Effect of boundary conditions on pressure behavior of finite-conductivity fractures in bounded stratified reservoirs

Abstract

In this study, a mathematical model was developed to model the pressure behavior of a well located in a bounded multilayer reservoir and crossed by a finite-conductivity vertical fracture. It was found that the dimensionless pressure function and its derivative strongly depend on fracture conductivity and fracture extension during early times. The effect of reservoir heterogeneity on the pressure function is negligible compared to that on the pressure derivative. Both functions exhibit four flow periods: bilinear, formation linear, pseudoradial and pseudosteady-state which are separated by transition periods. One or more of these flow periods may be missing. Data obtained from a long test and which are characterized by a unit slope line indicate that the well is intercepted by deeply extended fractures. It has been found that the fractional production rates of different layers are a good measure of reservoir and fracture characteristics. Flowmeter survey data can be used to eliminate the non-uniqueness problem when using the type curves presented in this study.