Use of Stochastic and Flow Simulation to Improve Reservoir Characterization and Production Forecasts
Authors: Rodrigues L.G. , Remacre A.Z. , Schiozer D.J. 
Published: December 2007

Abstract
Integration analysis between geology and engineering is obtained by the methodology cited in this paper and applies to stochastic and flow simulation for the improvement of reservoir characterization. Variograms kriging and stochastic simulation are used for horizontal and vertical permeability. Grid simulation, used in geostatistic analysis, works in coordination with flow simulation by preventing scaling-up problems. This is possible because the analysis is done in only one well and its drainage area. A tridimensional variographic analysis, modeled with a sin-cardinal function and a Sequential Gaussian Simulation (SGS), is used to fit heterogeneity and continuity of horizontal and vertical permeability. All generated images are used and selected by using the production obtained from flow simulation. Simulated and real water production are compared in history matching by using the classical methodology of fixed petrophysic properties in every layer and the methodology of stochastic image generation. A minimized objective function is used for image selection and for comparing methodologies. Mathematically, this represents the quality of the obtained history matching. Parallelization of flow simulation is used to reduce the total time of the process.

Introduction
Heterogeneities significantly influence flow in reservoirs, complicate history matching, and introduce errors in production forecasts. One of the most important variables is permeability. Permeability, as exemplified in this paper, directly influences flow equations and greatly impacts history matching.
Many researchers have demonstrated vertical permeability to be more influenced by distribution of shales, among properties of flow transport. Campozana, 1990, describes the distribution of shales using stochastic simulation joining with flow simulation in a real petroleum field. The variable Vsh (volume of shale) is used and is sufficient in revealing reservoir's heterogeneity. Other authors try effective integration between geology and reservoir engineering to improve the description of a petroleum reservoir. However, they fail to analyze the behavior of representative images of reservoir in flow simulation.
The aim of this paper is to present a methodology which improves reservoir characterization. This paper is divided in two main parts. The first analyzes field data and constructs a geologic model. This model is constructed using variographic analysis of horizontal and vertical permeability and stochastic simulation of these variables into a pre-defined mesh. The second is the analysis of the responses obtained using these images in a flow simulator.
Results are obtained from flow simulation using the traditional method of kriging and a set of ten representative stochastic images in two different production times and in the two cases studied. The first case consists of history matching, with one curve of relative water permeability used for the whole field. The second case consists of refining the adjustment of introducing another curve of relative water permeability around a TE10 well.
To accelerate the comparison process of simulated images a package (PVM) is used, allowing a computer net to function as a parallel computer. When simulation parallelizations in a net of workstations is used, the time for historical adjustment and the generation of stochastic images is reduced.