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.

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

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.

Review and Modeling of Two-Phase Frictional Pressure Gradient at Microgravity Conditions

2010 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Gradient ◽  
Single Phase ◽  
Present Model ◽  
Theoretical Method ◽  
Asymptotic Model ◽  
Pressure Gradients ◽  
Two Phase ◽  
Proposed Model ◽  
Microgravity Conditions ◽  
Phase Liquid

First, a detailed review of two-phase frictional pressure gradient at microgravity conditions is presented. Then, a simple semi-theoretical method for calculating two-phase frictional pressure gradient at microgravity conditions 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. Comparison of the asymptotic model with experimental data at microgravity conditions is presented.

Modeling of Interfacial Component for Two-Phase Frictional Pressure Gradient in Microchannels and Minichannels

2011 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Single Phase ◽  
Simple Approach ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Interfacial Pressure ◽  
Proposed Model ◽  
Phase Liquid

A simple approach for calculating the interfacial component of frictional pressure gradient in two-phase flow in microchannels and minichannels is presented. This approach is developed using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. The proposed model can be transformed in two different ways. First, two-phase interfacial multiplier for liquid flowing alone (φl,i2) as a function of two-phase frictional multiplier for liquid flowing alone (φl2) and the Lockhart-Martinelli parameter, X. Second, two-phase interfacial multiplier for gas flowing alone (φg,i2) as a function of two-phase frictional multiplier for gas flowing alone (φg2) and the Lockhart-Martinelli parameter, X. This proposed model allows for the interfacial pressure gradient to be easily modeled. Comparisons of the proposed model with experimental data for microchannels and minichannels and existing correlations for both φl and φg versus X are presented.

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.

Combination of Petroleum Correlations and Drift-Flux Approaches: A New Model for Two-Phase Flow Pressure Gradient Calculation for Horizontal and Slightly Inclined Upward Flowlines

2014 ◽  
Author(s):  
Rinaldo Antonio de Melo Vieira ◽  
Artur Posenato Garcia
Keyword(s):  
Pressure Gradient ◽  
Single Phase ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
New Model ◽  
One Dimensional ◽  
Drift Flux Model ◽  
Drift Flux ◽  
Flux Model

One-dimensional single-phase flow has only one characteristic velocity, which is the area-averaged velocity. On the other hand, one-dimensional two-phase flow has several characteristics velocities, such as center of volume mixture velocity and center of mass mixture velocity. Under slip condition, usually they are quite different. In a simple way, one may think that the petroleum correlations and the drift-flux model are an attempt to “adapt” the single-phase momentum equation for a mixture of more than one phase, where the several parameters in the single-phase equation are replaced by average-mixture ones. These two models use different considerations for this “adaptation”. For instance, for friction loss calculation, petroleum correlations use the mixture volume velocity while drift-flux models use the mixture mass velocity. Normally, the volume velocity is higher than the mass velocity, and petroleum correlations may calculate friction gradients higher than the ones obtained by drift-flux models. This is very important, especially for horizontal and slightly inclined upward flows, where the friction pressure gradient is dominant. This work compares the pressure gradient evaluated by these two models for horizontal and slightly inclined upward flowlines using available data found in literature. The comparison shows that, depending on the situation, one model gives better results than the other. Based on the results, a new approach for two-phase flow friction calculation is proposed. The new model represents a combination of the approach used by the Petroleum Correlations and the Drift-Flux Model, using different characteristic velocities (volume, mass and a new one defined by the authors). The new model is very simple to implement and shows good agreement with the tested data.

An efficient discontinuous Galerkin method for two-phase flow modeling by conservative velocity projection

2016 ◽  
Vol 26 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Mehdi Jamei ◽  
H Ghafouri
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type ◽  
Proposed Model ◽  
Dg Method ◽  
Velocity Projection

Purpose – The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection. Design/methodology/approach – The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations. Findings – The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements. Research limitations/implications – The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible. Practical implications – The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media. Originality/value – The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.

Asymptotic Generalizations of the Lockhart-Martinelli Method for Two Phase Flows

2009 ◽  
Author(s):  
Y. S. Muzychka ◽  
M. M. Awad
Keyword(s):  
Pressure Drop ◽  
Single Phase ◽  
Two Phase Flow ◽  
Point Of View ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Interfacial Pressure ◽  
Phase Liquid ◽  
Flow Pressure

The Lockhart-Martinelli method for predicting two phase flow pressure drop is examined from the point of view of asymptotic modelling. Comparisons are made with the Lockhart-Martinelli method, the Chisholm method, and the Turner-Wallis method. An alternative approach for predicting two phase flow pressure drop is developed using superposition of three pressure gradients: single phase liquid, single phase gas, and interfacial pressure drop. This new approach allows for the interfacial pressure drop to be easily modelled for each type of flow regime such as: bubbly, mist, churn, plug, stratified, and annular, or based on the classical laminar-laminer, turbulent-turbulent, laminar-turbulent and turbulent-laminar flow regimes proposed by Lockhart and Martinelli.

scholarly journals An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

2020 ◽  
Author(s):  
Jing-Fa Li ◽  
Bo Yu ◽  
Dao-Bing Wang ◽  
Shu-Yu Sun ◽  
Dong-Liang Sun
Keyword(s):  
Porous Media ◽  
Equation Of State ◽  
Single Phase ◽  
Reduced Order Model ◽  
Flow In Porous Media ◽  
Order Model ◽  
Reduced Order ◽  
Proposed Model ◽  
Speed Up ◽  
Robinson Equation

Abstract In this paper, an efficient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible flow in porous media. The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of flow equation in original full-order space, and the discrete empirical interpolation method (DEIM) is applied to speed up the solution of Peng–Robinson equation of state in reduced-order subspace. The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reduced-order subspace, which not only preserves good prediction accuracy of full-order model, but also gains dramatic computational acceleration by multigrid and DEIM. Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method. In addition, the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng–Robinson equation of state is demonstrated and carried out in detail. Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors. The general acceleration is up to 50–60 times faster than that of standard semi-implicit method in two-dimensional simulations, but the average relative errors of numerical results between these two methods only have the order of magnitude 10−4–10−6%.

A NOVEL FRACTAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY IN POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550017 ◽  
Author(s):  
G. LEI ◽  
P. C. DONG ◽  
S. Y. MO ◽  
S. H. GAI ◽  
Z. S. WU
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Fractal Dimension ◽  
Multiphase Flow ◽  
Relative Permeability ◽  
Structural Parameters ◽  
Flow In Porous Media ◽  
Fluid Viscosity ◽  
Two Phase ◽  
Proposed Model

Multiphase flow in porous media is very important in various scientific and engineering fields. It has been shown that relative permeability plays an important role in determination of flow characteristics for multiphase flow. The accurate prediction of multiphase flow in porous media is hence highly important. In this work, a novel predictive model for relative permeability in porous media is developed based on the fractal theory. The predictions of two-phase relative permeability by the current mathematical models have been validated by comparing with available experimental data. The predictions by the proposed model show the same variation trend with the available experimental data and are in good agreement with the existing experiments. Every parameter in the proposed model has clear physical meaning. The proposed relative permeability is expressed as a function of the immobile liquid film thickness, pore structural parameters (pore fractal dimension Dfand tortuosity fractal dimension DT) and fluid viscosity ratio. The effects of these parameters on relative permeability of porous media are discussed in detail.

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