Finite Volume TVD Scheme for a Nonlinear Gas Transport Model in Shale Rocks

Ultra small permeability is the main feature of the rocks containing the shale gas. The shale rocks are composed of a network of fractures that trap a large amount of gas. Expensive procedures such as hydraulic fracturing and horizontal drilling are used to release gas from the shale rocks. The process of gas extraction is augmented with the use of transport models and experimental techniques. The gas transport models are developed so that they can capture the physics and the complexity of the fluid flow through shale rocks. In this work, a conservative finite volume TVD scheme is developed to obtain the numerical solutions of the gas transport model. Numerical model is validated against a time dependent advection diffusion equation whose exact solution is available, and then it is applied to a nonlinear gas transport model to find it's numerical solutions. The numerical solutions, in the steady state case, are compared against the experimental results that are obtained from pressure-pulse decay tests.