Mathematical Modeling of the Single-Phase Multicomponent Flow in Porous Media

2021 ◽  
pp. 200-214
Author(s):  
Petr Gális ◽  
Jiří Mikyška
Keyword(s):  
Mathematical Modeling ◽  
Porous Media ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Multicomponent Flow

Shock–like structure of phase-change flow in porous media

1981 ◽  
Vol 104 ◽  
pp. 467-482 ◽  
Author(s):  
L. A. Romero ◽  
R. H. Nilson
Keyword(s):  
Porous Media ◽  
Phase Change ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Flows In Porous Media ◽  
Dissipative Effects ◽  
Condensing Flows ◽  
Self Similar ◽  
Phase Change Flows

Shock-like features of phase-change flows in porous media are explained, based on the generalized Darcy model. The flow field consists of two-phase zones of parabolic/hyperbolic type as well as adjacent or imbedded single-phase zones of either parabolic (superheated, compressible vapour) or elliptic (subcooled, incompressible liquid) type. Within the two-phase zones or at the two-phase/single-phase interfaces, there may be steep gradients in saturation and temperature approaching shock-like behaviour when the dissipative effects of capillarity and heat-conduction are negligible. Illustrative of these shocked, multizone flow-structures are the transient condensing flows in porous media, for which a self-similar, shock-preserving (Rankine–Hugoniot) analysis is presented.

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

A Robust Asymptotically Based Modeling Approach for Two-Phase Flow in Porous Media

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
M. M. Awad ◽  
S. D. Butt
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Single Phase ◽  
Present Model ◽  
Flow In Porous Media ◽  
Pressure Gradients ◽  
Two Phase ◽  
New Model ◽  
Proposed Model ◽  
Phase Liquid

A simple semitheoretical method for calculating the two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x≅0 is nearly identical to the single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x≅1 is nearly identical to the single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (ϕl2) or a two-phase frictional multiplier for gas flowing alone (ϕg2) as a function of the Lockhart–Martinelli parameter X. The advantage of the new model is that it has only one fitting parameter (p), while the other existing correlations, such as the correlation of Larkins et al., Sato et al., and Goto and Gaspillo, have three constants. Therefore, calibration of the new model to the experimental data is greatly simplified. The new model is able to model the existing multiparameter correlations by fitting the single parameter p. Specifically, p=1/3.25 for the correlation of Midoux et al., p=1/3.25 for the correlation of Rao et al., p=1/3.5 for the Tosun correlation, p=1/3.25 for the correlation of Larkins et al., p=1/3.75 for the correlation of Sato et al., and p=1/3.5 for the Goto and Gaspillo correlation.

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