Pressure Behavior of Laterally Composite Reservoirs

Abstract

Summary This paper presents a new general method for solving the pressure diffusion equation in laterally composite reservoirs, where rock and fluid properties may change laterally as a function of y in the x − y plane. Composite systems can be encountered as a result of many different types of depositional and tectonic processes. For example, meandering point bar reservoirs may be approximated as lateral composite systems. Reservoirs with edgewater encroachment are another example of such systems. The new solution method presented is based on the reflection-transmission concept of electromagnetics to solve fluid-flow problems in 3D nonhomogeneous reservoirs, where heterogeneity is in only one (y) direction. A general Green's function for a point source in 3D laterally composite systems is developed by using the reflection-transmission method. The solutions in the Laplace transform domain are then developed from the Green's function for the pressure behavior of specific composite reservoirs. The solution method can also be applied to many different types of wells, such as vertical, fractured, and horizontal in composite reservoirs. The pressure behavior of a few well-known laterally composite systems are investigated. It is shown that a network of partially communicating faults and fractures in porous medium can be modeled as composite systems. It is also shown that the existing solutions for a partially communicating fault are not valid when the fault permeability is substantially larger than the formation permeability. The derivative plots are presented for selected faulted, fractured, channel, and composite reservoirs as diagnostic tools for well-test interpretation. It is also shown that if the composite system's permeability varies moderately in the x or y direction, it exhibits a homogeneous system behavior. However, it does not yield the system's average permeability. Furthermore, the composite systems with distributed low-permeability zones behave as if the system has many two no-flow boundaries.