Modeling of anomalous gas transport in heterogeneous unconventional reservoirs using a nonlinear generalized diffusivity equation

Abstract

Exploitation of unconventional reservoirs is enabled by multi-fractured horizontal wells. Hydraulic fractures are created with the purpose of enhancing fluid conductivity in such low permeability formation. These hydraulic fractures, along with the intricate structure of the reservoir, such as the presence of natural fractures, result in a highly heterogeneous system and introduces significant challenges with respect to obtaining a proper description of fluid movement. This paper proposes the use of anomalous transport concept based on fractional-time derivative to model gas flow through highly heterogeneous unconventional reservoirs. A modified Darcy’s law that accounts for non-local temporal effects, i.e. history, is adopted to account for the complex flow mechanisms encountered in such disordered media with a wide range of heterogeneity scales. Studies previously developed on this topic solely focused on slightly-compressible fluid transport without further consideration of the nonlinear dependency of fluid properties to pressure. In this regard, the development of predictive models simultaneously considering reservoir heterogeneity and the nonlinear nature of gas transport is yet to be accomplished. In this work, transient pressure diffusion is modeled by the so-called nonlinear Generalized Diffusivity Equation (nGDE), and an integral solution is derived based on Green’s function method. It is observed that for the cases of higher heterogeneity level, higher pressure drawdown is required to maintain a given specified (constant) rate, significantly increasing the deviation of the system response from its linear (slightly-compressible) behavior. This finding corroborates the importance of properly accounting for the nonlinear behavior of gas properties and highlights that available analytical solutions suffer drawbacks when extrapolated to compressible flow scenarios.