Abstract
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space. © 2017 The Authors
Authors
El Amin M.F., Radwan A.G., Sun S.
Keywords
Fractional derivative; Infinite series solutions; Natural gas; Porous media; Reservoir modeling
Document Type
Journal
Source
Results in Physics, Vol. 7, PP. 2432 to 2438, Doi: 10.1016/j.rinp.2017.06.051