A new approach to fracturing test interpretation using the PKN model

Abstract

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG 0 −2/3 , CG 0 1/3 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G 0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G 0 are found somehow, the fracture length and the fracture volume at the end of pumping can be calculated.