Abstract

Complex geometry reservoirs can be encountered in the field for variety of depositional and tectonic processes. For example, fluvial depositional environments may produce inter-branching channel reservoirs, or reservoirs consisting of relatively high permeability channels in communication with low-permeability splays.

This paper presents a general methodology for computing pressure responses and flow characteristics in complex geometry reservoirs. The proposed method consists of decomposing the original complex-geometry reservoir into a set of simple-geometry reservoirs, which interact with each other by transfer of fluid and equality of pressure over the regions where they are in hydraulic contact. Analytical solutions are written down for each of the simple reservoir components in terms of the unknown pressures and fluxes at their boundaries, and the coupled systems are solved for the desired wellbore pressure responses.

The method of sources and sinks is used to compute the pressure response in the Laplace domain and the results are inverted numerically using the Stehfest Inversion algorithm1. We present fast accurate methods of taking numerical Laplace transforms of the source/sink solutions that make the computations reasonably fast and efficient.

The proposed methodology can be extended to any system where the Laplace-space solution can be easily written in terms of integrals of real-space source/sink functions, including production at constant bottom-hole pressure, wellbore storage effects or naturally fractured systems. We demonstrate the applicability of the method by modeling branching channels and channel/splay systems.

Introduction

Classical well test analysis has long been used as a valuable tool in characterizing reservoirs using transient pressure versus time behavior. In most classical well test models, the reservoir is idealized as a "homogeneous" single or dual porosity system with a simple reservoir and well geometry. This is done in order to facilitate generation of analytical solutions to the reservoir problem. In fluvial-deltaic reservoir systems, however, the complex geometry precludes idealizing the reservoir as a simple-shaped homogeneous system and in general, the transient pressure responses do not resemble those of classical simple-geometry systems. Fluvial-deltaic reservoir systems are one example of general complex-geometry reservoirs for which classical well test analysis models may not be applicable.

Except for work presented by Larsen2,3 on a network of interconnected linear reservoirs, there appears to have been very little presented in the literature in modeling or describing the pressure transient pressure behavior of these types of reservoirs. Larsen's work was primarily concerned with the long time productivity of a network of intersecting linear reservoirs, with no special consideration given to the geometry at the regions of intersection. Larsen's work indicated that proper understanding of reservoir type is critical in situations where extrapolation of short-time test data to possible late-time production characteristics is attempted.

Sealing and/or non-sealing faults have been a major research topic in pressure transient analysis literature. Instead of focusing on the communication between reservoirs, most of the studies have been focused on the effect of the sealing and/or non-sealing faults. Both numerical and analytical solutions have been presented in the literature to model the pressure behavior in faulted reservoirs and some pertinent papers are listed in the references4–9.

Modeling Philosophy and Methodology

In the following, we illustrate our general modeling approach by applying it to a simple reservoir system. The physical model considered in Fig. 1 consists of two semi-infinite reservoirs separated over most of their extent by a hydraulically sealing barrier. One has flow properties of a "channel", while the other has properties of a "splay". The reservoirs are in hydraulic contact only over a small area. A well is producing from one of the reservoirs.

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