Surfactant induced one dimensional unsaturated flow through porous media: a classical mathematical approach

2013 ◽  
Vol 51 (9) ◽  
pp. 2423-2431
Author(s):  
Rakhee Kuperkar ◽  
D. M. Patel
Keyword(s):  
Porous Media ◽  
Unsaturated Flow ◽  
Mathematical Approach ◽  
Flow Through Porous Media ◽  
One Dimensional ◽  
Flow Through

Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media

2003 ◽  
Vol 133 (1) ◽  
pp. 177-196 ◽  
Author(s):  
Kenji Nishihara
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Compressible Flow ◽  
Convergence Rates ◽  
Flow Through Porous Media ◽  
Optimal Convergence Rate ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Optimal Convergence ◽  
Flow Through

Consider the Cauchy problem for a one-dimensional compressible flow through porous media, Hsiao and Liu showed that the solution (υ, u) behaves as the diffusion wave (ῡ, ū), i.e. the solution of the porous-media equation due to the Darcy law. The optimal convergence rates have been obtained by Nishihara and co-workers. When υ0(x) has the same constant state at x = ±∞, the convergence rate ‖(υ − ῡ)(·,t)‖L∞ = O(t−1) obtained is ‘optimal’, since ‖ῡ(·,t)‖∞ = O(t−1/2). However, this ‘optimal’ convergence rate is less sufficient to determine the location of the diffusion wave. Our aim in this paper is to obtain the ‘truly optimal’ convergence rate by choosing suitably located diffusion waves.

scholarly journals A new approach to Bäcklund transformations for longitudinal dispersion of miscible fluid flow through porous media in oil reservoir during secondary recovery process

2011 ◽  
Vol 38 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Ramakanta Meher ◽  
M.N. Mehta ◽  
S.K. Meher
Keyword(s):  
Porous Media ◽  
Nonlinear Partial Differential Equations ◽  
Recovery Process ◽  
Flow Through Porous Media ◽  
New Approach ◽  
One Dimensional ◽  
Secondary Recovery ◽  
Miscible Fluid ◽  
Dispersion Problem ◽  
Flow Through

In this paper a theoretical model has developed for the dispersion problem in porous media in which the flow is one dimensional and the average flow is unsteady. The Solution of the dispersion problem is presented by means of a new approach to B?cklund transformations of nonlinear partial differential equations.

Solubility effects on surfactant-induced unsaturated flow through porous media

1999 ◽  
Vol 223 (3-4) ◽  
pp. 164-174 ◽  
Author(s):  
E.J. Henry ◽  
J.E. Smith ◽  
A.W. Warrick
Keyword(s):  
Porous Media ◽  
Unsaturated Flow ◽  
Flow Through Porous Media ◽  
Flow Through

Principles of Unsaturated Flow in Tight Gas Reservoirs

2013 ◽  
Vol 772 ◽  
pp. 761-764
Author(s):  
Zhi Kai Lv ◽  
Dai Hong Gu ◽  
Shun Li He ◽  
Hai Yong Zhang ◽  
Shao Yuan Mo
Keyword(s):  
Porous Media ◽  
Unsaturated Flow ◽  
Water Saturation ◽  
Gas Production ◽  
Reservoir Rock ◽  
Residual Water ◽  
Flow Through Porous Media ◽  
Production Flow ◽  
Gas Seepage ◽  
Flow Through

The future of the energy sector in the coming years is expected to be significantly affected by unconventional gas resources. Flow through porous media has many applications in the chemical, petroleum, gas, and pulp and paper industries, as well as in soil remediation and material characterization. In petroleum and natural gas production, flow through porous media has significance in the production of gas and/or oil. There are many characteristics of tight reservoir rock resulting in high and complex water saturation such as tiny pore throat, poor sorting, high displacement pressure, and so on. The one hand, the gas seepage is affected by the slippage effect, resulting in the abnormal gas relative permeability. On the other hand, the residual water of the tight core is controlled by displacement pressure. This study is directly related to gas reservoir engineering and is specifically focused to obtain fundamental information for two phase flow through low permeability porous media (Tight Sand Gas).

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