Patent Publication Number: US-2022228961-A1

Title: Method for measuring rheological property of drilling fluid by using curved pipe on site

Description:
CROSS REFERENCE TO THE RELATED APPLICATIONS 
     This application is the continuation application of International Application No. PCT/CN2020/138476, filed on Dec. 23, 2020, the entire contents of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to the field of oil well construction and, in particular, to a method for measuring a rheological property of a drilling fluid by using a curved pipe on site. 
     BACKGROUND 
     The properties of the drilling fluid (mud) play a crucial role in optimizing drilling operations. Among them, the density and rheological properties of the drilling fluid play a significant role in the optimal management of wellbore pressure. Therefore, it is necessary to carry out accurate measurement of the density and rheological properties of the drilling fluid in narrow-window drilling operations, especially in advanced drilling techniques, including managed pressure drilling (MPD) and dual gradient drilling (DGD). 
     At present, the rheological properties of the drilling fluid are mainly measured by a rotation method and a pipe flow method. In the pipe flow method, the online rheological measurement device uses a straight pipe for measurement. However, due to its large size, it requires significant changes to the site space, resulting in greatly limited on-site applications and poor measurement accuracy. 
     SUMMARY 
     A technical problem to be solved by the present invention is to provide a method for measuring a rheological property of a drilling fluid by using a curved pipe on site, so as to improve the accuracy of the rheological measurement of the drilling fluid. 
     To solve the above technical problem, the present invention adopts the following technical solution: a method for measuring a rheological property of a drilling fluid by using a curved pipe on site, including the following steps: 
     step  1 : deriving relationship constants between friction coefficients of a drilling fluid through offline checking; 
     step  2 : calculating a Reynolds number R ei  of the drilling fluid in an on-site curved pipe according to a friction coefficient f ci  of the drilling fluid in the on-site curved pipe; 
     step  3 : calculating an actual shear stress τw i  of the drilling fluid in the on-site curved pipe according to the relationship constants between the friction coefficients of the drilling fluid and the Reynolds number R ei  of the drilling fluid in the on-site curved pipe, where i denotes a number of times the drilling fluid flows through the on-site curved pipe, which is a positive integer not less than 2; 
     step  4 : establishing a plurality of on-site models according to the actual shear stress τw i  and a shear rate γ of the drilling fluid; 
     step  5 : determining an optimal on-site model according to correlations between the actual shear stress τw i  and predicted shear stresses of the plurality of on-site models; and 
     step  6 : performing on-site measurement on the rheological property of the drilling fluid according to the optimal on-site model. 
     The working principle and beneficial effects of the present invention are as follows: The present invention derives the relationship constants between the friction coefficients of the drilling fluid through offline checking and can derive the relationship constants for different types of drilling fluids. The present invention avoids inaccurate rheological measurement due to different types of drilling fluids and improves the measurement accuracy for different types of drilling fluids. In addition, the present invention determines the optimal on-site model according to the correlations between the actual shear stress τw i  and the predicted shear stresses of the plurality of on-site models, so as to ensure the accuracy of on-site measurement of the drilling fluid. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, step  1  may include: 
     step  11 : calculating a friction coefficient f ck  of the drilling fluid in an offline curved pipe and a friction coefficient f sk  of the drilling fluid in an offline straight pipe, where, k denotes a number of times the drilling fluid flows through an offline pipe, which is a positive integer not less than 2; 
     step  12 : establishing a plurality of prediction models according to an actual friction coefficient ratio y k , where y k =f ck /f sk ; 
     step  13 : determining an optimal prediction model according to correlations between the actual friction coefficient ratio y k  and predicted friction coefficient ratios of the plurality of prediction models; and 
     step  14 : deriving the relationship constants between the friction coefficients of the drilling fluid according to the optimal prediction model. 
     The beneficial effects of the above further solution are as follows. The present invention measures and calculates the actual friction coefficients of the drilling fluid in offline curved and straight pipes and establishes the plurality of prediction models. The present invention determines the optimal prediction model according to the correlations between the actual friction coefficient ratio y i  and the predicted friction coefficient ratios of the plurality of prediction models. The present invention ensures the accuracy of selecting the prediction model. The present invention uses the relationship constants between the friction coefficients of the selected prediction model for subsequent on-site measurement on the rheological property of the drilling fluid. The present invention analyzes the correlations through the plurality of prediction models to ensure the accuracy of the relationship constants between the friction coefficients of different types of drilling fluids. Therefore, the present invention avoids the inaccuracy caused when a single relationship constant between the friction coefficients is applied to the on-site measurement of the drilling fluid. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, in step  11 , f ck  may be expressed by formula (1): 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where, d tc1  denotes an inner diameter of the offline curved pipe, and has a unit of m; 
     ρ 1  denotes a density of an offline drilling fluid, and has a unit of kg/m 3 ; 
     v ck  denotes a flow velocity of the drilling fluid at the k-th time in the offline curved pipe, and has a unit of m/s; and 
     ΔP ck /ΔL ck  denotes a measured average pressure difference in the offline curved pipe, and has a unit of kPa/m; and ΔP ck  denotes a total pressure difference in a pipe section with a length of ΔL ck , and has a unit of kPa; 
     in step  1 , f sk  may be expressed by formula (2): 
     
       
         
           
             
               
                 
                   
                     f 
                     sk 
                   
                   = 
                   
                     
                       
                         d 
                         
                           ts 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           sk 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           sk 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           sk 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where, d ts1  denotes an inner diameter of the offline straight pipe, and has a unit of m; 
     ρ 1  denotes a density of the drilling fluid, and has a unit of kg/m 3 ; 
     v sk  denotes a flow velocity of the drilling fluid at the k-th time in the offline straight pipe, and has a unit of m/s; and 
     ΔP sk /ΔL sk  denotes a measured average pressure difference in the offline straight pipe, and has a unit of kPa/m; and ΔP sk  denotes a total pressure difference in a pipe section with a length of ΔL sk , and has a unit of kPa. 
     The beneficial effects of the above further solution are as follows. The present invention measures the average pressure differences of the straight pipe and the curved pipe and calculates the friction coefficient f ck  of the drilling fluid in the curved pipe and the friction coefficient f sk  thereof in the straight pipe, so as to ensure the calculation accuracy of the friction coefficients. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     there may be at least three prediction models, namely: 
     a first prediction model: 
         ŷ   1k   =a*D   nk   b   +C   (3)
 
     a second prediction model: 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ^ 
                     
                     
                       2 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         a 
                         * 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                           b 
                         
                       
                       
                         
                           7 
                           ⁢ 
                           0 
                         
                         + 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     a third prediction model: 
         ŷ   3k =1+ a *(log 10   D   nk ) b   (5)
 
     where 
     ŷ 1k  denotes a predicted friction coefficient of the first prediction model; 
     ŷ 2k  denotes a predicted friction coefficient of the second prediction model; 
     ŷ 3k  denotes a predicted friction coefficient of the third prediction model; and 
     a, b and c denote the relationship constants between the friction coefficients of the drilling fluid, respectively; 
     where, D nk  denotes a Dean number of the drilling fluid at the k-th time in the offline curved pipe, and is expressed by formula (6): 
     
       
         
           
             
               
                 
                   
                     D 
                     
                       n 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           ck 
                         
                         * 
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       
                         μ 
                         1 
                       
                     
                     * 
                     
                       
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         
                           D 
                           
                             c 
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     where 
     μ 1  denotes a viscosity of an offline drilling fluid, and has a unit of Pa·s; and 
     v ck  denotes a flow velocity of the drilling fluid at the k-th time in the offline curved pipe, and has a unit of m/s. 
     The advantages of the above further solution are as follows. The present invention designs a plurality of prediction models involving the Dean number, which ensures the calculation accuracy. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     step  13  may specifically include: 
     expressing a correlation R 11   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the first prediction model by formula (7): 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       1 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     1 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     expressing a correlation R 12   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the second prediction model by formula (8): 
     
       
         
           
             
               
                 
                   
                     R 
                     12 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     2 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     expressing a correlation R 13   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the third prediction model by formula (9): 
     
       
         
           
             
               
                 
                   
                     R 
                     13 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     3 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     comparing R 11   2 , R 12   2  and R 13   2  in terms of magnitude, and selecting a prediction model with a maximum correlation as an optimal prediction model; 
     where 
     m denotes a number of samples; 
     y k  denotes the actual friction coefficient ratio; and 
       y  denotes an average actual friction coefficient ratio. 
     The beneficial effects of the above further solution are as follows: The present invention selects the final model for offline calibration through the correlations between the actual friction coefficient ratio y i  and the predicted friction coefficient ratios of the prediction models, which ensures the accuracy of selecting the offline model. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     in step  2 , f ci  may be expressed by formula (10): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           2 
                         
                         * 
                         
                           v 
                           ci 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           ci 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           ci 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where, d tc2  denotes an inner diameter of the on-site curved pipe, and has a unit of m; 
     ρ 2  denotes a density of an on-site drilling fluid, and has a unit of kg/m 3 ; 
     v ci  denotes a flow velocity of the drilling fluid at the i-th time in the on-site curved pipe, and has a unit of m/s; and 
     ΔP ci /ΔL ci  denotes a measured average pressure difference in the on-site curved pipe, and has a unit of kPa/m; and ΔP ci  denotes a total pressure difference in a pipe section with a length of ΔL ci , and has a unit of kPa. 
     The beneficial effects of the above further solution are as follows. The present invention can accurately calculate the friction coefficient f ci  of the drilling fluid in the on-site curved pipe. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     in step  2 , the Reynolds number R ei  of the drilling fluid in the on-site curved pipe may be calculated as follows: 
     when an offline model is the first prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (12): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           a 
                           * 
                           
                             
                               ( 
                               
                                 
                                   R 
                                   ei 
                                 
                                 * 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             b 
                           
                         
                         + 
                         c 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     when the offline model is the second prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (13): 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       ci 
                     
                     = 
                     
                       
                         
                           1 
                           ⁢ 
                           6 
                         
                         
                           R 
                           ei 
                         
                       
                       * 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               a 
                               * 
                               
                                 
                                   ( 
                                   
                                     
                                       R 
                                       ei 
                                     
                                     * 
                                     
                                       
                                         
                                           d 
                                           
                                             tc 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             2 
                                           
                                         
                                         
                                           D 
                                           
                                             c 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                 b 
                               
                             
                             
                               
                                 7 
                                 ⁢ 
                                 0 
                               
                               + 
                               
                                 ( 
                                 
                                   
                                     R 
                                     ei 
                                   
                                   * 
                                   
                                     
                                       
                                         d 
                                         
                                           tc 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                       
                                         D 
                                         
                                           c 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     and 
     when the offline model is the third prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (14): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     * 
                     
                       
                         [ 
                         
                           1 
                           + 
                           
                             a 
                             * 
                             
                               
                                 ( 
                                 
                                   
                                     log 
                                     10 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         R 
                                         ei 
                                       
                                       * 
                                       
                                         
                                           
                                             d 
                                             
                                               tc 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               2 
                                             
                                           
                                           
                                             D 
                                             
                                               c 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                               b 
                             
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The beneficial effects of the above further solution are as follows. The present invention calculates the Reynolds number R ei  of the drilling fluid in the on-site curved pipe and adopts different calculation methods according to different offline models, thereby ensuring the accuracy of the calculation of the Reynolds number R ei  of the drilling fluid in the on-site curved pipe. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     in step  3 , the actual shear stress τw i  of the drilling fluid in the on-site curved pipe may be expressed by formula (15): 
     
       
         
           
             
               
                 
                   
                     τ 
                     
                       w 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       8 
                       ⁢ 
                       
                         ρ 
                         2 
                       
                       * 
                       
                         v 
                         
                           c 
                           ⁢ 
                           i 
                         
                         2 
                       
                     
                     
                       R 
                       
                         e 
                         ⁢ 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     where 
     v ci  denotes the flow velocity of the drilling fluid at the i-th time in the on-site curved pipe, and has a unit of m/s; and 
     ρ 2  denotes the density of the on-site drilling fluid, and has a unit of kg/m 3 ; 
     the shear rate γ i  of the drilling fluid is expressed by formula (16): 
     
       
         
           
             
               
                 
                   
                     γ 
                     i 
                   
                   = 
                   
                     
                       
                         8 
                         * 
                         
                           v 
                           ci 
                         
                       
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     * 
                     
                       
                         
                           3 
                           * 
                           
                             N 
                             i 
                           
                         
                         + 
                         1 
                       
                       
                         4 
                         * 
                         
                           N 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where, N is expressed by formula (17): 
     
       
         
           
             
               
                 
                   
                     N 
                     i 
                   
                   = 
                   
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                             τ 
                             
                               w 
                               i 
                             
                           
                         
                         ) 
                       
                     
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                             
                               8 
                               * 
                               
                                 v 
                                 ci 
                               
                             
                             
                               d 
                               
                                 tc 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     The beneficial effects of the above further solution are as follows. The present invention ensures the calculation accuracy. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     there may be at least three on-site models, namely: 
     a first on-site model: 
       τ ŵ   1i   =YP−PV*γ   i   (18)
 
     a second on-site model: 
       τ ŵ   2i   =K*γ   i   n   (19)
 
     a third on-site model: 
       τ ŵ   2i =τ 0   +K*γ   i   n   (20)
 
     where 
     YP denotes a yield strength of the on-site drilling fluid, and has a unit of Pa; 
     PV denotes a plastic viscosity of the on-site drilling fluid, and has a unit of Pa·s; 
     n denotes a fluidity index of the on-site drilling fluid, and is dimensionless; 
     K denotes a consistency coefficient of the on-site drilling fluid, and has a unit of Pa·s{circumflex over ( )}n; and 
     τ 0  denotes a dynamic shear stress of the on-site drilling fluid, and has a unit of Pa. 
     The beneficial effects of the above further solution are as follows. The present invention selects the rheological parameters through three different on-site models to ensure the optimal on-site models available for different drilling fluids. 
     The following improvement may be further made by the present invention based on the above technical solution. 
     Further, 
     step  5  may specifically include: 
     expressing a correlation R 21   2  between the actual shear stress τw i  and a predicted shear stress of the first on-site model by formula (21): 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ^ 
                                   
                                   
                                     1 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     expressing a correlation R 22   2  between the actual shear stress τw i  and a predicted shear stress of the second on-site model by formula (22): 
     
       
         
           
             
               
                 
                   
                     R 
                     22 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ^ 
                                   
                                   
                                     2 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     expressing a correlation R 23   2  between the actual shear stress τw i  and a predicted shear stress of the third on-site model by formula (23): 
     
       
         
           
             
               
                 
                   
                     R 
                     23 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ^ 
                                   
                                   
                                     3 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     comparing R 21   2 , R 22   2  and R 23   2  in terms of magnitude, and selecting an on-site model with a maximum correlation as a final model; 
     where 
     m denotes a number of samples; 
     τw i  denotes the actual shear stress; and 
       τw  denotes an average actual shear stress. 
     The beneficial effects of the above further solution are as follows: The present invention selects the final model for on-site measurement through the correlations between the actual shear stress τw i  and the predicted friction coefficient ratios of the on-site models, ensuring the accuracy of selecting the on-site model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a flowchart of an on-site measurement method according to a first embodiment of the present invention; and 
         FIG. 2  is a flowchart of an offline checking method according to the first embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Principles and features of the present invention are described below with reference to the drawings. The described embodiments are only used to explain the present invention, rather than to limit the scope of the present invention. 
       FIG. 1  is a flowchart of an on-site measurement method according to a first embodiment of the present invention. 
     A method for measuring a rheological property of a drilling fluid by using a curved pipe on site includes the following steps: 
     Step  1 : Derive relationship constants between friction coefficients of a drilling fluid through offline checking. 
     Step  2 : Calculate a Reynolds number R ei  of the drilling fluid in an on-site curved pipe according to a friction coefficient f ci  of the drilling fluid in the curved pipe. 
     Step  3 : Calculate an actual shear stress τw i  of the drilling fluid in the on-site curved pipe according to the relationship constants between the friction coefficients of the drilling fluid and the Reynolds number R ei  of the drilling fluid in the on-site curved pipe, where i denotes a number of times the drilling fluid flows through the on-site curved pipe, which is a positive integer not less than 2. 
     Step  4 : Establish a plurality of on-site models according to the actual shear stress τw i  and a shear rate γ of the drilling fluid. 
     Step  5 : Determine an optimal on-site model according to correlations between the actual shear stress τw i  and predicted shear stresses of the plurality of on-site models. 
     Step  6 : Perform on-site measurement on the rheological property of the drilling fluid according to the optimal on-site model. 
     The working principle and beneficial effects of the embodiment of the present invention are as follows. The present invention derives the relationship constants between the friction coefficients of the drilling fluid through offline checking and can derive the relationship constants for different types of drilling fluids. The present invention avoids inaccurate rheological measurement due to different types of drilling fluids and improves the measurement accuracy for different types of drilling fluids. In addition, the present invention determines the optimal on-site model according to the correlations between the actual shear stress τw i  and the predicted shear stresses of the plurality of on-site models, so as to ensure the accuracy of on-site measurement of the drilling fluid. 
     In this embodiment, when the on-site measurement on the rheological property of the drilling fluid is carried out by the optimal on-site model, if the friction of the curved pipe changes, Step  7  is performed. That is, according to the friction of the curved pipe, the entire method starting from Step  1  is repeated outside a fixed operation time. The fixed operation time refers to a normal operation time of the on-site measurement equipment. 
       FIG. 2  is a flowchart of an offline checking method according to the embodiment of the present invention. 
     Step  1  includes: 
     Step  11 : Calculate a friction coefficient f ck  of the drilling fluid in an offline curved pipe and a friction coefficient f sk  of the drilling fluid in an offline straight pipe, where, k denotes a number of times the drilling fluid flows through an offline pipe, which is a positive integer not less than 2. 
     Step  12 : Establish a plurality of prediction models according to an actual friction coefficient ratio y k , where, y k =f ck /f sk . 
     Step  13 : Determine an optimal prediction model according to correlations between the actual friction coefficient ratio y k  and predicted friction coefficient ratios of the plurality of prediction models. 
     Step  14 : Derive the relationship constants between the friction coefficients of the drilling fluid according to the optimal prediction model. 
     The present invention measures and calculates the actual friction coefficients of the drilling fluid in offline curved and straight pipes and establishes the plurality of prediction models. The present invention determines the optimal prediction model according to the correlations between the actual friction coefficient ratio y i  and the predicted friction coefficient ratios of the plurality of prediction models. The present invention ensures the accuracy of selecting the prediction model. The present invention uses the relationship constants between the friction coefficients of the selected prediction model for subsequent on-site measurement on the rheological property of the drilling fluid. The present invention analyzes the correlations through the plurality of prediction models to ensure the accuracy of the relationship constants between the friction coefficients of different types of drilling fluids. Therefore, the present invention avoids the inaccuracy caused when a single relationship constant between the friction coefficients is applied to the on-site measurement of the drilling fluid. 
     Specifically, in step  11 , f ck  is expressed by formula (1): 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where, d tc1  denotes an inner diameter of the offline curved pipe, and has a unit of m; 
     ρ 1  denotes a density of an offline drilling fluid, and has a unit of kg/m 3 ; 
     v ck  denotes a flow velocity of the drilling fluid at the k-th time in the offline curved pipe, and has a unit of m/s; and 
     ΔP ck /ΔL ck  denotes a measured average pressure difference in the offline curved pipe, and has a unit of kPa/m; and ΔP ck  denotes a total pressure difference in a pipe section with a length of ΔL ck , and has a unit of kPa; 
     in step  1 , f sk  is expressed by formula (2): 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           ts 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           sk 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           sk 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           sk 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where, d ts1  denotes an inner diameter of the offline straight pipe, and has a unit of m; 
     ρ 1  denotes a density of the drilling fluid, and has a unit of kg/m 3 ; 
     v sk  denotes a flow velocity of the drilling fluid at the k-th time in the offline straight pipe, and has a unit of m/s; and 
     ΔP sk /ΔL sk  denotes a measured average pressure difference in the offline straight pipe, and has a unit of kPa/m; and ΔP sk  denotes a total pressure difference in a pipe section with a length of ΔL sk , and has a unit of kPa. 
     where, 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         4 
                         * 
                         
                           V 
                           1 
                         
                       
                       
                         π 
                         * 
                         le 
                         ⁢ 
                         
                           n 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     where, V 1  denotes a total volume of the offline curved pipe, and has a unit of m 3 ; and 
     len 1  denotes an length of the offline curved pipe, and has a unit of m. 
     In this embodiment, there are at least three prediction models, namely: 
     a first prediction model: 
         ŷ   1k   =a*D   nk   b   +c   (3)
 
     a second prediction model: 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ^ 
                     
                     
                       2 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         a 
                         * 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                           b 
                         
                       
                       
                         
                           7 
                           ⁢ 
                           0 
                         
                         + 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     a third prediction model: 
         ŷ   3k =1+ a *(log 10   D   nk ) b   (5)
 
     where 
     ŷ 1k  denotes a predicted friction coefficient of the first prediction model; 
     ŷ 2k  denotes a predicted friction coefficient of the second prediction model; 
     ŷ 3k  denotes a predicted friction coefficient of the third prediction model; and 
     a, b and c denote the relationship constants between the friction coefficients of the drilling fluid, respectively; 
     where, D nk  denotes a Dean number of the drilling fluid at the k-th time in the offline curved pipe, and is expressed by formula (6): 
     
       
         
           
             
               
                 
                   
                     D 
                     
                       n 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           v 
                           ck 
                         
                         * 
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       
                         μ 
                         1 
                       
                     
                     * 
                     
                       
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         
                           D 
                           
                             c 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     where 
     μ 1  denotes a viscosity of an offline drilling fluid, and has a unit of Pa·s; and 
     v ck  denotes a flow velocity of the drilling fluid at the k-th time in the offline curved pipe, and has a unit of m/s. 
     Step  13  specifically includes: 
     Express a correlation R 11   2  between the actual friction coefficient ratio yk and a predicted friction coefficient ratio of the first prediction model by formula (7): 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       1 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     1 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     express a correlation R122 between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the second prediction model by formula (8): 
     
       
         
           
             
               
                 
                   
                     R 
                     12 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     2 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     express a correlation R132 between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the third prediction model by formula (9): 
     
       
         
           
             
               
                 
                   
                     R 
                     13 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   y 
                                   
                                     3 
                                     ⁢ 
                                     k 
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                           
                           m 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 y 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     compare R 11   2 , R 12   2  and R 13   2  in terms of magnitude, and select a prediction model with a maximum correlation as an optimal prediction model; 
     where 
     m denotes a number of samples; 
     y k  denotes the actual friction coefficient ratio; and 
       y  denotes an average actual friction coefficient ratio. 
     In this embodiment, in step  2 , f ci  is expressed by formula (10): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         d 
                         
                           t 
                           ⁢ 
                           c 
                           ⁢ 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ρ 
                           2 
                         
                         * 
                         
                           v 
                           ci 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           ci 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           ci 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where, d tc2  denotes an inner diameter of the on-site curved pipe, and has a unit of m; 
     ρ 2  denotes a density of an on-site drilling fluid, and has a unit of kg/m 3 ; 
     v ci  denotes a flow velocity of the drilling fluid at the i-th time in the on-site curved pipe, and has a unit of m/s; and 
     ΔP ci /ΔL ci  denotes a measured average pressure difference in the on-site curved pipe, and has a unit of kPa/m; and ΔP ci  denotes a total pressure difference in a pipe section with a length of ΔL ci , and has a unit of kPa; and 
     d tc2  is expressed by formula (11): 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       t 
                       ⁢ 
                       c 
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         4 
                         * 
                         
                           V 
                           2 
                         
                       
                       
                         π 
                         * 
                         
                           len 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where, V 2  denotes a total volume of the on-site curved pipe, and has a unit of m 3 ; and 
     len 2  denotes a length of the on-site curved pipe, and has a unit of m; 
     Specifically, in step  2 , the Reynolds number R ei  of the drilling fluid in the on-site curved pipe is calculated as follows: 
     when an offline model is the first prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (12): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           a 
                           * 
                           
                             
                               ( 
                               
                                 
                                   R 
                                   ei 
                                 
                                 * 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             b 
                           
                         
                         + 
                         c 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     when the offline model is the second prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (13): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     * 
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             
                               
                                 a 
                                 * 
                               
                               ( 
                               
                                 
                                   R 
                                   ei 
                                 
                                 * 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             b 
                           
                           
                             
                               7 
                               ⁢ 
                               0 
                             
                             + 
                             
                               ( 
                               
                                 
                                   R 
                                   ei 
                                 
                                 * 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     when the offline model is the third prediction model, the Reynolds number R ei  of the drilling fluid in the on-site curved pipe satisfies formula (14): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     * 
                     
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               
                                 a 
                                 * 
                               
                               ( 
                               
                                 
                                   log 
                                   10 
                                 
                                 ( 
                                 
                                   
                                     R 
                                     ei 
                                   
                                   * 
                                   
                                     
                                       
                                         d 
                                         
                                           tc 
                                           ⁢ 
                                           2 
                                         
                                       
                                       
                                         D 
                                         
                                           c 
                                           ⁢ 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                               ) 
                             
                             b 
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Specifically, in step  3 , the actual shear stress τw i  of the drilling fluid in the on-site curved pipe is expressed by formula (15): 
     
       
         
           
             
               
                 
                   
                     τ 
                     
                       w 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         8 
                         ⁢ 
                         
                           ρ 
                           2 
                         
                       
                       ⋆ 
                       
                         v 
                         
                           c 
                           ⁢ 
                           i 
                         
                         2 
                       
                     
                     
                       R 
                       
                         e 
                         ⁢ 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     where 
     v ci  denotes the flow velocity of the drilling fluid at the i-th time in the on-site curved pipe, and has a unit of m/s; and 
     ρ 2  denotes the density of the on-site drilling fluid, and has a unit of kg/m 3 ; 
     the shear rate γ i  of the drilling fluid is expressed by formula (16): 
     
       
         
           
             
               
                 
                   
                     γ 
                     i 
                   
                   = 
                   
                     
                       
                         
                           8 
                           * 
                         
                         ⁢ 
                         
                           v 
                           ci 
                         
                       
                       
                         d 
                         
                           t 
                           ⁢ 
                           c 
                           ⁢ 
                           2 
                         
                       
                     
                     * 
                     
                       
                         
                           
                             3 
                             * 
                           
                           ⁢ 
                           
                             N 
                             i 
                           
                         
                         + 
                         1 
                       
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           N 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where, N is expressed by formula (17): 
     
       
         
           
             
               
                 
                   
                     N 
                     i 
                   
                   = 
                   
                     
                       d 
                       ⁡ 
                       ( 
                       
                         ln 
                         ⁢ 
                            
                         
                           τ 
                           
                             w 
                             i 
                           
                         
                       
                       ) 
                     
                     
                       d 
                       ⁡ 
                       ( 
                       
                         ln 
                         ⁢ 
                         
                           
                             
                               8 
                               * 
                             
                             ⁢ 
                             
                               v 
                               ci 
                             
                           
                           
                             d 
                             
                               t 
                               ⁢ 
                               c 
                               ⁢ 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, there are at least three on-site model, namely: 
     a first on-site model: 
       {circumflex over (τ)} w   1i   =YP+PV*γ   i   (18)
 
     a second on-site model: 
       {circumflex over (τ)} w   2i   =K*γ   i   n   (19)
 
     a third on-site model: 
       {circumflex over (τ)} w   2i =τ 0   K*γ   i   n   (20)
 
     where 
     YP denotes a yield strength of the on-site drilling fluid, and has a unit of Pa; 
     PV denotes a plastic viscosity of the on-site drilling fluid, and has a unit of Pa·s; 
     n denotes a fluidity index of the on-site drilling fluid, and is dimensionless; 
     K denotes a consistency coefficient of the on-site drilling fluid, and has a unit of Pa·s{circumflex over ( )}n; and 
     τ 0  denotes a dynamic shear stress of the on-site drilling fluid, and has a unit of Pa. 
     Specifically, step  5  includes: 
     express a correlation R 21   2  between the actual shear stress τw i  and a predicted shear stress of the first on-site model by formula (21): 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     1 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     express a correlation R 22   2  between the actual shear stress τw i  and a predicted shear stress of the second on-site model by formula (22): 
     
       
         
           
             
               
                 
                   
                     R 
                     22 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     2 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     express a correlation R 23   2  between the actual shear stress τw i  and a predicted shear stress of the third on-site model by formula (23): 
     
       
         
           
             
               
                 
                   
                     R 
                     23 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     3 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     compare R 21   2 , R 22   2  and R 23   2  in terms of magnitude, and selecting an on-site model with a maximum correlation as a final model; 
     where 
     m denotes a number of samples; 
     τw i  denotes the actual shear stress; and 
       τw  denotes an average actual shear stress. 
     The application of the first embodiment of offline checking of the present invention is described below. 
     In this embodiment, the offline curved pipe is a helical pipe, which has a total volume V 1 =1.04 l and a length len 1 =5.57476 m; the offline straight pipe has an inner diameter d ts1 =0.01056 m; and a first offline drilling fluid has a density ρ 1 =1,003 kg/m 3 . 
     The inner diameter of the offline curved pipe is calculated as: d tc1 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           V 
                           1 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         
                           len 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, the first offline drilling fluid flows through the pipe for k=24 times. 
     A flow velocity v sk  of the first offline drilling fluid at the k-th time in a straight pipe and a flow velocity v ck  thereof at the k-th time in the curved pipe are shown in the table below. 
     An average pressure difference ΔP ck /ΔL ck  of the offline curved pipe and an average pressure difference ΔP sk /ΔL sk  of the offline straight pipe are also shown in the table below. 
     The first offline drilling fluid flows through for 24 times, and its friction coefficient f ck  in the offline curved pipe and friction coefficient f sk  in the offline straight pipe are calculated by formulas (1) and (2) and are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           1 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             1 
                           
                         
                         ⋆ 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     f 
                     sk 
                   
                   = 
                   
                     
                       
                         d 
                         
                           ts 
                           ⁢ 
                           1 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             1 
                           
                         
                         ⋆ 
                         
                           v 
                           sk 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           sk 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           sk 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The corresponding actual friction coefficient ratios y k  are shown in the table below, where y k =f ck /f sk . 
     In this embodiment, an average viscosity of the first offline drilling fluid is μ 1 =0.00711 Pa·s. 
     The Dean numbers D nk  of the first offline drilling fluid flowing through the curved pipe for 24 times are calculated according to formula (6) and are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     D 
                     
                       n 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         ⋆ 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                         ⋆ 
                         
                           d 
                           
                             tc 
                             ⁢ 
                             1 
                           
                         
                       
                       
                         μ 
                         1 
                       
                     
                     * 
                     
                       
                         
                           d 
                           
                             tc 
                             ⁢ 
                             1 
                           
                         
                         
                           D 
                           
                             c 
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Number 
                 ΔP ck / 
                 ΔP sk / 
                   
                   
                   
                   
                   
                   
               
               
                 of times 
                 ΔL ck   
                 ΔL sk   
                 v sk   
                 
                   vck 
                 
                 f sk   
                 f ck   
                 y k   
                 D nk   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.576 
                 0.590 
                 0.169 
                 0.170 
                 0.106 
                 0.106 
                 1.001 
                  29.557 
               
               
                 2 
                 0.651 
                 0.727 
                 0.235 
                 0.237 
                 0.062 
                 0.068 
                 1.091 
                  50.588 
               
               
                 3 
                 0.674 
                 0.777 
                 0.264 
                 0.266 
                 0.051 
                 0.058 
                 1.127 
                  61.461 
               
               
                 4 
                 0.691 
                 0.830 
                 0.274 
                 0.276 
                 0.049 
                 0.057 
                 1.175 
                  64.702 
               
               
                 5 
                 0.718 
                 0.873 
                 0.304 
                 0.307 
                 0.041 
                 0.049 
                 1.187 
                  76.722 
               
               
                 6 
                 0.748 
                 0.927 
                 0.327 
                 0.330 
                 0.037 
                 0.045 
                 1.211 
                  85.333 
               
               
                 7 
                 0.777 
                 0.979 
                 0.348 
                 0.351 
                 0.034 
                 0.042 
                 1.231 
                  92.785 
               
               
                 8 
                 0.807 
                 1.023 
                 0.374 
                 0.377 
                 0.030 
                 0.038 
                 1.240 
                 103.122 
               
               
                 9 
                 0.827 
                 1.064 
                 0.397 
                 0.401 
                 0.028 
                 0.035 
                 1.257 
                 113.686 
               
               
                 10 
                 0.909 
                 1.169 
                 0.440 
                 0.444 
                 0.025 
                 0.031 
                 1.257 
                 126.935 
               
               
                 11 
                 0.936 
                 1.242 
                 0.482 
                 0.486 
                 0.021 
                 0.028 
                 1.297 
                 147.922 
               
               
                 12 
                 0.973 
                 1.295 
                 0.503 
                 0.508 
                 0.020 
                 0.026 
                 1.301 
                 155.213 
               
               
                 13 
                 0.999 
                 1.350 
                 0.543 
                 0.548 
                 0.018 
                 0.024 
                 1.321 
                 176.185 
               
               
                 14 
                 1.031 
                 1.408 
                 0.571 
                 0.576 
                 0.017 
                 0.022 
                 1.334 
                 188.652 
               
               
                 15 
                 1.071 
                 1.468 
                 0.591 
                 0.597 
                 0.016 
                 0.022 
                 1.340 
                 194.715 
               
               
                 16 
                 1.111 
                 1.525 
                 0.616 
                 0.622 
                 0.015 
                 0.021 
                 1.341 
                 203.773 
               
               
                 17 
                 1.111 
                 1.589 
                 0.631 
                 0.637 
                 0.015 
                 0.021 
                 1.398 
                 213.799 
               
               
                 18 
                 1.142 
                 1.627 
                 0.665 
                 0.671 
                 0.014 
                 0.019 
                 1.393 
                 230.859 
               
               
                 19 
                 1.178 
                 1.694 
                 0.696 
                 0.703 
                 0.013 
                 0.018 
                 1.405 
                 245.566 
               
               
                 20 
                 1.196 
                 1.785 
                 0.723 
                 0.729 
                 0.012 
                 0.018 
                 1.459 
                 260.502 
               
               
                 21 
                 1.243 
                 1.845 
                 0.769 
                 0.776 
                 0.011 
                 0.016 
                 1.450 
                 283.448 
               
               
                 22 
                 1.262 
                 1.904 
                 0.778 
                 0.785 
                 0.011 
                 0.016 
                 1.475 
                 286.099 
               
               
                 23 
                 1.294 
                 1.977 
                 0.809 
                 0.817 
                 0.010 
                 0.016 
                 1.494 
                 301.892 
               
               
                 24 
                 1.360 
                 2.089 
                 0.879 
                 0.887 
                 0.009 
                 0.014 
                 1.502 
                 338.859 
               
               
                   
               
            
           
         
       
     
     Three prediction models are fitted by the actual friction coefficient ratios yk and the Dean numbers D nk  as follows: 
     a first prediction model: 
         ŷ   1k   =a*D   nk   b   +c   (3)
 
     where, a=0.035966, b=0.5, and c=0.855298. 
     a second prediction model: 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ˆ 
                     
                     
                       2 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         
                           a 
                           * 
                         
                         ⁢ 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                           b 
                         
                       
                       
                         
                           7 
                           ⁢ 
                           0 
                         
                         + 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where, a=0.052896, and b=1.421332. 
     a third prediction model: 
         ŷ   3k =1+ a *(log 10   D   nk ) b   (5)
 
     where, a=0.016495, and b=3.709336. 
     The predicted friction coefficients of the third prediction models are shown in the table below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Number  
                   
                   
                   
               
               
                   
                 of times 
                 ŷ 1k   
                 ŷ 2k   
                 ŷ 3k   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 
                 1.051 
                 1.065 
                 1.069 
               
               
                   
                 2 
                 1.111 
                 1.116 
                 1.119 
               
               
                   
                 3 
                 1.137 
                 1.140 
                 1.143 
               
               
                   
                 4 
                 1.145 
                 1.147 
                 1.149 
               
               
                   
                 5 
                 1.170 
                 1.172 
                 1.173 
               
               
                   
                 6 
                 1.188 
                 1.189 
                 1.189 
               
               
                   
                 7 
                 1.202 
                 1.203 
                 1.203 
               
               
                   
                 8 
                 1.221 
                 1.222 
                 1.221 
               
               
                   
                 9 
                 1.239 
                 1.241 
                 1.239 
               
               
                   
                 10 
                 1.261 
                 1.262 
                 1.260 
               
               
                   
                 11 
                 1.293 
                 1.295 
                 1.292 
               
               
                   
                 12 
                 1.303 
                 1.305 
                 1.303 
               
               
                   
                 13 
                 1.333 
                 1.335 
                 1.332 
               
               
                   
                 14 
                 1.349 
                 1.351 
                 1.348 
               
               
                   
                 15 
                 1.357 
                 1.359 
                 1.356 
               
               
                   
                 16 
                 1.369 
                 1.370 
                 1.368 
               
               
                   
                 17 
                 1.381 
                 1.382 
                 1.380 
               
               
                   
                 18 
                 1.402 
                 1.402 
                 1.401 
               
               
                   
                 19 
                 1.419 
                 1.418 
                 1.418 
               
               
                   
                 20 
                 1.436 
                 1.434 
                 1.435 
               
               
                   
                 21 
                 1.461 
                 1.458 
                 1.460 
               
               
                   
                 22 
                 1.464 
                 1.461 
                 1.463 
               
               
                   
                 23 
                 1.480 
                 1.476 
                 1.479 
               
               
                   
                 24 
                 1.517 
                 1.510 
                 1.516 
               
               
                   
                   
               
            
           
         
       
     
     A correlation R 11   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the first prediction model, a correlation R 12   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the second prediction model and a correlation R 13   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the third prediction model are calculated according to formulas (7), (8) and (9), respectively. 
     Through calculation, R 11   2 =0.976421, R 12   2 =0.972209 and R 13   2 =0.971412. 
     To sum up, in this embodiment, for the first offline drilling fluid, the first prediction model is the optimal prediction model. According to the optimal prediction model, the relationship constants between the friction coefficients are a=0.035966, b=0.5 and c=0.855298, which are used for the on-site measurement on the rheological property of the drilling fluid. 
     The on-site measurement on the rheological property of the drilling fluid in the curved pipe is described below. 
     In a first embodiment of the on-site measurement, the density of a first on-site drilling fluid is ρ 2 =1,003 kg/m 3 . 
     The on-site curved pipe is a helical pipe, which has a total volume V 2 =1.04 l and a length len 2 =5.57476 m. 
     An inner diameter of the on-site curved pipe is calculated as d tc2 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           V 
                           2 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         
                           len 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, a first offline drilling fluid flows through the on-site pipe for i=24 times. 
     A flow velocity v ci  of the first on-site drilling fluid at the i-th time in the curved pipe and an average pressure difference thereof in the curved pipe ΔP ci /ΔL ci  are shown in the table below. 
     The measured parameters of the on-site drilling fluid in the curved pipe are shown in the table below. The flow velocity of the drilling fluid is increased in the curved pipe in an ascending order to keep a laminar flow state of the drilling fluid. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                   
                 Rate  
                   
                   
                   
                   
               
               
                 Number 
                 of flow 
                 Temperature  
                   
                   
                   
               
               
                 of times 
                 (lpm) 
                 (° C.) 
                 ΔP ci /ΔL ci   
                 ρ 2   
                 v ci   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 0.8882 
                 32.5 
                 0.590 
                 1003.9 
                 0.1705 
               
               
                 2 
                 1.2356 
                 32.5 
                 0.727 
                 1002.7 
                 0.2372 
               
               
                 3 
                 1.3858 
                 32.5 
                 0.777 
                 1002.5 
                 0.2660 
               
               
                 4 
                 1.4388 
                 32.5 
                 0.830 
                 1003.4 
                 0.2762 
               
               
                 5 
                 1.5973 
                 32.5 
                 0.873 
                 1004.1 
                 0.3066 
               
               
                 6 
                 1.7200 
                 32.5 
                 0.927 
                 1003.3 
                 0.3302 
               
               
                 7 
                 1.8269 
                 32.5 
                 0.979 
                 1004.2 
                 0.3507 
               
               
                 8 
                 1.9638 
                 32.5 
                 1.023 
                 1002.7 
                 0.3770 
               
               
                 9 
                 2.0876 
                 32.5 
                 1.064 
                 1002.9 
                 0.4007 
               
               
                 10 
                 2.3133 
                 32.5 
                 1.169 
                 1002.6 
                 0.4441 
               
               
                 11 
                 2.5336 
                 32.5 
                 1.242 
                 1002.8 
                 0.4864 
               
               
                 12 
                 2.6463 
                 32.5 
                 1.295 
                 1002.7 
                 0.5080 
               
               
                 13 
                 2.8562 
                 32.5 
                 1.350 
                 1002.8 
                 0.5483 
               
               
                 14 
                 3.0025 
                 32.5 
                 1.408 
                 1003.2 
                 0.5764 
               
               
                 15 
                 3.1087 
                 32.5 
                 1.468 
                 1002.9 
                 0.5968 
               
               
                 16 
                 3.2385 
                 32.5 
                 1.525 
                 1003.5 
                 0.6217 
               
               
                 17 
                 3.3183 
                 32.5 
                 1.589 
                 1002.9 
                 0.6370 
               
               
                 18 
                 3.4960 
                 32.5 
                 1.627 
                 1002.6 
                 0.6711 
               
               
                 19 
                 3.6600 
                 32.5 
                 1.694 
                 1003.7 
                 0.7026 
               
               
                 20 
                 3.7989 
                 32.5 
                 1.785 
                 1003.3 
                 0.7293 
               
               
                 21 
                 4.0419 
                 32.5 
                 1.845 
                 1002.6 
                 0.7759 
               
               
                 22 
                 4.0901 
                 32.5 
                 1.904 
                 1002.9 
                 0.7852 
               
               
                 23 
                 4.2535 
                 32.5 
                 1.977 
                 1003.3 
                 0.8165 
               
               
                 24 
                 4.6207 
                 32.5 
                 2.089 
                 1003.0 
                 0.8870 
               
               
                   
               
            
           
         
       
     
     The first on-site drilling fluid flows through the curved pipe for 24 times, and its friction coefficient f ci  in the curved pipe is calculated by formula (11), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           2 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             2 
                           
                         
                         ⋆ 
                         
                           v 
                           ci 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           ci 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           ci 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is calculated according to the selected optimal offline model. In this embodiment, the optimal prediction model is the first prediction model: ŷ 1k =a*D nk   b +c, where the relationship constants between the friction coefficients are respectively: a=0.035966, b=0.5, and c=0.855298. 
     The Reynolds number R ei  of the on-site curved pipe is expressed by formula (12): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               a 
                               * 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     R 
                                     ei 
                                   
                                   * 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           b 
                         
                         + 
                         c 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is shown in the table below. 
     According to the Reynolds number R ei  of the on-site curved pipe, a shear stress τw i  of the drilling fluid in the on-site curved pipe is calculated, which is expressed by formula (15), and is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     τ 
                     wi 
                   
                   = 
                   
                     
                       8 
                       ⁢ 
                       
                         
                           ρ 
                           2 
                         
                         * 
                       
                       ⁢ 
                       
                         v 
                         ci 
                         2 
                       
                     
                     
                       R 
                       ei 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, an intermediate parameter N i  is calculated by a binomial fitting method according to formula (17), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     N 
                     i 
                   
                   = 
                   
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             τ 
                             
                               w 
                               i 
                             
                           
                         
                         ) 
                       
                     
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                             
                               
                                 8 
                                 * 
                               
                               ⁢ 
                               
                                 v 
                                 ci 
                               
                             
                             
                               d 
                               
                                 tc 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     A shear rate γ i  of the first drilling fluid in the on-site curved pipe is calculated according to formula (16), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     γ 
                     l 
                   
                   = 
                   
                     
                       
                         
                           8 
                           * 
                         
                         ⁢ 
                         
                           v 
                           ci 
                         
                       
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     * 
                     
                       
                         
                           
                             3 
                             * 
                           
                           ⁢ 
                           
                             N 
                             i 
                           
                         
                         + 
                         1 
                       
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           N 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Number  
                   
                   
                   
                   
                   
               
               
                   
                 of times 
                 f ci   
                 R ci   
                 τw i   
                 N i   
                 γ i   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 1 
                 0.11 
                 158.92 
                 1.47 
                 0.47 
                 166.99 
               
               
                   
                 2 
                 0.07 
                 263.11 
                 1.72 
                 0.50 
                 225.78 
               
               
                   
                 3 
                 0.06 
                 316.51 
                 1.79 
                 0.51 
                 250.91 
               
               
                   
                 4 
                 0.06 
                 320.14 
                 1.91 
                 0.51 
                 259.74 
               
               
                   
                 5 
                 0.05 
                 384.57 
                 1.96 
                 0.53 
                 286.06 
               
               
                   
                 6 
                 0.05 
                 425.27 
                 2.06 
                 0.53 
                 306.33 
               
               
                   
                 7 
                 0.04 
                 459.71 
                 2.15 
                 0.54 
                 323.95 
               
               
                   
                 8 
                 0.04 
                 516.12 
                 2.21 
                 0.55 
                 346.44 
               
               
                   
                 9 
                 0.04 
                 569.37 
                 2.26 
                 0.55 
                 366.69 
               
               
                   
                 10 
                 0.03 
                 649.48 
                 2.44 
                 0.56 
                 403.50 
               
               
                   
                 11 
                 0.03 
                 751.29 
                 2.53 
                 0.57 
                 439.27 
               
               
                   
                 12 
                 0.03 
                 793.06 
                 2.61 
                 0.58 
                 457.51 
               
               
                   
                 13 
                 0.02 
                 908.07 
                 2.66 
                 0.58 
                 491.39 
               
               
                   
                 14 
                 0.02 
                 975.29 
                 2.73 
                 0.59 
                 514.94 
               
               
                   
                 15 
                 0.02 
                 1008.00 
                 2.84 
                 0.59 
                 532.01 
               
               
                   
                 16 
                 0.02 
                 1064.98 
                 2.91 
                 0.60 
                 552.83 
               
               
                   
                 17 
                 0.02 
                 1073.93 
                 3.03 
                 0.60 
                 565.62 
               
               
                   
                 18 
                 0.02 
                 1186.55 
                 3.05 
                 0.61 
                 594.03 
               
               
                   
                 19 
                 0.02 
                 1267.02 
                 3.13 
                 0.61 
                 620.20 
               
               
                   
                 20 
                 0.02 
                 1301.98 
                 3.28 
                 0.61 
                 642.33 
               
               
                   
                 21 
                 0.02 
                 1458.08 
                 3.31 
                 0.62 
                 680.96 
               
               
                   
                 22 
                 0.02 
                 1444.81 
                 3.42 
                 0.62 
                 688.62 
               
               
                   
                 23 
                 0.02 
                 1521.06 
                 3.52 
                 0.63 
                 714.54 
               
               
                   
                 24 
                 0.01 
                 1750.53 
                 3.61 
                 0.63 
                 772.62 
               
               
                   
                   
               
            
           
         
       
     
     According to the shear stress τw i  and the shear rate γ i  of the first on-site drilling fluid, at least three on-site models are fitted, which are respectively: 
     a first on-site model: 
       {circumflex over (τ)} w   1i   =YP+PV*γ   i   (18)
 
     where, PV=0.00354, and YP=0.95267. 
     a second on-site model: 
       {circumflex over (τ)} w   2i   =K*γ   i   n   (19),
 
     where K=0.0622, and n=0.6105. 
     a third on-site model: 
       {circumflex over (τ)} w   2i =τ 0   +K*γ   i   n   (20),
 
     where, n=0.7991, K=0.0151, and τ 0 =0.581. 
     Then the following parameters are respectively calculated: 
     a correlation R 21   2  between the shear stress τw i  of the first on-site drilling fluid and a predicted shear stress of the first on-site model; 
     a correlation R 22   2  between the shear stress τw i  of the first on-site drilling fluid and a predicted shear stress of the second on-site model; and 
     a correlation R 23   2  between the shear stress τw i  of the first on-site drilling fluid and a predicted shear stress of the third on-site model. 
     These parameters are calculated according to formulas (21), (22) and (23), respectively. 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     w 
                                     
                                       1 
                                       ⁢ 
                                       i 
                                     
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 w 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     22 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     w 
                                     
                                       2 
                                       ⁢ 
                                       i 
                                     
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 w 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     23 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   w 
                                   i 
                                 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     w 
                                     
                                       3 
                                       ⁢ 
                                       i 
                                     
                                   
                                 
                                 ^ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 τ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 w 
                               
                               - 
                               
                                 
                                   τ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   w 
                                 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Through calculation, R 21   2 =0.9950, R 22   2 =0.9951 and R 23   2 =0.9964. The third on-site model has the maximum correlation and is most in line with the actual situation, so the third on-site model is selected as the final model for calculating other viscosity data. 
     The on-site measurement results of the third on-site model are compared with those of a 6-speed viscometer (Fann35), which shows that the third on-site model is the most suitable. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Measurement 
                 Measuring 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
                 PV 
                 YP 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 34 
                 7 
                 5 
                 4 
                 3 
                 1 
                 0.5 
                 0.002 
                 1.533 
               
               
                 System measurement  
                 34 
                 8.6 
                 5.4 
                 4.3 
                 2.9 
                 1.3 
                 1.2 
                 0.0032 
                 1.1538 
               
               
                 device 
               
               
                   
               
            
           
         
       
     
     If the viscosity data calculated by the first on-site model is directly selected without performing on-site model optimization, as shown in the table below, the deviation will increase significantly. The difference percentage of viscosity corresponding to θ6 is 0.9/1=90%, the difference percentage of viscosity corresponding to θ3 is 1.4/0.5=280%, and the difference percentage of YP is 0.5804/1.533=38%. The calculation of the preferred third model of the present invention shows that the difference percentage of viscosity corresponding to θ6 is 0.3/1=30%, the difference percentage of viscosity corresponding to θ3 is 0.7/0.5=140%, and the difference percentage of YP is 0.3792/1.533=25%. 
     In conclusion, compared with the measurement results of Fann35, the calculation results of the optimal on-site model (third on-site model) determined by the correlations of the actual shear stress τw i  and the predicted shear stresses of the on-site models are the most accurate. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Measurement  
                 Measuring 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
                 PV 
                 YP 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 34 
                 7 
                 5 
                 4 
                 3 
                 1 
                 0.5 
                 0.002 
                 1.533 
               
               
                 System measurement  
                 34 
                 9.0 
                 5.4 
                 4.2 
                 3.0 
                 1.9 
                 1.9 
                 0.0035 
                 0.9526 
               
               
                 device 
               
               
                   
               
            
           
         
       
     
     A second embodiment is described below. 
     In the second embodiment of offline checking, the offline curved pipe has a total volume V 1 =1.04 and a length len 1 =5.57476 m; the offline straight pipe has an inner diameter d ts1 =0.01056 m; and a second offline drilling fluid has a density ρ 1 =1,953 kg/m 3 . 
     The inner diameter of the offline curved pipe is calculated as: d tc1 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           V 
                           1 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         
                           len 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, the second offline drilling fluid flows through the pipe for k=17 times. 
     A flow velocity v sk  of the second offline drilling fluid at the k-th time in a straight pipe and a flow velocity v ck  thereof at the k-th time in the curved pipe are shown in the table below. 
     An average pressure difference ΔP ck /ΔL ck  of the offline curved pipe and an average pressure difference ΔP sk /ΔL sk  of the offline straight pipe are also shown in the table below. 
     The second offline drilling fluid flows through for 17 times, and its friction coefficient f ck  in the offline curved pipe and friction coefficient f sk  in the offline straight pipe are calculated by formulas (1) and (2), and are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     ck 
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           
                             ρ 
                             1 
                           
                           * 
                         
                         ⁢ 
                         
                           v 
                           ck 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           ck 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     sk 
                   
                   = 
                   
                     
                       
                         d 
                         
                           ts 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           
                             ρ 
                             1 
                           
                           * 
                         
                         ⁢ 
                         
                           v 
                           sk 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           sk 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The corresponding actual friction coefficient ratios y k  are shown in the table below, where y k =f ck /f sk . 
     In this embodiment, an average viscosity of the second offline drilling fluid is μ 1 =0.02639 Pa·s. 
     The Dean numbers D nk  of the second offline drilling fluid flowing through the curved pipe for 17 times are calculated according to formula (6), which are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     D 
                     nk 
                   
                   = 
                   
                     
                       
                         
                           
                             ρ 
                             1 
                           
                           * 
                         
                         ⁢ 
                         
                           
                             v 
                             ck 
                           
                           * 
                         
                         ⁢ 
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       
                         μ 
                         1 
                       
                     
                     * 
                     
                       
                         
                           d 
                           
                             tc 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         
                           D 
                           
                             c 
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Number 
                 ΔP ck / 
                 ΔP sk / 
                   
                   
                   
                   
                   
                   
               
               
                 of times 
                 ΔL ck   
                 ΔL sk   
                 v sk   
                 v ck   
                 f sk   
                 f ck   
                 y k   
                 D nk   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 1 
                  6.249 
                  8.759 
                 0.80 
                 0.81 
                 0.03 
                 0.04 
                 1.37 
                 119.74 
               
               
                 2 
                  7.020 
                  9.999 
                 0.91 
                 0.91 
                 0.02 
                 0.03 
                 1.39 
                 135.57 
               
               
                 3 
                  7.447 
                 10.907 
                 0.97 
                 0.98 
                 0.02 
                 0.03 
                 1.43 
                 145.85 
               
               
                 4 
                  8.008 
                 12.182 
                 1.07 
                 1.08 
                 0.02 
                 0.03 
                 1.49 
                 166.80 
               
               
                 5 
                  8.420 
                 12.888 
                 1.11 
                 1.12 
                 0.02 
                 0.03 
                 1.50 
                 167.88 
               
               
                 6 
                  8.583 
                 13.091 
                 1.13 
                 1.14 
                 0.02 
                 0.03 
                 1.49 
                 172.00 
               
               
                 7 
                  9.179 
                 14.505 
                 1.21 
                 1.22 
                 0.02 
                 0.03 
                 1.54 
                 184.56 
               
               
                 8 
                  9.603 
                 15.250 
                 1.29 
                 1.30 
                 0.02 
                 0.02 
                 1.55 
                 199.90 
               
               
                 9 
                 10.128 
                 16.783 
                 1.37 
                 1.38 
                 0.01 
                 0.02 
                 1.62 
                 215.73 
               
               
                 10 
                 10.338 
                 17.224 
                 1.41 
                 1.43 
                 0.01 
                 0.02 
                 1.63 
                 224.42 
               
               
                 11 
                 10.880 
                 18.257 
                 1.47 
                 1.48 
                 0.01 
                 0.02 
                 1.64 
                 230.18 
               
               
                 12 
                 13.825 
                 24.076 
                 1.82 
                 1.83 
                 0.01 
                 0.02 
                 1.70 
                 277.64 
               
               
                 13 
                 13.706 
                 24.131 
                 1.83 
                 1.85 
                 0.01 
                 0.02 
                 1.72 
                 284.93 
               
               
                 14 
                 14.606 
                 26.401 
                 1.96 
                 1.98 
                 0.01 
                 0.02 
                 1.77 
                 305.94 
               
               
                 15 
                 15.228 
                 27.892 
                 2.07 
                 2.09 
                 0.01 
                 0.02 
                 1.79 
                 326.25 
               
               
                 16 
                 16.025 
                 29.395 
                 2.14 
                 2.16 
                 0.01 
                 0.02 
                 1.79 
                 333.56 
               
               
                 17 
                 16.940 
                 30.332 
                 2.21 
                 2.23 
                 0.01 
                 0.02 
                 1.75 
                 333.69 
               
               
                   
               
            
           
         
       
     
     Three prediction models are fitted by the actual friction coefficient ratios yk and the Dean numbers D nk  as follows: 
     a first prediction model: 
         ŷ   1k   =a*D   nk   b   +c   (3)
 
     where, a=0.0576, b=0.5, and c=0.745. 
     a second prediction model: 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ^ 
                     
                     
                       2 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         
                           a 
                           * 
                         
                         ⁢ 
                         
                           D 
                           nk 
                           b 
                         
                       
                       
                         
                           7 
                           ⁢ 
                           0 
                         
                         + 
                         
                           D 
                           nk 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where, a=0.0644, and b=1.4654. 
     a third prediction model: 
         ŷ   3k =1+ a *(log 10   D   nk ) b   (5)
 
     where, a=0.0231, and b=3.8241. 
     The predicted friction coefficients of the third prediction models are shown in the table below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Number  
                   
                   
                   
               
               
                   
                 of times 
                 ŷ 1k   
                 ŷ 2k   
                 ŷ 3k   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 
                 1.376 
                 1.377 
                 1.379 
               
               
                   
                 2 
                 1.416 
                 1.417 
                 1.418 
               
               
                   
                 3 
                 1.441 
                 1.442 
                 1.443 
               
               
                   
                 4 
                 1.489 
                 1.491 
                 1.490 
               
               
                   
                 5 
                 1.492 
                 1.493 
                 1.492 
               
               
                   
                 6 
                 1.501 
                 1.502 
                 1.501 
               
               
                   
                 7 
                 1.528 
                 1.529 
                 1.528 
               
               
                   
                 8 
                 1.560 
                 1.561 
                 1.560 
               
               
                   
                 9 
                 1.591 
                 1.593 
                 1.591 
               
               
                   
                 10 
                 1.608 
                 1.610 
                 1.608 
               
               
                   
                 11 
                 1.619 
                 1.620 
                 1.619 
               
               
                   
                 12 
                 1.705 
                 1.705 
                 1.704 
               
               
                   
                 13 
                 1.718 
                 1.717 
                 1.717 
               
               
                   
                 14 
                 1.753 
                 1.752 
                 1.752 
               
               
                   
                 15 
                 1.786 
                 1.784 
                 1.785 
               
               
                   
                 16 
                 1.797 
                 1.795 
                 1.796 
               
               
                   
                 17 
                 1.798 
                 1.795 
                 1.797 
               
               
                   
                   
               
            
           
         
       
     
     A correlation R 11   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the first prediction model, a correlation R 12   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the second prediction model and a correlation R 13   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the third prediction model are calculated according to formulas (7), (8) and (9), respectively. 
     Through calculation, R 11   2 =0.9833, R 12   2 =0.9843 and R 13   2 =0.9828. 
     To sum up, in this embodiment, for the second offline drilling fluid, the first prediction model is the optimal prediction model. According to the optimal prediction model, the relationship constants between the friction coefficients are a=0.0644 and b=1.4654, which are used for the on-site measurement on the rheological property of the drilling fluid. 
     The on-site measurement on the rheological property of the drilling fluid in the curved pipe is described below. 
     In a second embodiment of the on-site measurement, the density of a second on-site drilling fluid is ρ 2 =1,300 kg/m 3 . 
     The on-site curved pipe has a total volume V 2 =1.04 l and a length len 2 =5.57476 m. 
     An inner diameter of the on-site curved pipe is calculated as d tc2 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           ∇ 
                           2 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         
                           len 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, a second offline drilling fluid flows through the on-site pipe for i=17 times. 
     A i-th flow velocity v ci  of the second on-site drilling fluid at the i-th time in the curved pipe and an average pressure difference thereof in the curved pipe ΔP ci /ΔL ci  are shown in the table below. 
     The measured parameters of the on-site drilling fluid in the curved pipe are shown in the table below. The flow velocity of the drilling fluid is increased in the curved pipe in an ascending order to keep a laminar flow state of the drilling fluid. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                   
                 Rate  
                   
                   
                   
                   
               
               
                 Number 
                 of flow 
                 Temperature 
                   
                   
                   
               
               
                 of times 
                 (lpm) 
                 (° C.) 
                 ΔPci/ΔLci 
                 ρ2 
                 vci 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 4.212 
                 29 
                 8.759 
                 1960.5 
                 0.809 
               
               
                 2 
                 4.761 
                 29 
                 9.999 
                 1951.0 
                 0.914 
               
               
                 3 
                 5.088 
                 29 
                 10.907 
                 1950.2 
                 0.977 
               
               
                 4 
                 5.642 
                 29 
                 12.182 
                 1950.2 
                 1.083 
               
               
                 5 
                 5.813 
                 29 
                 12.888 
                 1944.5 
                 1.116 
               
               
                 6 
                 5.933 
                 29 
                 13.091 
                 1949.2 
                 1.139 
               
               
                 7 
                 6.358 
                 29 
                 14.505 
                 1947.9 
                 1.221 
               
               
                 8 
                 6.776 
                 29 
                 15.250 
                 1943.1 
                 1.301 
               
               
                 9 
                 7.207 
                 29 
                 16.783 
                 1955.0 
                 1.384 
               
               
                 10 
                 7.425 
                 29 
                 17.224 
                 1956.0 
                 1.425 
               
               
                 11 
                 7.716 
                 29 
                 18.257 
                 1955.1 
                 1.481 
               
               
                 12 
                 9.544 
                 29 
                 24.076 
                 1958.6 
                 1.832 
               
               
                 13 
                 9.631 
                 29 
                 24.131 
                 1956.9 
                 1.849 
               
               
                 14 
                 10.306 
                 29 
                 26.401 
                 1955.3 
                 1.978 
               
               
                 15 
                 10.868 
                 29 
                 27.892 
                 1955.2 
                 2.086 
               
               
                 16 
                 11.263 
                 29 
                 29.395 
                 1958.4 
                 2.162 
               
               
                 17 
                 11.595 
                 29 
                 30.332 
                 1954.3 
                 2.226 
               
               
                   
               
            
           
         
       
     
     The second on-site drilling fluid flows through the curved pipe for 17 times, and its friction coefficient f ci  in the curved pipe is calculated by formula (11), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           
                             ρ 
                             2 
                           
                           * 
                         
                         ⁢ 
                         
                           v 
                           ci 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           P 
                           ci 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           L 
                           ci 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is calculated according to the selected optimal offline model. In this embodiment, the optimal prediction model is the second prediction model: 
     
       
         
           
             
               
                 
                   y 
                   ^ 
                 
                 
                   2 
                   ⁢ 
                   k 
                 
               
               = 
               
                 1 
                 + 
                 
                   
                     
                       a 
                       * 
                     
                     ⁢ 
                     
                       D 
                       nk 
                       b 
                     
                   
                   
                     
                       7 
                       ⁢ 
                       0 
                     
                     + 
                     
                       D 
                       nk 
                     
                   
                 
               
             
             , 
           
         
       
     
     where the relationship constants between the friction coefficients are respectively: a=0.0644 and b=1.4654. 
     The Reynolds number R ei  of the on-site curved pipe is expressed by formula (12): 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         ei 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               a 
                               * 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     R 
                                     ei 
                                   
                                   * 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       d 
                                       
                                         tc 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                     
                                       D 
                                       
                                         c 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           b 
                         
                         + 
                         c 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is shown in the table below. 
     According to the Reynolds number R ei  of the on-site curved pipe, a shear stress τw i  of the drilling fluid in the on-site curved pipe is calculated, which is expressed by formula (15), and is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     τ 
                     wi 
                   
                   = 
                   
                     
                       8 
                       ⁢ 
                       
                         
                           ρ 
                           2 
                         
                         * 
                       
                       ⁢ 
                       
                         v 
                         ci 
                         2 
                       
                     
                     
                       R 
                       ei 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     An intermediate parameter N i  is calculated according to formula (17), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     N 
                     i 
                   
                   = 
                   
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             τ 
                             
                               w 
                               i 
                             
                           
                         
                         ) 
                       
                     
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           ln 
                           ⁢ 
                           
                             
                               
                                 8 
                                 * 
                               
                               ⁢ 
                               
                                 v 
                                 ci 
                               
                             
                             
                               d 
                               
                                 tc 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     A shear rate γ i  of the second drilling fluid in the on-site curved pipe is calculated according to formula (16), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     γ 
                     i 
                   
                   = 
                   
                     
                       
                         
                           8 
                           * 
                         
                         ⁢ 
                         
                           v 
                           ci 
                         
                       
                       
                         d 
                         
                           t 
                           ⁢ 
                           c 
                           ⁢ 
                           2 
                         
                       
                     
                     * 
                     
                       
                         
                           
                             3 
                             * 
                           
                           ⁢ 
                           
                             N 
                             i 
                           
                         
                         + 
                         1 
                       
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           N 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of times 
                 f ci   
                 R ei   
                 τw i   
                 N i   
                 γ i   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 0.0359 
                 614.0792 
                 16.6964 
                 0.9448 
                 624.1797 
               
               
                 2 
                 0.0322 
                 707.0957 
                 18.4418 
                 0.9517 
                 704.3091 
               
               
                 3 
                 0.0308 
                 750.4231 
                 19.8311 
                 0.9554 
                 751.8029 
               
               
                 4 
                 0.0280 
                 852.8917 
                 21.4602 
                 0.9612 
                 832.4728 
               
               
                 5 
                 0.0280 
                 853.1906 
                 22.7020 
                 0.9628 
                 857.2334 
               
               
                 6 
                 0.0272 
                 885.4715 
                 22.8450 
                 0.9640 
                 874.7194 
               
               
                 7 
                 0.0263 
                 928.1204 
                 25.0111 
                 0.9678 
                 936.3869 
               
               
                 8 
                 0.0244 
                 1026.7406 
                 25.6190 
                 0.9714 
                 997.0713 
               
               
                 9 
                 0.0236 
                 1074.6661 
                 27.8581 
                 0.9748 
                 1059.5306 
               
               
                 10 
                 0.0228 
                 1125.6006 
                 28.2435 
                 0.9765 
                 1091.0656 
               
               
                 11 
                 0.0224 
                 1153.9089 
                 29.7386 
                 0.9786 
                 1133.1933 
               
               
                 12 
                 0.0193 
                 1418.3999 
                 37.0815 
                 0.9905 
                 1397.4120 
               
               
                 13 
                 0.0190 
                 1448.0218 
                 36.9546 
                 0.9910 
                 1409.9395 
               
               
                 14 
                 0.0181 
                 1540.8543 
                 39.7384 
                 0.9948 
                 1507.3717 
               
               
                 15 
                 0.0172 
                 1654.1138 
                 41.1553 
                 0.9978 
                 1588.2620 
               
               
                 16 
                 0.0169 
                 1702.5492 
                 43.0205 
                 0.9998 
                 1645.2677 
               
               
                 17 
                 0.0165 
                 1761.7294 
                 43.9646 
                 1.0014 
                 1692.9891 
               
               
                   
               
            
           
         
       
     
     According to the shear stress τw i  and the shear rate γ i  of the second on-site drilling fluid, at least three on-site models are fitted, which are respectively: 
     a first on-site model: 
       {circumflex over (τ)} w   1i   =YP+PV*γ   i   (18)
 
     where, PV=0.026, and YP=0.241. 
     a second on-site model: 
       {circumflex over (τ)} w   2i   =K*γ   i   n   (19),
 
     where K=0.0278, and n=0.9917. 
     a third on-site model: 
       {circumflex over (τ)} w   2i =τ 0   +K*γ   i   n   (20),
 
     Where, n=0.9991, K=0.0262, and τ 0 =0.2146. 
     Then the following parameters are respectively calculated: 
     a correlation R 21   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the first on-site model; 
     a correlation R 22   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the second on-site model; and 
     a correlation R 23   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the third on-site model. 
     These parameters are calculated according to formulas (21), (22) and (23), respectively. 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     1 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       2 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     2 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       3 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     3 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Through calculation, R 21   2 =0.998873, R 22   2 =0.996445 and R 23   2 =0.998873. The first and third on-site models have the maximum correlation and are most in line with the actual situation, so the first and third on-site models are selected as the final models for calculating other viscosity data. 
     The on-site measurement results of the first on-site model are compared with those of the 6-speed viscometer, which shows that the first on-site model is the most suitable. 
     
       
         
           
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 29 
                 50 
                 27 
                 19 
                 11 
                 1 
                 0.5 
               
               
                 System measurement 
                 29 
                 52.42 
                 26.45 
                 17.79 
                 9.13 
                 0.99 
                 0.73 
               
               
                 device 
               
               
                   
               
            
           
         
       
     
     The on-site measurement results of the third on-site model are compared with those of the 6-speed viscometer, which shows that the third on-site model is the most suitable. 
     
       
         
           
               
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
                 n 
                 K 
                 τ0 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 29 
                 50 
                 27 
                 19 
                 11 
                 1 
                 0.5 
                 0.9015 
                 0.0490 
                 0.26 
               
               
                 System measurement 
                 29 
                 52.42 
                 26.44 
                 17.77 
                 9.10 
                 0.94 
                 0.68 
                 0.9991 
                 0.0262 
                 0.21 
               
               
                 device 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     If the viscosity data calculated by the second on-site model is directly selected without performing on-site model optimization, as shown in the table below, the deviation will increase significantly. The difference percentage of viscosity corresponding to θ100 is 2.13/11=19% and the difference percentage of viscosity corresponding to θ6 is 0.46/1=46%. The calculation of the preferred third model of the present invention shows that the difference percentage of viscosity corresponding to θ100 is 1.9/11=17% and the difference percentage of viscosity corresponding to θ6 is 0.06/1=6%. The calculation of the preferred first model of the present invention shows that the difference percentage of viscosity corresponding to θ100 is 1.83/11=17% and the difference percentage of viscosity corresponding to θ6 is 0.01/1=1%. 
     
       
         
           
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 29 
                 50 
                 27 
                 19 
                 11 
                 1 
                 0.5 
               
               
                 System 
                   
                   
                   
                   
                   
                   
                   
               
               
                 measurement 
                 29 
                 52.43 
                 26.37 
                 17.64 
                 8.87 
                 0.54 
                 0.27 
               
               
                 device 
               
               
                   
               
            
           
         
       
     
     In conclusion, compared with the measurement results of Fann35, the calculation results of the optimal on-site models (the first and third on-site models) determined by the correlations of the actual shear stress τw i  and the predicted shear stresses of the on-site models are the most accurate. 
     A third embodiment is described below. 
     In the third embodiment of offline checking, the offline curved pipe has a total volume V 1 =1.04 l and a length len 1 =5.57476 m; the offline straight pipe has an inner diameter d ts1 =0.01056 m; and a third offline drilling fluid has a density ρ 1 =1,227 kg/m 3 . 
     The inner diameter of the offline curved pipe is calculated as: d tc1 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       tc 
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           V 
                           1 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         
                           len 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, the third offline drilling fluid flows through the pipe for k=13 times. 
     A flow velocity v sk  of the third offline drilling fluid at the k-th time in a straight pipe and a flow velocity v ck  thereof at the k-th time in the curved pipe are shown in the table below. 
     An average pressure difference ΔP ck /ΔL ck  of the offline curved pipe and an average pressure difference ΔP sk /ΔL sk  of the offline straight pipe are also shown in the table below. 
     The third offline drilling fluid flows through the pipe for 13 times, and its friction coefficient f ck  in the curved pipe and friction coefficient f sk  in the straight pipe are calculated by formulas (1) and (2), and are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           tc 
                           ⁢ 
                           1 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             1 
                           
                         
                         ⋆ 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     f 
                     
                       s 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         d 
                         
                           ts 
                           ⁢ 
                           1 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             1 
                           
                         
                         ⋆ 
                         
                           v 
                           sk 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           sk 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           sk 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The corresponding actual friction coefficient ratios y k  are shown in the table below, where y k =f ck /f sk . 
     In this embodiment, an average viscosity of the third offline drilling fluid is μ 1 =0.01455 Pa·s. 
     The Dean numbers D nk  of the third offline drilling fluid flowing through the curved pipe for 13 times are calculated according to formula (6), which are shown in the table below. 
     
       
         
           
             
               
                 
                   
                     D 
                     
                       n 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         ⋆ 
                         
                           v 
                           
                             c 
                             ⁢ 
                             k 
                           
                         
                         ⋆ 
                         
                           d 
                           
                             tc 
                             ⁢ 
                             1 
                           
                         
                       
                       
                         μ 
                         1 
                       
                     
                     * 
                     
                       
                         
                           d 
                           
                             tc 
                             ⁢ 
                             1 
                           
                         
                         
                           D 
                           
                             c 
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Number 
                 ΔP ck / 
                 ΔP sk / 
                   
                   
                   
                   
                   
                   
               
               
                 of times 
                 ΔL ck   
                 ΔL sk   
                 v sk   
                 
                   vck 
                 
                 f sk   
                 f ck   
                 y k   
                 D nk   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 2.634 
                 3.108 
                 0.56 
                 0.56 
                 0.04 
                 0.04 
                 1.15 
                  85.88 
               
               
                 2 
                 2.788 
                 3.381 
                 0.61 
                 0.61 
                 0.03 
                 0.04 
                 1.19 
                  96.66 
               
               
                 3 
                 2.881 
                 3.555 
                 0.64 
                 0.65 
                 0.03 
                 0.04 
                 1.21 
                 105.05 
               
               
                 4 
                 3.050 
                 3.808 
                 0.69 
                 0.70 
                 0.03 
                 0.03 
                 1.22 
                 114.64 
               
               
                 5 
                 3.363 
                 4.360 
                 0.79 
                 0.80 
                 0.02 
                 0.03 
                 1.27 
                 134.93 
               
               
                 6 
                 3.447 
                 4.622 
                 0.83 
                 0.84 
                 0.02 
                 0.03 
                 1.31 
                 145.22 
               
               
                 7 
                 3.555 
                 4.894 
                 0.87 
                 0.88 
                 0.02 
                 0.03 
                 1.35 
                 154.57 
               
               
                 8 
                 3.664 
                 5.160 
                 0.91 
                 0.92 
                 0.02 
                 0.03 
                 1.38 
                 166.17 
               
               
                 9 
                 3.784 
                 5.453 
                 0.96 
                 0.97 
                 0.02 
                 0.03 
                 1.41 
                 176.43 
               
               
                 10 
                 3.909 
                 5.734 
                 1.01 
                 1.02 
                 0.02 
                 0.02 
                 1.43 
                 190.62 
               
               
                 11 
                 4.036 
                 6.001 
                 1.05 
                 1.06 
                 0.02 
                 0.02 
                 1.45 
                 198.90 
               
               
                 12 
                 4.177 
                 6.287 
                 1.09 
                 1.10 
                 0.02 
                 0.02 
                 1.47 
                 208.59 
               
               
                 13 
                 4.215 
                 6.420 
                 1.11 
                 1.12 
                 0.01 
                 0.02 
                 1.49 
                 211.66 
               
               
                   
               
            
           
         
       
     
     Three prediction models are fitted by the actual friction coefficient ratios y k  and the Dean numbers D nk  as follows: 
     a first prediction model: 
         ŷ   1k   =a*D   nk   b   +c   (3)
 
     where, a=0.0645, b=0.5, and c=0.5424. 
     a second prediction model: 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ˆ 
                     
                     
                       2 
                       ⁢ 
                       k 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         a 
                         ⋆ 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                           b 
                         
                       
                       
                         
                           7 
                           ⁢ 
                           0 
                         
                         + 
                         
                           D 
                           
                             n 
                             ⁢ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where, a=0.0045, and b=1.9298. 
     a third prediction model: 
         ŷ   3k =1+ a *(log 10   D   nk ) b   (5)
 
     where, a=0.0025, and b=6.2539. 
     The predicted friction coefficients of the third prediction models are shown in the table below. 
     
       
         
           
               
               
               
               
             
               
                   
               
               
                 Number  
                   
                   
                   
               
               
                 of times 
                 ŷ 1k   
                 ŷ 2k   
                 ŷ 3k   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 1 
                 1.1401 
                 1.1555 
                 1.1547 
               
               
                 2 
                 1.1765 
                 1.1827 
                 1.1822 
               
               
                 3 
                 1.2035 
                 1.2042 
                 1.2040 
               
               
                 4 
                 1.2330 
                 1.2292 
                 1.2291 
               
               
                 5 
                 1.2916 
                 1.2828 
                 1.2830 
               
               
                 6 
                 1.3196 
                 1.3103 
                 1.3106 
               
               
                 7 
                 1.3443 
                 1.3354 
                 1.3358 
               
               
                 8 
                 1.3738 
                 1.3668 
                 1.3671 
               
               
                 9 
                 1.3991 
                 1.3946 
                 1.3948 
               
               
                 10 
                 1.4329 
                 1.4332 
                 1.4333 
               
               
                 11 
                 1.4520 
                 1.4557 
                 1.4557 
               
               
                 12 
                 1.4739 
                 1.4822 
                 1.4819 
               
               
                 13 
                 1.4807 
                 1.4905 
                 1.4902 
               
               
                   
               
            
           
         
       
     
     A correlation R 11   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the first prediction model, a correlation R 12   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the second prediction model and a correlation R 13   2  between the actual friction coefficient ratio y k  and a predicted friction coefficient ratio of the third prediction model are calculated according to formulas (7), (8) and (9), respectively. 
     Through calculation, R 11   2 =0.9923, R 12   2 =0.9948 and R 13   2 =0.9949. 
     To sum up, in this embodiment, for the third offline drilling fluid, the third prediction model is the optimal prediction model. According to the optimal prediction model, the relationship constants between the friction coefficients are a=0.0025 and b=6.2539, which are used for the on-site measurement on the rheological property of the drilling fluid. 
     The on-site measurement on the rheological property of the drilling fluid in the curved pipe is described below. 
     In the third embodiment of the on-site measurement, the density of a third on-site drilling fluid is ρ 3 =1,227 kg/m 3 . 
     The on-site curved pipe has a total volume V 2 =1.04 l and a length len 2 =5.57476 m. 
     An inner diameter of the on-site curved pipe is calculated as d tc2 =0.01051 m: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       t 
                       ⁢ 
                       c 
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           V 
                           2 
                         
                       
                       
                         
                           π 
                           * 
                         
                         ⁢ 
                         le 
                         ⁢ 
                         
                           n 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, the third offline drilling fluid flows through the on-site pipe for i=13 times. 
     A i-th flow velocity v ci  of the second on-site drilling fluid at the i-th time in the curved pipe and an average pressure difference thereof in the curved pipe ΔP ci /ΔL ci  are shown in the table below. 
     The measured parameters of the on-site drilling fluid in the curved pipe are shown in the table below. The flow velocity of the drilling fluid is increased in the curved pipe in an ascending order to keep a laminar flow state of the drilling fluid. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                   
                 Rate  
                   
                   
                   
                   
               
               
                 Number  
                 of flow 
                 Temperature 
                   
                   
                   
               
               
                 of times 
                 (lpm) 
                 (° C.) 
                 ΔP ci /ΔL ci   
                 ρ 2   
                 vc i   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 2.926 
                 29 
                 3.11 
                 1227.7 
                 0.5617 
               
               
                 2 
                 3.195 
                 29 
                 3.38 
                 1227.5 
                 0.6133 
               
               
                 3 
                 3.385 
                 29 
                 3.55 
                 1228.0 
                 0.6497 
               
               
                 4 
                 3.640 
                 29 
                 3.81 
                 1226.4 
                 0.6988 
               
               
                 5 
                 4.146 
                 29 
                 4.36 
                 1227.3 
                 0.7958 
               
               
                 6 
                 4.355 
                 29 
                 4.62 
                 1226.6 
                 0.8360 
               
               
                 7 
                 4.563 
                 29 
                 4.89 
                 1226.8 
                 0.8759 
               
               
                 8 
                 4.802 
                 29 
                 5.16 
                 1227.3 
                 0.9218 
               
               
                 9 
                 5.028 
                 29 
                 5.45 
                 1227.5 
                 0.9652 
               
               
                 10 
                 5.313 
                 29 
                 5.73 
                 1226.9 
                 1.0199 
               
               
                 11 
                 5.512 
                 29 
                 6.00 
                 1227.9 
                 1.0582 
               
               
                 12 
                 5.741 
                 29 
                 6.29 
                 1228.7 
                 1.1021 
               
               
                 13 
                 5.815 
                 29 
                 6.42 
                 1226.2 
                 1.1163 
               
               
                   
               
            
           
         
       
     
     The second on-site drilling fluid flows through the curved pipe for 13 times, and its friction coefficient f ci  in the curved pipe is calculated by formula (11), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     f 
                     ci 
                   
                   = 
                   
                     
                       
                         d 
                         
                           t 
                           ⁢ 
                           c 
                           ⁢ 
                           2 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                             ρ 
                             2 
                           
                         
                         ⋆ 
                         
                           v 
                           ci 
                           2 
                         
                       
                     
                     * 
                     
                       
                         Δ 
                         ⁢ 
                         
                           P 
                           ci 
                         
                       
                       
                         Δ 
                         ⁢ 
                         
                           L 
                           ci 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is calculated according to the selected optimal offline model. In this embodiment, the optimal prediction model is the third prediction model: ŷ 3k =1+a*(log 10  D nk ) b , where the relationship constants between the friction coefficients are respectively: a=0.0025 and b=6.2539. 
     The Reynolds number R ei  of the on-site curved pipe is expressed by formula (12): 
     
       
         
           
             
               
                 
                   
                     f 
                     
                       c 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         1 
                         ⁢ 
                         6 
                       
                       
                         R 
                         
                           e 
                           ⁢ 
                           i 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           a 
                           * 
                           
                             
                               ( 
                               
                                 
                                   log 
                                   
                                     1 
                                     ⁢ 
                                     0 
                                   
                                 
                                 ( 
                                 
                                   
                                     R 
                                     
                                       e 
                                       ⁢ 
                                       i 
                                     
                                   
                                   * 
                                   
                                     
                                       
                                         d 
                                         
                                           t 
                                           ⁢ 
                                           c 
                                           ⁢ 
                                           2 
                                         
                                       
                                       
                                         D 
                                         
                                           c 
                                           ⁢ 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                               ) 
                             
                             b 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The Reynolds number R ei  of the on-site curved pipe is shown in the table below. 
     According to the Reynolds number R ei  of the on-site curved pipe, a shear stress τw i  of the drilling fluid in the on-site curved pipe is calculated, which is expressed by formula (15), and is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     τ 
                     
                       w 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         8 
                         ⁢ 
                         
                           ρ 
                           2 
                         
                       
                       ⋆ 
                       
                         v 
                         ci 
                         2 
                       
                     
                     
                       R 
                       
                         e 
                         ⁢ 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     An intermediate parameter N i  is calculated according to formula (17), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     N 
                     i 
                   
                   = 
                   
                     
                       d 
                       ⁡ 
                       ( 
                       
                         ln 
                         ⁢ 
                            
                         
                           τ 
                           wi 
                         
                       
                       ) 
                     
                     
                       d 
                       ⁡ 
                       ( 
                       
                         ln 
                         ⁢ 
                         
                           
                             
                               8 
                               * 
                             
                             ⁢ 
                             
                               v 
                               ci 
                             
                           
                           
                             d 
                             
                               tc 
                               ⁢ 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     A shear rate γ i  of the third drilling fluid in the on-site curved pipe is calculated according to formula (16), which is shown in the table below. 
     
       
         
           
             
               
                 
                   
                     γ 
                     i 
                   
                   = 
                   
                     
                       
                         
                           8 
                           * 
                         
                         ⁢ 
                         
                           v 
                           ci 
                         
                       
                       
                         d 
                         
                           t 
                           ⁢ 
                           c 
                           ⁢ 
                           2 
                         
                       
                     
                     * 
                     
                       
                         
                           
                             3 
                             * 
                           
                           ⁢ 
                           
                             N 
                             i 
                           
                         
                         + 
                         1 
                       
                       
                         
                           4 
                           * 
                         
                         ⁢ 
                         
                           N 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
               
               
                 Number  
                   
                   
                   
                   
               
               
                 of times 
                 f ci   
                 R ei   
                 τw i   
                 γ i   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 0.042 
                 438.213 
                 7.072 
                 474.696 
               
               
                 2 
                 0.038 
                 491.082 
                 7.521 
                 518.882 
               
               
                 3 
                 0.036 
                 534.109 
                 7.764 
                 550.185 
               
               
                 4 
                 0.033 
                 589.713 
                 8.124 
                 592.341 
               
               
                 5 
                 0.029 
                 699.632 
                 8.888 
                 675.882 
               
               
                 6 
                 0.028 
                 739.707 
                 9.271 
                 710.482 
               
               
                 7 
                 0.027 
                 779.393 
                 9.661 
                 744.922 
               
               
                 8 
                 0.026 
                 838.195 
                 9.953 
                 784.520 
               
               
                 9 
                 0.025 
                 885.939 
                 10.327 
                 822.071 
               
               
                 10 
                 0.024 
                 970.584 
                 10.518 
                 869.288 
               
               
                 11 
                 0.023 
                 1016.091 
                 10.825 
                 902.452 
               
               
                 12 
                 0.022 
                 1075.315 
                 11.102 
                 940.432 
               
               
                 13 
                 0.022 
                 1080.252 
                 11.316 
                 952.785 
               
               
                   
               
            
           
         
       
     
     According to the shear stress τw i  and the shear rate γ i  of the third on-site drilling fluid, at least three on-site models are fitted, which are respectively: 
     a first on-site model: 
       {circumflex over (τ)} w   1i   =YP+PV*γ   i   (18)
 
     where, PV=0.0088, and YP=2.98. 
     a second on-site model: 
       {circumflex over (τ)} w   2i   =K*γ   i   n   (19),
 
     where, K=0.6715, and n=0.1126. 
     a third on-site model: 
       {circumflex over (τ)} w   2i =τ 0   +K*γ   i   n   (20),
 
     where, n=0.6716, K=0.1126, and τ 0 =0.001. 
     Then the following parameters are respectively calculated. 
     a correlation R 21   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the first on-site model; 
     a correlation R 22   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the second on-site model; and 
     a correlation R 23   2  between the shear stress τw i  of the second on-site drilling fluid and a predicted shear stress of the third on-site model. 
     These parameters are calculated according to formulas (21), (22) and (23), respectively. 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       1 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     1 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       2 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     2 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     R 
                     
                       2 
                       ⁢ 
                       3 
                     
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τ 
                                 ⁢ 
                                 
                                   
                                     w 
                                     ˆ 
                                   
                                   
                                     3 
                                     ⁢ 
                                     i 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                           
                         
                           
                             ( 
                             
                               
                                 τw 
                                 i 
                               
                               - 
                               
                                 τw 
                                 _ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Through calculation, R 21   2 =0.996314, R 22   2 =0.997775 and R 23   2 =0.997775. The second and third on-site models have the maximum correlation and are most in line with the actual situation, so the second and third on-site models are selected as the final models for calculating other viscosity data. 
     The on-site measurement results of the second on-site model are compared with those of the 6-speed viscometer, which shows that the third on-site model is the most suitable. 
     
       
         
           
               
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
                 n 
                 K 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 29 
                 22 
                 14 
                 10 
                 6.5 
                 1 
                 0.8 
                 0.6521 
                 0.1226 
               
               
                 System measurement 
                 29 
                 23.1 
                 14.5 
                 11.1 
                 6.9 
                 1.0 
                 0.7 
                 0.6715 
                 0.1126 
               
               
                 device 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     The on-site measurement results of the third on-site model are compared with those of the 6-speed viscometer, which shows that the third on-site model is the most suitable. 
     
       
         
           
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
                 n 
                 K 
                 τ0 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Fann35 (control) 
                 29 
                 22 
                 14 
                 10 
                 6.5 
                 1 
                 0.8 
                 0.6835 
                 0.0950 
                 0.4088 
               
               
                 System measurement 
                 29 
                 23.1 
                 14.5 
                 11.1 
                 6.9 
                 1.0 
                 0.7 
                 0.6716 
                 0.1126 
                 0.001  
               
               
                 device 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     If the viscosity data calculated by the first on-site model is directly selected without performing on-site model optimization, as shown in the table below, the deviation will increase significantly. The difference percentage of viscosity corresponding to θ100 is 2.2/6.5=35%, the difference percentage of viscosity corresponding to θ6 is 5/1=500%, and the difference percentage of viscosity corresponding to θ3 is 5.1/0.8=639%. The calculation results of the preferred second and third models of the present invention show that the difference percentage of viscosity corresponding to θ100 is 0.4/6.5=7%, the difference percentage of viscosity corresponding to θ6 is 0.1/5=5% and the difference percentage of viscosity corresponding to θ3 is −0.1/0.8=−17%. 
     
       
         
           
               
               
               
            
               
                   
               
               
                 Measurement 
                 Measuring 
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 instrument 
                 temperature/° C. 
                 θ600 
                 θ300 
                 θ200 
                 θ100 
                 θ6 
                 θ3 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Fann35  
                 29 
                 22 
                 14 
                 10 
                 6.5 
                 1 
                 0.8 
               
               
                 (control) 
                   
                   
                   
                   
                   
                   
                   
               
               
                 System  
                 29 
                 23.4 
                 14.6 
                 11.7 
                 8.7 
                 6.0 
                 5.9 
               
               
                 measurement 
                   
                   
                   
                   
                   
                   
                   
               
               
                 device 
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     In conclusion, compared with the measurement results of Fann35, the calculation results of the optimal on-site models (the second and third on-site models) determined by the correlations of the actual shear stress τw i  and the predicted shear stresses of the on-site models are the most accurate. 
     The above described are merely preferred embodiments of the present invention, which are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.