Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM

Abstract

In the last 10 years, Multiple-Point Statistics (MPS) modeling has emerged in Geostatistics as a valuable alternative to traditional variogram-based and object-based modeling. In contrast to variogram-based simulation, which is limited to two-point correlation reproduction, MPS simulation extracts and reproduces multiple-point statistics moments from training images; this allows modeling geologically realistic features, such as channels that control reservoir connectivity and flow behavior. In addition, MPS simulation works on individual pixels or small groups of pixels (patterns), thus does not suffer from the same data conditioning limitations as object-based simulation. The Single Normal Equation Simulation program SNESIM was the first implementation of MPS simulation to propose, through the introduction of search trees, an efficient solution to the extraction and storage of multiple-point statistics moments from training images. SNESIM is able to simulate three-dimensional models; however, memory and speed issues can occur when applying it to multimillion cell grids. Several other implementations of MPS simulation were proposed after SNESIM, but most of them manage to reduce memory demand or simulation time only at the expense of data conditioning exactitude and/or training pattern reproduction quality. In this paper, the original SNESIM program is revisited, and solutions are presented to eliminate both memory demand and simulation time limitations. First, we demonstrate that the time needed to simulate a grid node is a direct function of the number of uninformed locations in the conditioning data search neighborhood. Thus, two improvements are proposed to maximize the ratio of informed to uniformed locations in search neighborhoods: a new multiple-grid approach introducing additional intermediary subgrids; and a new search neighborhood designing process to preferentially include previously simulated node locations. Finally, because SNESIM memory demand and simulation time increase with the size of the data template used to extract multiple-point statistics moments from the training image and build the search tree, a simple method is described to minimize data template sizes while preserving training pattern reproduction quality.