Abstract

This work deals with the problem of estimating reservoir permeability and porosity distribution from multiple sources, including production data and well logging data. The work focuses on integrating long-term resistivity data into the parameter estimation problem, investigating its resolution power both in the depth direction and in area.

The resistivity logging tool considered in this project is a new tool proposed for permanent installation. The tool is installed in the cement around the well when the well is completed, and is capable of recording the long-term resistivity variation around the wellbore.

In this work, the Poisson equation with mixed boundary condition was used to model the infinite potential field around the resistivity logging tool. The behavior of the reservoir was modeled with a standard three-dimensional, two-phase, black-oil model. The resistivity response simulator was integrated into the flow simulator through Archie's law.

The Gauss-Newton algorithm was used to solve the inverse problem. This algorithm requires the calculation of the derivatives of the observation data with respect to the unknown parameters. These derivatives are called the sensitivity coefficients.

By running several simple inverse problems, it was concluded that the resistivity data has high resolution power in the depth direction and is capable of sensing the areal heterogeneity.

Introduction

In reservoir engineering, some of the most important tasks are to monitor reservoir conditions and design optimal production strategies. These tasks require knowledge of the spatial distributions of reservoir properties. Traditional well test methods assume very simple reservoir models and can only reveal overall average reservoir properties rather than spatial distributions. Also it is expected that the more information we have, the better we can describe our reservoir. However, the traditional well test technology only uses a short period of pressure transient information, thus does not use other available information, such as water production history, well logging data, etc.

In order to address the limitations encountered in traditional well test methods, nonlinear regression technology has been used to infer spatially dependent reservoir properties such as the distribution of permeability and porosity from multiple sources, both dynamic and static.

There are several active research areas in this problem. One approach is to bring more complex reservoir models into consideration, find a suitable or more efficient optimization algorithm to reduce the computation time, speed up the convergence rate, and achieve numerical stability. Another approach is to try to integrate more data, hard and soft, static and dynamic, to obtain a more reasonable set of reservoir parameter estimates.

In 1997, Landa and Horne [1] [2] demonstrated a way to integrate 4-D or 3-D seismic data into the two-dimensional parameter estimation problem, and showed that using such information combined with the traditional production data is a very powerful way to determine spatially distributed reservoir properties. Later Phan and Horne (1999) [3] applied this method to three-dimensional problems and focused on determining depth-dependent reservoir properties using integrated data analysis. Phan and Horne (1999) [3] showed that depth-averaged seismic data resolves reservoir properties poorly in the depth dimension while layer data reveals most depth- and space-dependent information. Phan and Horne (1999) [3] also concluded that we can not estimate layer properties unless we measure layer information. The 4-D seismic data usually have insufficient resolution in the depth direction to reveal the layer by layer properties. Also 4-D seismic data surveys are usually expensive, and sometimes infeasible. In this project, we focus on integrating long-term resistivity data into parameter estimation problem as an alternative means of providing depth-dependent information. Resistivity data has high resolution in the depth direction, and is easy and cheap to measure.

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