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

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.

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

Journal of Heat Transfer ◽

10.1115/1.3180808 ◽

2009 ◽

Vol 131 (10) ◽

Cited By ~ 5

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

Volume 1: Offshore Technology ◽

10.1115/omae2008-57792 ◽

2008 ◽

Author(s):

M. M. Awad ◽

S. D. Butt

Keyword(s):

Porous Media ◽

Pressure Gradient ◽

Single Phase ◽

Theoretical Method ◽

Flow In Porous Media ◽

Pressure Gradients ◽

Two Phase ◽

New Model ◽

Proposed Model ◽

Phase Liquid

A simple semi-theoretical method for calculating two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. 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 single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x ≅ 1 is nearly identical to 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 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 Larkins et al. correlation, Sato et al. correlation, and Goto and Gaspillo correlation have three constants. Therefore, calibration of the new model to experimental data is greatly simplified. The new model is able to model the existing multi parameters correlations by fitting the single parameter p. Specifically, p = 1/3.25 for Midoux et al. correlation, p = 1/3.25 for Rao et al. correlation, p = 1/3.5 for Tosun correlation, p = 1/3.25 for Larkins et al. correlation, p = 1/3.75 for Sato et al. correlation, and p = 1/3.5 for Goto and Gaspillo correlation.

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Self-similar condensing flows in porous media

International Journal of Heat and Mass Transfer ◽

10.1016/0017-9310(80)90150-7 ◽

1980 ◽

Vol 23 (11) ◽

pp. 1461-1470 ◽

Cited By ~ 5

Author(s):

R.H. Nilson ◽

L.A. Romero

Keyword(s):

Porous Media ◽

Flows In Porous Media ◽

Condensing Flows ◽

Self Similar

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NUMERICAL ALGORITHMS FOR SOLVING PROBLEMS OF MULTIPHASE FLOWS IN POROUS MEDIA

Mathematical Modelling and Analysis ◽

10.3846/13926292.2006.9637308 ◽

2006 ◽

Vol 11 (2) ◽

pp. 133-148 ◽

Cited By ~ 5

Author(s):

R. Èiegis ◽

O. Iliev ◽

V. Starikovièius ◽

K. Steiner

Keyword(s):

Porous Media ◽

Numerical Algorithms ◽

Software Tool ◽

Flow In Porous Media ◽

Nonlinear Pdes ◽

Two Phase ◽

Flows In Porous Media ◽

Time Stepping ◽

Realistic Problem ◽

Volume Method

In this paper we discuss numerical algorithms for solving the system of nonlinear PDEs, arising in modelling of two‐phase flows in porous media, as well as the proper object oriented implementation of these algorithms. Global pressure model for isothermal two‐phase immiscible flow in porous media is considered in this paper. Finite‐volume method is used for the space discretization of the system of PDEs. Different time stepping discretizations and linearization approaches are discussed. The main concepts of the PDE software tool MfsolverC++ are given. Numerical results for one realistic problem are presented.

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Exact Solution for Non-Self-Similar Wave-Interaction Problem during Two-Phase Four-Component Flow in Porous Media

Abstract and Applied Analysis ◽

10.1155/2014/731567 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 8

Author(s):

S. Borazjani ◽

P. Bedrikovetsky ◽

R. Farajzadeh

Keyword(s):

Exact Solution ◽

Porous Media ◽

Oil Recovery ◽

Environmental Flows ◽

Wave Interaction ◽

Flow In Porous Media ◽

Two Phase ◽

Multicomponent Flows ◽

Phase Saturation ◽

Self Similar

Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for3×3hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to2×2system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.

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