Abstract:
Estimates are formed of reservoir pressure between the wells for subsurface hydrocarbon producing reservoir. The estimation is based on field data and physical laws governing the hydrocarbon flow in porous media. Information from 3-dimensional fine geological and numerical reservoir simulation models, statistical interpolation between the wells, and static bottom-hole pressure (SBHP) surveys (measurement) at wells are used to more rapidly determine 2-dimensional isobaric reservoir pressure maps for times of interest during the reservoir simulation.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is a continuation in part of, and claims priority to, Applicant&#39;s co-pending, commonly owned U.S. patent application Ser. No. 14/014,658, filed Aug. 30, 2013, which is incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to determination or mapping of reservoir pressure over a region of interest in a subsurface reservoir with integration of static bottom-hole pressure survey data and simulation modeling. 
         [0004]    2. Description of the Related Art 
         [0005]    In the oil and gas industries, massive amounts of data are required to be processed for computerized simulation, modeling and analysis for exploration and production purposes. For example, the development of underground hydrocarbon reservoirs typically includes development and analysis of computer simulation models of the reservoir. These underground hydrocarbon reservoirs are typically complex rock formations which contain both a petroleum fluid mixture and water. The reservoir fluid content usually exists in two or more fluid phases. The petroleum mixture in reservoir fluids is produced by wells drilled into and completed in these rock formations. 
         [0006]    A computer reservoir model with realistic geological features and properties, appropriate distribution of in-situ fluids, as well as initial pressure conditions of the fluids also help in forecasting the optimal future oil and gas recovery from hydrocarbon reservoirs. Oil and gas companies have come to depend on such models as an important tool to enhance the ability to exploit a petroleum reserve. 
         [0007]    It is desirable to be able to monitor pressure conditions in such a reservoir so that production is optimized. Adjustments can be made in production or injection rates to remove undesirable high or low pressure regions that might be observed from such monitoring. For reservoir planning purposes, the reservoir is simulated in a computer and runs are made of estimated production for a range of times over the projected life of the reservoir. 
         [0008]    In simulation models, the reservoir is organized into a number of individual cells. Seismic data with increasing accuracy has permitted the cells to be on the order of 25 meters areal (x and y axis) intervals. For what are known as giant reservoirs, the number of cells is at least hundreds of millions, and reservoirs of what is known as giga-cell size (a billion cells or more) are encountered. 
         [0009]    An example reservoir of the type for which production data are simulated over the expected reservoir life as illustrated by the model M ( FIG. 1 ) is usually one which is known to those in the art as a giant reservoir. A giant reservoir may be several miles in length, breadth and depth in its extent beneath the earth and might, for example, have a volume or size on the order of three hundred billion cubic feet. 
         [0010]    The reservoir is organized into a matrix which corresponds to the three dimensional extent of the reservoir and is composed of a number of contiguous 3-dimensional cells. It is common for a reservoir matrix to contain millions of cells to obtain as accurate an indication of reservoir conditions as feasible. Actual reservoir models may have several millions of such cells. 
         [0011]    For reservoirs of this type, the actual number of wells may also be on the order of a thousand, with each well having a number of perforations into producing formations. Typically, not all of the wells in a reservoir have what are known as permanent downhole pressure gauges in them to monitor reservoir at those locations. This however represents a pressure measurement at only one point in the huge volume of the reservoir. 
         [0012]    Thus, only a relatively small number of wells in a reservoir have such pressure gauges and as mentioned, the reservoir may have a substantial extent in terms of subsurface breadth, width and depth, leading to a very large number of cells in the model. The data points are extremely scarce when compared to the reservoir volume. 
         [0013]    Therefore, the conditions and spatial quantity under which the actual well pressure is measured are completely different than the reservoir pressure which reservoir engineers are interested in for reservoir production optimization. Pressure measurements at the limited number of wells having gauges in the reservoir do not provide an accurate indication of reservoir pressure conditions of interest over the full 3-dimensional extent of the reservoir. 
         [0014]    So far as is known, in previous isobaric mapping techniques, the well&#39;s static bottom-hole pressure (SBHP) readings were used to generate isobaric maps. Each SBHP reading was a control point based on which the isobaric map was generated. The interpolation between the control points was a simple linear interpolation that did not account for geological features or for reservoir dynamics during production. 
       SUMMARY OF THE INVENTION 
       [0015]    Briefly, the present invention provides a new and improved computer implemented method of forming a two-dimensional pressure map with a data processing system of reservoir pressures in a region of interest in a subsurface hydrocarbon producing reservoir partitioned for modeling purposes into a reservoir model partitioned as an array of a grid of cells extending over the three dimensions of the reservoir, the reservoir having a plurality of wells with perforations for fluid passage from the reservoir into the wells, with selected ones of the wells having downhole pressure measurement systems installed therein, the array of a grid of cells of the reservoir model comprising well cells at the locations of the wells and reservoir cells at the remaining cells of the grid. 
         [0016]    The computer processing receives pressure data from the wells based on measurements from the downhole pressure measurement systems, and performs simulated pressure calculations on a reservoir simulator in the data processing system for the cells in an array of well cells for an area of interest of the reservoir. Well cells at an uppermost perforation of each of the wells are populated with assigned pressure values from the received pressure data. Pressure values are propagated for the well cells of the wells below the uppermost perforations and for the reservoir cells of the area of interest to form a three-dimensional grid pressure array for the area of interest. The three-dimensional grid pressure array is then collapsed or transformed to a two-dimensional layer of pressure values for the region of interest. The two-dimensional layer of pressure values for the region of interest are assembled in memory of the data processing system and an output image map is formed of the two-dimensional layer of pressure values for the region of interest. 
         [0017]    The present invention also provides a new and improved data processing system for forming a two-dimensional pressure map with a data processing system of reservoir pressures in a region of interest in a subsurface hydrocarbon producing reservoir partitioned for modeling purposes into a reservoir model partitioned as an array of a grid of cells extending over the three dimensions of the reservoir, the reservoir having a plurality of wells with perforations for fluid passage from the reservoir into the wells, with selected ones of the wells having downhole pressure measurement systems installed therein, the array of a grid of cells of the reservoir model comprising well cells at the locations of the wells and reservoir cells at the remaining cells of the grid. 
         [0018]    The data processing system includes a processor which receives pressure data from the wells based on measurements from the downhole pressure measurement systems, and performs simulated pressure calculations on a reservoir simulator in the data processing system for the cells in an array of well cells for an area of interest of the reservoir. The processor then populates well cells at an uppermost perforation of each of the wells with assigned pressure values from the received pressure data, and propagates pressure values for the well cells of the wells below the uppermost perforations and to the reservoir cells of the area of interest to form a three-dimensional grid pressure array for the area of interest. The processor then reduces the three-dimensional grid pressure array to a two-dimensional layer of pressure values for the region of interest, and assembles in memory of the data processing system the measure of two-dimensional layer of pressure values of the region of interest. The data processing system also includes a memory storing the two-dimensional layer of pressure values for the region of interest an output display forming a display of the two-dimensional layer of pressure values for the region of interest of the reservoir. 
         [0019]    The present invention also provides a new and improved data storage device which has stored in a computer readable medium non-transitory computer operable instructions for causing a data processing system to form a two-dimensional pressure map with a data processing system of reservoir pressures in a region of interest in a subsurface hydrocarbon producing reservoir partitioned for modeling purposes into a reservoir model partitioned as an array of a grid of cells extending over the three dimensions of the reservoir. The reservoir has a plurality of wells with perforations for fluid passage from the reservoir into the wells, with selected ones of the wells having downhole pressure measurement systems installed therein, the array of a grid of cells of the reservoir model comprising well cells at the locations of the wells and reservoir cells at the remaining cells of the grid. 
         [0020]    The instructions stored in the data storage device cause the data processing system to receive pressure data from the wells based on measurements from the downhole pressure measurement systems, and perform simulated pressure calculations on a reservoir simulator in the data processing system for the cells in an array of well cells for an area of interest of the reservoir. The instructions also cause the data processing system to populate well cells at an uppermost perforation of each of the wells with assigned pressure values from the received pressure data, and then propagate pressure values for the well cells of the wells below the uppermost perforations and to the reservoir cells of the area of interest to form a three-dimensional grid pressure array for the area of interest. The instructions further cause the data processing system to reduce the three-dimensional grid pressure array to a two-dimensional layer of pressure values for the region of interest, and assemble in memory of the data processing system the two-dimensional layer of pressure values for the region of interest, then form an output image map of the two-dimensional layer of pressure values for the region of interest. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0021]      FIG. 1  is a schematic diagram of a model of a subsurface hydrocarbon reservoir. 
           [0022]      FIG. 2  is a schematic diagram showing a pressure downhole measuring system installed in a selected number of wells in the reservoir of  FIG. 1 . 
           [0023]      FIG. 3  is a functional block diagram of a set of data processing steps performed in a data processing system for two dimensional reservoir pressure estimation with integrated static bottom-hole pressure survey data and simulation modeling according to the present invention. 
           [0024]      FIGS. 4, 5 and 6  are functional block diagrams of a set of data processing steps performed in connection with processing according to  FIG. 3 . 
           [0025]      FIGS. 7A, 7B and 7C  are schematic diagrams of grid cells of a subsurface reservoir model illustrative of the workflow according to  FIGS. 3 and 4  for propagating pressure determinations to each perforation in a vertical well. 
           [0026]      FIGS. 8A and 8B  are schematic diagrams of grid cells of a subsurface reservoir model illustrative of the workflow according to  FIGS. 3 and 5  for propagating pressure determinations for a single perforation in a vertical well to other grid cells in the reservoir. 
           [0027]      FIG. 9  is a schematic diagram of a subsurface reservoir model illustrative of the workflow according to  FIGS. 3 and 6  for propagating pressure determinations for a single perforation in a horizontal well to other grid cells in the reservoir. 
           [0028]      FIGS. 10A and 10B  are schematic diagrams illustrating notations for directions and for grid nomenclature in a reservoir model. 
           [0029]      FIG. 11  is a schematic block diagram of a data processing system for two dimensional reservoir pressure estimation with integrated static bottom-hole pressure survey data and simulation modeling according to the present invention. 
           [0030]      FIG. 12  is an example simulated plot of a 2-dimensional isobaric pressure map based on governing reservoir actual thermodynamics and geophysics relationships according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0031]    In the drawings, the letter M designates a simplified model of a portion of a subsurface hydrocarbon reservoir for which production results based on operating conditions and parameters are simulated over an estimated production life according to the present invention based on geological and fluid characterization information obtained for the cells of the reservoir. The results obtained are thus available and used for simulation of historical performance and for forecasting of production from the reservoir. Based on the results of such simulation, models such as those described and shown in U.S. Pat. No. 7,526,418 are then formed and are available for evaluation and analysis. U.S. Pat. No. 7,526,418 is owned by the assignee of the present invention and is incorporated herein by reference. 
         [0032]    For a giant reservoir, the physical size of the reservoir may be several miles in length, breadth and depth in its extent beneath the earth and might, for example, have a volume or size on the order of three hundred billion cubic feet. The number of cells for a reservoir of this size is, for example, typically on the order of hundreds of millions. 
         [0033]    For reservoirs of this type, the actual number of wells may also be on the order of a thousand, with each well having a number of perforations into producing formations. Typically, a limited number of the wells in a reservoir have what are known as permanent downhole pressure gauges in them to monitor reservoir at those locations. This, however, represents a pressure measurement at only one point in the volume of the reservoir. 
         [0034]    Thus, only key wells in a reservoir have such pressure gauges and as mentioned, the reservoir may have a substantial extent in terms of subsurface breadth, width and depth, leading to a very large number of cells in the model. The reservoir pressure data points are extremely scarce when compared to the reservoir volume. 
         [0035]      FIG. 2  illustrates an example placement of a group G of wells W from a portion of a large reservoir R of the type and size exemplified by the model M of  FIG. 1 . The wells in the group G typically include production wells, injection wells and observation wells and are spaced over the extent of the reservoir. As indicated, certain ones of the wells W represented by the group G are provided with permanent downhole measurement systems  20 , which are known as PDHMS. The PDHMS  20  may, for example be of the type described in U.S. Pat. Nos. 8,078,328 and 8,312,320, commonly owned by the assignee of the present application. The subject matter disclosed in U.S. Pat. Nos. 8,078,328 and 8,312,320 is incorporated herein by reference. 
         [0036]    The PDHMS  20  include surface units which receive reservoir and well data in real time from downhole sensors  22 . The downhole sensors  22  obtain data of interest, and for the purposes of the present invention the downhole sensors include downhole pressure and temperature sensors located in the wells W at selected depths and positions in the selected group G of wells among the much larger number of wells in the reservoir. 
         [0037]    The downhole sensors  22  furnish the collected real-time pressure and temperature data from the wells W in which they are installed, and a supervisory control and data acquisition (SCADA) system with a host computer or data processing system D ( FIG. 4 ) collects and organizes the collected data form the wells in the group G. The PDHMS  20  also includes sensors to record production and injection data for the injection wells in the group G, which data is also collected and organized by the supervisory control and data acquisition. 
       NOMENCLATURE 
       [0038]      
         [0000]    
       
         
               
               
             
           
               
                   
               
             
             
               
                 P av   
                 Average reservoir pressure 
               
               
                 P colav   
                 Average reservoir pressure for a column of grid blocks 
               
               
                 P SBHP   
                 Static Bottom-hole pressure 
               
               
                 ΔP cf   
                 Pressure correction factor for a column of cells 
               
               
                 P cal   
                 i-Reservoir calculated pressure 
               
               
                 (PV i ) 
                 Pore volume of cell or grid block i, where i = 1, 2 . . . n 
               
               
                 (BV) i   
                 Bulk Volume of cell or grid block i, where i = 1, 2 . . . n 
               
               
                 PV i  = 
                 (Gridblock Bulk Volume) * porosity of grid block i where 
               
               
                 (BV) I  * Ø i   
                 i = 1, 2 . . . n 
               
               
                 (S w ) i   
                 Water saturation 
               
               
                 (1 − S w ) i   
                 Hydrocarbon Saturation at grid block i where i = 1, 2 . . . n 
               
               
                 I 
                 Grid block index in x-direction with reference to a layer 
               
               
                   
                 in the 3D reservoir grid 
               
               
                 J 
                 Grid block index in y-direction with reference to a 
               
               
                   
                 layer in the 3D reservoir grid 
               
               
                 K 
                 Grid block index in z-direction with reference to a column 
               
               
                   
                 in the 3D reservoir grid 
               
               
                   
               
             
          
         
       
     
       SUBSCRIPTS 
       [0039]      
         [0000]    
       
         
               
               
             
           
               
                   
               
             
             
               
                 C: 
                 column 
               
               
                 cf: 
                 correction factor 
               
               
                 cal: 
                 calculated 
               
               
                 colav: 
                 column average 
               
               
                 e: 
                 grid block index 
               
               
                 av: 
                 average 
               
               
                 i: 
                 grid block index 
               
               
                 s: 
                 start 
               
               
                 w: 
                 water 
               
               
                 HC: 
                 hydrocarbon 
               
               
                 avHC: 
                 hydrocarbon weighted average 
               
               
                 avWC: 
                 average pressure above contacts (free phase table) 
               
               
                 avHCWC: 
                 hydrocarbon average above contacts (free phase table) 
               
               
                   
               
             
          
         
       
     
         [0040]    Turning to  FIG. 3 , a flow chart F displays a set of processor steps performed according to the methodology of the present invention in a data processing system D ( FIG. 10 ) for three-dimensional reservoir pressure determination using real time pressure data from downhole gauges and reservoir simulation values determination to determine and form 2-dimensional isobaric pressure maps according to the present invention. The flowchart F indicates the basic computer processing sequence of the present invention and the computation taking place in the data processing system D for the 3-dimensional pressure determination reservoir simulation and map formation according to the present invention. 
         [0041]    Processing according to the flow chart F of  FIG. 3  is performed in conjunction with results of processing according to Applicant&#39;s co-pending, commonly owned U.S. patent application Ser. No. 14/014,658, filed Aug. 30, 2013, and in particular to the determination of an i-Reservoir calculated pressure P cal  and the pressure gradients between cells of the reservoir model. In connection with the processing according to the flow chart F, certain input parameters are provided as indicated at step  30  by users interested in reservoir management according to the present invention. The input parameters are identifications of each of the following: Field, Reservoir(s), Pressure Survey Data (SBHP), and Target Date for which a two dimensional reservoir pressure estimation map is to be formed. 
         [0042]    As shown at step  32 , input perforation and production/injection data obtained by the reservoir simulator R in the data processing system D are also provided and subjected to quality checking as shown at step  34 . The reservoir simulation model is thus updated with the latest perforations and production/injection data for the wells of interest in the reservoir or field. 
         [0043]    The reservoir simulation is then performed by reservoir simulator R ( FIG. 10 ) during step  36  with the quality-checked and verified updates to perforation and production/injection data which have been updated during step  34  to the date of interest. During step  36 , pressure gradients between the reservoir model grid blocks or reservoir cells of the model M are determined according to the techniques of U.S. patent application Ser. No. 14/014,658, mentioned above. The gradients between grid blocks are indicative of pressure changes in the reservoir due to geological heterogeneity, fluid dynamics, model constrains, and production/injection activities. 
         [0044]    During step  38 , the pressure gradients determined by reservoir simulator R as a result of step  36  are evaluated. In the evaluation during step  38 , a perforation file of the reservoir data in the reservoir data is parsed and stored. The perforation file is also sorted by depth for each well in the reservoir. Pressure survey or SBHP survey data is also parsed and stored during step  38 , as is needed data, which include samples of SBHP and of perforation data from the reservoir simulation model output. Inactive cells which are to be excluded from processing computation are then identified during step  38  and then discarded along with their data content. 
         [0045]    In step  39 , pressure survey data obtained from the reservoir in the manner described above as illustrated schematically in  FIG. 2  is then used to determine reservoir pressure values at well top perforations of the wells  22  in the reservoir according to the techniques of U.S. patent application Ser. No. 14/014,658, mentioned above. Then, in step  40 , pressure values are propagated for each of the perforations of each of the wells  22 . 
         [0046]    According to the present invention, there are three methods of performing step  40  for propagation of pressure values based on pressure survey data to be propagated to the perforations in the reservoir model and further to the reservoir models cells away from one or more of the wells. They are: an All Perforation Method as indicated schematically at  42  in  FIG. 4 ; a Single Perforation Column Method shown schematically at  44  in  FIG. 5 ; and an All-Perforation Column Method shown at  46  in  FIG. 6 . 
       All Perforation Method 
       [0047]    As shown in  FIG. 4 , the All Perforation processing  42  begins with step  48  where SBHP values are assigned to the first or uppermost perforation in a well. During step  50 , measures from the simulation model of pressure gradient between the perforated cells are used to propagate pressure calculation successively from the first or uppermost cells to last lowest cells in the well. All perforations thus used are control points used in step  52  to propagate pressure assignments to non-perforated cells according to suitable statistical methods as describe in U.S. patent application Ser. No. 14/014,658. A suitable such method is that known as Distance-Weighted Moving Average or DWMA. 
         [0048]    As shown schematically in  FIG. 7A , during All Perforation processing step  42  SBHP values are assigned to the first or uppermost perforation  54  in an example vertical well  56 .  FIG. 7B  illustrates schematically lower performance of step  52 , where pressure gradient measures for reservoir simulation are successively propagated from perforation  54  successively to lower perforations  58  and  60 . Since inactive cells have, as described above, been excluded from processing, perforations  54 ,  58  and  60  are shown vertically adjacent each other in  FIGS. 7A, 7B and 7C .  FIG. 7C  illustrates schematically the assignment of pressure values to non-perforated cells  62  according to Distance-Weighted Moving Average or DWMA methods, as will be described. 
       Single-Perforation Column Method 
       [0049]    In the Single-Perforation Column Method shown at  64  ( FIG. 5 ), only a first perforation of  56  well is considered as the pivot for calculating pressure along the well and away from it. As shown in  FIG. 5 , the All Perforation processing  64  begins with step  66  where after the first perforation is identified and the column of cells where, the first perforation is located is marked, the average column pressure (P colav ) is determined from the simulation model: 
         [0000]    
       
         
           
             
               P 
               colav 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   c 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     P 
                     i 
                   
                   ) 
                 
               
               c 
             
           
         
       
     
         [0050]    During step  68 , a correction factor (ΔP cf ) is determined by subtracting the pressure survey reading SBHP (P SBHP ) from the average column pressure P sim ) determined during step  66 : 
         [0000]      Δ P   cf   =P   colav   −P   SBHP  
 
         [0051]    During step  70 , for each cell pressure value from simulation model, the correction factor (ΔP cf ) is subtracted from cell pressure (P sim ) and the resultant i-Reservoir calculated pressure value P cal  assigned to i-Reservoir grid pressure, as follows: 
         [0000]    
       
      
       P 
       cal 
       =P 
       sim 
       −ΔP 
       cf  
      
     
         [0052]    In this manner pressure for each of the grid blocks is determined.  FIG. 8A  illustrates schematically the Single-Perforation Column Method step  64  where average column pressure measures as shown at  72  are determined and a pressure correction factor is subtracted as indicated at  74  resulting in an i-Reservoir pressure as shown at  76  and  78  for different cells in a column  80 . 
         [0053]      FIG. 8B  illustrates schematically step  82  where the resultant i-Reservoir calculated pressure value P cal  is determined for the cells  84  of the grid of the simulation model M. As a result, the average column pressure is the (P SBHP ). 
       All-Perforation Column Method 
       [0054]    For the All-Perforation Column Method as shown at  84  ( FIG. 6 ), each of the i perforations of a well are considered for calculating pressure along the well and away from it. The perforations of a well are identified, and measures of pressure along the perforations are determined according to the Single-Perforation Column Method described above. As shown in  FIG. 6 , the All Perforation processing begins with step  86 , where the average column pressure (P colayv     i   ) is determined for the perforations of each column i from the simulation model: 
         [0000]    
       
         
           
             
               ( 
               
                 P 
                 
                   colav 
                   i 
                 
               
               ) 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   c 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     P 
                     i 
                   
                   ) 
                 
               
               c 
             
           
         
       
     
         [0055]    During step  88 , a correction factor (ΔP cf     i   ) is determined for each column i by subtracting the pressure survey reading SBHP (P SBHP ) from the average column pressure (P colav     i   ) determined during step  86 : 
         [0000]      Δ P   cf     i     =P   colav     i     −P   SBHP  
 
         [0056]    Then, during step  90 , for each column i and for each cell pressure value from simulation model in that column, the correction factor (ΔP cf     i   ) is subtracted from cell pressure (P sim ) and assigned as the pressure value P cal  to i-Reservoir grid pressure: 
         [0000]    
       
      
       P 
       cal 
       =P 
       sim 
       −ΔP 
       cf 
       
         i  
       
      
     
         [0057]    Next, in step  92 , pressure assignments are determined and propagated to the remained or non-perforated grid blocks according to suitable statistical methods as described in U.S. patent application Ser. No. 14/014,658. For a vertical well, the All-Perforation Column Method produces the same results as the Single-Perforation Column Method, as illustrated schematically in  FIGS. 8A and 8B  and described above. 
         [0058]      FIG. 9  illustrates schematically the All-Perforation Column Method step  84  ( FIG. 6 ) for a horizontal well model  93  having a plurality of well perforations  94  as shown. In step  92  of the All-Perforation Column Method, pressure assignments are determined and propagated to the remained or non-perforated grid blocks  95  ( FIG. 9 ) of the horizontal well model  93  according to suitable statistical methods as described in U.S. patent application Ser. No. 14/014,658, as indicated schematically at  96 . 
         [0059]    After performance of step  40  ( FIG. 3 ) for pressure computation along the well completions of a selected one of the three alternatives: All Perforation Method; Single-Perforation Column Method or All-Perforation Column Method in the manner described above, the reservoir model has been adjusted. The reservoir model M indicates propagated pressure measures which incorporate measured reservoir pressures as adjusted to indicate the effects of physics and geology on the reservoir and its fluids indicated by reservoir simulation processing. 
         [0060]    During step  97  ( FIG. 3 ), a user is able to specify one of several techniques for data filtering, such as the type known as a Distance Weighted Moving Average or DWMA. The DWMA filtering is a nonlinear filter, designed to be a robust version of a traditional moving average. DWMA filtering is then performed during step  98  to reduce the impact of outlier propagated pressure measures in the reservoir model data. The result of step  98 , as indicated at  100  is a 3-dimensional pressure array of reservoir pressure data which is stored for further processing by the data processing system D. 
         [0061]    The 3-dimensional grid pressure array indicated at  100  is then in step  102  according to the present invention collapsed or changed in format from a 3-dimensional pressure array to 2-dimensional pressure of a region of interest (or entirety of the reservoir) in the reservoir M. There are a number of methods of collapsing the 3-dimensional grid to 2-dimensional maps, the simplest being simple averaging of the propagated pressure measures of the model adjacent the various specified map co-ordinates for 2-dimensional map being formed. 
         [0062]    Preferably, however, one of several forms of Pore-Volume Weighted Averaging for step  102  is utilized for collapsing the 3-dimensional grid to a 2-dimensional map of the region of interest. Examples of such pore-volume weighted averaging to indicate average reservoir pressure for 2-dimensional isobaric maps are set forth below. Reference is made to the Nomenclature Section for an explanation of the physical measures indicated in the relationships of pore-volume weighted averaging expressed. 
       Pore-Volume Weighted Average Reservoir Pressure 
       [0063]    
       
         
           
             
               P 
               av 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       P 
                       i 
                     
                      
                     
                       ( 
                       
                         PV 
                         i 
                       
                       ) 
                     
                   
                   ) 
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     PV 
                     i 
                   
                   ) 
                 
               
             
           
         
       
     
       Hydrocarbon Pore-Volume Weighted Average Reservoir Pressure 
       [0064]    
       
         
           
             
               P 
               avHC 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       P 
                       i 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             PV 
                             ) 
                           
                           i 
                         
                         * 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 S 
                                 w 
                               
                             
                             ) 
                           
                           i 
                         
                       
                       ] 
                     
                   
                   ) 
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   
                     ( 
                     PV 
                     ) 
                   
                   i 
                 
               
             
           
         
       
     
       Pore-Volume Weighted Average Reservoir Pressure Above Free Water Table 
       [0065]    
       
         
           
             
               P 
               avWC 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       P 
                       i 
                     
                      
                     
                       ( 
                       
                         PV 
                         i 
                       
                       ) 
                     
                   
                   ) 
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     PV 
                     i 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where i is the index of all grid block with depth greater than the specified contact&#39;s depth. 
       Hydrocarbon Pore-Volume Weighted Average Reservoir Pressure Above Free Water Table 
       [0066]    
       
         
           
             
               P 
               avHCWC 
             
             = 
             
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                     
                 
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                   ( 
                   
                     
                       P 
                       i 
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             PV 
                             ) 
                           
                           i 
                         
                         * 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 S 
                                 w 
                               
                             
                             ) 
                           
                           i 
                         
                       
                       ] 
                     
                   
                   ) 
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
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                     PV 
                     ) 
                   
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         [0000]    where i is the index of all grid block with depth greater than the specified contact&#39;s depth. 
         [0067]    As mentioned a user engineer or analyst is able to select an area of interest in the reservoir model M for which an isobaric 2-dimensional pressure map is to be formed. The display is formed by the data processing system D during performance of step  104  of  FIG. 3 . For this processing step, an engineer can specify an area of interest using an n-sided polygon where all variety of isobaric maps can be generated as indicated at step  106  along with average reservoir pressure calculations. 
         [0068]    As shown in  FIG. 12 , an example plot  140  represents a simulated 2-dimensional isobaric pressure map which could be obtained according to the present invention based on governing equations and relationships for a selected area of interest, and representing the interplay of principles of thermodynamics and geophysics formed according to the present invention. 
         [0069]    Example values of SBHP survey data and sample perforation location data according coordinates for perforations are set forth below: 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Sample SBHP Survey Data 
               
             
          
           
               
                   
                 FIELD 
                 WELL NO. 
                 Oct. 1, 2015 
               
               
                   
                   
               
             
          
           
               
                   
                 ABCD 
                 1 
                 1500 
               
               
                   
                 ABCD 
                 2 
                 1300 
               
               
                   
                 ABCD 
                 3 
                 2000 
               
               
                   
                 ABCD 
                 4 
                 1655 
               
               
                   
                 ABCD 
                 5 
                 1582 
               
               
                   
                 ABCD 
                 6 
                 1340 
               
               
                   
                 ABCD 
                 7 
                 1790 
               
               
                   
                 ABCD 
                 8 
                 2469 
               
               
                   
                 ABCD 
                 9 
                 4467 
               
               
                   
                 ABCD 
                 10 
                 1200 
               
               
                   
                 ABCD 
                 11 
                 1400 
               
               
                   
                 ABCD 
                 12 
                 4500 
               
               
                   
                 ABCD 
                 13 
                 3000 
               
               
                   
                 ABCD 
                 14 
                 1500 
               
               
                   
                 ABCD 
                 15 
                 4064 
               
               
                   
                 ABCD 
                 16 
                 3261 
               
               
                   
                 ABCD 
                 17 
                 2531 
               
               
                   
                 ABCD 
                 18 
                 5092 
               
               
                   
                 ABCD 
                 19 
                 2452 
               
               
                   
                 ABCD 
                 20 
                 2401 
               
               
                   
                 ABCD 
                 21 
                 2244 
               
               
                   
                 ABCD 
                 22 
                 2194 
               
               
                   
                   
               
             
          
         
       
     
       WELLS_BLOCK 
     WELL_Name=ABCD0001 
     PERF I=301 J=71 K=51 Rf=1.0 CD=‘Z’ Skin=1.0/MDEPTH=3873.5 
     PERF I=301 J=71 K=52 Rf=1.0 CD=‘Z’ Skin=2.0/MDEPTH=3880.5 
     PERF I=301 J=71 K=53 Rf=1.0 CD=‘Z’ Skin=1.0/MDEPTH=3887.5 
     PERF I=301 J=71 K=54 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=3898.5 
     PERF I=301 J=71 K=55 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=3913.5 
     PERF I=301 J=71 K=56 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=3928.5 
     PERF I=301 J=71 K=57 Rf=1.0 CD=‘Z’ Skin=1.0/MDEPTH=3941.5 
     WELL_Name=ABCD0002 
     PERF I=101 J=71 K=41 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=4873.0 
     PERF I=101 J=71 K=42 Rf=1.1 CD=‘Y’ Skin=0.0/MDEPTH=4880.0 
     PERF I=101 J=71 K=43 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=4887.0 
     PERF I=101 J=71 K=44 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=4898.0 
     PERF I=101 J=71 K=45 Rf=1.2 CD=‘Y’ Skin=0.0/MDEPTH=4913.0 
     PERF I=101 J=71 K=46 Rf=1.0 CD=‘Y’ Skin=0.0/MDEPTH=4928.0 
     PERF I=101 J=71 K=47 Rf=1.3 CD=‘Z’ Skin=0.0/MDEPTH=4941.0 
     ENDWELLS_BLOCK 
     DATE Dec. 1, 2010 
     WELLS_BLOCKS 
     WELL_Name=ABCD0005 
     PERF I=20 J=113 K=83 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=3890.50 
     PERF I=21 J=113 K=83 Rf=1.1 CD=‘X’ Skin=0.0/MDEPTH=3900.50 
     PERF I=21 J=113 K=84 Rf=1.0 CD=‘Z’ Skin=0.0/MDEPTH=3887.50 
     PERF I=22 J=113 K=81 Rf=1.0 CD=‘X’ Skin=3.0/MDEPTH=3887.50 
     PERF I=30 J=113 K=81 Rf=1.2 CD=‘X’ Skin=0.0/MDEPTH=3887.50 
     PERF I=31 J=113 K=83 Rf=1.0 CD=‘X’ Skin=0.0/MDEPTH=3887.50 
     PERF J=32 J=113 K=83 Rf=1.3 CD=‘Z’ Skin=0.0/MDEPTH=3890.50 
     ENDWELLS_BLOCK 
       [0070]    As can be seen in  FIG. 12 , the map plot  140  indicates by x, y co-ordinates the location in a reservoir model M of a selected area of interest and by contour lines  142 , areas of common isobaric pressures at the location. Indications of pressures represented as the 2-dimensional isobaric pressure areas in the reservoir map  140  may be indicated by variations in color, as schematically shown by varying stipple patterns in areas of common pressure within the contour lines. The pressures displayed indicate reservoir pressures over the area of interest while also taking into account geological features, aerial and vertical heterogeneity, and numerical model constraints. The maps formed according to the present invention are not merely estimates of reservoir pressures based only on readings from pressure measurement instrumentation located at a limited number of wells in a reservoir. 
         [0071]      FIG. 10A  is a graphical depiction of an example specification of I, J, and K co-ordinates, having reference to  FIG. 10B  for the orientation of the axial disposition of the co-ordinates. Set forth below are examples of numerical dimensions. 
       Example 1 
       [0072]    The area of interest, given model dimensions (I×J×K): 500×300×200, is bounded by 4-sided polygon indicated by these two corners (1, 1, 1) and (500, 300, 200) is basically the whole reservoir. Therefore the numerical co-ordinates of the user-specified region of interest in the reservoir model M are as set forth below in Table 1: 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 1 
                 1 
                 300 
                 1 
                 200 
               
               
                   
                 500 
                 500 
                 1 
                 300 
                 1 
                 200 
               
               
                   
                 1 
                 500 
                 1 
                 1 
                 1 
                 200 
               
               
                   
                 1 
                 500 
                 300 
                 300 
                 1 
                 200 
               
               
                   
                   
               
             
          
         
       
     
       Example 2 
       [0073]    The area of interest, given model dimensions (I×J×K): 500×300×200 is bounded by corners (1, 50, 10) and (350, 100, 190). The numerical co-ordinates of the user-specified region of interest in the reservoir model M are as set forth below in Table 2: 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 1 
                 50 
                 100 
                 10 
                 190 
               
               
                   
                 350 
                 350 
                 50 
                 100 
                 10 
                 190 
               
               
                   
                 1 
                 350 
                 50 
                 50 
                 10 
                 190 
               
               
                   
                 1 
                 350 
                 100 
                 100 
                 10 
                 190 
               
               
                   
                   
               
             
          
         
       
     
         [0074]    As illustrated in  FIG. 11 , the data processing system  1 ) according to the present invention includes a computer C having a processor  150  and memory  152  coupled to the processor  100  to store operating instructions, control information and database records therein. The data processing system D can be a computer of any conventional type of suitable processing capacity, such as a mainframe, a personal computer, laptop computer, or any other suitable processing apparatus. It should thus be understood that a number of commercially available data processing systems and types of computers may be used for this purpose. As indicated, the data processing system also operates as a reservoir simulator R for simulation of performance and for forecasting of production from the reservoir M. The simulator may thus be of the type described and shown in U.S. Pat. No. 7,526,418. 
         [0075]    The computer C has a user interface  154  and an output data display  156  for displaying output data or records of three-dimensional reservoir pressure deter using real time pressure data from downhole gauges according to the present invention. The output display  156  includes components such as a printer and an output display screen capable of providing printed output information or visible displays in the form of graphs, data sheets, graphical images, data plots and the like as output records or images. 
         [0076]    The user interface  154  of data processing system D also includes a suitable user input device or input/output control unit  158  to provide a user access to control or access information and database records and operate the computer C. Data processing system D further includes a database  160  stored in computer memory, which may be internal memory  152 , or an external, networked, or non-networked memory as indicated at  162  in an associated database server  164 . 
         [0077]    The data processing system D includes program code  166  stored in non-transitory form in memory  152  of the computer C. The program code  166  according to the present invention is in the form of non-transitory computer operable instructions causing the data processor  100  to perform the computer implemented method of the present invention in the manner described above and illustrated in  FIG. 3 . 
         [0078]    It should be noted that program code  166  may be in the form of microcode, programs, routines, or symbolic computer operable languages that provide a specific set of ordered operations that control the functioning of the data processing system D and direct its operation. The instructions of program code  166  may be stored in non-transitory form in memory  152  of the computer C, or on computer diskette, magnetic tape, conventional hard disk drive, electronic read-only memory, optical storage device, or other appropriate non-transitory data storage device having a computer usable medium stored thereon. Program code  166  may also be contained on a data storage device such as server  164  as a non-transitory computer readable medium. 
         [0079]    With the present invention, Bottom-Hole Pressure (SBHP) or pressure survey data measured at or near the depth of a producing formation interval data is entered and honored at the well locations with respect to the desired reference datum depth. Establishing the wells SBHP pressures as control points, the 3-dimensional pressure between the wells is estimated based on results of the numerical simulation by reservoir simulator R based on governing equations and relationships representing actual thermodynamics and geophysics, as well as the most updated geological realization of the subsurface reservoir illustrated as model M. The present invention reduces turnaround time for generation of maps and quality checking the data contents displayed in the maps and stored in the data processing system for evaluation of further processing or analysis. 
         [0080]    The integration between the SBHP pressure points and simulation pressure results in a 3D grid populated with estimated reservoir pressure based on appropriate reliability and conformance with statistical quality analysis and control methods (such as Distance-Weighted Moving Average or DWMA). The data processing system D then adjusts the pressure values to the datum reference depth, if needed. Several alternative methods are then available for collapsing the 3-dimensional pressure grid array into a single layer (2-dimensional) while also taking into account geological features, aerial and vertical heterogeneity, and numerical model constraints. The resultant product, a 2-dimensional isobaric map of a reservoir region of interest is the provided and made available to a variety of visualization and quality control tools for reservoir management engineers to utilize. 
         [0081]    The invention has been sufficiently described so that a person with average knowledge in the matter may reproduce and obtain the results mentioned in the invention herein Nonetheless, any skilled person in the field of technique, subject of the invention herein, may carry out modifications not described in the request herein, to apply these modifications to a determined methodology, or in the performance of the same, requires the claimed matter in the following claims; such techniques and procedures shall be covered within the scope of the invention. 
         [0082]    It should be noted and understood that there can be improvements and modifications made of the present invention described in detail above without departing from the spirit or scope of the invention as set forth in the accompanying claims.