Mathematical model of two-phase fluid nonlinear flow in low-permeability porous media with applications

Abstract In this paper, we present a computational fluid dynamics (CFD) model to perform single- and two-phase fluid flow simulation on two- and three-dimensional perforated porous media with different perforation geometries. The finite volume method (FVM) has been employed to solve the equations governing the fluid flow through the porous media and obtain the pressure and velocity profiles. The volume of fluid (VOF) method has also been utilized for accurate determination of the volume occupied by each phase. The validity of the model has been achieved via comparing the simulation results with the available experimental data in the literature. The model was used to analyze the effect of perforation geometrical parameters (length and diameter), degree of heterogeneity, and also crushed zone properties (permeability and thickness) on the pressure and velocity profiles. The two-phase fluid flow around the perforation tunnel under the transient flow regime was also investigated by considering a constant mass flow boundary condition at the inlet. The developed model successfully predicted the pressure drop and resultant temperature changes for the system of air–water along clean and gravel-filled perforations under the steady-state conditions. The presented model in this study can be used as an efficient tool to design the most appropriate perforation strategy with respect to the well characteristics and reservoir properties.

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An Efficient Hybrid Model for Nonlinear Two-Phase Flow in Fractured Low-Permeability Reservoir

Energies ◽

10.3390/en12152850 ◽

2019 ◽

Vol 12 (15) ◽

pp. 2850 ◽

Cited By ~ 5

Author(s):

Daigang Wang ◽

Jingjing Sun ◽

Yong Li ◽

Hui Peng

Keyword(s):

Porous Media ◽

Pressure Drop ◽

Hybrid Model ◽

Two Phase Flow ◽

Low Permeability ◽

Phase Flow ◽

Two Phase ◽

Fracture Length ◽

Wellbore Pressure ◽

Horizontal Wellbore

The staged fracturing horizontal well has proven to be an attractive alternative for improving the development effect of a low permeability waterflood reservoir. Due to the coexistence of matrix, fracture, and horizontal wellbore, it remains a great challenge to accurately simulate the nonlinear flow behaviors in fractured porous media. Using a discrete fracture model to reduce the dimension of the fracture network, a two-parameter model is used to describe the nonlinear two-phase flow behavior, and the equivalent pipe flow equation is selected to estimate the horizontal wellbore pressure drop in the fractured low-permeability reservoir. A hybrid mathematical model for the nonlinear two-phase flow, including the effect of horizontal wellbore pressure drop in fractured porous media, is developed. A numerical scheme of the hybrid model is derived using the mimetic finite difference method and finite volume method. With a staggered five-spot flood system, the accuracy of the proposed model and the effect of fracture properties on nonlinear two-phase flow behaviors are further investigated. The results also show that with an increase of fracture length near injectors, the breakthrough time of injected water into the horizontal wellbore will be shorter, indicating a faster rise of the water cut, and a worse development effect. The impact of shortening fracture spacing is consistent with that of enlarging fracture length. Successful practice in modeling the complex waterflood behaviors for a 3-D heterogeneous reservoir provides powerful evidence for the practicability and reliability of our model.

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Erratum to “Immiscible two-phase fluid flows in deformable porous media” [Advances in Water Resources 25 (2002) 1105–1117]

Advances in Water Resources ◽

10.1016/s0309-1708(03)00007-1 ◽

2003 ◽

Vol 26 (4) ◽

pp. 473

Author(s):

Wei-Cheng Lo ◽

Garrison Sposito ◽

Ernest Majer

Keyword(s):

Porous Media ◽

Water Resources ◽

Fluid Flows ◽

Two Phase ◽

Deformable Porous Media ◽

Phase Fluid

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Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽

10.1155/2017/3602593 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Mohamed F. El-Amin ◽

Ahmed M. Saad ◽

Amgad Salama ◽

Shuyu Sun

Keyword(s):

Magnetic Field ◽

Mathematical Model ◽

Porous Media ◽

Magnetic Nanoparticles ◽

Additional Term ◽

Flow In Porous Media ◽

Phase System ◽

Two Phase ◽

The Mathematical Model ◽

Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

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A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

Revista de Engenharia Térmica ◽

10.5380/reterm.v1i2.3504 ◽

2002 ◽

Vol 1 (2) ◽

pp. 09

Author(s):

J. C. Da Mota ◽

A. J. De Souza ◽

D. Marchesin ◽

P. W. Teixeira

Keyword(s):

Mathematical Model ◽

Porous Media ◽

Wave Structure ◽

Thermal Recovery ◽

Flow In Porous Media ◽

Low Temperature Oxidation ◽

Two Phase ◽

Temperature Oxidation ◽

Physical Effects ◽

The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

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Fabrication of a Microchannel Device With a Three-Dimensional Pore Network Using a Sacrificial Sugar Template

Volume 3: Computational Fluid Dynamics; Micro and Nano Fluid Dynamics ◽

10.1115/fedsm2020-20356 ◽

2020 ◽

Author(s):

Haipeng Zhang ◽

Tomer Palmon ◽

Seunghee Kim ◽

Sangjin Ryu

Keyword(s):

Porous Media ◽

Fluid Flow ◽

Pore Structure ◽

Three Dimensional ◽

Pore Network ◽

Compressed Air ◽

Microfluidic Channels ◽

Two Phase ◽

Flow Through ◽

Phase Fluid

Abstract Porous media compressed air energy storage (PM-CAES) is an emerging technology that stores compressed air in an underground aquifer during the off-peak periods, to mitigate the mismatch between energy supplies and demands. Thus, PM-CAES involves repeated two-phase fluid flow in porous media, and ensuring the success of PM-CAES requires a better understanding of repetitive two-phase fluid flow through porous media. For this purpose, we previously developed microfluidic channels that retain a two-dimensional (2D) pore network. Because it was found that the geometry of the pore structure significantly affects the patterns and occupational efficiencies of a non-wetting fluid during the drainage-imbibition cycles, a more realistic microfluidic model is needed to reflect the three-dimensional (3D) nature of pore structures in the underground geologic formation. In this study, we developed an easy-to-adopt method to fabricate a microfluidic device with a 3D random pore network using a sacrificial sugar template. Instead of using a master mold made in photolithography, a sacrificial mold was made using sugar grains so that the mold could be washed away after PDMS curing. First, we made sugar templates with different levels of compaction load, and found that the thickness of the templates decreased as the compaction load increased, which suggests more packing of sugar grains and thus lower porosity in the template. Second, we fabricated PDMS porous media using the sugar template as a mold, and imaged their pore structure using micro computed tomography (micro-CT). Pores within PDSM samples appeared more tightly packed as the compacting force increased. Last, we fabricated a prototype PDMS channel device with a 3D pore network using a sugar template, and visualized flow through the pore network using colored water. The flow visualization result shows that the water was guided by the random pores and that the resultant flow pattern was three dimensional.

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