Optimal Coarsening of 3D Reservoir Models for Flow Simulation

Abstract

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.

Numerical models for ground deformation and gravity changes during volcanic unrest: simulating the hydrothermal system dynamics of a restless caldera

“…Representing the effects of such heterogeneity, and in particular the strong local contrasts in the vicinity of the faults, is difficult using standard gridding approaches (Geiger and Matthäi, 2014). Small-scale geological heterogeneities observed in nature, usually modelled by geostatistical methods (Journel et al, 1998;Strebelle, 2002), cannot be correctly represented by a coarse cell blocks and identifying appropriate upscaling methods is challenging (Gerritsen and Durlofsky, 2005;King et al, 2006). On the other hand, using an extremely fine grid would radically increase the computational cost, making the model unusable for practical purposes where a number of simulation runs is required, such as optimisation and uncertainty reduction (Oliver and Chen, 2011).…”

About the Use of Quality Indicators to Reduce Information Loss When Performing Upscaling

“…Thus, we prefer to refer to formulae 1 and 2 because they apply to any grids, whatever the coarse grid. This definition is very general and is independent of the upgridding method used to create the coarse grid [17,18]. Upgridding methods make it possible to adapt the gridding to geological heterogeneity.…”

Recent Advances in Upgridding

“…The "missing physics" in a single phase flow calculation is the multiphase frontal speed. As discussed in King et al (2006) we have used the net rock volume weighted variance of the distribution of about its mean as a measure of the error introduced in this upscaling calculation. Specifically, we perform a sequential coarsening calculation, based on merging the layer pair which minimizes the increase of variation within the coarse cell.…”

“…We acknowledge the use of Figures originally presented in King et al (2006) scheduled for publication in the August 2006 issue of SPE Reservoir Evaluation & Engineering, and the contributions of our co-authors to that work. In addition, we acknowledge the unpublished work of Chen et al (2005), and thank BP America, Inc., for permission to publish this work.…”

“…The latter have many of the advantages of unstructured PEBI grids whilst retaining the integrated project workflow and numerical advantages of an underlying regular gridding structure. Many of these case studies appeared in King et al (2006), but we expand upon those discussions in terms of a generalized approach to a priori error estimates for developing appropriate coarsened models. …”