Rapid Simulation of Multiphase Flow Through Fine-Scale Geostatistical Realizations Using a New, 3-D, Streamline Model: A Field Example
Authors: Peddibhotla Sriram , Cubillos Helber , Datta-Gupta Akhil , Wu Ching H. 
Published: December 2007

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Abstract
Geostatistical techniques generate fine-scale reservoir description that can integrate a variety of data such as cores, logs, and seismic traces. However, predicting dynamic behavior of fluid flow through multiple fine-scale realizations has still remained an illusive goal. Typically an upscaling algorithm is applied to obtain a coarse scale heterogeneity model. Most of the upscaling algorithms are based on single phase pressure solution and are thus questionable at best for multiphase flow applications. Pseudo-relative permeabilities have often been used as a tool for multiphase flow upscaling But such approaches are highly process dependent and thus, have limited applicability. We describe a powerful, versatile, multiphase three dimensional streamline simulator for integrating fine-scale reservoir descriptions with dynamic performance predictions. Unlike conventional streamtube models, the proposed 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. Thus, the method can be easily applied in 3-D and incorporated into conventional finite-difference simulators. Once streamlines are generated in three dimensions, a variety of one dimensional problems can be solved analytically along the streamlines. The power and utility of the streamline simulator is demonstrated through application to a detailed characterization and waterflood performance of the La Cira field, Colombia, South America. We illustrate the advantage of the streamline simulator through comparisons with a commercial simulator for a waterflood pattern. The streamline simulator is shown to be orders of magnitude faster than traditional numerical simulators and does not suffer from numerical dispersion or instability. We illustrate the use of this simulator for evaluation of multiple, fine-scale realizations of heterogeneity models and quantification of uncertainty in predicting dynamic behavior of fluid flow.

Introduction
A geostatistical approach is commonly used to reproduce reservoir heterogeneities1. The objective is to generate a few "typical descriptions incorporating heterogeneity elements that are difficult to include by conventional methods. Conditional simulation is used for creating property (permeability, porosity, etc.) distribution with a prescribed spatial correlation structure that honors measured data at well locations. Stochastic reservoir modeling provides multiple equiprobable, reservoir models, all data intensive, rather than a single, smooth usually data poor deterministic model. Experience has shown that these data intensive, stochastic reservoir models yield a better history match of production data, yet provide a measure of uncertainty in prediction of future performance.
Fine-scale realizations are the most detailed representation of the heterogeneities that exist in the petroleum reservoir. The ideal flow simulation process would be to input this fine-scale data in its entirety. However conventional numerical simulators do not allow this readily. Reservoir models built for conventional simulators using the fine-scale data are huge and unmanageable. The flow simulation process thus becomes very tedious, slow and expensive. This is in addition to any hardware limitations that may exist. Typically an upscaling algorithm is applied to obtain a coarse-scale heterogeneity model. This coarse-scale model is then input into the conventional simulators. However, most of the upscaling algorithms are based on single phase pressure solution and are thus questionable at best for multiphase flow applications. Pseudo-relative permeabilities have often been used as a tool for multiphase flow upscaling But such approaches are highly process dependent and have limited applicability. There is a definite need for a fast and powerful simulator that allows the easy use of fine-scale realizations as such without the need for any upscaling.
In this paper we describe a new, fully three-dimensional, multiphase, streamline simulator for modeling waterflood performance.
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