Pressure Transient Analysis in Partially Penetrating Infinite Conductivity Hydraulic Fractures in Naturally Fractured Reservoirs

Abstract

Abstract Although the effect of partial penetration of an infinite conductivity hydraulic fracture has been considered in a homogeneous reservoir, there is no study in similar problem in naturally fractured reservoirs. This paper presents the analysis of the solution to such problem in naturally fractured reservoirs. The method of analysis with or without type curve that enables us to evaluate the permeability in the three principal axes directions is also presented. The solution to the mathematical model was obtained in Laplace domain with elliptical flow model. Several type curves were generated to study the pressure behavior. Both the early linear and pseudo-radial flow regimes are observed. The duration of the early linear flow regime is a function of the natural fractures storativity ratio, interporosity flow coefficient and the dimensionless hydraulic fracture's height. The effect of the dimensionless hydraulic fracture's height on the duration of the linear flow becomes negligible as its dimensionless height approaches unity. Therefore there is no single unique value of a dimensionless time for the end of the linear flow regime as in the case of homogeneous reservoir. Raghavan et al (1978) determined the end of the linear flow regime in fully penetrating hydraulic fractures in homogeneous reservoir to be 0.016. This value is based on the dimensionless pressure drop only. In this study, this value was found to be 0.01 and it was evaluated with pressure derivative curve which is more accurate. Two simulated examples were used to validate the method of the analysis developed. The results obtained are in agreement with the input data.