Abstract

The current requirement of geologic detail to be built into reservoir descriptions has been exceeding the computational capabilities of reservoir simulation due to a need of huge number of simulation grids. This has motivated the development of a variety of upscaling techniques for flow simulation.

This paper presents an efficient upscaling method effective for an oil-wet heterogeneous reservoir, which offers a means of simulating multiple geostatistical realizations. A new effective permeability correlation is developed through application of one of the non-parametric regression techniques to the results of intensive numerical experiments. The developed empirical correlation enables us to compute effective permeabilities fast and accurately for a wide variety of heterogeneous permeability fields from layered to random system and can be easily extended for averaging two-phase flow properties under viscous limit or capillary limit.

The paper describes the developed technique in detail and demonstrates how the overall upscaling procedure can be speeded up with the desired accuracy.

Introduction

Upscaling is a technique that transforms a detailed fine geologic model to a coarse-grid simulation model such that the coarse model can capture the fluid flow behavior in the detailed model. This technique has become an increasingly important tool for reservoir simulation.

There are two key components to implement accurate upscaling: upgridding and averaging. The former focuses on maintaining the global geologic feature of a fine grid model, while the latter calculates the effective properties for a coarse simulation grid that preserves fine grid fluid flow dynamics.

In the literature, there are two major approaches in the existing methods to average flow properties: dynamic approaches and effective properties approaches1. Dynamic approaches are developed to generate pseudo functions based on the simulation results of an entire reservoir model or representative portion of a fine grid model. Thus, these approaches give accurate results under an imposed flow condition from which pseudo functions are derived but are too time-consuming to upscale very large geological models. On the other hand, effective properties approaches average flow properties from the information on sub-grid scale heterogeneity and the assumption of local flow regime. These approaches, which work on the isolated coarse grid block, enable us to compute effective properties much more promptly than dynamic approaches and give accurate results if the appropriate assumption is made for the actual flow field.

The objective of this study is to develop a fast and accurate upscaling method suitable to an oil-wet heterogeneous reservoir. Toward this end, effective properties approaches are intensively evaluated in the course of our study. Numerous numerical experiments are first conducted using 20,000 test cubes with various permeability fields. Second, a new effective permeability correlation is derived through application of a non-parametric regression technique to the collected data. It is shown that the resultant correlation gives high prediction quality and much more accurate results than the existing methods without direct simulation. Third this new technique is extended to two-phase upscaling problems under limiting conditions such as viscous limit or capillary limit.2,3 Its practical application is demonstrated through single-phase and two-phase flow simulations against stochastic fine grid models. Finally, some other aspects of the upscaling procedure are discussed.

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