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.

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.

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.

A Robust Asymptotically Based Modeling Approach for Two-Phase Liquid-Liquid Flow in Pipes

2009 ◽  
Author(s):  
M. M. Awad ◽  
S. D. Butt
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Viscous Liquid ◽  
Oil Recovery ◽  
Liquid Flow ◽  
Petroleum Industry ◽  
Theoretical Method ◽  
Two Phase ◽  
New Model ◽  
Recovery Processes

The flow of two immiscible liquids such as oil and water is very important in the petroleum industry like oil recovery processes. For example, the injection of water into the oil flowing in the pipeline reduces the resistance to flow and the pressure gradient. Thus, there is no need for large pumping units. In the present study, a simple semi-theoretical method for calculating the two-phase frictional pressure gradient for liquid-liquid flow in pipes using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for the more viscous liquid and the less viscous liquid flowing alone. The proposed model can be transformed into either a two-phase frictional multiplier for the more viscous liquid flowing alone (φ12) or two-phase frictional multiplier for the less viscous liquid flowing alone (φ22) as a function of the Lockhart-Martinelli parameter, X. The advantage of the new model is that it has only one fitting parameter (p). 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. Comparison with experimental data for two-phase frictional multiplier versus the Lockhart-Martinelli parameter (X) is presented.

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.

Two-Phase Flow Modeling in Microchannels and Minichannels

2008 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Gradient ◽  
Two Phase Flow ◽  
Effective Property ◽  
Theoretical Method ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Flow Modeling ◽  
Two Phase ◽  
Asymptotic Modeling ◽  
Modeling Approach

In the present paper, three different methods for two-phase flow modeling in microchannels and minichannels are presented. They are effective property models for homogeneous two-phase flows, an asymptotic modeling approach for separated two-phase flow, and bounds on two-phase frictional pressure gradient. In the first method, new definitions for two-phase viscosity are proposed using a one dimensional transport analogy between thermal conductivity of porous media and viscosity in two-phase flow. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. In the second method, a simple semi-theoretical method for calculating two-phase frictional pressure gradient 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 final method, simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient in minichannels and microchannels. In all cases, the proposed modeling approaches are validated using the published experimental data.

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.

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