Application of superposition principle to variable rate/pressure production analysis of multi-fractured horizontal wells in unconventional gas reservoirs

Application of superposition principle to non-linear gas governing equations has been an elusive goal in early-transient production data analysis and has been so far limited to the use of empirical and approximate methods best applicable to boundary-dominated flow conditions. This paper presents a novel and rigorous semi-analytical model that is applicable for the analysis of production data from multi-fractured horizontal gas wells (MFHWs) producing under early-transient variable rate/pressure production conditions. Nonlinear, pressure-dependent hydraulic diffusivity retained in pseudo-pressure-based gas diffusivity equation is straightforwardly and rigorously captured without approximation. The resulting formulation of superposition applied in nonlinear gas system is written in terms of the classical solution for the governing linear partial differential equation (PDE) plus an analytical adjustment factor that quantifies the nonlinearity of the system. Numerical examples and field cases are presented to test the validity and showcase the capabilities of proposed approach. Comparisons against available empirical and approximate models are also provided for these cases.