TY - JOUR
T1 - Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
AU - El-Amin, Mohamed
AU - Radwan, Ahmed G.
AU - Sun, Shuyu
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2017/7/6
Y1 - 2017/7/6
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/625174
UR - http://www.sciencedirect.com/science/article/pii/S2211379717309038
UR - http://www.scopus.com/inward/record.url?scp=85024852835&partnerID=8YFLogxK
U2 - 10.1016/j.rinp.2017.06.051
DO - 10.1016/j.rinp.2017.06.051
M3 - Article
SN - 2211-3797
VL - 7
SP - 2432
EP - 2438
JO - Results in Physics
JF - Results in Physics
ER -