Scale Up of Heterogeneous Three Dimensional Reservoir Descriptions

Abstract

A general method for the scale up of highly detailed, heterogeneous, three dimensional reservoir descriptions is developed and applied. The method entails the nonuniform coarsening of the original detailed description, with finer resolution introduced in regions of potentially high flow rate (as identified through computationally efficient single phase flow calculations) arid coarser, homogenized property descriptions applied throughout the bulk of the model. The method is applied to the simulation of three actual reservoirs and is demonstrated to provide coarsened reservoir models which give simulation results in close agreement with those of the original fine scale description but at considerable computational savings (speedups of nearly two orders of magnitude). In addition, it is shown that the method can provide geologically realistic coarse scale reservoir descriptions, which can be subsequently history matched to field data via geologically sensible modifications. Introduction Through the use of sophisticated geological and geostatistical modeling tools, engineers and geologists can now generate highly detailed, three dimensional representations of reservoir properties. Such models can be particularly important for reservoir management, as fine scale details in formation properties, such as thin, high permeability layers or thin shale barriers, can dominate reservoir behavior. The direct use of these highly resolved models for reservoir simulation is not generally feasible because their fine level of detail (up to millions of grid blocks) places prohibitive demands on computational resources. Therefore, the ability to coarsen these highly resolved geologic models to levels of detail appropriate for reservoir simulation (tens of thousands to one hundred thousand grid blocks), while maintaining the integrity of the model for purposes of flow simulation (i.e., avoiding the loss of important details), is clearly needed. We previously developed and applied such a technique for the scale up of detailed cross sectional models. Given a highly detailed reservoir cross section, this method was designed to generate a coarsened model that is capable of providing simulation predictions in close agreement with results using the original, detailed reservoir description. More specifically, we require agreement in (1) the global pressure-flow rate behavior of the reservoir; (2) the breakthrough characteristics of the displacing fluid and; (3) the post-breakthrough fractional flows of all reservoir fluids. The cross sectional method achieves such a scale up by efficiently identifying the likely regions of high fluid velocities (via single phase flow calculations), which can lead to the early breakthrough of displacing fluids. These regions are then modeled in detail, using a fine scale permeability description, within the coarsened reservoir model. The remainder of the fine scale description is coarsened using a general technique, based on homogenization theory, for the calculation of effective, directional permeabilities. The resulting coarsened reservoir description is able to model both average reservoir behavior as well as some important effects due to extremes in reservoir properties (such as the early breakthrough of injected fluids), without prior knowledge of the global flow field. This indicates that the scaled up model is largely process independent. The method is implemented as an interactive workstation application, with various diagnostics to allow for an assessment of the accuracy of the coarsened reservoir model relative to the original fine scale description.

Modeling of subgrid effects in coarse‐scale simulations of transport in heterogeneous porous media

“…These methods act to generate coarsened models with more resolution in high-flow regions and less resolution in slower regions [Durlofsky et al, 1996. The coarse model is therefore capable of capturing effects due to the high extremes of the permeability field, such as the early breakthrough of injected fluids.…”

“…Most such methods either attempt to minimize, and then neglect, subgrid effects [Durlofsky et al, 1996 or require the a priori estimate of the global flow field from which upscaled (or pseudo) flux functions are computed [Christie, 1996;Barker and Thibeau, 1997]. The present method does model subgrid effects, but it does not require a priori estimates of the global flow field.…”

“…However, in our upscaling of the underlying pressure equation we apply a nonuniform coarsening procedure [Durlofsky et al, 1996. This method introduces variable degrees of coarsening throughout the domain, with more refinement in active regions (typically connected regions of high permeability leading to high flow rates and early breakthrough) and more coarsening in less active regions.…”

Multiscale finite element methods for porous media flows and their applications

“…These kinds of upscaling techniques in conjunction with the upscaling of absolute permeability is commonly used in applications (see e.g. [13,12,11]). The difference of our approach is that the coupling of the small scales is performed through the finite volume element formulation of the global problem and the small scale information of the velocity field can be easily recovered.…”

Upscaled modeling in multiphase flow applications

“…This kind of technique in conjunction with the upscaling of absolute permeability is commonly used in applications (e.g., [12,11,10]). The difference of our approach is that the coupling of the small scales is performed through the finite volume element formulation of the global problem and the small scale information of the velocity field can be easily recovered.…”