Laplace-domain multiwell convolution for simulating pressure interference response of multiple fractured horizontal wells by use of modified Stehfest algorithm

Abstract

In the multiwell-pad-production scheme, it is a critical task for petroleum engineers to provide an understanding of various interwell communications to quantify well-to-well interference. The focus of this study is put on transient pressure simulation of interwell interference communicated by connecting fracture (i.e. fracture hit) during interference testing of wells with variable operating conditions. On the basis of a framework generalized model of capturing discrete-fracture-network (DFN) flowing, this paper established a rigorous Laplace-transform solution for multiwell pad interfered through fracture-hit connection. In Laplace-transform domain, the variable-rate operating conditions are directly incorporated to integrate with constant-unit-rate solution by using convolution method. Based on the fundamental Stehfest algorithm modified by Chen and Raghavan (1994), which was originally applicable to single-well model, an inverse algorithm was devised to provide the results of transient pressure response of multiwell pad in the real-time domain.The approach is validated by comparing with reservoir numerical simulators with regard to interference pressure response of two-well case producing in piecewise-continuous rate sequences. The results are all in an excellent agreement. By conducting sensitivity analysis where the effects of connecting fracture properties (i.e., conductivity, azimuth, number, and geometrical complexity etc.) and rate-sequence changing are considered, detailed discussions on interference diagnostic and identification are presented to capture the physics of interwell interference by utilizing various visualized approaches including pressure profile, flux distribution along fracture face and pressure field. Finally, a field example of multiwell-pad completion, communicated by fracture hit, is used to demonstrate the advantage and improvement of this model over single-isolated-well model and matrix-communication-multiwell model in achieving accurate history matching and providing reasonable fracturing-parameter explanation.The new approach combines the flexibility of presenting complex fracture-hit connection and the convenience of convolution of Laplace transformation. The corresponding inverse numerical algorithm has the ability of overcoming difficulties in handling sudden changes in flow rate in well-test-analysis applications. In summary, the study provides a well understanding and insight into the physics of interference mechanisms by using semi-analytical approach.