Optimal Coarsening of 3D Reservoir Models for Flow Simulation
- Michael J. King (BP America Inc) | Karam S. Burn (BP America Inc) | Pengju Wang (BP) | Venkataramanan Muralidharan (BP America Inc) | Freddy E. Alvarado (BP America Inc.) | Xianlin Ma (Texas A&M U.) | Akhil Datta-Gupta (Texas A&M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2006
- Document Type
- Journal Paper
- 317 - 334
- 2006. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 4.1.2 Separation and Treating, 5.1 Reservoir Characterisation, 5.5.8 History Matching, 5.8.1 Tight Gas, 5.1.2 Faults and Fracture Characterisation, 5.8.5 Oil Sand, Oil Shale, Bitumen, 4.1.5 Processing Equipment, 5.3.2 Multiphase Flow, 5.3.1 Flow in Porous Media, 5.5 Reservoir Simulation, 5.6.5 Tracers, 5.5.1 Simulator Development, 5.4.1 Waterflooding, 5.1.1 Exploration, Development, Structural Geology, 1.6.9 Coring, Fishing, 5.5.3 Scaling Methods, 5.1.5 Geologic Modeling, 4.6 Natural Gas, 5.2 Reservoir Fluid Dynamics, 4.3.4 Scale
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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.
The development of (coarsened) reservoir simulation models from high-resolution geologic models remains an active field of research (Darche et al. 2005; Nilsson et al. 2005; Fincham et al. 2004; Li and Beckner 2000; Stern and Dawson 1999; Li et al. 1995; Durlofsky et al. 1996). These studies are motivated by a desire to understand the errors introduced when a high-resolution model is upscaled or, equivalently, to use an error analysis to find the optimal coarsened grid. If coarsened too far, the reservoir description many be overly homogenized, providing biased performance predictions. If coarsened too little, the cost of the simulation model may remain too high, limiting the utility of the model for detailed engineering or sensitivity studies. In the current study, we propose a statistical error analysis for layer coarsening, which guides us to an optimal layering scheme. Specifically, the error analysis provides us with a sequence of possible layering schemes, with a calculated error for each. The scheme with the minimum number of layers that reduces variance but does not introduce bias into the solution by over-homogenization is the optimal scheme.
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