Pressure Transient Analysis of Wells with Finite Conductivity Vertical Fractures in Double Porosity Reservoirs

Abstract

This paper presents the results obtained in the study of the transient behavior of a well intersected by a finite conductivity vertical fracture in a double porosity reservoir. Two models are considered to take into account the fluid transfer between matrix blocks and fractures: the pseudo-steady-state matrix flow mode and the transient matrix flow model. A general semianalytical model and simplified fully analytical models are presented. It is demonstrated that these systems exhibit the basic behavior of a well with a finite conductivity fracture: that is bilinear flow, pseudolinear flow and pseudoradial flow in addition to the transition flow periods. Each of these flow periods is under the influence of the different states of the fluid transfer between matrix and fractures; that is fracture dominated period, transition period and total system dominated period. It is shown that correlating parameters are the dimensionless fracture conductivity (), the fracture storativity coefficient and the interporosity flow parameter (or the dimensionless matrix hydraulic diffusivity). It was found, for the transient matrix flow model, that the pressure behavior exhibits 1/8 slope in a log-log graph during the bilinear flow dominated by the transition period of the fluid transfer. Hence a graph of pressure versus yields a straight line passing through the origin. During the pseudolinear flow, and if the fluid transfer is in the transition period, a log-log graph of the pressure versus time exhibits 1/4 slope straight line. This means that a graph of p versus yields a straight line. Hence it is concluded that bilinear flow is not the only type of flow that exhibits the one quarter slope type of behavior. Type curves are presented to analyze data falling in the bilinear pseudolinear flow regions. The effect of wellbore storage are also included. The general semianalytical models yields simultaneous the constant flow rate and the constant pressure solutions as well as the pressure derivative function for the constant rate case. Introduction In recent years interest has been growing for the evaluation of hydraulically fractured wells producing in double porosity reservoirs. Although considerable efforts have been dedicated to study either fractured wells in homogeneous reservoirs or wells producing in double porosity reservoirs, there is not a complete study that includes fractures in double porosity reservoirs. It has been shown in the past that well intersected by finite conductivity vertical fracture in a homogeneous reservoir can exhibit several flow periods: bilinear, pseudolinear and pseudo-radial in addition to the transition between them. For each of these flow periods there is a specific graph of interpretation that produces a straight line portion for the pressure data. The pressure data within the bilinear flow, the pseudolinear flow and the pseudoradial flow exhibit a straight line in a graph of pressure versus, and log t, respectively. The complete behavior of the system can be correlated by a parameter called dimensionless fracture conductivity (). In order to identify the different flow regimes type curves have been presented in terms of pressure or pressure derivative. On the other hand, the studies on the behavior of wells in double porosity reservoirs have considered two kinds of models for the matrix-fracture fluid transfer: the pseudo-steady-state flow model (Warren and Root) and the transient matrix flow model (de Swaan and Kazemi). P. 645^

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