A New Model for Flow in Shale-gas Reservoirs including Natural and Hydraulic Fractures - Application to Well Tests

Abstract

In this paper we develop a new model to describe the hydrodynamics of gas flow in a multiporosity shale reservoir including natural and hydraulic fractures. The shale matrix is envisioned as a medium composed of four levels of porosity associated with nanopores, micropores, natural and hydraulic fractures and five distinct length scales. The bridging between the hydrodynamics at the different length scales is accomplished within the framework of the homogenization procedure. At the finest (nano) scale, gas is absorbed in the intra-kerogen nanopores. The upscaling of this level gives rise to gas storativity in the organic aggregates, where kerogen particles and nanopores are viewed as overlaying continua coexisting, at the microscale lying in the vicinity of the inorganic matter (considered impermeable) and the network of the interparticle pores where free gas flow takes place. We then upscale the microscopic problem to the mesoscale, where interparticle pores, organic and inorganic matters are homogenized giving rise to a new pressure equation for gas hydrodynamics in the shale matrix. The pressure equation in the shale matrix is coupled with the flow equations in the network of natural fractures leading, after averaging, to a micro-structured model of dual porosity type. Finally the dual porosity model is coupled with flow in the network of hydraulic fractures which are treated as (n-1) interfaces (n=2,3) with flow equation posed in a domain of reduced dimension. The closure of the coupled system hinges on the constitutive law for the partition coefficient which rules gas adsorption in the intra-kerogen nanopores. Usually such constitutive law is based on the classical Langmuir model whose accuracy is restricted to the monolayer adsorption portrait. The entire coupled system is discretized by the finite element method and applied to numerically simulate gas wells pressure transient analysis for the identification of petrophysical shale parameters. Different flow regimes (linear and bilinear) with its characteristics behavior in time are obtained for the pressure in a horizontal well for a prescribed mass flux. An approximate analytical solution was also derived including the gas adsorption in nanopores. A set of solutions parametrized by different adsorption equilibrium parameters is developed and compared with the numerical solution. These solutions show the effects of adsorbed gas in the parameters estimation.