Semi-analytical model for pumping tests in discretely fractured aquifers

Abstract In this paper, a novel semi-analytical model for pumping tests in discretely fractured aquifers with randomly distributed and finitely conductive fractures is presented to investigate the wellbore drawdown transient behaviour. An aquifer model and discrete fracture model are established. The flux and drawdown equivalent conditions in the Laplace space are applied in the fracture wall to couple the fluid flow in both systems. The advantage of the proposed semi-analytical model is that only fractures must be separated into segments, not the entire domain. Then, a matrix of the fracture segment in Laplace space can be built and solved by using Gauss's elimination method. A final solution for wellbore drawdown can be easily evaluated using the numerical Laplace inversion algorithm of Stehfest. The model is compared with a previous result of an extended well. The proposed model allows us to consider the problems of pumping tests in complex fracture networks, including parallel uncrossed fracture networks, arbitrary distribution non-intersected fracture networks, and intersected fracture networks with isolated fractures. In the past studies, some scholars have found that the drawdown or pressure derivative curve will present only one dip valley which looks like a V-shaped curve for the naturally fractured confined aquifer or reservoirs, and number of dip valleys are only related to porous media type. However, this study illustrates that the drawdown transient behaviour and the number of dip valleys are closely related to fracture density, fracture conductivity, fracture length, fracture orientation, fracture distribution, position of a pumping well, and the distance between the pumping well and fracture.