We have developed a new constrained optimization approach to the coarsening of 3D reservoir models for flow simulation. The optimization maximally preserves a statistical measure of the heterogeneity of a fine scale model. Constraints arise from the reservoir fluids, well locations, pay/non-pay juxtaposition, and large scale reservoir structure and stratigraphy. The approach has been validated for a number of oil and gas projects, where flow simulation through the coarsened model is shown to provide an excellent approximation to high resolution calculations performed in the original model. The optimal layer coarsening is related to the analyses of Li and Beckner (2000), Li, Cullick and Lake (1995), and Testerman (1962). It differs by utilizing a more accurate measure of reservoir heterogeneity and by being based on recursive sequential coarsening, instead of sequential refinement. Recursive coarsening is shown to be significantly faster than refinement: the cost of the calculation scales as (NX·NY·NZ) instead of (NX·NY·NZ)[2]. The more accurate measure of reservoir heterogeneity is very important; it provides a more conservative estimate of the optimal number of layers than the analysis of Li et.al.. The latter is shown to be too aggressive and does not preserve important aspects of the reservoir heterogeneity. Our approach also differs from the global methods of Stern (1999) and Durlofsky (1994). It does not require the calculation of a global pressure solution and it does not require the imposition of large scale flow fields, which may bias the analysis, Fincham (2004). Instead, global flow calculations are retained only to validate the reservoir coarsening. Our approach can generate highly unstructured, variable resolution, computational grids. The layering scheme for these grids follows from the statistical analysis of the reservoir heterogeneity. Locally variable resolution follows from the constraints (reservoir structure, faults, well locations, fluids, pay/non-pay juxtaposition). Our reservoir simulator has been modified to allow a fine scale model to be initialized and further coarsened at run time. This has many advantages in that it provides both simplified and powerful workflows, which allow engineers and geoscientists to work with identical shared models. Introduction The development of (coarsened) reservoir simulation models from high resolution geologic models remains an active field of research [1–7]. In the current study we will report upon our success in the use of coarsening algorithms to determine a ‘best’ reservoir simulation grid obtained by grouping fine scale geologic model cells into effective simulation cells. Our results differ from previous studies in that we have found a statistical analysis of the static properties of the model that appears to identify the best grid for dynamic reservoir simulation. Coarsening beyond the degree indicated by our analysis discards too much of the underlying heterogeneity. It will overly homogenize the properties on the simulation grid. Finer models will, of course, retain at least as much reservoir heterogeneity, but are more costly. Our analysis uses a statistical technique for layer grouping and a constrained approach for areal gridding. The resulting composite corner point grid (CCPG) has many of the advantages of unstructured PEBI grids in that they can follow major features of the geologic description [8]. Compared to PEBI grids, they have the advantage of exact alignment of the simulation cells with the geologic model, which will minimize property upscaling errors, and the practical advantage that they may be utilized without the development of new simulation pre and post processing applications. This approach also moves us closer to having an Earth Model shared between the reservoir engineer and the reservoir geologist: the 3D geologic model will provide the grid on which the high resolution initialization of the simulation model will be calculated.

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The field development of a clastic reservoir in Siberia has been optimized. Uncertainties in geological description have been incorporated into the optimization process. A reservoir modeling study was undertaken to ascertain the impact of subsurface uncertainties on field production predictions and to evaluate a large range of field development options. Many exploratory wells have been drilled in this field covering a large areal extent. Pressure data from pressure buildup and well interference tests are available from these wells. BP's powerful Top Down Reservoir Modeling technology (TDRM™) has been used for assisted history matching. Multiple geological descriptions matching historical pressure data have been generated. The calibrated multiple reservoir models representing uncertainties in reservoir geology have been evaluated over a large range of field development options and for the definition of uncertainties in future production performance. BP's Top Down Depletion Planning technology (TDDP™) has been used for the optimization of well patterns, well spacing, well types (vertical versus high angle wells), lengths of high angle wells, order of well pad development, etc. The net present value (NPV) of the project has been maximized whilst meeting field development constraints. Thousands of potential field development options meeting field development constraints have been automatically evaluated. Multiple reservoir models have been run for every evaluated field development option to determine uncertainties in future production performance. As a result, an optimized field development option has been proposed with significant incremental net present value and oil recovery in the comparison with the current technical development scheme. Field BackgroundDiscovered in the late 1970s, this clastic reservoir is located in the eastern region of Siberia. The field is areally extensive with a large footprint covering about ~2000 square km. To date over 100 exploratory wells have been drilled at an average distance of 4 km between locations. Of these exploratory wells, 54 are productive. This field is currently at the select stage of depletion planning.The geological models for the reservoir were built by DeGolyer and MacNaughton, of Dallas, Texas (D&M). The current D&M models used for this study are based on an alluvial and lacustrine depositional environment system with channel complexes as described in their report to the operating company. The sandstone sits directly on the basement with weak aquifer and scattered perched water. The gross interval averages ~30m with an average net pay of ~15m. The reservoir is laminated and characterized with small but very productive sands (e.g., 1m thick Darcy rock). The average net-to-gross ratio is 50% and average permeability of ~115 md. As typical of clastic reservoirs of East Siberia, pore filling halite has also been observed in core analysis. The reservoir temperature is low, ranging from 10 to 20 degree Celsius with an in-situ oil viscosity of ~4 CP at reservoir conditions...

Summary We have developed a new constrained optimization approach to the coarsening of 3D reservoir models for flow simulation. The optimization maximally preserves a statistical measure of the heterogeneity of a fine-scale model. Constraints arise from the reservoir fluids, well locations, pay/nonpay juxtaposition, and large-scale reservoir structure and stratigraphy. The approach has been validated for a number of oil and gas projects, where flow simulation through the coarsened model is shown to provide an excellent approximation to high-resolution calculations performed in the original model. The optimal layer coarsening is related to the analyses of Li and Beckner (2000), Li et al. (1995), and Testerman (1962). It differs by using a more accurate measure of reservoir heterogeneity and by being based on recursive sequential coarsening instead of sequential refinement. Recursive coarsening is shown to be significantly faster than refinement: the cost of the calculation scales as (NX·NY·NZ) instead of (NX·NY·NZ)2. The more accurate measure of reservoir heterogeneity is very important; it provides a more conservative estimate of the optimal number of layers than the analysis of Li et al. The latter is shown to be too aggressive and does not preserve important aspects of the reservoir heterogeneity. Our approach also differs from the global methods of Stern and Dawson (1999) and Durlofsky et al. (1996). It does not require the calculation of a global pressure solution, nor does it require the imposition of large-scale flow fields, which may bias the analysis (Fincham et al. 2004). Instead, global flow calculations are retained only to validate the reservoir coarsening. Our approach can also be used to generate highly unstructured, variable-resolution computational grids. The layering scheme for these grids follows from the statistical analysis of the reservoir heterogeneity. Locally variable resolution follows from the constraints (reservoir structure, faults, well locations, fluids, pay/ nonpay juxtaposition). Our reservoir simulator has been modified to allow a fine-scale model to be initialized and further coarsened at run time. This has many advantages in that it provides both simplified and powerful workflows, which allow engineers and geoscientists to work with identical shared models.

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