A robust semi-analytical method based on integral formulations for modeling unconventional gas wells with variable production constraints

Abstract

Modeling real multi-fractured horizontal gas wells with variable rate/pressure conditions has always been a challenging task. Previous studies demonstrated the advantages of integral solutions for modeling natural gas flow problems with variable inner boundary constraints, enabled by the convolution nature of such formulations. In this approach, the system's nonlinear behavior is captured through a rigorously-derived adjustment factor which becomes part of the final superimposed solution. The introduction of such a correction term captures additional complexities in the formulation that extends the applicability of classical Green's function techniques. This paper presents a robust and iterative semi-analytical method that solves the associated integral formulation used to model gas flow in porous media. The performance of our proposed method is compared against other Green's function-based solution protocols available in the literature. Validation against numerical simulations corroborated the robustness of our proposed approach in predicting reservoir performance. The method consistently provides the best predictive performance for all cases under study, which include variable and constant production constraints.