Multiphase Fluids In Porous Media Research Articles

Probing the generation mechanism of emulsion based on shearing actions between multiphase fluids in porous media

The generation, migration, and coalescence processes of emulsions in porous media of the actual formations are relatively complex. However, few studies have been reported about the generation mechanism of emulsions under shearing action, especially under shearing action between multiphase fluids. In this paper, the concept of emulsification caused by fluid shearing was proposed for the first time. An oil-water two phases flow model in porous media was established to study the generation process of emulsion caused by shearing actions between oil and water. Fluid flow velocity, pressure and distribution characteristics of oil and water during this process were recorded. The effects of flow velocity and oil-water interface properties on the generation process of emulsion were investigated. Combined with the microscopic visualization oil displacement model, the generation characteristics of emulsions in porous media were further explored. The results indicated that the complex flow between oil and water in porous media would cause shear emulsification of crude oil. With the increase of flow velocity of oil-water two phases, the shear emulsification capacity was gradually enhanced. The generation capacity of emulsion in the micro shearing unit was mainly affected by the flow velocity of the displacing phase, and the particle size of the emulsion was mainly affected by the flow velocity of the shearing phase. When the interfacial tension between oil and water was lower than 10−1 mN/m, the shear emulsification rate did not change significantly. These results are of great significance for the supplement and improvement of the generation mechanism of emulsions in porous media, providing theoretical guidance for further enhancing oil recovery by regulating emulsification.

Wettability control on imbibition behavior of oil and water in porous media

Wettability determines the spreading or adherence behavior of fluids at the solid surface and significantly influences the displacement and entrapment of multiphase fluids in porous media. The present study sets out to determine how wettability controls the imbibition physics of oil and water in a matrix–fracture medium. The displacement and distribution characteristics of fluids, the types of flow regimes, and the fluid morphology under various conditions were revealed in depth. The influences of wettability on oil recovery and energy conversion were analyzed. Finally, the application of the conventional scaling model to simulated imbibition data was also discussed. Results show that the imbibition front is complete and stable in a water-wet medium with the one-end open boundary condition. There are three flow regimes occurring in countercurrent imbibition, depending on the wettability and Ca (capillary number) situations. Increasing θ (contact angle, the affinity of wetting phase to the solid) or Ca can shift the flow pattern from the capillary regime to the capillary-viscous regime to the viscous regime. Additionally, the imbibition oil recovery is greatly affected by wettability, and a more water-wet state does not signify a larger oil recovery. There is a power-law relationship between the oil recovery and the fractal dimension of the nonwetting phase. On the other hand, we performed the energy conversion analysis in the strongly water-wet condition. The external work is positive for both the capillary-viscous and viscous regimes and declines with the decreased Ca. Oil recovery could be linked to the surface energy ratio to some degree, which is relevant to Ca. For the capillary regime, oil recovery is proportional to the final reduced surface energy and does not have an evident relationship with the dissipation energy ratio. Through scaling the recovery factor data vs time via the linear, the power-law, and the conventional models, we find that the conventional scaling model can be used to fit the data point, and the fitting performance is good when Ca is relatively high. However, the linear model is more appropriate when scaling the data in low Ca. Overall, our pore-scale simulation study could pave the way for a further step toward investigating other influencing factors on imbibition behaviors of fluids in more complex media like natural rock materials, which exhibit strong heterogeneity of wettability and pore structure.

Analysis of a finite volume element scheme for solving the model two-phase nonequilibrium flow problem

The paper proposes a hybrid numerical method for solving a model problem of two-phase nonequilibrium flow of an incompressible fluid in a porous medium. This problem is relevant in the modern theory of the motion of multiphase fluids in porous media and has many applications. The studied model is based on the assumption that the relative phase permeabilities and capillary pressure depend not only on saturation, but also on its time derivative. The saturation equation in this problem refers to the type of convection-diffusion with a predominance of convection, which also includes a third-order term to account for the nonequilibrium effects. Due to the hyperbolic nature of the equation, its solution is accompanied by a number of difficulties that lead to the need for an appropriate choice of the solution method. In contrast to previous works, this paper uses a finite volume element method for solving the problem, the construction of which is based on integral balance equations, and an approximate solution is chosen from the finite element space. To discretize the problem, two different dual grids are used based on the main triangulation. In this paper, a number of a priori estimates are obtained which yields the unconditional stability of the scheme as well as its convergence with the second order. The advantages of the approach used include the local conservatism of the scheme, as well as the comparative simplicity of the software implementation of the method. These results are confirmed by a numerical test carried out on the example of a model problem.

GPU-based Real-time Porous Medium Dynamic Network Simulation

Porous medium network simulation is to accurately describe the seepage law of multiphase fluids in porous media. Researchers have studied the relationship between various macroscopic physical properties of multiphase fluids (e.g. relative permeability, capillary pressure and fluid saturation) from theoretical, experimental, and computer simulation. This research introduces the construction method of stochastic pore network model and describes the calculation steps of pore network pressure field. In this research, the computational efficiency of the GPU-based pore network was compared with CPU. The calculation speed and simulation model scale of the pressure domain of the random pore network were improved.

(Invited) Modelling Electrochemical Cells with Porous Electrodes. The Proton Exchange Membrane Fuel Cell

The purpose of a good physical-chemical model is to aid cell design and operation. All such models must obey balance equations as well as constitutive equations of transport. The set of transport equations must conform with the entropy balance. The difficulty is to choose the right scale of description. The pore scale may be too small, when the cell’s overall performance is of interest. But the variables given by classical thermodynamics are obviously too crude, when we want to know the location, say, of hot spots. For the material designer, knowledge of hot spots is central. The method of coarse-graining of the porous medium or the choice of the representative elementary volume (REV) becomes then central [1,2]. In this work, we present a method for integration across various porous electrodes and heterogeneous layers of a fuel cell. This entropy balance is used to check the model for consistency [1]. The REV is defined in terms of Gibbs excess properties [1,2]. The electrode surfaces appear as dynamic boundary conditions for the transport processes in the electrolyte, and connecting leads. We show how the theory of non-equilibrium thermodynamics can be used to find a consistent thermodynamic model. The fuel cell is taken as example, and we show a simultaneous set of cell profiles for electric potential, concentration, temperature, entropy production and simultaneous heat fluxes out of the cell on both sides. The heat flux through the cell is illustrated in Fig.1. The figure shows how the heat flux varies through the membrane-electrode assembly for various current densities, 500, 2500 and 5000 A.m-2. The electrode regions are indicated as finite slabs. The external temperature is kept constant at 340 K. Heat is leaving the cell on both sides, slightly more on the anode side that the cathode side. One advantage of this formulation is the insight provided by the link from molecular mechanisms, via coupling coefficients for heat, mass and charge transport, to the integrated overall performance. The importance of the boundary conditions for the results will be demonstrated in the talk, in particular the effect of changing the boundary temperature. We conclude that the formulation gives a good base for cell performance optimization [3,4]. Acknowledgement The authors are grateful to the Research Council of Norway through its Center of Excellence funding scheme, PoreLab project no. 262644. References Signe Kjelstrup and Dick Bedeaux, Nonequilibrium thermodynamics of heterogeneous systems, World Scientific, Singapore, 2008, Chapter 19Signe Kjelstrup, Dick Bedeaux, Alex Hansen, Bjørn Hafskjold, Olav Galteland, Non-isothermal transport of multi-phase fluids in porous media. The entropy production. Frontiers in Physics 6 (2018) 126S. Kjelstrup, M-O Coppens, J. G. Pharoah and P. Pfeifer, Nature-Inspired Energy- and Material- Efficient Design of a Polymer Electrolyte Membrane Fuel Cell, Energy & Fuels, 24 (2010) 5097-5108A. Zlotorowicz, Kaushik. Jayasayeed, P.I. Dahl, M. S. Thomassen and S. Kjelstrup, Tailored Porosities of the Cathode Layer for Improved Polymer Electrolyte Fuel Cells, J. Power Sources, 287 (2015) 472-477 Fig. 1. The heat flux through the polymer electrolyte fuel cell at various current densities (in A.m-2) 500 (unbroken line), 2500(dotted curve) and 5000 (dashed curve). The membrane is sandwiched between electrode layers at positions around 0.2 and 0.3 mm. We see a discontinuity in the heat flux at the electrode interfaces due to the reaction. The temperatures at both end points are here the same, 340 K. Figure 1

Corrigendum: Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations

Corrigendum: Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations

Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations

We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.

Non-isothermal Transport of Multi-phase Fluids in Porous Media. The Entropy Production

We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.

Estimation of relative permeability curves using an improved Levenberg-Marquardt method with simultaneous perturbation Jacobian approximation

Relative permeability controls the flow of multiphase fluids in porous media. The estimation of relative permeability is generally solved by Levenberg-Marquardt method with finite difference Jacobian approximation (LM-FD). However, the method can hardly be used in large-scale reservoirs because of unbearably huge computational cost. To eliminate this problem, the paper introduces the idea of simultaneous perturbation to simplify the generation of the Jacobian matrix needed in the Levenberg-Marquardt procedure and denotes the improved method as LM-SP. It is verified by numerical experiments and then applied to laboratory experiments and a real commercial oilfield. Numerical experiment indicates that LM-SP uses only 16.1% computational cost to obtain similar estimation of relative permeability and prediction of production performance compared with LM-FD. Laboratory experiment also shows the LM-SP has a 60.4% decrease in simulation cost while a 68.5% increase in estimation accuracy compared with the earlier published results. This is mainly because LM-FD needs 2n (n is the number of controlling knots) simulations to approximate Jacobian in each iteration, while only 2 simulations are enough in basic LM-SP. The convergence rate and estimation accuracy of LM-SP can be improved by averaging several simultaneous perturbation Jacobian approximations but the computational cost of each iteration may be increased. Considering the estimation accuracy and computational cost, averaging two Jacobian approximations is recommended in this paper. As the number of unknown controlling knots increases from 7 to 15, the saved simulation runs by LM-SP than LM-FD increases from 114 to 1164. This indicates LM-SP is more suitable than LM-FD for multivariate problems. Field application further proves the applicability of LM-SP on large real field as well as small laboratory problems.

Distribution of multiphase fluids in porous media: Comparison between lattice Boltzmann modeling and micro-x-ray tomography

A parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales.

Invasion percolation of single component, multiphase fluids with lattice Boltzmann models

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elements on a lattice. In reality, fluid interfaces and connectivity in porous media are naturally controlled by the details of the pore geometry, its dynamic interaction with the fluid, and the ambient fluid potential. The multiphase LBM approach admits realistic pore geometry derived from imaging techniques and incorporation of realistic hydrodynamics into invasion percolation models.

Critical Fluids in Porous Media

The behavior of fluids confined in porous materials has been of interest to engineers and scientists for many decades. Among the applications driving this research are the use of porous membranes to achieve liquid-liquid separations and to deionize water, the use of porous materials as beds for catalysis, and the need to extract liquids (especially oil and water) from such media. Many of these applications depend on transport, which is governed by flow or diffusion in the imbibed fluids. Both the flow and diffusion of multiphase fluids in porous media, however, strongly depend on the morphology of phase-separated domains, and on the kinetics of domain growth. Thus, it is worthwhile to study the behavior of multiphase fluids in porous media in the absence of flow. Recently, much attention has focused on even simpler systems that still capture these essential features, namely, near-critical binary liquid mixtures and vapor-liquid systems in model porous media, such as Vycor and dilute silica gels. Although near-critical fluids may seem rather artificial as models for multiphase liquids, there are several advantages associated with them. In general, domain morphology and growth kinetics are governed primarily by competition between interfacial tension and the preferential attraction of one phase to the surface of the medium. In near-critical fluids, the relative strength of these two energy scales is sensitive to temperature, and can therefore be altered in a controlled fashion. In addition, the kinetics of domain growth are sensitive to the temperature quench depth, and can be controlled.

Thermodynamics of multiphase fluids in porous media

The basic thermodynamics of multiphase fluids in porous media is formulated, starting from equations originally derived by Laplace, Gauss, Young, and Kelvin. Special attention is paid to the conditions of hydrostatic (Laplace) equilibrium and diffusional (Kelvin) equilibrium, and to the stability of the equilibrium states with respect to displacements arising from flow or condensation/evaporation processes. Detailed discussion is given of capillary condensation in both uniform and nonuniform capillaries, for the case of zero and finite contact angles, and for both one and two liquid components. Immiscible displacement is considered briefly.