Abstract:
A method of history matching a simulation model is disclosed comprising: (a) defining regions exhibiting similar behavior in the model thereby generating the model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; (b) introducing historically known input data to the model; (c) generating output data from the model in response to the historically known input data; (d) comparing the output data from the model with a set of historically known output data; (e) adjusting the model when the output data from the model does not correspond to the set of historically known output data, the adjusting step including the step of arithmetically changing each of the regions of the model; and (f) repeating steps (b), (c), (d), and (e) until the output data from the model does correspond to the set of historically known output data.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This is a Utility Application of prior pending Provisional Application Ser. No. 60/774,589, filed Feb. 17, 2006, and entitled “Method for History Matching a Simulation Model using Self Organizing Maps to generate Regions in the Simulation Model”. 
    
    
     BACKGROUND 
     This specification discloses a method, and its associated System and Program Storage Device and Computer Program, adapted for ‘history matching’ of numerical simulation models using a Self Organizing Map (SOM) software, the SOM being used to generate and define the ‘Regions’ among the grid blocks of the numerical simulation model during the history matching procedure. 
     History matching of numerical models is an inverse problem. That is, a numerical simulation model is adjusted such that, when a set of historically known input parameters are input to the model, a set of historically known output parameters or data will be generated by the model. History matching is therefore a trial and error procedure. 
     When ‘history matching’ a numerical simulation model, a set of historically known output parameters should be generated by the model in response to a set of historically known input parameters. However, when the set of historically known output parameters are not generated by the model in response to the set of historically known input parameters, it is necessary to multiply the value of a parameter (e.g. permeability) associated with each grid block of the numerical simulation model by a certain value. However, it is clear that the multiplier cannot be the same number for each grid block of the model. Therefore, when the simulation model represents a reservoir field, such as an oil or gas reservoir field, the engineer defines one or more ‘regions’ of the reservoir, wherein the same multiplier within a particular ‘region’ can be used to improve the history match. The selection of the ‘regions’ of the reservoir field can be accomplished in accordance with a geological model of the reservoir. Very often, one or more ‘rectangular boxes’ are used to define the ‘regions’ of the reservoir field. However, the selection of ‘rectangular boxes’ to define the ‘regions’ of the reservoir field does not ordinarily comply with nature. 
     In addition, the selection of ‘regions’ in accordance with a geological model is very often based on ‘static geological information’, that is, geological information that is not directly related to hydraulic parameters associated with production from a reservoir or other changes over time (e.g. permeability is derived from a correlation with porosity after the creation of the geological model). 
     SUMMARY 
     One aspect of the present invention involves a method of history matching a simulation model, comprising: (a) defining regions exhibiting similar behavior in the model thereby generating the model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; (b) introducing historically known input data to the model; (c) generating output data from the model in response to the historically known input data; (d) comparing the output data from the model with a set of historically known output data; (e) adjusting the model when the output data from the model does not correspond to the set of historically known output data, the adjusting step including the step of arithmetically changing each of the regions of the model; and (f) repeating steps (b), (c), (d), and (e) until the output data from the model does correspond to the set of historically known output data. 
     Another aspect of the present invention involves a program storage device readable by a machine tangibly embodying a program of instructions executable by the machine to perform method steps for history matching a simulation model, the method steps comprising: (a) defining regions exhibiting similar behavior in the model thereby generating the model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; (b) introducing historically known input data to the model; (c) generating output data from the model in response to the historically known input data; (d) comparing the output data from the model with a set of historically known output data; (e) adjusting the model when the output data from the model does not correspond to the set of historically known output data, the adjusting step including the step of arithmetically changing each of the regions of the model; and (f) repeating steps (b), (c), (d), and (e) until the output data from the model does correspond to the set of historically known output data. 
     Another aspect of the present invention involves a computer program adapted to be executed by a processor, the computer program, when executed by the processor, conducting a process for history matching a simulation model, the process comprising: (a) defining regions exhibiting similar behavior in the model thereby generating the model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; (b) introducing historically known input data to the model; (c) generating output data from the model in response to the historically known input data; (d) comparing the output data from the model with a set of historically known output data; (e) adjusting the model when the output data from the model does not correspond to the set of historically known output data, the adjusting step including the step of arithmetically changing each of the regions of the model; and (f) repeating steps (b), (c), (d), and (e) until the output data from the model does correspond to the set of historically known output data. 
     Another aspect of the present invention involves a system adapted for history matching a simulation model, comprising: first apparatus adapted for defining regions exhibiting similar behavior in the model thereby generating the model having a plurality of regions, each of the plurality of regions exhibiting a similar behavior; second apparatus adapted for introducing historically known input data to the model; third apparatus adapted for generating output data from the model in response to the historically known input data; fourth apparatus adapted for comparing the output data from the model with a set of historically known output data; fifth apparatus adapted for adjusting the model when the output data from the model does not correspond to the set of historically known output data, the fifth apparatus including sixth apparatus adapted for arithmetically changing each of the regions of the model; and seventh apparatus adapted for repeating the functions performed by the second, third, fourth, fifth, and sixth apparatus until the output data from the model does correspond to the set of historically known output data. 
     Further scope of applicability will become apparent from the detailed description presented hereinafter. It should be understood, however, that the detailed description and the specific examples set forth below are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention, as described and claimed in this specification, will become obvious to one skilled in the art from a reading of the following detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A full understanding will be obtained from the detailed description presented hereinbelow, and the accompanying drawings which are given by way of illustration only and are not intended to be limitative to any extent, and wherein: 
         FIG. 1  illustrates a workstation or other computer system wherein the numerical simulation model and the Self Organizing Map (SOM) software is stored; 
         FIG. 2  illustrates a grid block of the numerical simulation model which has a ‘parameter’ associated therewith; 
         FIG. 3  illustrates the numerical simulation model including a plurality of grid blocks and a method for history matching the numerical simulation model including the method as disclosed in this specification for history matching a simulation model using Self Organizing Maps to generate Regions in the simulation model; 
         FIG. 3A  illustrates a realistic example of the numerical simulation model including the plurality of grid blocks; 
         FIG. 4  illustrates the numerical simulation model including a plurality of grid blocks, the model including a plurality of ‘regions’ where each ‘region’ of the model further includes one or more of the grid blocks of the numerical simulation model; 
         FIG. 5  illustrates how the ‘parameters’ (in addition to ‘all available information’) associated with each grid block of the numerical simulation model are introduced, as input data, to the Self Organizing Map (SOM) software, and the SOM software responds by defining the ‘regions’ of the numerical simulation model which are illustrated in  FIG. 4 ; 
         FIG. 6  illustrates how ‘all available information’ associated with each of the grid blocks of the numerical simulation model is used by the SOM software to generate and define ‘regions’ of similar behavior among the grid blocks of the numerical simulation model, and, responsive thereto, the SOM software organizes the grid blocks of the numerical simulation model into one or more of the defined ‘regions’ as illustrated in  FIG. 4 ; and 
         FIG. 7  illustrates a block diagram which describes how the SOM software will define ‘regions’ of similar behavior among the grid blocks of the numerical simulation model. 
     
    
    
     DETAILED DESCRIPTION 
     This specification discloses a ‘Method for history matching using Self Organizing Maps (SOM) to generate regions’, wherein the novel method uses Self Organizing Maps (“SOM”) to compute ‘regions’ of similar behavior among the grid blocks of a numerical simulation model when ‘history matching’ the numerical simulation model. This leads to a much faster approach to a correct solution. Instead of hundreds of simulation runs, less than 20 simulation runs are generally necessary in order to achieve a good understanding of the parameter values within the grid blocks of the model. When a good understanding of such parameter values is achieved, a good ‘history match’ of the numerical simulation model is the result. 
     A first step associated with the ‘Method for history matching using Self Organizing Maps (SOM) to generate regions’, as disclosed in this specification, uses SOM to build a set of ‘regions’ among the grid blocks of the numerical simulation model. That is, instead of grouping grid blocks in accordance with geology, the grid blocks are grouped in accordance with ‘regions of similar behavior based on all available information’ (hereinafter called ‘regions’). The method of Self Organizing Maps (SOM) is used to cluster grid blocks of similar behavior. SOMs can handle all different types of parameters, including model parameters from the initialization, such as initial pressure and saturation. This ‘new approach’ (i.e., using SOMS to generate ‘regions’) takes into account several different ‘parameters’ of each grid block of the model reflecting different physical and numerical processes of hydrocarbon production, including:
         geological description: such as lithofacies type   hydraulic flow units (HFU): such as permeabilities, porosities   initialization: such as water saturations (initial and critical), initial pressure   discretization: such as spatial discretization (e.g. DZ), grid block pore volumes   PVT regions   drainage   secondary phase movement: relative permeability endpoints.       

     Depending on the importance of the parameter of each grid block, its influence can be controlled using a weight factor. This factor is normalized between 0 and 1. The parameter gets the highest weight when the weight factor is one. A parameter has no influence on the clustering when the weight factor is set to 0. The SOM generates rules which are used to identify ‘regions’ automatically. For example, a rule for one specific ‘region’ might be:
         IF DZ&gt;10.23 AND DZ&lt;27.48 AND   IF PERMX&gt;9.03 AND PERMX&lt;2496.5 AND   IF PERMY&gt;8.53 AND PERMY&lt;665.9 AND   IF PERMZ&gt;0.89 AND PERMZ&lt;440.8 AND   IF PORO&gt;0.077 AND PORO&lt;0.25 AND   IF PORV&gt;1.38e+5 AND PORV&lt;5.26e+5 AND   IF PINI&gt;2485.5 AND PINI&lt;2874.4 AND   IF SWAT&gt;0.06 AND SWAT&lt;0.74   THEN Grid-Block belongs to REGION  1         

     The advantage of this ‘new approach’ is its simplicity. Since the Self Organizing Map (SOM) is a self-learning approach, it does not need any expert knowledge to use this technology. The only decision which the user has to make is how many ‘regions’ the user wants to create. 
     A second step associated with the ‘Method for history matching using Self Organizing Maps (SOM) to generate regions’, as disclosed in this specification, includes calculating a Root Mean Square (RMS) error based on ‘regions’. To accelerate the match progress, it is necessary to calculate the root mean square (RMS) error based on regions. This means that the direct impact of a parameter change of a region can be compared to the quality of the match in that region. To do that, it is necessary to split up the RMS error per well into the fractions which are contributed by each individual region. Each region, in which a well is perforated, contributes in a different way to the well behavior. As the well behavior is mainly driven by its production, it is also clear that the importance of a region in the well is depending on the product of permeability and thickness (kh). The higher the kh of a region in the perforated part of a well is, the higher its contribution to production will be. This principle is used to split up the well RMS error into an error for each region in which the well is perforated. Summing up all well RMS for one region can be used to determine a regional RMS value. In this way, the direct impact of a change in the region input parameter can be quantified directly. 
     The ‘Method for history matching using Self Organizing Maps (SOM) to generate regions’, as disclosed in this specification, represents a clear improvement to: the ‘quality of the history match’ and the ‘number of runs needed to achieve the history match’ of the numerical simulation model. 
     Referring to  FIG. 1 , a workstation, personal computer, or other computer system  10  is illustrated adapted for storing a numerical simulation model  12  and a Self Organizing Map (SOM) software  14 . The computer system  10  of  FIG. 1  includes a processor  10   a  operatively connected to a system bus  10   b , a memory or other program storage device  10   c  operatively connected to the system bus  10   b , and a recorder or display device  10   d  operatively connected to the system bus  10   b . The memory or other program storage device  10   c  stores the numerical simulation model  12  and the Self Organizing Map (SOM) software  14  which provides an input to and receives an output from the numerical simulation model  12 . The numerical simulation model  12  and the Self Organizing Map (SOM) software  14  which is stored in the memory  10   c  of  FIG. 1  can be initially stored on a CD-ROM, where that CD-ROM is also a ‘program storage device’. That CD-ROM can be inserted into the computer system  10 , and the numerical simulation model  12  and the Self Organizing Map (SOM) software  14  can be loaded from that CD-ROM and into the memory/program storage device  10   c  of the computer system  10  of  FIG. 1 . The computer system  10  of  FIG. 1  receives ‘input data’  16  which includes ‘historically known input data’  18 . The processor  10   a  will execute the numerical simulation model  12  and the Self Organizing Map (SOM) software  14  stored in memory  10   c  while simultaneously using the ‘input data’  16  including the ‘historically known input data’  18 ; and, responsive thereto, the processor  10   a  will generate ‘Output Data’  20  which is adapted to be recorded by or displayed on the Recorder or Display device  10   d  in  FIG. 1 . The computer system  10  of  FIG. 1  will attempt to ‘history match’ the numerical simulation model  12  with respect to the ‘historically known input data’  18  and the ‘output data’  20  (to be discussed later in this specification) by using the SOM software  14  to achieve the match. The computer system  10  of  FIG. 1  may be a personal computer (PC), a workstation, a microprocessor, or a mainframe. Examples of possible workstations include a Silicon Graphics Indigo 2 workstation or a Sun SPARC workstation or a Sun ULTRA workstation or a Sun BLADE workstation. The memory or program storage device  10   c  (including the above referenced CD-ROM) is a computer readable medium or a program storage device which is readable by a machine, such as the processor  10   a . The processor  10   a  may be, for example, a microprocessor, microcontroller, or a mainframe or workstation processor. The memory or program storage device  10   c , which stores the numerical simulation model  12  and the Self Organizing Map (SOM) software  14 , may be, for example, a hard disk, ROM, CD-ROM, DRAM, or other RAM, flash memory, magnetic storage, optical storage, registers, or other volatile and/or non-volatile memory. 
     Referring to  FIGS. 2 , a grid block  22  is illustrated. The grid block  22  is only one grid block among a multitude of other grid blocks which comprise the numerical simulation model  12 , each grid block including grid block  22  having one or more ‘parameters’  24  associated therewith. For example, the ‘parameters’  24  associated with the grid blocks (including grid block  22 ) may include permeability or transmissibility or pore volume, as fully described and set forth in U.S. Pat. Nos. 6,078,869 and 6,018,497 to Gunasekera, the disclosures of which are incorporated by reference into this specification. As noted above, the ‘parameters’ could also include: geological description, such as lithofacies type, hydraulic flow units (HFU), such as permeabilities, porosities, initialization, such as water saturations (initial and critical), initial pressure discretization, such as spatial discretization (e.g. DZ), grid block pore volumes, PVT regions, drainage, and secondary phase movement, such as relative permeability endpoints. 
     Referring to  FIG. 3 , a method for ‘history matching’ the numerical simulation model  12  with respect to the ‘historically known input data’  18  and the ‘output data’  20  of  FIG. 1  is discussed below with reference to  FIG. 3 . In  FIG. 3 , the numerical simulation model  12  includes a plurality of the grid blocks  22 , each of the plurality of grid blocks  22  of  FIG. 3  having one or more ‘parameters’  24  associated therewith, such as permeability or transmissibility or pore volume. In  FIG. 3 , when ‘history matching’ the numerical simulation model  12 , the ‘historically known input data’ is introduced as ‘input data’ to the model  12  and, responsive thereto, the ‘output data’  20  is generated. That ‘output data’  20  is compared against a set of ‘historically known output data’ which was previously generated (in the past) in response to the ‘historically known input data’. When the ‘output data’  20  does not substantially match the ‘historically known output data’, the numerical simulation model  12  must first be ‘adjusted’ before the ‘historically known input data’  18  can again be introduced as ‘input data’ to the model  12 . In order to ‘adjust’ the model  12 , refer to steps or block  26   a  and  26   b  of  FIG. 3 . In step  26   a , to ‘adjust’ the model  12 , certain ‘regions’ must be defined in the numerical simulation model  12 . When the ‘regions’ are defined in the numerical simulation model  12 , in step  26   b , it is necessary to multiply the ‘parameters’  24  in each grid block of each ‘region’ by a certain value. At this point, the model  12  has been ‘adjusted’. Then, the ‘historically known input data’  18  is reintroduced, as ‘input data’, to the model  12 , and, responsive thereto, the ‘output data’  20  is generated once again. That ‘output data’  20  is compared against a set of ‘historically known output data’ which was previously generated (in the past) in response to the ‘historically known input data’. When the ‘output data’  20  does not substantially match the ‘historically known output data’, the numerical simulation model  12  must be ‘re-adjusted’ before the ‘historically known input data’  18  can again be introduced as ‘input data’ to the model  12 . In step  26   b , in order to ‘re-adjust’ the model  12 , it is necessary to multiply the parameters  24  in each grid block of each ‘region’ by a certain value. At this point, the model  12  has been ‘re-adjusted’. Then, the ‘historically known input data’  18  is reintroduced, as ‘input data’, to the model  12 , and, responsive thereto, the ‘output data’  20  is generated once again. This process repeats until the ‘output data’  20  does, in fact, substantially match the ‘historically known output data’. At this point, the numerical simulation model  12  has been ‘history matched’. 
     Referring to  FIG. 3A , a realistic illustration of a typical numerical simulation model  12  of  FIG. 3  is illustrated. Note the multitude of grid blocks  22  which have the ‘parameters’  24  of  FIG. 2  associated therewith. 
     Referring to  FIG. 4 , the numerical simulation model  12  of  FIG. 3  is illustrated including a plurality of grid blocks  22 . In  FIG. 4 , the model  12  includes a plurality of ‘regions’  30  where each ‘region’  30  of the model  12  further includes one or more of the grid blocks  22 , each grid block  22  having ‘parameters’  24  of  FIG. 2  associated therewith. Recall that, in order to ‘history match’ the numerical simulation model  12 , certain ‘regions’  30  must be defined in the numerical simulation model  12 . When the ‘regions’  30  are defined in the numerical simulation model  12 , in step  26   b  of  FIG. 3 , it is necessary to multiply the ‘parameters’  24  (of  FIG. 2 ) in each grid block  22  of the ‘region’  30  by a certain value. At this point, the model  12  has been ‘adjusted’. 
     Referring to  FIGS. 4 and 5 , referring initially to  FIG. 5 , the ‘parameters’ P 1 , P 2 , . . . , and P 10  associated with each grid block  22  (in addition to ‘all available information’ associated with each grid block  22 ) of the numerical simulation model  12  are introduced, as input data, to the Self Organizing Map (SOM) software  14 , and, responsive thereto, the SOM software  14  responds by defining the ‘regions’  30  of the numerical simulation model  12  which are illustrated in  FIG. 4 . In particular, the SOM software  14  will define the ‘regions’  30  ‘of similar behavior’ within the numerical simulation model  12 . For example, in  FIG. 4 , the SOM software  14  of  FIG. 5  will define: (1) a first ‘region 1’  30   a  having a first particular type of similar behavior, (2) a second ‘region 2’  30   b  having a second particular type of similar behavior, (3) a third ‘region 3’  30   c  having a third particular type of similar behavior, (4) a fourth ‘region 4’  30   d  having a fourth particular type of similar behavior, (5) a fifth ‘region 5’  30   e  having a fifth particular type of similar behavior, (6) a sixth ‘region 6’  30   f  having a sixth particular type of similar behavior, and (7) a seventh ‘region 7’  30   g  having a seventh particular type of similar behavior. 
     Referring to  FIGS. 4 and 6 , referring initially to  FIG. 6 , note that ‘all available information’ associated with each of the grid blocks  22  of the numerical simulation model  12  is used by the SOM software  14  to generate and define ‘regions’  30  of similar behavior among the grid blocks  22  of the numerical simulation model  12 , and, responsive thereto, the SOM software  14  organizes the grid blocks  22  of the numerical simulation model  12  into one or more of the defined ‘regions’  30   a ,  30   b ,  30   c ,  30   d ,  30   e ,  30   f , and  30   g  as illustrated in  FIG. 4 . In  FIG. 6 , for example, ‘all available information about grid block 1’  32 , and ‘all available information about grid block 2’  34 , . . . , and ‘all available information about grid block N’  36  is received by the SOM software  14 . In response thereto, the SOM software  14  will ‘generate and define regions of similar behavior based on all available information associated with the grid blocks’ as indicated by step  38  in  FIG. 6 . When the ‘regions of similar behavior’ are defined, as indicated by step  40  in  FIG. 6 , the SOM software  14  will organize the grid blocks  22  into one or more ‘regions’ of similar behavior, as shown in  FIG. 4 . For example, as illustrated in  FIG. 4 , the SOM software  14  of  FIGS. 1 ,  5 , and  6  will: (1) organize the grid blocks  22  into a ‘region 1’  30   a  having a first type of similar behavior, (2) organize the grid blocks  22  into a ‘region 2’  30   b  having a second type of similar behavior, (3) organize the grid blocks  22  into a ‘region 3’  30   c  having a third type of similar behavior, (4) organize the grid blocks  22  into a ‘region 4’  30   d  having a fourth type of similar behavior, (5) organize the grid blocks  22  into a ‘region 5’  30   e  having a fifth type of similar behavior, (6) organize the grid blocks  22  into a ‘region 6’  30   f  having a sixth type of similar behavior, and (7) organize the grid blocks  22  into a ‘region 7’  30   g  having a seventh type of similar behavior. 
     Referring to  FIG. 7 , a block diagram  38  is illustrated which describes how the SOM software  14  of  FIGS. 1 ,  5 , and  6  will ‘Define Regions of Similar Behavior’, as indicated by step  38  in  FIG. 6 . The block diagram  38  of  FIG. 7  representing step  38  in  FIG. 6  includes the following sub-steps: step  38   a , step  38   b , step  38   c , and step  38   d . In order to fully understand step  38  of  FIG. 6  which includes sub-steps  38   a - 38   d  as shown in  FIG. 7 , it would be helpful to read U.S. Pat. No. 6,950,786 to Sonneland et al (hereinafter, the &#39;786 Sonneland et al patent), issued Sep. 27, 2005, entitled “Method and Apparatus for Generating a Cross Plot in Attribute Space from a Plurality of Attribute Data Sets and Generating a Class Data Set from the Cross Plot”, with particular reference to FIGS. 16 through 21 of the &#39;786 Sonneland et al patent, the disclosure of which is incorporated by reference into the specification of this application. In  FIG. 7 , the SOM Software  14  will ‘define regions of similar behavior’ (as indicated by step  38  in  FIG. 6 ) by executing the following steps: (1) Crossplot the parameters of the grid cells, step  38   a  of  FIG. 7 , such as the parameters  24  of the grid cells  22  of  FIG. 2 , (2) Identify clusters of points within the crossplot—the points within a cluster represent grid cells having parameters which have similar behavior, step  38   b , (3) Plot the grid cells on a multidimensional plot while recalling the identity of those grid cells within the cluster which have similar behavior, step  38   c , and (4) group together those grid cells on the multidimensional plot which clustered together on the crossplot—that group is called a ‘region’, step  38   d.    
     A functional description of the operation of the present invention will be set forth below with reference to  FIGS. 1 through 7  of the drawings. 
     In  FIG. 3 , when ‘history matching’ the numerical simulation model  12 , the ‘historically known input data’ is introduced as ‘input data’ to the model  12  and, responsive thereto, the ‘output data’  20  is generated. That ‘output data’  20  is compared against a set of ‘historically known output data’ which was previously generated (in the past) in response to the ‘historically known input data’. When the ‘output data’  20  does not substantially match the ‘historically known output data’, the numerical simulation model  12  must first be ‘adjusted’ before the ‘historically known input data’  18  can again be introduced as ‘input data’ to the model  12 . In order to ‘adjust’ the model  12 , refer to steps or block  26   a  and  26   b  of  FIG. 3 . In step  26   a , in order to ‘adjust’ the model  12 , certain ‘regions’  30  of the model  12  of  FIG. 4  must be defined and generated in the numerical simulation model  12 . The ‘regions’  30  of the numerical simulation model  12  of  FIG. 4  are defined and generated by the SOM software  14  of  FIGS. 1 ,  5 , and  6 . The SOM software  14  will define and generate the ‘regions’  30  of  FIG. 4  by executing the following steps of  FIG. 7  (refer to U.S. Pat. No. 6,950,786 to Sonneland et al, with particular reference to FIGS. 16 through 21 of the &#39;786 Sonneland et al patent, the disclosure of which has already been incorporated herein by reference): (1) Crossplot the parameters of the grid cells, step  38   a  of  FIG. 7 , such as the parameters  24  of the grid cells  22  of  FIG. 2 , (2) Identify clusters of points within the crossplot—the points within a cluster represent grid cells having parameters which have similar behavior, step  38   b , (3) Plot the grid cells on a multidimensional plot while recalling the identity of those grid cells within the cluster which have similar behavior, step  38   c , and (4) group together those grid cells on the multidimensional plot which clustered together on the crossplot—that group is called a ‘region’, step  38   d . When the ‘regions’ are defined by the SOM software  14  in the numerical simulation model  12 , in step  26   b  of  FIG. 3 , it is necessary to multiply the ‘parameters’  24  in each grid block of each ‘region’ by a certain ‘value’. However, the ‘value’ for one ‘region’ may be different from the ‘value’ for another ‘region’ because ‘it is clear that the multiplier cannot be the same number for each grid block of the model’. At this point, the model  12  has been ‘adjusted’. Then, the ‘historically known input data’  18  is reintroduced, as ‘input data’, to the model  12 , and, responsive thereto, the ‘output data’  20  is generated once again. That ‘output data’  20  is compared against a set of ‘historically known output data’ which was previously generated (in the past) in response to the ‘historically known input data’. When the ‘output data’  20  does not substantially match the ‘historically known output data’, the numerical simulation model  12  must be ‘re-adjusted’ in the same manner as discussed above before the ‘historically known input data’  18  can again be introduced as ‘input data’ to the model  12 . In step  26   b , in order to ‘re-adjust’ the model  12 , it may be necessary to: (1) use the SOM software  14  to define the ‘regions’  30  of the numerical simulation model  12  of  FIG. 4  by executing the steps  38   a - 38   d  of  FIG. 7  (a step which may have already been accomplished and therefore may not be necessary), and (2) multiply the parameters  24  in each grid block of each newly defined ‘region’ by a certain value. Again, the ‘value’ for one ‘region’ may be different from the ‘value’ for another ‘region’ because ‘it is clear that the multiplier cannot be the same number for each grid block of the model’. At this point, the model  12  has been ‘re-adjusted’. Then, the ‘historically known input data’  18  is reintroduced, as ‘input data’, to the model  12 , and, responsive thereto, the ‘output data’  20  is generated once again. This process repeats until the ‘output data’  20  does, in fact, substantially match the ‘historically known output data’. At this point, the numerical simulation model  12  has been ‘history matched’. 
     The above description, pertaining to the use of SOM&#39;s to define ‘regions’ during the ‘history matching’ of numerical simulation models, being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the claimed method or apparatus or program storage device, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.