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BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to reservoir simulation by computer processing and more particularly to processing data relating to a subsurface reservoir to compress the reservoir simulation grids, and subsequently to decompress the grids for study and analysis of the simulation results. 
     2. Description of the Related Art 
     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. A realistic simulation model of the reservoir, and the presence of its fluids, helps in forecasting the optimal future oil and gas recovery from hydrocarbon reservoirs. Oil and gas companies have come to depend on simulation models as an important tool to enhance the ability to exploit a petroleum reserve. 
     The 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. Sometimes, fluids such as water and/or gases are also injected into these rock formations to improve the recovery of the petroleum fluids. 
     Reservoir simulation belongs to the general domain of flow in porous media simulation. However, reservoir simulation normally involves multiple hydrocarbon components and multiple fluid phases in an underground geological formation which is under high pressure and temperature. The chemical phase behavior of these hydrocarbon fluids and the included groundwater has to be taken into account in these simulators. 
     The simulation models contain volumetric data which describe the specific geometry of the rock formations and the wells, and also reservoir properties data, such as the fluid and rock properties, as well as production and injection history pertaining to the specific reservoirs of the oil or gas field in question. The simulation models are formed by a simulator (known as a reservoir simulator) which is a suite of computer programs run on a data processing system. 
     The reservoir simulator which runs these models is a computer implemented numerical methodology, or coded algorithms and data constructs of an underlying mathematical model. The mathematical model which represents the physics of fluid movements in these hydrocarbon reservoirs is a system of nonlinear partial differential equations which describe the transient multiple-phase, multiple-component fluid flow, and material balance behaviors in these reservoirs induced by the production and/or injection of fluids, as well as the pressure-volume-temperature (PVT) relationships of the reservoir fluids. 
     A reservoir simulator simulates the multiphase multicomponent fluid flow and material balance in subterranean reservoirs and the included surrounding porous rock formations by subdividing the volume into contiguous cells, also known as grid blocks. In simulation models, the reservoir is thus organized into a number of individual cells. A cell or grid block is the basic finite volume where the underlying mathematical model is applied. The number of cells varies depends on the resolution needed for the simulation and the size of the reservoirs in question. 
     For a large reservoir, such as the type known in the industry as a giant reservoir, which may have multi-billion barrels of original oil-in-place (OOIP), the number of grid cells can be in the hundreds of millions to over a billion. This number of cells is required in order to have adequate resolution to represent flow dynamics, formation rock porosity and permeability heterogeneity, and many other geologic and depositional complexities within the reservoir. Simulation of this size reservoir can be termed giga-cell reservoir simulation. 
     The challenges in hydrocarbon reservoir simulation require the use of the latest technology to maximize recovery in a cost-effective manner. Reservoir simulators such as GigaPOWERS have been described in the literature. See, for example articles by Dogru, A. H. et al., “ A Next - Generation Parallel Reservoir Simulator for Giant Reservoirs ,” SPE 119272, proceedings of the 2009 SPE Reservoir Simulation Symposium, The Woodlands, Tex., USA, Feb. 2-4, 2009 and by Dogru, A. H., Fung, L. S., Middya, U., Al-Shaalan, T. M., Byer, T., Hoy, H., Hahn, W. A., Al-Zamel, N., Pita, J., Hemanthkumar, K., Mezghani, M., Al-Mana, A., Tan, J, Dreiman, T., Fugl, A, Al-Baiz, A., “ New Frontiers in Large Scale Reservoir Simulation ,” SPE 142297, Proceedings of the 2011 SPE Reservoir Simulation Symposium, The Woodlands, Tex., USA, Feb. 21-23, 2011. GigaPOWERS reservoir simulation is capable of fine-scale grid simulation that exceeds a billion-cell barrier for post-processing while utilizing hundreds of GB footprint per scenario. 
     The total number of simulation runs for a company with a number of hydrocarbon reservoirs and appreciable reserves exceeds multiple tens of thousands per year, and one or more petabytes of high performance storage is required to host these data. For full simulation studies, it is required to maintain and store for subsequent use and analysis all of the simulation visualization data that are represented by the hundreds or thousands gigabytes of reservoir simulations. 
     Consider the case of a single volumetric grid of 1024 3  grid points (on the order of a billion cells) that is processed by a solver such as GigaPowers. Storing volumetric data alone requires 3 times 1024 3  floats (4 bytes each) for space coordinates (x, y, z). State of the art data formats would imply a memory space or capacity of 12.88 GB for volumetric data alone. 
     This memory space for volumetric data coordinates is required without even considering the many other properties attached to each cell as a result of simulation, such as oil saturation, water saturation, etc. Serious maintenance issues arise due to the vast file size, such as time delays for I/O, file disk size limitations, and required support for increasing or expanding the available memory space capacity as petroleum engineers and reservoir analysts generate more simulation data on a continuing basis. 
     SUMMARY OF THE INVENTION 
     Briefly, the present invention provides a new and improved computer implemented method of compressing reservoir simulation data representative of a subterranean reservoir organized into a three dimensional grid of reservoir cells arranged in a set of layers in a vertical dimension of the three dimensional grid. The computer implemented method according to the present invention selects a layer from the three dimensional grid, and batch compresses the reservoir simulation grid data to a compressed layer file representation. The compressed layer file representation is stored in memory. The steps of selecting, batch compressing and storing are repeated for the set of layers of the three dimensional grid; and a reduced representation is formed of the reservoir from the stored compressed layer file representations of the layers of the three dimensional grid for analysis. 
     The present invention also provides a new and improved data processing system for compressing reservoir simulation data representative of a subterranean reservoir organized into a three dimensional grid of reservoir cells arranged in a set of layers in a vertical dimension of the three dimensional grid. The data processing system includes a processor which selects a layer from the three dimensional grid; and batch compresses the reservoir simulation grid data to a compressed layer file representation. The data processing system also includes memory which storing the compressed layer file representation. The processor further repeats the steps of selecting, batch compressing and storing for the set of layers of the three dimensional grid. An interface of the data processing system forms a reduced representation of the reservoir from the stored compressed layer file representations of the layers of the three dimensional grid for analysis. 
     The present invention further provides a new and improved data storage device having stored in a non-transitory computer readable medium computer operable instructions for causing a data processing system to compress reservoir simulation data representative of a subterranean reservoir organized into a three dimensional grid of reservoir cells arranged in a set of layers in a vertical dimension of the three dimensional grid. The instructions stored in the data storage device cause the data processing system to select a layer from the three dimensional grid, and batch compress the reservoir simulation grid data to a compressed layer file representation. The instructions also cause the data processing system to store in memory the compressed layer file representation, and to repeat the steps of selecting, batch compressing and storing for the set of layers of the three dimensional grid. The instructions also cause the data processing system to form a reduced representation of the reservoir from the stored compressed layer file representations of the layers of the three dimensional grid for analysis. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of the organization of the processing methodology according to the present invention. 
         FIG. 2  is a functional block diagram of data processing steps for the processing methodology of data compression of hydrocarbon reservoir simulation grids according to the present invention. 
         FIG. 3  is a schematic diagram of a computer network for data compression of hydrocarbon reservoir simulation grids according to the present invention. 
         FIG. 4  is a functional block diagram of data processing steps for data compression for individual layers of hydrocarbon reservoir simulation grids according to  FIG. 2 . 
         FIG. 5  is a schematic diagram of the computer network of  FIG. 3  configured to perform the data processing steps of  FIG. 4 . 
         FIG. 6  is a functional block diagram of data processing steps for layer by layer data decompression of hydrocarbon reservoir simulation grids according to  FIG. 1 . 
         FIG. 7  is a schematic diagram of the computer network of  FIG. 3  configured to perform the data processing steps of  FIG. 2 . 
         FIG. 8  is a functional block diagram of data processing steps for data visualization of hydrocarbon reservoir simulation grids according to  FIG. 1 . 
         FIG. 9  is a schematic diagram of the computer network of  FIG. 3  configured to perform the data processing steps of  FIG. 8 . 
         FIG. 10  is an example of a full display of a volume of reservoir simulation input data organized into a three dimensional grid of cells for processing according to the present invention. 
         FIG. 11  is an example display of a single layer of the reservoir simulation input data of  FIG. 10 . 
         FIG. 12  is a graphical plot of a parametric cubic boundary curve representing an approximation of one side of the layer of  FIG. 11 . 
         FIG. 13  is a graphical plot of the actual data of the side of the layer of  FIG. 11  approximated in  FIG. 12 . 
         FIG. 14  is a plot of a smoothed boundary curve formed from data points of the data of  FIG. 13 . 
         FIG. 15  is a representation of four sides of a reservoir layer plotted in parametric space. 
         FIG. 16  is a plot of corresponding sides of the parameterization of  FIG. 15 . 
         FIG. 17  is a plot of a four sided surface defined with corners and tangent vectors during processing according to the present invention. 
         FIGS. 18, 19, 20 and 21  are example plots of different levels of compression and surfaces per layer according to the present invention. 
         FIG. 22  is a schematic diagram illustrating the selection of boundary tangents during processing according to the present invention. 
         FIG. 23  is a schematic diagram of an example color mapping function applied during processing according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the drawings,  FIG. 1  illustrates schematically as indicated at A the organization of the computerized processing methodology for data compression of hydrocarbon reservoir simulation grids in accordance with the present invention. The processing is composed of three segments or parts as shown generally in  FIG. 1 . 
     As indicated at C, reservoir simulation grid data is subjected to a compression sequence. Batch compression is performed during segment or stage C, as will be set forth, and compresses reservoir simulation grid data from spatial xyz coordinates of the reservoir to mathematical coefficients. The compression methodology during stage C reads layer by layer a volumetric unstructured grid and computes coefficients layer by layer. The coefficients so obtained represent a main compressed grid file. The grid file is stored in computer memory and can be shared quickly given its relatively small size (in comparison to the original grid file size). The operational sequence of the compression processing C is set forth in  FIG. 2 , with the batch compression methodology processing B illustrated schematically in  FIG. 4 . 
     As indicated at stage or segment D in  FIG. 1 , the stored compressed grid data is available to be subjected to decompression processing. Processing during decompression stage D opens the main compressed grid file and extracts grid information to evaluate the basic functions and re-generate a surface of interest to a user reservoir analyst or engineer. The operational sequence of the decompression processing D is set forth in  FIG. 6 . 
     During stage or segment V, the decompressed grid data resulting from decompression processing in stage D is subject to visualization processing. Surfaces of interest selected after decompression from the stored compressed grid data are mapped to geometric primitives and displayed to the user at a specified display resolution, in interactive time. The operational sequence of the visualization processing V is set forth in  FIG. 8 . 
     Data Processing Methodology and System 
     The computerized reservoir grid data processing of the present invention according to  FIGS. 1, 2, 4, 6 and 8  is adapted for deployment on a variety of presently available high performance computing or HPC platforms. An example HPC environment for the present invention is a multi-node, multi-CPU, multi-core computer cluster system illustrated at R in a data processing system S of  FIG. 3 . More detailed schematic diagrams of the data processing system S showing components or units involved in the processing sequences of  FIGS. 4, 6 and 8  are shown in  FIGS. 5, 7 and 9 , respectively. 
     The cluster R of the data processing system S ( FIG. 3 ) is formed of a plurality of computer nodes indicated at  50  operating in parallel under control of one or more cluster terminals or router servers  52 . The computer nodes  50  are provided with reservoir grid data in parallel as indicated by arrows  54  from disk storage  56  under control of cluster terminal server or servers  52 . Original reservoir grid simulation input data is stored in a suitable number of data storage/file servers  56 . The reservoir grid data in disk storage  56  is obtained from long term data storage memory  58  in the form of a suitable number of data storage memory units. The computer system S also includes a number of client work stations such as shown at  60  in  FIG. 3  for user reservoir analysts and engineers. The work stations  60  are in data communication with reservoir grid data stored in disk storage  56  over a network, as indicated at  62 . 
     The cluster terminal  52  operates during performance of the compression processing C under control of program code  64  ( FIG. 5 ) stored in terminal  52 . Similarly, the work station or stations  60  operate during performance of decompression processing D and visualization processing V under control of program code  66  and  68  ( FIGS. 7 and 9 ) stored in each work station or stations. The program codes  64 ,  66  and  68  according to the present invention are in the form of non-transitory computer operable instructions causing associated terminal  52  or work station  60  to perform the respective reservoir grid data processing sequences, as will be described. 
     It should be noted that program codes  64 ,  66  and  68  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 associated cluster terminal  52  or work station  60  of the data processing system S and direct its operation. The instructions of program codes  64 ,  66  and  68  may be stored in memory of the associated terminal or work station or on a data storage device such as computer diskette, magnetic tape, conventional hard disk drive, electronic read-only memory, optical storage device, or other appropriate data storage device having a non-transitory computer usable medium stored thereon. 
     Compression 
     With reference to  FIG. 2 , a high-level logic flowchart of a preferred sequence of steps for performing computer-implemented reservoir grid data compression processing C according to the present invention is illustrated schematically. As shown in  FIG. 2 , during step  100  of compression processing C the complete reservoir grid of interest is obtained from disk storage  56  after retrieval from long term data storage memory  58 . A layer of interest is the reservoir grid is selected during step  102  for performance during step  104  of the batch compression processing B ( FIG. 4 ) of the layer grid data by the computer cluster R. 
     During step  106 , a lightweight or reduced data volume footprint representative of the compressed layer grid resulting from batch compression is formed. During step  108 , a determination is made whether all layers of the reservoir grid of interest have been batch compressed. If not, processing returns to step  102  and another layer in the grid is select for batch compression. 
     If all layers of the grid of interest are indicated to have been processed during step  108 , the layer&#39;s compressed parameters are retrieved during step  110  and the compressed parameters are sent during step  112  to storage disk  56 . 
     The general process of compression implies a one by one transformation of each layer of a large volumetric grid coming from the discretization of an oil/gas reservoir. The final output is a lightweight file containing information about connectivity points and directions. This information in form of a file is then stored in a database on storage disk  56  of frequent access, or to long term storage  58 , and is thereafter accessible to users at work stations  60  as reservoir information for use in day to day operations and for decision making. 
     The compression process is triggered in batch, possibly automatically right after simulation is over, launched by a user or client with access to a parallel cluster able to leverage the parallel nature of the processing. The processing is highly recursive in the sense that the same computational process is applied to equally divided regions of the layer of interest. A limit in the recursion process would be the size of the original grid, but for general visualization purposes and considering the highly adaptive basis, functions with only a few subdivisions are necessary to achieve a visually fair reconstruction. 
     Batch Compression 
       FIG. 4  illustrates a high-level logic flowchart sequence of steps for performing computer-implemented batch compression processing B during step  104  of compression processing C according to the present invention. As indicated at step  120 , for a layer of interest selected during step  102 , the corners of the layer are identified and set as control points. 
     As an example, a volume data set V of 49×104×69 cells (or about 25,000) reservoir grid cells is shown in shown in  FIG. 10 . The volume data set V is represented by 70 layers of 50×105 points. This means the other layers have similar shape and characteristics. The methodology of the present invention compresses the data layer by layer; therefore the first step is to decompose a single layer for compression. 
     Because of the small size of the image shown in  FIG. 10  the seventy layers appear to be generally level or flat horizontal layers. However, an individual layer L shown in  FIG. 11  is seen to be significantly arched from a high center portion to four lower corners. 
     Reservoirs are usually thin in the vertical axis or Z direction of the three dimensional coordinate system, compared to the areal size of the reservoirs. The 70 layers of  FIG. 10  are assembled from actual real reservoir simulation data. The single layer L of  FIG. 11  is scaled which is typical for reservoir visualization purposes. The layer L has a different scale on the Z axes than the stacked layers of  FIG. 10  to emphasize the layer shape and results in the highly curved image of  FIG. 11 . 
     Layer L in  FIG. 11  can be seen to have four sides, each of which represents a two dimensional or 2-D surface, as shown in  FIG. 12 . Referring to a first side  121  of layer L, it can be seen to be composed of a set of boundary points (as shown schematically in  FIG. 13 ) that can be approximated by an appropriately determined parametric cubic boundary curve  122 , as shown in  FIG. 14  in superposition with selected boundary points for the side  121  from the set of  FIG. 13 . 
     For the purposes of the present invention, a mathematical representation in the form of a cubic Hermite spline function is utilized to represent the set of boundary points in compressed form. The spline function utilized can be defined with two points P and a tangent m per point. The result is a one dimensional or 1-D function in parameter space t, according to the following expression:
 
 p ( t )=(2 t   3 +3 t   2 +1) p   0 +( t   3 −2 t   2   +t ) m   0 +(−2 t   3 +3 t   2 ) p   1 +( t   3   −t   2 ) m   1  
 
where p 0  and p 1  represent the two points P and m 0  and m 1  represent the two tangents.  FIG. 15  is an illustration of each of the four sides of layer L in parametric space u and w.
 
     During step  124  ( FIG. 4 ), a determination of the degree of a compression factor n is made in response to a user query. For a layer side, a reduced representation is found. For example, a tolerance of 1.5 and Error=4 (units) results in 95.2% less data points. This represents a compression ratio of 20:1 per layer. With processing for the level 0 of compression, tangents are subsequently chosen for best fit (in a least square manner) to approximate the given data per layer. Additional levels of compression subdivide the layer to minimize the approximation error. Compression varies depending on topology, and thus each layer model may have a unique compression rate. Level zero of compression accounts for the 4 corner points and approximate tangents directions. 
     Level one of compression accounts for a subdivision by half in each horizontal direction (x-y plane) of the previous level. In the present example, this results in four new domains, as shown schematically in  FIG. 16 . 
     The selected layer is divided during step  126  into a number of subdomains, as shown in  FIG. 16 , and during step  128  one of the domains of the layer being processed is selected. Sub-domains are computed separately according to the compression level selected and then retrieved in order for subsequent decompression (reconstruction) and visualization. 
     Computation of additional levels of compression can be done in parallel one subdomain per node of the cluster R of the data processing system S. The output of the compression computation is the spatial position of the joint or juncture of sub-surfaces and connectivity information for the subsurface, in order to merge the subsurface junctions together in decompression. 
     Using the formulation of the one dimensional expression for the problem now that each side can be represented by a mathematical function with fewer points than the whole set of points. This results in significant data storage requirement savings according to the present invention. 
     The formulation for a single layer side is extended to four parametric curves which describe the four boundaries which form a surface or layer L. The formulation is as follows: 
     
       
         
           
             
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     A two dimensional or 2-D surface is thus defined that approximates the layer L based on four corners points and eight tangents with the formulation set forth above.  FIG. 17  is a plot of the results obtained, from a four sided surface with four corners and eight tangent vectors, with level 0 of compression, one surface per layer. This is done by using what is known as a Coons patch, with 16 degrees of freedom. Coons&#39; patches, for example, represent a general multi-sided surface definition that allows a curve formulation to be used for a composite surface. It should be understood that other forms of surface patches may be used, as well. 
     The curve formulation performed during step  122  is general enough to support any type of curve. A simpler form known as Ferguson patch may also be used, which has 12 degrees of freedom, namely 4 corners and 2 tangent vectors. Ferguson patches, for instance, make use of cubic polynomial curves. 
       FIG. 18  shows schematically a level 1 of compression by equally subdividing a layer into four regions.  FIGS. 19, 20 and 21  schematically represent subsequent levels of compression by further dividing the layers by increasing powers of two in order to provide final reconstruction. Different shading in sub regions denotes an independent subdomain of the underlying grid at a higher resolution than the previous subdivision level. During step  130 , approximate tangent vectors at the corners of the layer being processed are selected. This is accomplished by assembling in the computer a suitable surface patch for the layer, based on the assembled sets of compressed data points for the four layer sides. 
     After visual and error requirements are met surfaces are joined together choosing boundary tangents so that continuity is preserved. Boundary tangents are selected or obtained by computer processing during step  130  as shown in  FIG. 22 . There are many conventional alternative techniques to approximate tangents across neighboring pieces of data. An example of one is the use of a general second order function such as a parabola to compute the slope of the middle point as shown in  FIG. 22 . It should be understood, as mentioned, that a number of conventional techniques to approximate tangents across neighboring pieces of data may be used for this purpose. The general second order function technique is illustrative. 
     A color mapping function is then applied during step  132  to the number of elements of the original data set properties (e.g. oil saturation, permeability, pressure, etc.) A 1  through A n , with a new lower number B 1  through B m  for the new cells according to the level of compression, as the schematic multivalued function diagram of  FIG. 23  indicates. 
     Color mapping of the type indicated in  FIG. 23  is a conventional computer implemented functionality used to visualize a scalar of interest over an underlying grid. A description color mapping methodology and its implementation is presented, for example, at: http://en.wikipedia.org/wiki/Color_mapping. 
     During step  134 , the control points and tangent vectors and the applied color mapping determined in the cluster R are stored in memory. During step  136 , a determination is made whether all of the n domains of the identified layer have been batch compressed. If not, processing returns to step  126  and another domain is then processed according to steps  126 ,  128 ,  130  and  132  in the manner described above. 
     If all of the n domains of the identified layer are indicated to have been processed during step  134 , a layer temporal file with control points and tangents is formed and stored during step  136  in memory. 
     Decompression 
     Decompression during the sequence or stage D is the middle step between retrieval and visualization; it opens up and reconstructs the underlying grid. The result is a set of geometric primitives in form of triangles or quadrangles that can be rendered in any modern graphics library such as OPENGL, DIRECTX, COIND3d, VTK, among others. 
       FIG. 6  illustrates a high-level logic flowchart of a preferred sequence of steps for performing computer-implemented decompression processing D of compression processing C according to the present invention. The decompression processing sequence D is performed in work station  60  under control of decompression operating instructions  66  stored in work station  60 . As indicated at step  140 , the compressed grid reservoir file of interest is retrieved by the work station  60  ( FIG. 7 ) from storage disk  56 . 
     In step  142 , the number of layers in the reservoir grid is identified. During step  144 , a layer is selected by a user and the control points and tangents resulting from step  136  of compression processing are retrieved. During step  146 , the surface layer is reconstructed by processor  70  of the user work station  60 , and during step  148 , geometric primitives are generated for display or rendition on graphical user interface  72  of the work station  60 . 
     During step  150 , a determination is made whether all layers of the reservoir grid have completed decompression processing. If not, processing returns to step  144  and another layer is selected and then processed according to steps  146  and  148  in the manner described above. When each identified layer has been decompressed, a temporary file or dataset of geometric primitives is generated during step  152 . 
     Visualization 
     Considering the visualization processing sequence V ( FIG. 8 ), during step  160  a user selected compressed or lightweight file of interest in the reservoir is selected and downloaded to work station  60  from disk storage  52 . The processing sequence V is performed by work station  60  under control of visualization routines operating instructions stored in work station  60 . During step  162 , the decompression processing sequence D shown in  FIG. 6  is performed in the work station  60  under control of operating instructions  66  stored in memory of work station. 
     During step  164 , the geometric primitives generated during step  152  ( FIG. 6 ) are loaded into memory of work station  60  for processing. During step  166 , a user selects a scalar field of interest in the reservoir. In step  168 , the selected scalar field is mapped for surface reconstruction, and during step  170 , the reservoir geometric primitives are rendered for display on graphical user interface  72  of the work station  60 . 
     Rendering of the geometric primitives by graphical user interface  72  allows a client user to select the layer of interest to visualize and the scalar field of interest, e.g. oil saturation, water saturation, pressure, etc. With the present invention, it can thus be seen that due to the small size of the compressed grid file, the user client at the work station  60  is able to download and interact in real time with the grid. 
     A comparison of data storage reductions P with other well-known algorithms for mesh compression and certain standard computer graphics test models is provided and contrasted with current data in the chart below: 
     
       
         
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Processing 
                 Model 
                 Gain 
               
               
                   
                   
               
             
             
               
                   
                 Compressing 
                 triceratops 
                 43.800% 
               
               
                   
                 Polygon Mesh 
                 cessna 
                 10.500% 
               
               
                   
                 Connectivity with 
                 beethoven 
                 27.300% 
               
               
                   
                 Degree Duality 
                 sandal 
                 18.700% 
               
               
                   
                 Prediction 
                 shark 
                 54.700% 
               
               
                   
                   
                 al 
                 17.000% 
               
               
                   
                   
                 cupie 
                 28.900% 
               
               
                   
                   
                 tommygun 
                 13.500% 
               
               
                   
                   
                 cow 
                 19.500% 
               
               
                   
                   
                 teapot 
                 32.500% 
               
               
                   
                 Binary 
                 wolf 
                 88.889% 
               
               
                   
                 Compression 
                 raptor 
                 88.889% 
               
               
                   
                 Rates for ASCII 
                 fish 
                 94.118% 
               
               
                   
                 Formats 
                 snake 
                 92.308% 
               
               
                   
                   
                 horse 
                 90.909% 
               
               
                   
                   
                 cat 
                 87.500% 
               
               
                   
                   
                 dog 
                 90.010% 
               
               
                   
                 Present 
                 Reservoir 
                 95.010% 
               
               
                   
                 Invention 
                 Layer 
               
               
                   
                   
               
             
          
         
       
     
     The present invention forms a smooth representation of the reservoir of interest that preserves the data grid shape with significantly less data storage footprint requirements. The present invention thus has less storage memory requirements. Fewer I/O or input/output operations are required when a user is interacting with a compressed grid according to the present invention. The present invention allows faster data retrieval for visualization. 
     The present invention can thus be seen to provide an effective simulation grid methodology that reduces data footprint. The present invention has the potential to reduce the cost of new storage and retain generated scenarios after completion of simulation studies. 
     The invention has been sufficiently described so that a person with average knowledge in the field of reservoir modeling and simulation 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 structure, or in the manufacturing process of the same, requires the claimed matter in the following claims; such structures shall be covered within the scope of the invention. 
     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.

Summary:
A dense volumetric grid coming from an oil/gas reservoir simulation output is translated into a compact representation that supports desired features such as interactive visualization, geometric continuity, color mapping and quad representation. A set of four control curves per layer results from processing the grid data, and a complete set of these 3-dimensional surfaces represents the complete volume data and can map reservoir properties of interest to analysts. The processing results yield a representation of reservoir simulation results which has reduced data storage requirements and permits quick performance interaction between reservoir analysts and the simulation data. The degree of reservoir grid compression can be selected according to the quality required, by adjusting for different thresholds, such as approximation error and level of detail. The processions results are of potential benefit in applications such as interactive rendering, data compression, and in-situ visualization of large-scale oil/gas reservoir simulations.