Immiscible Fluids In Porous Media Research Articles

Degenerate two-phase incompressible flow V: characteristic finite element methods

This is the fifth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we study a finite element procedure for numerically solving this system. This procedure uses a mixed finite element method for the elliptic equation of the pressure and velocity and the modified method of characteristics for the degenerate parabolic equation of the saturation. Sharp error estimates in energy norms are obtained for this procedure. The error analysis does not use any regularization of the saturation equation and does not impose any restriction on the nature of degeneracy; these error estimates are derived directly from this degenerate saturation equation. Other characteristic finite element methods such as the modified method of characteristics with adjusted advection (MMOCAA) are also considered.

Non‐Darcy displacement of immiscible fluids in porous media

This paper presents a Buckley‐Leverett analytical solution for non‐Darcy displacement of two immiscible fluids in porous media. The multiphase non‐Darcy displacement is described using a Forchheimer equation or other non‐Darcy flow correlations under multiphase flow conditions. The analytical solution is used to obtain some insight into the physics of displacement involving non‐Darcy flow effects in porous media. The solution reveals how non‐Darcy displacement is controlled not only by relative permeability curves but also by non‐Darcy flow coefficients as well as injection or flow rates. This analytical solution is then applied to verify a numerical simulator for modeling multiphase non‐Darcy flow.

Degenerate two-phase incompressible flow

This is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we consider a finite element approximation for this system. The elliptic equation for the pressure and velocity is approximated by a mixed finite element method, while the degenerate parabolic equation for the saturation is approximated by a Galerkin finite element method. A fully discrete approximation is analyzed. Sharp error estimates in energy norms are obtained for this approximation. The error analysis does not use any regularization of the saturation equation; the error estimates are derived directly from the degenerate equation. Also, the analysis does not impose any restriction on the nature of degeneracy. Finally, it respects the minimal regularity on the solution of the differential system.

A stochastic analysis of the flow of two immiscible fluids in porous media: The case when the viscosities of the fluids are equal

A new stochastic theory is developed to explain the flow of two immiscible fluids in porous medium when the viscosity difference between two fluids is zero. In an individual micropore the radius of curvature of the interface separating the fluids is assumed constant and flow is modeled by the random jumping of microscopic interfaces. A one dimensional model composed of an array of parallel capillary tubes of constant radius is analyzed in detail. For the case in which two fluids have equal viscosity an analytical solution is obtained. The fluid displacement process is Fickian and dispersion is described in terms of a diffusion or spreading constant.

Experimental studies on the flow of two immiscible fluids in porous media using X-ray computed tomography: The case when the viscosities of the fluids are equal

Experiments were carried out to demonstrate the dispersion that occurs at the interface between fluids when two immiscible fluids flow in porous structures. In this work the porous medium was cellulosic absorbent and the fluids, decyl alcohol and water, were modified so as to cover a range of flow rates and identical fluid viscosities. Computerized Tomography (CT) was used to generate dynamic three-dimensional images of two-phase saturations and provided quantitative information of time evolution of fluid saturation at each position. Thus, use of CT made characterization of two-phase displacement history in cellulosic porous media possible. This work could relate experimental fluid saturation to theoretical model of immiscible fluids flow.

A New Approach for Obtaining J-Function in Clean and Shaly Reservoir Using In Situ Measurements

Abstract Leverett's capillary J-function has been widely used in the petroleum industry as an effective tool for correlating capillary pressure data with rock properties. The major goals of this study are: (1) to investigate the effect of stress on the calculated values of J-function, and (2) to develop new models capable of obtaining the J-function using in situ measurements in clean and shaly heterogeneous reservoirs. Two models are developed, in which well-logging data, a good source of in situ measurements, are used to calculate the Jfunction. The first model was obtained using Tixier's permeability equation and Archie's equation for water saturation. The second model was derived using Tixier's permeability equation in combination with the Schlumberger shale model for water saturation determination. These models were validated using actual field data from two reservoirs in Oklahoma and Louisiana. Introduction Leverett's capillary pressure J-function has been widely used in the petroleum industry as an effective tool for correlating capillary pressure data with rock properties. Capillary pressure data is a very useful tool, since it reflects the pore size distribution, the radius of the largest pore, the rock wettability, and the interfacial tension of fluids in the system. Leverett(1) developed the basic theory for the behaviour of the flow of fluid mixtures in reservoir rocks. He used well established thermodynamic and physical principles in the development of his theory. He divided the problems into two groups:Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids (gravitational forces), andDynamic problems, involving analysis of the flow of immiscible fluids in porous media under the effect of gravity, capillary, and external differential pressure forces. The J-function is a very useful tool for correlating capillary pressure data and rock properties. Hence, it is an effective tool for the better description of reservoir rock and the behaviour of the capillary retention of the wetting fluid. The Concept of J-Function Leverett conducted several experiments using unconsolidated clean and clayey sands for the development of a dimensionless group called the "Leverett J-function." He used the J-function to correlate capillary pressure (PC), interfacial tension (σ), in addition to permeability (K) and porosity (φ) of the porous rock. He found, from the results of his experiments, that a dimensionless group of the form [PC / σ* √ (K/ φ)] vs. water saturation (SW) gives two satisfactory but closed curves, one for imbibition of water and the other for drainage. Leverett's data showed that a plot of this dimensionless group vs. the wetting-phase saturation (SW) yielded a unique curve describing the capillary retention of the wetting liquid existing in the clean, unconsolidated sands, when capillary forces were at equilibrium, as shown in Figure 1. Later, Leverett et al.(2) proved theoretically, using the dimensionless analysis technique, that capillary pressure is proportional to the interfacial tension, to the radical v(K/ φ), and to the dimensionless function of the water saturation J(SW).

Degenerate Two-Phase Incompressible Flow: I. Existence, Uniqueness and Regularity of a Weak Solution

This is the first paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we first show that this system possesses a weak solution under physically reasonable hypotheses on the data. Then we prove that this weak solution is unique. Finally, we establish regularity on the weak solution which is needed in the uniqueness proof. In particular, the Hölder continuity of the saturation in space and time and the Lipschitz continuity of the pressure in space are obtained.

Determining effective interfacial tension and predicting finger spacing for DNAPL penetration into water-saturated porous media

The difficulty in determining the effective interfacial tension limits the prediction of the wavelength of fingering of immiscible fluids in porous media. A method to estimate the effective interfacial tension using fractal concepts was presented by Chang et al. [Water Resour. Res. 30 (1994) 125]. We modified the method in that the macroscopic interface length was used instead of the system width. Methods to determine the macroscopic and the microscopic interface length are given. Lab experiments of dense nonaqueous phase liquid (DNAPL) penetrating into water-saturated glass beads were carried out in a two-dimensional (2-D) transparent chamber. The displacement processes were recorded using a 35-mm camera or a video camera, which was directly connected to and controlled by a computer. Unlike the method of Chang et al. (1994), the modified method used here gives a constant value of the effective interfacial tension over time. The predicted wavelengths of fingering are relatively close to those observed except for the fine beads.

Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media

The behavior of two-dimensional binary and ternary amphiphilic fluids under flow conditions is investigated using a hydrodynamic lattice-gas model. After the validation of the model in simple cases (Poiseuille flow, Darcy's law for single component fluids), attention is focused on the properties of binary immiscible fluids in porous media. An extension of Darcy's law which explicitly admits a viscous coupling between the fluids is verified, and evidence of capillary effects is described. The influence of a third component, namely, surfactant, is studied in the same context. Invasion simulations have also been performed. The effect of the applied force on the invasion process is reported. As the forcing level increases, the invasion process becomes faster and the residual oil saturation decreases. The introduction of surfactant in the invading phase during imbibition produces new phenomena, including emulsification and micellization. At very low fluid forcing levels, this leads to the production of a low-resistance gel, which then slows down the progress of the invading fluid. At long times (beyond the water percolation threshold), the concentration of remaining oil within the porous medium is lowered by the action of surfactant, thus enhancing oil recovery. On the other hand, the introduction of surfactant in the invading phase during drainage simulations slows down the invasion process-the invading fluid takes a more tortuous path to invade the porous medium-and reduces the oil recovery (the residual oil saturation increases).

Concentration profiles of reactant in a viscous finger formed during the interfacially reactive immiscible displacements in porous media

A simple unsteady-state convective-diffusion model was employed to simulate reactant concentration profiles in a viscous finger, which is created during interfacially reactive displacement of two immiscible fluids in porous media. A two-dimensional system was considered. It was assumed that the finger grew in one direction at a constant flow rate and that a fast chemical reaction was taking place at the oil–water interface layer. Interaction with reservoir rock was also taken into account. Two types of convective flow were studied: steady-state laminar flow with a parabolic velocity profile and plug flow with a flat velocity profile. The numerical method of lines was used to solve the model equation. A significant decrease of reactant concentration in the water phase, especially in the fingertip area was observed. This can cause important changes in interfacial behavior and influence the efficiency of fluid displacement. The model numerically confirmed previous visual observations of displacing patterns during the displacement of acidified oil by alkaline solutions.

The spreading of immiscible fluids in porous media under the influence of gravity.

We use an approach based on invasion percolation in a gradient (IPG) to describe the displacement patterns that develop when a fluid spreads on an impermeable boundary in a porous medium under the influence of gravity (buoyancy) forces in a drainage process. The approach is intended to simulate applications, such as the spreading of a DNAPL in the saturated zone and of a NAPL in the vadose zone on top of an impermeable layer, or the classical problems of gravity underruning and gravity override in reservoir engineering. As gravity acts in a direction transverse to the main displacement direction, a novel form of IPG develops. We study numerically the resulting patterns for a combination of transverse and parallel Bond numbers and interpret the results using the concepts of gradient percolation. A physical interpretation in terms of the capillary number, the viscosity ratio and the gravity Bond number is also provided. In particular, we consider the scaling of the thickness of the spreading gravity ‘tongue’, for the cases of gravity‐dominated and viscous‐unstable displacements, and of the propagating front in the case of stabilized displacement at relatively high rates. It is found that the patterns have percolation (namely fractal‐like) characteristics, which cannot be captured by conventional continuum equations. These characteristics will affect, for example, mass transfer and must be considered in the design of remediation processes.

On a method of calculation of the first phase saturation during the process of displacement of oil by water from porous media

A method for calculation of the first phase saturation in the process of joint filtration of incompressible, immiscible fluids in porous media is suggested in this paper. The method suggested also enables to find the position of the front, which is formed inside the initial continuous flux. Some components of exploration of a homogeneous layer have been calculated end on a basis of the method suggested.

Measurement of Specific Fluid−Fluid Interfacial Areas of Immiscible Fluids in Porous Media

ADVERTISEMENT RETURN TO ISSUEPREVCommunicationNEXTMeasurement of Specific Fluid−Fluid Interfacial Areas of Immiscible Fluids in Porous MediaK. Prasad Saripalli, Heonki Kim, P. Suresh C. Rao, and Michael D. AnnableView Author Information Inter-Disciplinary Program in Hydrologic Science, Department of Environmental Engineering Science and Department of Soil and Water Science, University of Florida, Gainesville, Florida 32611-0290 Cite this: Environ. Sci. Technol. 1997, 31, 3, 932–936Publication Date (Web):February 27, 1997Publication History Received26 July 1996Accepted5 December 1996Revised4 December 1996Published online27 February 1997Published inissue 1 March 1997https://doi.org/10.1021/es960652gCopyright © 1997 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views595Altmetric-Citations91LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (156 KB) Get e-AlertsSUBJECTS:Adsorption,Amorphous materials,Fluids,Interfaces,Surfactants Get e-Alerts

Pore-Scale Prototypes of Multiphase Flow in Porous Media

Understanding the motion of immiscible fluids in porous media is a challenging problem in low-Reynolds-number hydrodynamics that is relevant to many processes of technological and biological interest. Simple representations of the flow on the scale of individual pores or channels have proven useful in exposing effects of various parameters on fluid motion and in identifying flow-induced changes in the spatial configurations of the fluids, which can affect the mobilities of the phases. This paper examines a hierarchy of such prototype flows, paying special attention to phenomena that cannot be described completely by the equations of motion, such as flow-induced breakup and coalescence of fluid phases. In these cases, connections between numerical computations and experiments are especially significant, which is apparent in the studies reviewed here.

Pore scale spatial analysis of two immiscible fluids in porous media

A conceptual model is introduced describing the spatial distribution of two immiscible fluids in the pore space of sphere packings. The model is based on the ideal soil concept of homogeneous arrangement of identical spheres but is generalized to include random packing. It quantitatively analyzes the interfacial area between wetting and nonwetting fluids and between the fluids and the solid spheres, as a function of the saturation degree. These relationships depend on the packing arrangement of the spheres, the sphere radius, and the fluid‐solid contact angle. The model focuses on the region of low saturation of the wetting phase, where the wetting phase is comprised of pendular rings. When the nonwetting phase appears as ganglia, the model assumes single‐chamber ganglia. Three‐dimensional graphical illustrations are provided. Three potential applications are pointed out: (1) to quantify the water‐air interface in the unsaturated zone; (2) to analyze connate water interfacial area in petroleum reservoirs and to assess the effect of surfactants during enhanced oil recovery; and (3) to estimate the interface between groundwater and floating nonaqueous phase liquids above the water table.

The statistical properties of immiscible fluid displacement in bond/site correlated network models of porous media

A statistical formulation is introduced which allows the determination of capillary pressure and relative permeability curves from lattice properties and, by extension, possibly core properties. Comparisons of statistical results to simulation results generally show good agreement for both drainage and imbibition. These processes turn out to be two different formulations of a single problem in one view presented here. Both agreement and disagreement between statistics and simulation results provide insight into the characteristics of the flow of immiscible fluids in porous media. A considerable amount of topological information on the fluids is also obtainable by these methods.

Liquids in porous media

The basic mechanisms which take place during the displacement of immiscible fluids in porous media have been observed in micromodels and have been modelled. At the pore level, in drainage, the invading fluid chooses the largest throat. In imbibition, the displacement depends on the local geometry. For a large pore-to-throat ratio (aspect ratio), the main mechanism is the collapse of the invading fluid in the smallest channel, without entering the pore. For a small aspect ratio, the wetting fluid invades the pore first, and then the adjacent channels. From observations at the pore level, the author has modelled the displacement on a large scale in some extreme cases by using statistical theories. The different behaviours are then displayed as domains in three phase diagrams: one for drainage and two for imbibition (large and small aspect ratios). At a high rate, when viscous forces are dominant, all the diagrams show a stable domain (described by anti-DLA) and a viscous fingering domain (DLA). In drainage, low capillary numbers lead to capillary fingering represented by invasion percolation. In imbibition, the capillary domain is described either by a compact cluster growth (small aspect ratio) or percolation theory (large aspect ratio). In addition the possibility of flow by film along the roughness of the walls leads to disconnected structures.

Data interpretation problems to be expected in the study of coupled fluid flow in porous media

On the basis of recent work, it would appear that the transport coefficients descriptive of certain idealized cases of coupled flow of immiscible fluids in porous media, can be determined in principle by calculations employing well-defined experimental data. Other considerations show, however, that even small errors inherent in laboratory observations sometimes will have an enormously large effect on the accuracy of the calculated values. On the other hand, it often will be the case that values for the transport coefficients are not needed individually, as long as those particular functions which appear lumped together in the equations of motion, can be calculated from the same data but with less error. In any case, it will be clear that error problems will be, to some extent, mitigated when very accurate instrumentation is available to control and measure the fluxes and driving forces that give rise to the transport processes under study. Thus, the aim of this paper is to present an error analysis that will facilitate laboratory design in preparation for experimental work, and will also facilitate the interpretation of the data that eventually are to be obtained. Another aim is to underscore the risks taken by those who fail to take coupling effects into account just because the potential importance of them is not appreciated or not clearly revealed by existing data.

The study of displacement of immiscible fluids in porous media with constant pressure drop by means of nuclear tracers

A laboratory technique based on the use of nuclear tracers has been developed for studying the displacement of immiscible fluids in a porous medium. Water tagget with 131 I is injected in a porous medium initially filled with kerosene (a non wetting fluid for the medium). The saturation profiles are obtained by recording the nuclear activity as a function of position and time. The technique is aplied to first and second inhibition separated by a phase of drainage. The porous media are non consolidated packings of microspheres and Berea sandstones. Similar results are obtained in both cases. The results are compared with theorical models. We present a simple analysis emphasizing the dominant role of capillary effects in the slow invasion experiments performed by us under a constant pressure head Nous presentons des mesures de deplacement de fluides immiscibles dans les milieux poreux realisees a l'aide de traceurs radioactifs. Nous avons injecte de l'eau marquee avec 131 I dans ce milieu, d'abord rempli de kerosene (qui est ici le fluide le moins mouillant pour le poreux). On obtient les profils de saturation en mesurant la variation de l'activite nucleaire en fonction du temps et de la distance suivant l'ecoulement. Nous avons applique cette technique a une premiere et a une seconde inhibition separees par une phase de drainage

Measuring transport coefficients necessary for the description of coupled two-phase flow of immiscible fluids in porous media

In the simplist cases of coupled two-phase flow of immiscible fluids in porous media, the governing equations usually are written to show that there are four independent transport coefficients that implicitly have to be separately measured. The analysis presented here accordingly indicates that two types of known experiments involving two measurements apiece are needed at each fluid saturation condition in order to provide the necessary and sufficient information by which the unsteady as well as the steady states of ensuing transport processes can be established and characterized. Apparently, however, the fact that methodologies are already available for the required laboratory work either is not widely appreciated or it is being overlooked. For this reason and others, mention is made of the surprising fact that the experimental difficulties to be confronted in the actual study of coupled transport processes are no greater than those that have already been dealt with by the advocates of classical relative permeability theory (i.e. the traditionalists who simplistically model two-phase flow as though no coupling effects are involved).