Rapid simulation of multiphase flow in heterogeneous reservoirs using 3D streamlines

Abstract

Geostatistical techniques generate fine-scale reservoir description that integrates data from cores, logs, and seismic traces. However, predicting dynamic behavior of fluid flow through multiple fine-scale realizations has remained an illusive goal. Typically an upscaling algorithm is applied to obtain a coarse scale heterogeneity model. Most upscaling algorithms are based on single phase pressure solution and are questionable for multiphase flow applications. Pseudo-curves have been used for multiphase flow upscaling, but these are highly process dependent and have limited applicability. There is a need for an efficient, three dimensional, multiphase flow simulator for use in reservoir simulation and reservoir characterization. We present a new, powerful simulator for multiphase flow in heterogeneous reservoirs using 3D streamlines. Unlike streamtube models, this approach relies on the observation that in a velocity field derived by finite difference, streamlines can be approximated by piece-wise hyperbolas within grid blocks. Once streamlines are generated in 3D, one dimensional problems can be solved along streamlines. The streamline model has been generalized to handle changing well configurations resulting from infill drilling, zone isolations, recompletions, etc.. Important here is the remapping of streamlines and fluid saturations as dynamics of field conditions dictate. The past approach of averaging streamlines over an underlying grid and then performing numerical computations along streamlines undermines a major strength of streamline modeling, i.e., to preserve the self-sharpening nature of saturation fronts during waterflooding. We present two major modifications for large-scale field application. First, during changing well conditions, a 3D interpolation algorithm is used to map saturations from streamlines to streamlines, thus avoiding unnecessary smearing of front. Second, for modeling multiphase flow along streamlines, a third-order Total Variation Diminishing scheme is implemented, thus minimizing numerical dispersion and nonphysical oscillations. We illustrate the advantages of this approach through the use of synthetic and field examples. The approach is compared with a commercial numerical simulator or field data where available. The power and utility of the streamline simulator is demonstrated through detailed characterization and waterflood simulation of the La Cira field, Colombia. Streamline simulation is found to be orders of magnitude faster than numerical simulation, and significantly reduces numerical dispersion and instability. The approach is then applied to North Robertson Unit in West Texas--a highly heterogeneous carbonate reservoir with multiple patterns comprising of 58 wells. This example illustrates the ability of streamline simulation to perform field scale simulations efficiently taking into account changing operating conditions and well configurations.