Phase Saturation Control on Mixing-Driven Reactions in 3D Porous Media

In this work we aim to develop a theoretical framework for evaluating the feasibility of attaining significant improvement of fuel cells performance and stability by enhancing the transport processes in porous partially-fluid-filled cathode compartments through applying acoustic and structural excitations. A generic unified model has been derived of the structural/acoustic wave propagation in the porous media with consideration of its coupling with mass transfer. It has been demonstrated that the phase saturation has a strong impact on the wave dynamics in porous media. Explicit expressions have been obtained for the generalized multiphase Biot-type coefficients. A generalized filtration equation has been derived that takes into account the effects on mass transfer of dynamic loading, varying saturation, and solid structure distortion in this complex system. For model calibration a series of tests has been conducted to measure water flows through porous media with and without acoustic excitations. It has been demonstrated that the excitations may result in a net change of the saturation inside the porous medium and the applied structural/acoustic loading can intensify the transportation process. Based on the numerical and experimental results, certain recommendations have been made in regards to the selection of materials and the optimization of performance regime.

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Scaling of Transport Properties of Reservoir Material at Low Saturations of a Wetting Phase

MRS Proceedings ◽

10.1557/proc-367-255 ◽

1994 ◽

Vol 367 ◽

Cited By ~ 1

Author(s):

Y. Carolina Araujo ◽

Pedro G. Toledo ◽

Hada Y. Gonzalez

Keyword(s):

Electrical Conductivity ◽

Porous Media ◽

Transport Properties ◽

Capillary Pressure ◽

Power Law ◽

Scaling Laws ◽

Pore Space ◽

Conductivity Data ◽

Phase Saturation ◽

Electrical Conductivity Data

AbstractTransport properties of natural porous media have been observed to obey scaling laws in the wetting phase saturation. Previous work relates power-law behavior at low wetting phase saturations, i.e., at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of porous media. Here, we present recent combined porousplate capillary pressure and electrical conductivity data of Berea sandstone at low saturations that lend support to the scaling laws. Power law is interpreted in terms of the exponent m in the relation of surface forces and film thickness and the fractal dimension D of the interface between pore space and solid matrix. Simple determination of D from capillary pressure and m from electrical conductivity data can be used to rapidly determine wetting phase relative permeability and capillary dispersion coefficient at low wetting phase saturations.

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Wettability Effects on Capillary Pressure, Relative Permeability, and Irredcucible Saturation Using Porous Plate

Journal of Petroleum Engineering ◽

10.1155/2014/465418 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Olugbenga Falode ◽

Edo Manuel

Keyword(s):

Porous Media ◽

Capillary Pressure ◽

Relative Permeability ◽

Water Saturation ◽

Porous Plate ◽

Reservoir Rock ◽

Flow In Porous Media ◽

Wettability Alteration ◽

Initial Water ◽

Phase Saturation

An understanding of the mechanisms by which oil is displaced from porous media requires the knowledge of the role of wettability and capillary forces in the displacement process. The determination of representative capillary pressure (Pc) data and wettability index of a reservoir rock is needed for the prediction of the fluids distribution in the reservoir: the initial water saturation and the volume of reserves. This study shows how wettability alteration of an initially water-wet reservoir rock to oil-wet affects the properties that govern multiphase flow in porous media, that is, capillary pressure, relative permeability, and irreducible saturation. Initial water-wet reservoir core samples with porosities ranging from 23 to 33%, absolute air permeability of 50 to 233 md, and initial brine saturation of 63 to 87% were first tested as water-wet samples under air-brine system. This yielded irreducible wetting phase saturation of 19 to 21%. The samples were later tested after modifying their wettability to oil-wet using a surfactant obtained from glycerophtalic paint; and the results yielded irreducible wetting phase saturation of 25 to 34%. From the results of these experiments, changing the wettability of the samples to oil-wet improved the recovery of the wetting phase.

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A parallel second-order adaptive mesh algorithm for incompressible flow in porous media

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0160 ◽

2009 ◽

Vol 367 (1907) ◽

pp. 4633-4654 ◽

Cited By ~ 17

Author(s):

George S. H. Pau ◽

Ann S. Almgren ◽

John B. Bell ◽

Michael J. Lijewski

Keyword(s):

Porous Media ◽

Incompressible Flow ◽

Second Order ◽

Flow In Porous Media ◽

Recursive Procedure ◽

Phase Form ◽

Phase Saturation ◽

Multi Phase ◽

Coarse Grids ◽

Total Velocity

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy’s law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm’s accuracy and convergence properties and to illustrate the behaviour of the method.

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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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Complex Electrical Resistivity and Dielectric Permittivity Responses to Dense Non-aqueous Phase Liquids' Imbibition and Drainage in Porous Media: A Laboratory Study

Journal of Environmental and Engineering Geophysics ◽

10.32389/jeeg20-050 ◽

2020 ◽

Vol 25 (4) ◽

pp. 557-567

Author(s):

Mohammad Ali Iravani ◽

Jacques Deparis ◽

Hossein Davarzani ◽

Stéfan Colombano ◽

Roger Guérin ◽

...

Keyword(s):

Porous Medium ◽

Porous Media ◽

Electrical Resistivity ◽

Dielectric Permittivity ◽

Aqueous Phase ◽

Relative Permittivity ◽

Time Domain Reflectometry ◽

High Resistivity ◽

Complex Resistivity ◽

Phase Saturation

The effective techniques for remediation of sites polluted by dense non-aqueous phase liquids (DNAPLs) remains a challenge. Among the various technical monitoring methods, there is an increasing interest in studying the geophysical characteristics of contaminated soils, as indicators of the progress in clean-up programs. This work sought to investigate the variation of the electrical complex resistivity and the relative permittivity by analyzing the results obtained from spectral induced polarization (SIP) and time domain reflectometry (TDR). Different series of measurements during drainage and imbibition of DNAPLs in porous media were done to validate the clean-up process on sites polluted by DNAPLs. Therefore, a methodology based on laboratory work was designed and carried out to study the electrical complex resistivity (both in magnitude and phase) in the frequency range 0.183 Hz to 20 kHz, and the relative dielectric permittivity at 70 MHz. The experiments were done on small 1D cells. In these cells, glass beads were used as a porous medium. Two different fluid couples, i.e., coal tar (CT)/water and canola oil (CO)/salty ethanol (SE), were used to produce two-phase flow. Our findings highlight that due to the high resistivity of CO and CT, an increase in water saturation led to decrease in amplitude and phase. Saturation change of SE had the same effect on resistivity but no relationship was found for phase and saturation for the mixture CO and SE. It is also showed that the complex resistivity and relative permittivity measurements were compatible with generalized Archie's law and complete complex refractive index method (CRIM) model as two empirical models for defining the correlation between the electrical resistivity, relative permittivity, and saturation of each phase in the multiphase porous medium.

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Microscopic Imbibition Characterization of Sandstone Reservoirs and Theoretical Model Optimization

10.21203/rs.3.rs-200028/v1 ◽

2021 ◽

Author(s):

Xuan Xu ◽

Yujing Wan ◽

Xizhe Li ◽

yong Hu ◽

qingyan mei ◽

...

Keyword(s):

Porous Media ◽

Transition Zone ◽

Oil And Gas ◽

Large Deviation ◽

Water Saturation ◽

Experimental Studies ◽

Theoretical Models ◽

Gas Reservoirs ◽

Phase Saturation ◽

Oil And Gas Reservoirs

Abstract Traditional porous media imbibition models deviate from the actual imbibition process in oil and gas reservoirs. Experimental studies on gas-water imbibition in reservoirs were carried out to describe the dynamic profile variation process of wet phase saturation in reservoirs and to further reveal the variation of the imbibition front and the imbibition amount. Optimization and correction methods were established, and experimental verifications were performed. Studies have shown the following: (1) Unlike homogeneous porous media, the water phase imbibition process in oil and gas reservoirs is more complicated, and it is impossible for the maximum saturation of imbibition to reach 100%. (2) Contrary to the theoretical hypothesis, the imbibition of water is not piston-like, and there is a clear transition zone at the imbibition front. This transition zone is the main cause of water saturation variations in the imbibition zone; with the expansion of the imbibition zone, the influence of the transition zone on water saturation weakens. (3) Traditional theoretical models predict a positive correlation between the imbibition amount and the measurements; however, there is a large deviation in the numerical values, which must be corrected. (4) The L-W model was optimized and the parameter group fluid factor and the reservoir factor were proposed to characterize the properties of the fluid and the reservoir, respectively. These two parameters have a clear physical significance and are easy to accurately test. After experimental correction, the parameters are favourably suitable for oil and gas reservoirs.

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Evaluation of Scale-Up Laws for Two-Phase Flow Through Porous Media

Society of Petroleum Engineers Journal ◽

10.2118/494-pa ◽

1963 ◽

Vol 3 (02) ◽

pp. 164-176 ◽

Cited By ~ 5

Author(s):

Russell L. Nielsen ◽

M.R. Tek

Keyword(s):

Porous Media ◽

Capillary Pressure ◽

Relative Permeability ◽

Scaling Laws ◽

Laboratory Model ◽

Gas Reservoir ◽

Two Phase ◽

Phase Saturation ◽

Water Coning ◽

Capillary Pressure Curves

The scaling laws as formulated by Rapport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions.Two hypothetical systems - a gas reservoir subject to water drive and the laboratory scaled model of that reservoir - were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these particular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system.This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. Introduction Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models.To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoport and others. Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems.It will be recalled that these scaling laws presuppose three conditions:the relative permeability curves must be identical for the model and prototype;the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; andboundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because:The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media.The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent.Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible.The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible.The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. SPEJ P. 164^

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