Patent Publication Number: US-11378474-B2

Title: Predict brake horsepower for a pump for viscous applications

Description:
TECHNICAL FIELD 
     This application is directed, in general, to determining pump parameters and, more specifically, to determining a brake horsepower (BHP) of a pump for provided design parameters. 
     BACKGROUND 
     Centrifugal pumps have been developed and used for centuries in handling viscous fluids. Performance of a centrifugal pump is affected by many factors such as viscosity, speed (rotations per minute), stage diameter, flow rate, and hydraulic design of the pump. Generally, a pump is tested in water at atmospheric conditions and its performance, as measured at one or two fixed speeds, is used for the selection of the pump type and a number of pump stages. Predicting a performance of a pump in a viscous application, e.g., where the pumped fluid has a higher viscosity than water, may be difficult as the performance is dependent upon the speed of the pump, viscosity of the fluid, and the fluid flow rate. For a given viscous application, a pump is generally tested using various viscosity fluids at a range of speeds and its test data is interpolated. This testing has been found to be lengthy and costly. Additionally, interpolating and modelling the performance for use in a practical application can be a complex process and can introduce inaccuracies in the prediction of the performance. 
     SUMMARY 
     In one aspect a method to predict a design BHP of a pump is disclosed. In one embodiment, the method, includes: (1) selecting a design RPM of the pump, (2) computing an original K-R number using a viscosity of a fluid, and an original flow rate and a first BHP of the pump, wherein the computing is performed under controlled environmental conditions, (3) generating a normalized K-R number utilizing the original K-R number and a BEP K-R number, and a normalized flow rate utilizing the original flow rate and a BEP flow rate, wherein the BEP K-R number and the BEP flow rate are computed for the pump using water performance specifications, and (4) calculating the design BHP for the design RPM, wherein a BEP BHP is determined for the design RPM, and the design BHP is equal to ((the normalized flow rate{circumflex over ( )}B*the BEP BHP)/the normalized K-R number), wherein B is equal to two when the viscosity is an absolute viscosity and B is equal to one when the viscosity is a kinematic viscosity. 
     In a second aspect, a system to determine a design BHP of a pump is disclosed. In one embodiment, the system includes: (1) an interface capable of receiving benchmark specifications for the pump, and receiving user inputs, and (2) a BHP predictor, communicatively coupled to the interface and the memory, capable of computing one or more types of K-R numbers for a design RPM, determining BEP parameters, converting fluid viscosity, converting flow rates, normalizing the K-R numbers and the flow rates, and calculating a design BHP, utilizing benchmark specifications. 
     In a third aspect, a computer program product having a series of operating instructions stored on a non-transitory computer-readable medium that directs a data processing apparatus when executed thereby to perform operations to predict a design BHP of a pump is disclosed. In one embodiment, the computer program product operations include: (1) selecting a design RPM of the pump, (2) computing an original K-R number using a viscosity of a fluid, and an original flow rate and a first BHP of the pump, wherein the computing is performed under controlled environmental conditions, (3) generating a normalized K-R number utilizing the original K-R number and a BEP K-R number, and a normalized flow rate utilizing the original flow rate and a BEP flow rate, wherein the BEP K-R number and the BEP flow rate are computed for the pump using water performance specifications, and (4) calculating the design BHP for the design RPM, wherein a BEP BHP is determined for the design RPM, and the design BHP is equal to ((the normalized flow rate{circumflex over ( )}B*the BEP BHP)/the normalized K-R number), wherein B is equal to two when the viscosity is an absolute viscosity and B is equal to one when the viscosity is a kinematic viscosity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is an illustration of a diagram of an example well system; 
         FIG. 2  is an illustration of a diagram of an example pump system in a hydraulic fracturing well system; 
         FIG. 3  is an illustration of a diagram of an example pump system in an offshore well system; 
         FIG. 4A  is an illustration of a diagram of an example graph demonstrating a relationship between normalized flow rates and normalized Ketan-Roberts (K-R) numbers for a pump in water at a given rotations per minute (RPM) using absolute viscosity; 
         FIG. 4B  is an illustration of a diagram of an example graph demonstrating a relationship between normalized flow rates and normalized K-R numbers for a pump in water using kinematic viscosity; 
         FIG. 5A  is an illustration of a diagram of an example graph demonstrating a relationship between normalized flow rates and normalized K-R numbers for various viscous fluids using absolute viscosities; 
         FIG. 5B  an illustration of a diagram of an example graph demonstrating a relationship between normalized flow rates and normalized K-R numbers for various viscous fluids using kinematic viscosities; 
         FIG. 6  is an illustration of a diagram of an example graph demonstrating performance curves of an exemplary pump; 
         FIG. 7A  is an illustration of a flow diagram of an example method to predict a brake horsepower (BHP) of a pump for a viscous fluid; 
         FIG. 7B  is an illustration of a flow diagram of an example method, building on  FIG. 7A , to normalize best efficiency point K-R numbers; and 
         FIG. 8  is an illustration of a block diagram of an example BHP predictor system. 
     
    
    
     DETAILED DESCRIPTION 
     Pumps of various kinds can be utilized for pumping fluids in various industries and fields. For example, pumps can be centrifugal, rotary, displacement, metering, and other pump types. One type of pump, electrical submersible pumps (ESP), can be used to pump oil out of subterranean formations. An ESP is a multi-stage centrifugal pump having two or more stages, such as hundreds of stages, that can operate at variable speeds, e.g., from 1500 revolutions per minute (RPM) to 8000 RPM. The ESP operation can pump in or out a small amount of fluid, such as a few barrels per day (BPD) to hundreds of thousands of BPD. 
     Some types of pumps can also be utilized in non-subterranean formation applications such as in the medical field to pump blood or deliver medicine, in the chemical field, and in a broader hydrocarbon production field, for example, to pump mud, hydraulic fluid, brine, chemicals, oils, and other fluids into or out of a borehole. Selection of the pump, e.g., sizing the pump system, for one or more viscous applications include a selection of a stage type, stage diameter, flow rate, RPM range, a number of pump stages, seal (protector), motor, and optional components depending on the specific application, such as a gas separator. 
     Performance prediction of pumps in viscous applications, e.g., where the pumped fluid has a higher viscosity than water, especially in difficult environments such as an offshore application, requires higher accuracy than the accuracy provided by conventional prediction tools due to the cost of operating in the difficult environment. A discrepancy in the sizing and prediction of a pump type used an operating environment containing fluid of certain viscous properties can result in an increase in operating costs, such as in an offshore pumping operation where the increase can be several million dollars in additional time to pump the fluid or in additional maintenance costs. 
     For determining proper sizing of a pump for viscous applications, the pump&#39;s performance using various viscosities should be known. Generally, a pump having few stages can be built and tested in desired ranges of viscosities and RPMs in a test facility before the pump is sized and deployed in the actual application. The test results can be used for a prediction of the pump performance in the operating environment, such as an offshore production application. The prediction can be used to properly select the size of the pump and its motor before deployment. This building-testing-analyzing-modelling-predicting process can be costly and time-consuming, as well as inaccurate as viscosities and RPMs can vary widely based on the actual operating environment. 
     Introduced herein is a dimensionless relationship between a volumetric flow rate, a viscosity parameter, and a brake horsepower (BHP) that simplifies the prediction of horsepower (HP) requirements for a viscous pump performance. The estimated BHP, e.g., a preferred or design BHP, can be predicted from an analysis of the flow rate, head, speed (i.e., RPM), and viscosity of a pump derived from its water performance specifications. Water performance specifications are initially assumed to be at a viscosity of one centipoise (cP) and a temperature of 20 degrees Celsius. In aspects where the water has different specifications, the performance results can be normalized. The prediction of the BHP for a designed fluid viscosity can be derived from the water performance running at the same speed. The introduced relationship is referred through the disclosure as a Ketan-Robert (K-R) number and is derived in Equation 1 and Equation 2. 
     
       
         
           
             
               
                 
                   
                     Example 
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                   1 
                 
               
             
             
               
                 
                   
                     Example 
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                   Equation 
                   ⁢ 
                   
                       
                   
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                   2 
                 
               
             
           
         
       
         
         where Q is the mass flow rate of the viscous fluid;
       BHP is the brake HP of the pump;   RPM is the rotational speed of the pump;   μ is the absolute viscosity; and   v is the kinematic viscosity.   
     
       
    
     The kinematic viscosity and absolute viscosity are related through the conventional formula of 
             v   =       μ     fluid   ⁢           ⁢   density       .           
In addition, Equations 1 and 2 can utilize a volumetric flow rate, where the volumetric flow rate is proportional to the mass flow rate using the fluid density,
 
               volumetric   ⁢           ⁢   flow   ⁢           ⁢   rate     =       Q     fluid   ⁢           ⁢   density       .           
BHP is a function of the fluid flow rate, pump RPM, stage diameter of the pump, and hydraulic design of the pump. The flow rate is affected by the RPM, stage diameter, and hydraulic design of the pump. Equation 1 or Equation 2 can be utilized as the K-R number herein and the equation selected can be chosen for its ease of use, implementation need, available parameters, and other factors.
 
     A best efficiency point (BEP) is where the pump has the highest efficiency in the pump performance specifications at the design RPM for a flow rate of water. Water performance specifications of a given pump is generally available from the pump&#39;s manufacturer and are provided in the form of a pump curve, which is drawn with respect to flow rate, head, BHP, and efficiency at an RPM (see  FIG. 6  for an example BEP curve). For example, ESP industry water pump performance specifications of an ESP pump are published at 50 Hz (2917 RPM) or 60 Hz (3500 RPM) depending on the primary usage of the pump. In other aspects, the water performance specifications can be determined in a test environment, such as a lab or field experiment at a different RPM where the water performance specifications are adjusted using affinity laws. The lab or field tested results can be used in place of the published pump performance specifications. 
     The disclosure uses the K-R number to predict a recommended BHP for a pump. The K-R number is first calculated for one or more flow rates for a design RPM. Then the K-R number can be normalized by dividing it with the BEP K-R number. The K-R number of the viscous fluid, at the same RPM, is normalized against the K-R number at the BEP, see Equation 3. Similarly, the normalized flow rate can be calculated using the flow rate of the viscous fluid and the flow rate at the BEP, as shown in Equation 4. It is understood that flow rates other than the BEP flow rate, such as a near zero flow rate or near maximum flow rate or any other flow rate, can also be used for the normalization of the flow rates. 
     
       
         
           
             
               
                 
                   
                     Example 
                     ⁢ 
                     
                         
                     
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                     Example 
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                   ⁢ 
                   
                       
                   
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                   4 
                 
               
             
           
         
       
     
     Affinity laws can be utilized to transform the data from one RPM to another RPM for water performance, e.g., from the original or benchmark RPM to a specified or designed RPM. As the RPMs change, the K-R number for water performance also changes in an inverse proportional ratio, depending upon Equation 1 and 2. Typically, the K-R number for water performance at the BEP can be transformed to a different, e.g., designed, RPM using the inverse proportional ratio and the transformed K-R number can be utilized as the BEP K-R number for the designed RPM. Equation 5 demonstrates the inverse proportional ratio that can be used. 
     
       
         
           
             
               
                 
                   
                     Example 
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                   5 
                 
               
             
           
         
       
         
         where BEP K-R number orig RPM  is the BEP K-R number using the pump&#39;s BEP specifications;
       RPM orig  is the RPM used for the BEP specification;   RPM design  is the newly specified, i.e., second or design, RPM that is used to transform the other values; and   A is 4 when using Equation 1 and A is 2.5 when using Equation 2.   
     
       
    
     In another aspect, affinity laws can be applied to calculate water performance of a pump at a designed RPM using its original RPM. The set of equations in Equation 6 show examples of the affinity laws. 
     
       
         
           
             
               
                 
                   
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                   6 
                 
               
             
           
         
       
     
     Equation 5 and the set of equations in Equation 6 can be utilized for translating, e.g., transforming, pump specifications from one RPM to a second RPM using water as the fluid, prior to analyzing the system for another viscous fluid. These equations generally are not useful for calculation of pump performance at other RPMs using viscous fluids since the viscous losses follow a different relationship than the change in RPM alone would indicate. In hydrocarbon production applications, for example, oil, water, brine, gas, mud, sand, hydraulic fracturing fluid, and other fluids can mix in various proportions thereby affecting and continually changing the viscosity of the pumped fluid. 
     The disclosed process can follow the following steps to calculate a BHP of a selected pump for the design speed and design viscosity in the operating environment. (1) Computing a K-R number for the flow rates including BEP flow rate, using Equation 1 or 2 based on water performance at a pump&#39;s published specifications, e.g., parameters. The published, lab, and field determined specifications can be referred to as the benchmark specifications. 
     (2) The normalized K-R number and normalized flow rates for water performance are calculated by dividing each K-R number and flow rate with the respective BEP K-R number and flow rate, using Equation 3 and 4 respectively. 
     (3) A relationship is developed between the normalized K-R number and the normalized flow rate for the water performance, for example, as shown in  FIGS. 4A and 4B . This relationship is valid for all viscosities and RPMs, for example, as shown in  FIGS. 5A and 5B . 
     (4) A pump is designed to operate in different conditions and RPMs than the water specifications. Utilizing the operating specifications at implementation for the pump, speed, viscosity, and flow rate can be selected, and can be referenced as the design speed, the design BHP, and the design flow rate. The design speed can be different than the benchmark RPM. Water performance specifications at the design RPM can be determined using affinity laws and the published water performance specifications. 
     (5) The BEP K-R number for water performance at the design RPM can be calculated using the RPM inverse proportional ratio, such as using Equation 5. In an alternative aspect, the BEP K-R number can be determined by calculating the water performance at the design speed using the affinity laws of Equation 6, deriving new pump performance specifications, and then calculating the K-R number using Equation 1 or 2. 
     (6) Other parameters for the water performance can be adjusted using the design RPM and the benchmark RPM, such as using the affinity laws in Equation 6. 
     (7) From the relationship of BEP ratios of the flow and BHP with viscosity and speed, the design BEP flow rate and design BEP BHP is obtained from the BEP water performance parameters at the design RPM. 
     (8) The design flow rate can be normalized against the design BEP flow rate at design RPM and viscosity, such as using Equation 4. 
     (9) A normalized K-R number at the normalized flow rate can be computed, such demonstrated in  FIG. 5A or 5B . 
     (10) A BHP for the design viscous fluid and design RPM can be calculated. Equation 7 and Equation 8 are examples of calculating the predicted BHP. 
     
       
         
           
             
               
                 
                   
                     Example 
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                     calculation 
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                     Equation 
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                     1 
                   
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                                   RPM 
                                 
                                 , 
                                 viscosity 
                               
                             
                           
                         
                       
                       
                         K 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         
                           R 
                           
                             
                               normalized 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               at 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               design 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               RPM 
                             
                             , 
                             
                                 
                             
                             ⁢ 
                             viscosity 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
             
               
                 
                   
                     Example 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     calculation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     BHP 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     using 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       BHP 
                       
                         
                           design 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           RPM 
                         
                         , 
                         
                             
                         
                         ⁢ 
                         viscosity 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               flow 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   rate 
                                   
                                     
                                       normalized 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       at 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       design 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       RPM 
                                     
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     viscosity 
                                   
                                 
                                 2 
                               
                               * 
                             
                           
                         
                         
                           
                             
                               BHP 
                               
                                 BEP 
                                 , 
                                 
                                   design 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   RPM 
                                 
                                 , 
                                 viscosity 
                               
                             
                           
                         
                       
                       
                         K 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         
                           R 
                           
                             
                               normalized 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               at 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               design 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               RPM 
                             
                             , 
                             
                                 
                             
                             ⁢ 
                             viscosity 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
         
         where flow rate is the normalized flow rate derived from the pump&#39;s specifications or the flow rate as adjusted by a change in RPM selection;
       BHP is the BHP at the BEP as derived from the pump&#39;s specifications, or the BHP as adjusted by a change in RPM selection; and   K-R normalized  is the calculated K-R number, or the K-R number as adjusted by a change in RPM selection.   
     
       
    
     To demonstrate the process, an example pump and environment scenario is presented. In step 1, the pump performance characteristics are determined, such as from published materials and the expected operating environment as shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Example pump water performance characteristics 
               
            
           
           
               
               
               
            
               
                   
                 Stage 
                 SJ2800 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Speed 
                 2333 
                 RPM 
               
               
                   
                 Flow 
                 700 
                 BPD 
               
               
                   
                 Viscosity 
                 300 
                 cP 
               
               
                   
                   
               
            
           
         
       
     
     Steps 2 and 3 are performed to develop a K-R number for the viscous BHP correlation (see, for example, Equations 1 and 2, and  FIGS. 4A and 4B ). Steps 4 and 5 are performed to calculate the BEP water performance at the design (operating environment) RPM that was identified in step 1 as shown in Table 2, such as using affinity laws (see, for example, Equations 5 and 6). 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Example BEP calculations 
               
            
           
           
               
               
               
            
               
                   
                 40 Hz BEP water 
                 60 Hz BEP water 
               
               
                   
                 data 2333 RPM 
                 data 3500 RPM 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 water 
                 BEP flow rate 
                 1974 
                 BPD 
                 2961 
                 BPD 
               
               
                 water 
                 BEP Head 
                 24.88 
                 feet 
                 56.00 
                 feet 
               
               
                 water 
                 BEP BHP 
                 0.531 
                 HP 
                 1.793 
                 HP 
               
               
                   
               
            
           
         
       
     
     Step 7 can be utilized to calculate the BEP flow rate, head design at the design viscosity and design speed using the BEP and speed relationship, as shown in Table 3. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Example BEP calculations 
               
            
           
           
               
               
               
            
               
                   
                 Correction 
                   
               
               
                   
                 Factor for 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 40 Hz BEP water 
                 2333 RPM 
                 40 Hz BEP 300 cP 
               
               
                   
                 data 2333 RPM 
                 &amp; 300 cP 
                 data 2333 RPM 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 BEP flow rate 
                 1974 
                 BPD 
                 (X) 0.4678 
                 923.232 
                 BPD 
               
               
                 BEP Head 
                 24.88 
                 feet 
                 (X) 0.7112 
                 17.6961 
                 feet 
               
               
                 BEP BHP 
                 0.531 
                 HP 
                 (X) 2.2198 
                 1.1788 
                 HP 
               
               
                   
               
            
           
         
       
     
     Step 8 is performed to calculate the normalized flow rate at the design RPM and design viscosity as shown in Table 4 (see, for example, Equation 4). 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Example normalized flow rate 
               
            
           
           
               
               
               
            
               
                   
                 Original 
                 Normalized 
               
               
                   
                 flow rate 
                 flow rate 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                 Normalized flow at design RPM, viscosity 
                 700 
                 =0.7582 
               
               
                 (divide by 923.232, such as using 
               
               
                 Equation 4) 
               
               
                   
               
            
           
         
       
     
     Step 9 is performed to calculate the normalized K-R number using the relationships developed in Step 3 as shown in Table 5 (see, for example, Equation 3). 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Example K-R number normalization 
               
            
           
           
               
               
               
            
               
                   
                 Normalized 
                 Normalized 
               
               
                   
                 flow rate 
                 K-R number 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                 Normalized K-R number at design RPM, 
                 0.7582 
                 0.8152 
               
               
                 viscosity 
               
               
                 (Using equation 2, FIGS. 4B and 5B) 
               
               
                   
               
            
           
         
       
     
     Step 10 is performed to calculate the design BHP as shown in Table 6 (see, for example, Equations 7 and 8). 
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Example BHP calculation 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Design BHP = 
                 0.7582 * 1.1788/0.8152 
                 =1.0964 BHP 
               
               
                 (using equation 2 and 8) 
               
               
                   
               
            
           
         
       
     
     Once the predicted BHP is calculated, the information can be provided to a user, such as an engineer or operator. The user can utilize the information, combined with other parameters, data, factors, and information, in selecting and sizing the pump and determining the appropriate number of pump stages for the implementation. Some considerations the user can utilize in the pump selection analysis can be to maximize efficiency, minimize maintenance requirements, pump cost, pump operation cost, and other factors. 
     Turning now to the figures,  FIG. 1  is an illustration of a diagram of an example well system  100 , for example, an extraction system, a production system, a wireline system with a pump, and other hydrocarbon well systems. Well system  100  includes a derrick  105 , a well site controller  107 , a surface pump system  106 , and a computing system  108 . Well site controller  107  includes a processor and a memory and is configured to direct operation of well system  100 . Derrick  105  is located at a surface  104 . 
     Extending below derrick  105  is a borehole  110 , with two cased sections  115  and one uncased section  116 . Pipe  120  is inserted in borehole  110 . Located at the bottom of pipe  120  is a downhole tool  125 . Downhole tool  125  can include various downhole tools and bottom hole assemblies (BHA), such as one or more pumps  127  and valves. Other components of downhole tool  125  can be present, such as a local power supply, or batteries and capacitors to store power received from another system, as well as a transceiver and a control system. Borehole  110  is surrounded by subterranean formation  135 . Connecting surface pump system  106  and downhole tool  125  is the pipe  120 . Surface pump system  106  and pumps  127  can be sized using the processes described herein. 
     In this example, pumps  127  can have one or more stages to pump fluid  130  into or out of borehole  110 . Pumps  127  selected to be part of downhole tool  125  should be sized appropriately for the type of fluid and the viscosity of the fluid to be pumped. An inefficient pump could result in significant financial loss in terms of time used to pump the fluid, or a loss in time in replacing the pumps with ones of different specifications. 
     Computing system  108  or well site controller  107  can be utilized to perform the calculations and computations as described herein to predict an appropriate BHP which can be used to select and size pumps  127  to be used within borehole  110  as part. Computing system  108  can be proximate well site controller  107  or be a distance away, such as in a cloud environment, a data center, a lab, or a corporate office. Computing system  108  can be a laptop, smartphone, PDA, server, desktop computer, cloud computing system, and other computing systems that are operable to perform the process and methods described herein. The information generated from computing system  108  can be communicated by various conventional means to the well site operators and engineers so the predicted BHP can be used in selecting the pumps to be used in well system  100 . 
       FIG. 2  is an illustration of a diagram of an example pump system in a hydraulic fracturing (HF) well system  200 , which can be a well site where HF operations are occurring through the implementation of a HF treatment stage plan. HF well system  200  demonstrates a nearly horizontal wellbore undergoing a fracturing operation. 
     HF well system  200  includes a surface well equipment  205  located at a surface  204 , a well site control equipment  207 , a surface HF pump system  206 , and a computing system  208 . In some aspects, well site control equipment  207  is communicatively connected to separate computing system  208 , for example, a separate server, data center, cloud service, tablet, laptop, smartphone, or other types of computing systems capable of executing the processes and methods described herein. Computing system  208  can be located proximate to well site control equipment  207  or located a distance from well site control equipment  207 , and can be utilized by a well system engineer and operator to calculate the predicted BHP for a pump, such as pumps  227 , to be used within HF well system  200 . 
     Extending below surface  104  from surface well equipment  205  is a wellbore  210 . Wellbore  210  can have zero or more cased sections and a bottom section that is uncased. Inserted into wellbore  210  is a fluid pipe  220 . The bottom portion of fluid pipe  220  has the capability of releasing downhole material  230 , such as carrier fluid with diverter material, from fluid pipe  220  to subterranean formations  235  containing fractures  240 . The release of downhole material  230  can be by perforations in fluid pipe  220 , by valves placed along fluid pipe  220 , or by other release means. At the end of fluid pipe  220  is an end of pipe assembly  225 , which can be one or more downhole tools or an end cap assembly. End of pipe assembly  225  can include pumps  227  to pump fluid into or out of wellbore  210 . 
     In an alternative aspect, downhole material  230  can be pumped to the surface, such as removing HF fluid or removing hydrocarbon fluids. The fluid can be pumped through fluid pipe  220  using surface HF pump system  206 , pumps  227 , or a combination thereof. In some aspects, the computing system  208  and the well site control equipment  207  can be used to calculate the predicted BHP for the pumps used within HF well system  200 . The predicted BHP can be used as part of the analysis to select pumps for use within HF well system  200 . 
       FIG. 3  is an illustration of a diagram of an example pump system in an offshore well system  300 , where an ESP assembly  310  is placed downhole in a borehole  326  below a body of water  340 , such as an ocean or sea. Borehole  326  is surrounded by subterranean formation  345 . ESP assembly  310  can also be used for onshore operations. The ESP assembly  310  includes a speed controller  312 , an ESP motor  314 , and an ESP pump  330 . 
     Speed controller  312  is placed in a cabinet  306  inside a control room  307  on an offshore platform  305 , such as an oil rig. Speed controller  312  is configured to adjust the RPM of ESP motor  314  to improve well productivity. In the illustrated embodiment, ESP motor  314  is a two-pole, three-phase squirrel cage induction motor that operates to turn ESP pump  330 . ESP motor  314  is located near the bottom of ESP assembly  310 , just above downhole sensors within borehole  326 . A power cable  320  extends from speed controller  312  to ESP motor  314 . 
     ESP pump  330  can be a multi-stage centrifugal pump including an impeller and a diffuser at each stage. Before the deployment, the performance of ESP pump  330  is predicted using a viscous BHP prediction method, such as a method  701  in  FIG. 7A , by a computer system, such as BHP predictor system  800  in  FIG. 8 . Based on the prediction, ESP pump  330  can be sized for the implementation application of offshore well system  300 . ESP pump  330  should be sized and selected to enable efficient pumping of fluid of interest, such as oil or other hydrocarbons, through production tubing  322  to storage tanks onboard the offshore platform  305 . 
     In some embodiments, ESP pump  330  can be a horizontal surface pump, a progressive cavity pump or an electric submersible progressive cavity pump. A motor seal section and intake section may extend between ESP motor  314  and ESP pump  330 . A well casing  325  may separate ESP assembly  310  from water  340  and subterranean formation  345 . Perforations in well casing  325  can allow the fluid of interest from subterranean formation  345  to enter borehole  326 . 
       FIGS. 1 and 2  depict onshore operations. Those skilled in the art will understand that the disclosure is equally well suited for use in offshore operations.  FIGS. 1, 2, and 3  depict specific borehole configurations, those skilled in the art will understand that the disclosure is equally well suited for use in boreholes having other orientations including vertical boreholes, horizontal boreholes, slanted boreholes, multilateral boreholes, and other borehole types. 
       FIG. 4A  is an illustration of a diagram of an example graph  400  demonstrating a relationship between normalized flow rates and normalized K-R numbers for a pump in water at a given RPM using absolute viscosity as shown in Equation 1. The points shown in plot area  410  varies with a change in a pump design and is also a function of the pump specific design parameters. The points of plot area  410  can be used for a prediction of a BHP of the pump at a different RPM and in different fluid. 
     X-axis  405  shows the normalized flow rate determined using the water performance specifications of the pump. Flow rates from the water performance specifications are normalized using a flow rate at a reference point, e.g., BEP, for the given RPM. For the normalization, each of the flow rates can be divided by the BEP flow rate. 
     Y-axis  406  shows the normalized K-R numbers determined using the water performance specifications of the pump. Using Equation 1, the flow rates, and other parameters from the water performance specifications, K-R numbers can be calculated. This is shown as point  415  where the BEP flow rate and BEP K-R number are both one. The calculated K-R number for the viscous fluid are then normalized using the above K-R number and flow rate at the BEP. 
       FIG. 4B  is an illustration of a diagram of an example graph  430  demonstrating a relationship between normalized flow rates and normalized K-R numbers for a pump in water at a given RPM using kinematic viscosity as shown in Equation 2. The points shown in plot area  440  varies with a change in a pump design and is also a function of the pump specific design parameters. The points of plot area  440  can be used for a prediction of a BHP of the pump at a different RPM and in different fluid. 
     X-axis  435  shows the normalized flow rate determined using the water performance specifications of the pump. Flow rates from the water performance specifications are normalized using a flow rate at a reference point, e.g., BEP, for the given RPM. For the normalization, each of the flow rates can be divided by the BEP flow rate. 
     Y-axis  436  shows the normalized K-R numbers determined using the water performance specifications of the pump. Using Equation 2, the flow rates, and other parameters from the water performance specifications, K-R numbers can be calculated. This is shown as point  445  where the BEP flow rate and BEP K-R number are both one. The calculated K-R number for the viscous fluid are then normalized using the above K-R number and flow rate at the BEP. 
       FIG. 5A  is an illustration of a diagram of an example graph  500  demonstrating a relationship between normalized flow rates and normalized K-R numbers for various viscous fluids using absolute viscosities, as shown in Equation 1. X-axis  505  shows the normalized flow rates for the various viscous fluids. Y-axis  506  shows the corresponding normalized K-R numbers for the viscous fluids. Unlike graph  400  in  FIG. 4A , graph  500  are for fluids other than water. Plot area  510  shows data points for several different fluid viscosities. 
     The fluids include first fluid having 6 cP viscosity (hollow square), second fluid having 9 cP viscosity (hollow triangle), third fluid having 19 cP (solid rectangle), fourth fluid having a 35 cP (hollow diamond), fifth fluid having a 50 cP (X), sixth fluid having 90 cP (hollow circle), seventh fluid having a 100 cP (solid square), eighth fluid having 140 cP (solid triangle), ninth fluid having 190 cP (circle with square inside), tenth fluid having 244 cP (+), eleventh fluid having 285 cP (circle with angled lines), twelfth fluid having 426 cP (circle with intersecting lines), thirteenth fluid having 541 cP (X with a shaded background), and fourteenth fluid having 680 cP (gray circle). 
     As shown, while the fluids and their viscosities differ, the viscous performance correlation, i.e., the relationship between the normalized flow rates to the corresponding normalized K-R numbers, remains approximately equivalent. As such, a K-R number correlation of a pump in water at a given RPM, e.g., graph  400  and graph  500  in  FIGS. 4A and 5A  respectively, can be used in predicting a BHP of the pump in a viscous application, such as fluids of various viscosities in downhole operations. 
       FIG. 5B  is an illustration of a diagram of an example graph  530  demonstrating a relationship between normalized flow rates and normalized K-R numbers for various viscous fluids using kinematic viscosities, as shown in Equation 2. X-axis  535  shows the normalized flow rates for the various viscous fluids. Y-axis  536  shows the corresponding normalized K-R numbers for the viscous fluids. Unlike the graph  430  in  FIG. 4B , graph  530  are for fluids other than water. Plot area  540  shows data points for several different fluid viscosities. 
     The fluids include first fluid having 6 cP viscosity (hollow square), second fluid having 9 cP viscosity (hollow triangle), third fluid having 19 cP (solid rectangle), fourth fluid having a 35 cP (hollow diamond), fifth fluid having a 50 cP (X), sixth fluid having 90 cP (hollow circle), seventh fluid having a 100 cP (solid square), eighth fluid having 140 cP (solid triangle), ninth fluid having 190 cP (circle with squares inside), tenth fluid having 244 cP (+), eleventh fluid having 286 cP (circle with angled lines), twelfth fluid having 426 cP (circle with intersecting lines), thirteenth fluid having 541 cP (X with a shaded background), and fourteenth fluid having 680 cP (gray circle). 
     As shown, while the fluids and their viscosities differ, the viscous performance correlation, i.e., the relationship between the normalized flow rates to the corresponding normalized K-R numbers, remains approximately equivalent. As such, a K-R number correlation of a pump in water at a given RPM, e.g., graph  430  and graph  530  in  FIGS. 4B and 5B  respectively, can be used in predicting a BHP of the pump in a viscous application, such as fluids of various viscosities in downhole operations. 
       FIG. 6  is an illustration of a diagram of an example graph  600  demonstrating performance curves of an exemplary pump. Performance specifications, such as graph  600 , can be made available to a user of the exemplary pump and used to identify BEPs under various operating scenarios. Graph  600  has an x-axis  605  showing the flow rate in BPD, a primary y-axis  606  showing the head in feet per stage, a secondary y-axis  609  showing the BHP, e.g., horsepower per stage, and a graph key  608  showing different sample fluid viscosities at differing RPMs that are plotted in plot area  610 . 
     The exemplary pump operating characteristics are for water at room temperature, atmospheric pressure with specific gravity of 1.00 and viscosity of one cP. For the fixed speed as specified in graph key  608 , variations of head (e.g., pressure) and BHP with respect to change in flow rates are plotted. The performance characteristics also demonstrate an efficiency relationship with the flow rate demonstrating the optimal performance of the pump at the BEP, and demonstrating the operating range for optimal and reliable operation of the pump to maximize pump runlife. 
     BEP  620  shows the BEP points for some of the plotted performance curves. BEP  620  can be used to provide data inputs, i.e., pump characteristics or specifications, such as flow rates, to the equations used herein. The initial K-R number can be computed using the specifications at one of the data points of BEP  620 , depending on the viscosity and RPM selected. 
       FIG. 7A  is an illustration of a flow diagram of an example method  701  to predict BHP of a pump for a viscous fluid. Method  701  can utilize pump specifications determined in a lab, a field test, or published by the pump&#39;s manufacturer to perform calculations to predict an appropriate BHP for a pump for a specific implementation. Method  701  can be executed by a computing system, such as BHP predictor system  800  in  FIG. 8 . Method  700  starts at a step  705  and proceeds to a step  707 . 
     In step  707 , a design RPM can be selected. The design RPM can be the same as what was used in the published, lab, or field-tested specifications, e.g., benchmark specifications, for the pump. If the design RPM is different than the benchmark RPM, then algorithms can be applied, such as affinity laws, to transform various parameters from the benchmark RPM to the design RPM. 
     In step  710 , the K-R number for the BEP point can be computed for a design RPM. The viscosity can be assumed to be one for water. The parameters used for the computations can be received, such as receiving manufacturer&#39;s pump specifications or receiving specifications derived in lab or field testing. In addition, user inputs can be received, such as receiving a design RPM, flow rate, and other user design parameters. The various inputs can be entered by a user, received via an electronic communication, received from a memory or computing storage location, or a combination thereof. In other aspects, testing using other fluids can be used to determine the BEP point and that fluid&#39;s viscosity and pump specifications would be utilized. A second K-R number for the specific implementation can be computed, such as using Equation 1 or Equation 2. The specific implementation may have a different RPM, flow rate, or other parameter as compared to the original specifications used to determine the BEP specifications. The RPM and flow rate are data inputs, as well as the viscosity of the fluid. 
     In step  730 , the second K-R number is generated by normalizing the original K-R number using the BEP K-R number, such as using Equation 3. In addition, the normalized flow rate is generated using the original flow rate of the BEP, such as using Equation 4. In a step  750 , the design BHP is calculated using the normalized flow rate and the normalized K-R number, such as using Equation 7Method  701  ends at a step  770 . 
       FIG. 7B  is an illustration of a flow diagram of an example method  702 , building on  FIG. 7A , to normalize BEP K-R numbers. Method  702  incorporates the steps of method  700  and includes additional sub-steps. Method  701  can be executed by a computing system, such as BHP predictor system  800  in  FIG. 8 . Method  702  starts at step  705  and proceeds through step  707  and step  710  to step  730 . Step  730  includes two potential sub-steps that can be performed depending on the analysis being conducted and the parameters that are available. Method  702  can proceed to a step  732  or a step  740 , or both step  732  and step  740 . 
     Step  732  can generate a benchmark BEP K-R number. The benchmark K-R number can be the same as or modified from a tested or published set of pump specifications, such as to a design RPM. The transforming of the benchmark K-R number can allow pump operators to adjust the RPM, utilizing other factors, while being able to continue to predict a design BHP for the current operation plan. In a step  734 , the benchmark BEP K-R number can be normalized using the variation in pump RPM, such as using Equation 5. Method  700  can proceed to step  740  or to step  750 . 
     Step  740  can adjust the benchmark parameters using affinity laws or the set of equations in Equation 6. The flow rate, the head, and the BHP (such as the BEP BHP) can be adjusted using conventional affinity laws, for example, as shown in Equation 6. In a step  742 , the adjusted benchmark parameters can be normalized against the BEP parameters, such as the BEP K-R number and the BEP flow rate. These adjusted benchmark parameters can then be further used to perform the calculations to determine the design BHP for the viscous fluid. Method  702  proceeds to step  732  or to step  750 . Method  702  ends at step  770 . 
       FIG. 8  is an illustration of a block diagram of an example BHP predictor system  800  that has been constructed and configured to perform a BHP prediction method, such as method  701  and method  702 . BHP predictor system  800  includes a BHP predictor  820 , an interface  840  and a memory  860 . It is understood that the BHP predictor system  800  has been simplified for illustration purposes and may not illustrate some of the components that may be present in an actual system. 
     BHP predictor  820  can be one or more of a processing unit such as a central processing unit, a graphics processing unit, and other types of processing units, that are configured to predict a BHP of a given pump in a fluid of interest at a design RPM. BHP predictor  820  can be communicatively coupled to interface  840  and to memory  860 . 
     Interface  840  can be a user interface, a network interface, or a communications interface that is configured to receive water performance specifications of the given pump, such as benchmark, lab tested, field tested, and published specifications, and a design RPM and other user inputs. Interface  840  can output a design BHP for the pump for various viscosities fluid. In some aspects, a well system analyzer can be configured to receive the design BHP, and other parameters and specifications, and perform analysis to determine sizing and specifications for the pumps to be used in the implementation. Interface  840  can be a transceiver communications interface that is configured to communicate data, i.e., transmit and receive data. Interface  840  can include the logic, ports, terminals, and connectors to communicate data. The ports, terminals, connectors, may be conventional receptacles for communicating data via a communications network. 
     Memory  860  can be a computer memory such as cache, a read-only memory (ROM), a programmable ROM (PROM), an erasable PROM, a dynamic random-access memory (DRAM), a static random-access memory, and a flash memory. Memory  860  can be configured to store the received water performance specifications of the given pump and other calculated performance specifications from BHP predictor  820 . Memory  860  can also be configured to store computer executable instructions to direct the operation of BHP predictor  820  when initiated thereby. The operating instructions can correspond to an algorithm or algorithms that predict a BHP of a given pump in a fluid of interest at a design RPM. 
     BHP predictor system  800  can be part of another computing system, such as a laptop, tablet, smartphone, desktop computer, server, data center, cloud environment, well site controller, the well system analyzer, and other computing systems. BHP predictor system  800  can be implemented on a general computing system or a specialized computing system. BHP predictor can be located proximate the pump implementation location or be located a distance away, for example, a lab or office environment. BHP predictor system  800  can be implemented for different types of pumps, for example, centrifugal pumps, rotary pumps, and metering pumps. BHP predictor system  800  can be implemented for various industries and fields, such as hydrocarbon production industry, medical field, and chemical and petrochemical fields. These example implementations require the pumping of a viscous fluid in an environment where the pump&#39;s published specifications are not adequate to evaluate pump efficiency. 
     It is understood that methods and processes described herein can be applicable to a centrifugal pump and other types of pumps, such as a positive displacement pump, a rotary pump and a metering pump, that may be used in handling viscous fluid. It is also understood that in addition to well production, the methods and processes can be used in other oil industry applications, such as in mud pump performance control and monitoring, and chemical injection application in the oil well, e.g., for viscosity, scale inhibition, sand control. In some aspects, it can be used in non-hydrocarbon industry applications, such as in medical fields for blood flow control and monitoring, e.g., a measure of medicine transfer rate, and in chemical and petrochemical industry for control and monitoring injection and mixing of chemicals for proper chemical reactions. 
     A portion of the above-described apparatus, systems or methods may be embodied in or performed by various analog or digital data processors, wherein the processors are programmed or store executable programs of sequences of software instructions to perform one or more of the steps of the methods. A processor may be, for example, a programmable logic device such as a programmable array logic (PAL), a generic array logic (GAL), a field programmable gate arrays (FPGA), or another type of computer processing device (CPD). The software instructions of such programs may represent algorithms and be encoded in machine-executable form on non-transitory digital data storage media, e.g., magnetic or optical disks, random-access memory (RAM), magnetic hard disks, flash memories, and/or read-only memory (ROM), to enable various types of digital data processors or computers to perform one, multiple or all of the steps of one or more of the above-described methods, or functions, systems or apparatuses described herein. 
     Portions of disclosed examples or embodiments may relate to computer storage products with a non-transitory computer-readable medium that have program code thereon for performing various computer-implemented operations that embody a part of an apparatus, device or carry out the steps of a method set forth herein. Non-transitory used herein refers to all computer-readable media except for transitory, propagating signals. Examples of non-transitory computer-readable media include, but are not limited to: magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks; magneto-optical media such as floppy disks; and hardware devices that are specially configured to store and execute program code, such as ROM and RAM devices. Examples of program code include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. 
     In interpreting the disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. 
     Those skilled in the art to which this application relates will appreciate that other and further additions, deletions, substitutions and modifications may be made to the described embodiments. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present disclosure will be limited only by the claims. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present disclosure, a limited number of the exemplary methods and materials are described herein. 
     Aspects disclosed herein includes: 
     A. A method to predict a design BHP of a pump, including: (1) selecting a design RPM of the pump, (2) computing an original K-R number using a viscosity of a fluid, and an original flow rate and a first BHP of the pump, wherein the computing is performed under controlled environmental conditions, (3) generating a normalized K-R number utilizing the original K-R number and a BEP K-R number, and a normalized flow rate utilizing the original flow rate and a BEP flow rate, wherein the BEP K-R number and the BEP flow rate are computed for the pump using water performance specifications, and (4) calculating the design BHP for the design RPM, wherein a BEP BHP is determined for the design RPM, and the design BHP is equal to ((the normalized flow rate{circumflex over ( )}B*the BEP BHP)/the normalized K-R number), wherein B is equal to two when the viscosity is an absolute viscosity and B is equal to one when the viscosity is a kinematic viscosity. 
     B. A system to determine a design BHP of a pump, including: (1) an interface capable of receiving benchmark specifications for the pump, and receiving user inputs, and (2) a BHP predictor, communicatively coupled to the interface and the memory, capable of computing one or more types of K-R numbers for a design RPM, determining BEP parameters, converting fluid viscosity, converting flow rates, normalizing the K-R numbers and the flow rates, and calculating a design BHP, utilizing benchmark specifications. 
     C. A computer program product having a series of operating instructions stored on a non-transitory computer-readable medium that directs a data processing apparatus when executed thereby to perform operations to predict a design BHP of a pump, the operations include: (1) selecting a design RPM of the pump, (2) computing an original K-R number using a viscosity of a fluid, and an original flow rate and a first BHP of the pump, wherein the computing is performed under controlled environmental conditions, (3) generating a normalized K-R number utilizing the original K-R number and a BEP K-R number, and a normalized flow rate utilizing the original flow rate and a BEP flow rate, wherein the BEP K-R number and the BEP flow rate are computed for the pump using water performance specifications, and (4) calculating the design BHP for the design RPM, wherein a BEP BHP is determined for the design RPM, and the design BHP is equal to ((the normalized flow rate{circumflex over ( )}B*the BEP BHP)/the normalized K-R number), wherein B is equal to two when the viscosity is an absolute viscosity and B is equal to one when the viscosity is a kinematic viscosity. 
     Each of aspects A, B and C can have one or more of the following additional elements in combination. Element 1: wherein the BEP K-R number is a normalized BEP K-R number. Element 2: generating a benchmark BEP K-R number using the water performance specifications and a benchmark RPM of the pump. Element 3: modifying the normalized BEP K-R number for the design RPM. Element 4: wherein the normalized BEP K-R number is equal to (the benchmark BEP K-R number*(the benchmark RPM/the design RPM)AA)). Element 5: wherein A is equal to four when the viscosity is an absolute viscosity. Element 6: A is equal to 2.5 when the viscosity is a kinematic viscosity. Element 7: adjusting benchmark specifications using the design RPM. Element 8: where an adjusted flow rate is equal to (a benchmark flow rate*(the design RPM/a benchmark RPM)). Element 9: an adjusted BHP is equal to (a benchmark BHP*(the design RPM/a benchmark RPM){circumflex over ( )}3). Element 10: determining the normalized BEP K-R number using the adjusted flow rate and the adjusted BHP. Element 11: wherein the viscosity is an absolute viscosity and the original flow rate is a mass flow rate, and the computing of the original K-R number is equal to (the mass flow rate{circumflex over ( )}2.0)/(the BHP*the absolute viscosity). Element 12: wherein the viscosity is a kinematic viscosity and the original flow rate is a mass flow rate, and the original K-R number is equal to (the mass flow rate*the kinematic viscosity{circumflex over ( )}0.5)/(the design RPMA0.5*the BEP BHP). Element 13: wherein the original flow rate is a volumetric flow rate and the computing converts the volumetric flow rate to a mass flow rate using a density of the fluid. Element 14: wherein the pump is one of a centrifugal pump, a rotary pump, a positive displacement pump, or a metering pump. Element 15: wherein the pump is utilized in a medical field, a chemical field, a petrochemical field, or a hydrocarbon production field. Element 16: wherein the design BHP is utilized to predict a motor parameter for the pump, and the pump is one of a mud pump, an hydrocarbon pump, a slurry pump, a hydraulic pump, a sand pump, or a brine pump. Element 17: analyzing a well operation plan utilizing the design BHP, the pump, the viscosity of the fluid, and the motor parameter to determine parameters of the pump and a quantity of stages for the pump. Element 18: wherein the parameters of the pump include the design RPM, a stage diameter, a design flow rate, a hydraulic design, a head value, and a fluid viscosity handling. Element 19: wherein the BHP predictor is further capable of performing calculations. Element 20: a normalized BEP K-R number is equal to (a benchmark BEP K-R number*(a benchmark RPM*(a benchmark RPM/the design RPM){circumflex over ( )}5)). Element 21: an original K-R number is equal to (a mass flow rate{circumflex over ( )}2.0)/(a BEP BHP*an absolute viscosity). Element 22: an original K-R number is equal to (a mass flow rate*a kinematic viscosity{circumflex over ( )}0.5)/(the design RPMA0.5*a BEP BHP). Element 23: wherein the BHP predictor is further capable of implementing affinity laws. Element 24: an adjusted flow rate is equal to (a benchmark flow rate*(the design RPM/a benchmark RPM)). Element 25: an adjusted BHP is equal to (a benchmark BHP*(the design RPM/a benchmark RPM){circumflex over ( )}3). Element 26: wherein the design BHP is utilized to predict a motor parameter for the pump, and the pump is one of a mud pump, an hydrocarbon pump, a slurry pump, a hydraulic pump, a sand pump, or a brine pump. Element 27: a well system analyzer capable of analyzing a well operation plan utilizing the design BHP, the pump, the fluid viscosity, and the motor parameter to determine parameters of the pump and a quantity of stages of the pump, wherein the parameters of the pump include the design RPM, a stage diameter, the flow rate, a hydraulic design, a head value, and a fluid viscosity handling.