Effect of a Partially Communicating Fault on Transient Pressure Behavior
Authors: Yaxley L.M. 
Published: December 2007

Summary.
A mathematical model is presented that describes the effect of a partially communicating fault on transient pressure behavior. The well is partially communicating fault on transient pressure behavior. The well is treated as an infinite line source and the partially communicating fault as an infinitely long, vertical semipermeable barrier. Analytic solutions are given for the interference response at an observation well and the drawdown behavior of the active well. These solutions can improve the design and analysis of interference tests, which are affected by partially communicating faults. They are initially developed for constant formation thickness but are later extended to the case of unequal formation thickness on opposite sides of the fault.

Introduction
A question that arises frequently in the developmental planning of oil and gas fields is to what extent the faults that have been identified by seismic and geologic studies will act as barriers to fluid flow. The question is important because it may have a major impact on the number of wells required to exploit the field's reserves.
Faults in a hydrocarbon-bearing structure may be either sealing or nonsealing. A sealing fault will completely impede lateral fluid flow and may actually form part of the trapping mechanism for the hydrocarbon accumulation. The throw of a sealing fault is such that permeable strata on one side of the fault plane are juxtaposed against permeable strata on one side of the fault plane are juxtaposed against impermeable strata on the other side, as illustrated in Fig. 1.
A nonsealing fault, which will usually have insufficient throw to cause complete separation of the permeable strata on opposite sides of the fault plane, will always allow some degree of lateral fluid flow. Because of various mechanical processes, such as grain crushing, bed deformation. and clay smearing, however, the transmissibility of the fault zone may he much lower than the transmissibility of the undisturbed permeable strata. Such a situation, as illustrated in Fig. 2, is referred to as a partially communicating fault. Interference testing would seem to be an obvious method for measuring the transmissibility of a partially communicating fault. The design and analysis of conventional interference and pulse tests are based on the homogeneous reservoir model, however, which may be inadequate. At best, it may give an average interwell transmis-sibility, but it will not quantify separately the transmissibility of the fault and the transmissibility of the continuous reservoir.
In practice, though, many interference tests across faults have had the simple, qualitative objective of demonstrating whether communication exists. Such an application was suggested by Johnson et al. in respect of pulse testing. On the other hand, there have probably been many attempts to measure the transmissibility across a fault by interference or pulse tests, which have yielded no result. Qualitatively, a negative test result would imply that the fault was sealing, but the field pressure performance may later show that it was nonsealing. In such a case, the interference or pulse test may have failed because it was designed with an inappropriate flow model (i.e., the homogeneous reservoir model and exponential integral solution).
The influence of a partially communicating fault on interference testing was first considered by Stewart et al., who introduced the idea of modeling the fault zone as a linear, vertical semipermeable barrier of negligible capacity. Of course, the model is a great sim-plification of the complex physical nature of the fault zone, but a Stewart et al. noted, it has the essential property of imposing a linear flow pattern at the fault plane. It is also the way in which partially communicating faults are modeled in reservoir simulation partially communicating faults are modeled in reservoir simulation studies. In fact, the set of drawdown type curves Stewart et al. developed was obtained by numerical simulation.
In essence, the partially communicating fault is a type of linear discontinuity in reservoir properties. Although the subject of linear discontinuities has often been addressed in the transient well testing literature, it has usually been concerned with scaling faults. Bixel et al., however, considered the case of an abrupt, linear change of reservoir or fluid properties, as shown in Fig. 3a. For comparison, the vertical semipermeable barrier is shown in Fig. 3b. The two problems look similar, but the mathematical models needed to describe them are quite different. Nevertheless, the solution technique Bixel et al. used can also be used to solve the problem of the vertical semipermeable barrier. problem of the vertical semipermeable barrier. Problem Description and Definitions Problem Description and Definitions The problem being considered is the drawdown distribution resulting from constant-rate production from a well in an infinite reservoir that contains a linear, vertical semipermeable barrier.
The mathematical model relies on the assumptions thatthe reservoir fluid is single-phase and slightly compressible, having constant compressibility and viscosity;the reservoir is homogeneous in all rock properties and isotropic with respect to permeability on each side of the semipermeable barrier;the formation thickness is constant;the well can be approximated by an infinite line source;the semipermeable barrier is infinitely long and has negligible capacity; andthe fluid leakage rate through the semi-permeable barrier is always proportional to the instantaneous pressure difference across the barrier.
The last two assumptions allow the partially communicating fault to be approximated by a vertical plane. This should be valid, provided that the width of the fault zone is small compared with the provided that the width of the fault zone is small compared with the distance between the fault plane and the well. According to the last assumption, the leakage through the fault per unit time per unit length of the fault can be expressed by
(1)
where Tf =kfh/lf mu is defined as the specific transmissibility of the partially communicating fault, and the parameters kf and lf partially communicating fault, and the parameters kf and lf represent the effective permeability and effective width of the fault zone, respectively (see Figs. 3b and 4a).
Stewart et al. characterized the partially communicating fault by the parameter ratio kf/lf, which was defined as the fault conductivity. However, the specific transmissibility is preferred here because it simplifies the terminology required when the model is extended to the case of unequal formation thickness on opposite sides of the fault.
On both sides of the fault, the pressure behavior obeys the diffusivity equation, which is usually expressed in radial coordinatefor problems of fluid flow to a well in a porous medium. The problems of fluid flow to a well in a porous medium. The problem considered here, however, is more easily solved by problem considered here, however, is more easily solved by expression of the diffusivity equation in Cartesian coordinates with a separate formulation for each side of the semipermeable barrier.
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