A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

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A mathematical model for drug release from a two-phase system to a perfect sink

International Journal of Pharmaceutics ◽

10.1016/0378-5173(85)90200-5 ◽

1985 ◽

Vol 26 (1-2) ◽

pp. 57-76 ◽

Cited By ~ 9

Author(s):

H BODDE ◽

J JOOSTEN

Keyword(s):

Mathematical Model ◽

Drug Release ◽

Phase System ◽

Two Phase

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Enhanced Oil Recovery: Chemical Flooding

Geophysics and Ocean Waves Studies ◽

10.5772/intechopen.90335 ◽

2021 ◽

Author(s):

Ahmed Ragab ◽

Eman M. Mansour

Keyword(s):

Interfacial Tension ◽

Enhanced Oil Recovery ◽

Oil Recovery ◽

Recovery Phase ◽

Mobility Ratio ◽

Chemical Flooding ◽

Sweep Efficiency ◽

Oil Displacement ◽

Remaining Oil ◽

Oil Displacement Efficiency

The enhanced oil recovery phase of oil reservoirs production usually comes after the water/gas injection (secondary recovery) phase. The main objective of EOR application is to mobilize the remaining oil through enhancing the oil displacement and volumetric sweep efficiency. The oil displacement efficiency enhances by reducing the oil viscosity and/or by reducing the interfacial tension, while the volumetric sweep efficiency improves by developing a favorable mobility ratio between the displacing fluid and the remaining oil. It is important to identify remaining oil and the production mechanisms that are necessary to improve oil recovery prior to implementing an EOR phase. Chemical enhanced oil recovery is one of the major EOR methods that reduces the residual oil saturation by lowering water-oil interfacial tension (surfactant/alkaline) and increases the volumetric sweep efficiency by reducing the water-oil mobility ratio (polymer). In this chapter, the basic mechanisms of different chemical methods have been discussed including the interactions of different chemicals with the reservoir rocks and fluids. In addition, an up-to-date status of chemical flooding at the laboratory scale, pilot projects and field applications have been reported.

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Formulation of a General Multiphase, Multicomponent Chemical Flood Model

Society of Petroleum Engineers Journal ◽

10.2118/6727-pa ◽

1981 ◽

Vol 21 (01) ◽

pp. 63-76 ◽

Cited By ~ 15

Author(s):

Paul D. Fleming ◽

Charles P. Thomas ◽

William K. Winter

Keyword(s):

Phase Equilibrium ◽

Arbitrary Number ◽

Numerical Solutions ◽

Field Tests ◽

Reservoir Rock ◽

Phase System ◽

Surfactant Flooding ◽

Two Phase ◽

Special Cases ◽

Flood Model

Abstract A general multiphase, multicomponent chemical flood model has been formulated. The set of mass conservation laws for each component in an isothermal system is closed by assuming local thermodynamic (phase) equilibrium, Darcy's law for multiphase flow through porous media, and Fick's law of diffusion. For the special case of binary, two-phase flow of nonmixing incompressible fluids, the equations reduce to those of Buckley and Leverett. The Buckley-Leverett equations also may be obtained for significant fractions of both components in the phases if the two phases are sufficiently incompressible. To illustrate the usefulness of the approach, a simple chemical flood model for a ternary, two-phase system is obtained which can be applied to surfactant flooding, polymer flooding, caustic flooding, etc. Introduction Field tests of various forms of surfactant flooding currently are under way or planned at a number of locations throughout the country.1 The chemical systems used have become quite complicated, often containing up to six components (water, oil, surfactant, alcohol, salt, and polymer). The interactions of these components with each other and with the reservoir rock and fluids are complex and have been the subject of many laboratory investigations.2–22 To aid in organizing and understanding laboratory work, as well as providing a means of extrapolating laboratory results to field situations, a mathematical description of the process is needed. Although it seems certain that mathematical simulations of such processes are being performed, models aimed specifically at the process have been reported only recently in the literature.23–31 It is likely that many such simulations are being performed on variants of immiscible, miscible, and compositional models that do not account for all the facets of a micellar/polymer process. To help put the many factors of such a process in proper perspective, a generalized model has been formulated incorporating an arbitrary number of components and an arbitrary number of phases. The development assumes isothermal conditions and local phase equilibrium. Darcy's law32,33 is assumed to apply to the flow of separate phases, and Fick's law34 of diffusion is applied to components within a phase. The general development also provides for mass transfer of all components between phases, the adsorption of components by the porous medium, compressibility, gravity segregation effects, and pressure differences between phases. With the proper simplifying assumptions, the general model is shown to degenerate into more familiar special cases. Numerical solutions of special cases of interest are presented elsewhere.35

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Oil emulsion characteristics as significance in efficiency forecast of oil-displacing formulations based on surfactants

Oil and Gas Studies ◽

10.31660/0445-0108-2021-3-91-107 ◽

2021 ◽

pp. 91-107

Author(s):

E. A. Turnaeva ◽

E. A. Sidorovskaya ◽

D. S. Adakhovskij ◽

E. V. Kikireva ◽

N. Yu. Tret'yakov ◽

...

Keyword(s):

Oil Recovery ◽

Surfactant Concentration ◽

Chemical Flooding ◽

Optimal Salinity ◽

Oil Emulsion ◽

Oil Displacement ◽

Laboratory Selection ◽

Reservoir Conditions ◽

Selection Of ◽

Comprehensive Study

Enhanced oil recovery in mature fields can be implemented using chemical flooding with the addition of surfactants using surfactant-polymer (SP) or alkaline-surfactant-polymer (ASP) flooding. Chemical flooding design is implemented taking into account reservoir conditions and composition of reservoir fluids. The surfactant in the oil-displacing formulation allows changing the rock wettability, reducing the interfacial tension, increasing the capillary number, and forming an oil emulsion, which provides a significant increase in the efficiency of oil displacement. The article is devoted with a comprehensive study of the formed emulsion phase as a stage of laboratory selection of surfactant for SP or ASP composition. In this work, the influence of aqueous phase salinity level and the surfactant concentration in the displacing solution on the characteristics of the resulting emulsion was studied. It was shown that, according to the characteristics of the emulsion, it is possible to determine the area of optimal salinity and the range of surfactant concentrations that provide increased oil displacement. The data received show the possibility of predicting the area of effectiveness of ASP and SP formulations based on the characteristics of the resulting emulsion.

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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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Mathematical model of oil displacement by water in a plane channel

Multiphase Systems ◽

10.21662/mfs2020.3.131 ◽

2020 ◽

Vol 15 (3-4) ◽

pp. 208-211

Author(s):

A.D. Nizamova ◽

Valiev A.A. Valiev

Keyword(s):

Mathematical Model ◽

Oil Recovery ◽

Stokes Equations ◽

Plane Channel ◽

Navier Stokes ◽

Practical Applications ◽

Oil Displacement ◽

Hydrodynamic Approach ◽

Wide Range ◽

Comparison Of The Results

Unstable displacement of immiscible liquids in a plane channel is a topical research in both theoretical and practical applications. In this paper, we consider a plane channel filled with an incompressible fluid. Over time, another fluid is injected into the channel. The fluids are immiscible. The paper builds a mathematical model of the process of oil displacement by water in a plane channel, which allows further numerical studies and comparison of the results with the obtained experimental data using the example of the Hele-Show cell. The mathematical model for a multiphase, multicomponent flow consists of the Navier-Stokes equations, the equations of conservation of mass, momentum and energy. Modern methods for modeling the dynamics of "viscous fingers“ are based mainly on numerical methods for solving systems of differential equations using the pressure gradient, viscosity and capillary forces as parameters. The influence of these parameters must be determined experimentally. To solve the problem, a quasi-hydrodynamic approach is used, based on the addition of a certain small parameter and allowing one to describe stable schemes with central differences. The complexity of solving such problems lies in the size of the considered models, which in practice have a wide range of applications from micro-scale to orders of one centimeter. A comprehensive study will allow us to evaluate and analyze the entire process as a whole, as well as to establish flow parameters to improve the efficiency of displacement and increase oil recovery, since in the numerical modeling of the process it is easier to create many independent experiments with the same initial data, in contrast to the experimental study.

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Linear Oil Displacement by the Emulsion Entrapment Process

Society of Petroleum Engineers Journal ◽

10.2118/11333-pa ◽

1984 ◽

Vol 24 (03) ◽

pp. 351-360 ◽

Cited By ~ 15

Author(s):

D.P. Schmidt ◽

H. Soo ◽

C.J. Radke

Keyword(s):

Oil Recovery ◽

Mobility Control ◽

Phase Flow ◽

Permeability Reduction ◽

Filtration Theory ◽

Two Phase ◽

Oil Displacement ◽

Local Permeability ◽

Emulsion Flow

Abstract Lack of mobility control is a major impediment to successful EOR, especially for high-viscosity oils. This paper presents experimental and theoretical results for continuous, linear, secondary oil displacement using dilute, stable suspensions of oil drops. The major hypothesis is that the oil/water (O/W) emulsion provides microscopic mobility control through entrapment or local permeability reduction not through viscosity-ratio improvement. To describe the displacement process, previous emulsion filtration theory is extended to longer cores and to two-phase flow. Agreement between theory and experiment is satisfactory for continuous secondary oil displacement with 1- to 2-µm [1- to 2-micron] diameter drops of volume concentrations up to 5% in unconsolidated sand packs with permeabilities ranging from 1 to 3 µm2 [1 to 3 darcies]. Dilute suspensions of stable oil drops in water also are successful in diverting flow in parallel-core flooding to the lower-permeability core; therefore, they provide macroscopic mobility control. Introduction To date, two alkaline displacement processes employing stable emulsions have been suggested to improve oil recovery.1 In one process, emulsification with entrainment, oil drops are generated in situ upon reaction of alkali with acidic crude oil. Oil production occurs as an O/W emulsion. In emulsification with entrapment, the other process, oil drops that are generated in situ, or which are externally injected, aid in oil recovery by providing mobility control. These two processes are based on opposing views of how emulsions behave in porous media. According to the entrainment view, oil drops do not interact with the reservoir medium, and recovery of tertiary oil is a possibility.1 Conversely, according to the entrapment view, oil drops interact strongly with the reservoir medium, and improvement only in secondary recovery is sought. Recent work by Soo2 on silute emulsion flow in unconsolidated porous media shows that oil drops clog in pore constrictions and on pore walls, thereby restricting flow. Once captured, there is negligible particle reentrainment. Even drops smaller than the pore throats have a significant capture probability. Soo's study supports the entrapment picture as a more viable description of emulsion flow. However, in spit of field applications of the entrapment technique,3,4 no current methodology exists to predict quantitatively possible mobility-control improvement. This paper presents a theoretical framework for calculation of secondary oil displacement in linear systems with injection of dilute, stable O/W emulsions. Although we focus mainly on microscopic mobility control with dilute emulsions, some attention is given to macroscopic flow redistribution or sweep improvement in parallel cores. The basic premise is that dilute emulsions lower the mobility of the displacing phase through local permeability reduction, not through increasing the viscosity of the displacing phase. We rely heavily on filtration theory, which is successful in describing transient emulsion flow in water-saturated cores.2 The significance of the mathematical treatment is not restricted to the emulsion entrapment technique. It is well known that certain polymers, notably polyacrylamides, establish more mobility control than can be accounted for by bulk rheology.5–11 Large permeability reductions sometimes are observed following polymer injection. Adsorption does not appear to be the main cause of this flow restriction but rather mechanical entrapment - i.e., trapping of high-molecular-weight polymer molecules or, as likely, gels in pore constrictions. Willhite and Dominguez11 recognized the analogy between polymer mechanical entrapment and deep-bed filtration of liquid or solid particulate suspensions. However, they did not explore this analogy quantitatively. Polymer, solid particulate, and emulsion droplet entrapment are directly analogous. Hence, any theory devised for one phenomenon should, in principle, be applicable to the other. Moreover, macroemulsions, as distinguished from microemulsions, sometimes form in surfactant/polymer flooding. Larson et al.12 outline how such emulsion formation might be modeled in displacement calculations. They consider the emulsified oil drops to be retarded in percolating through the porous medium. Permanent capture is not envisioned. This study focused on the filtration and mobility-control aspects of emulsified oil flow. It, therefore, provides an alternative treatment to that of Larson et al. To model EOR with dilute emulsions requires extension of the filtration theory of Soo2 to long cores and to two-phase flow. Combination with classical Buckley-Leverett water flooding theory then permits transient displacement calculations. Before outlining the theory, we present the experimental procedures.

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Numerical Simulation of Water Imbibition in Fractured Cores

Society of Petroleum Engineers Journal ◽

10.2118/6895-pa ◽

1979 ◽

Vol 19 (03) ◽

pp. 175-182 ◽

Cited By ~ 33

Author(s):

Hossein Kazemi ◽

L.S. Merrill

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Oil Recovery ◽

Matrix System ◽

Two Dimensional ◽

Two Phase ◽

Flow Equations ◽

Water Imbibition ◽

The Matrix ◽

Numerical Simulator

Original manuscript received in Society f Petroleum Engineers office Sept. 15, 1977. Paper accepted for publication June 9, 1978. Revised manuscript received Feb. 19, 1979. Paper (SPE 6890) first presented at the SPE-AIME 52nd Annual Fall Technical Conference and Exhibition, held in Denver, Oct. 9-12, 1977. Abstract A two-dimensional, two-phase, semi-implicit, numerical simulator was used to simulate water imbibition and oil recovery in artificially fractured and unfractured cores. Experimental results were matched satisfactorily by the numerical simulator. These results provide evidence of the reliability of the concepts underlying an earlier numerical simulator, which was tailored specifically for field applications. We show that the flow equations used to match the laboratory data reduce to the equations used in the field simulator. In addition, the experiments themselves were conducted quite differently from those commonly used in imbibition experiments and provide added insight into oil recovery from fractured reservoirs. Introduction Previously, we reported on the development of a Previously, we reported on the development of a numerical reservoir simulator for use in field applications. In this paper, we examine the reliability of the concepts underlying the numerical simulation by matching experimental results of fractured and unfractured cores with a simulator that accounts for the fracture and the matrix components. The simulator is a conventional two-dimensional, two-phase, semi-implicit simulator, but we show that it reduces to the formulation used in the field simulator. Several studies have reported on water imbibition in fractured media. These studies were concerned primarily with the imbibition aspects of the flow primarily with the imbibition aspects of the flow mechanism in the matrix rather than the total flow problem in the fracture-matrix system. Mattax and problem in the fracture-matrix system. Mattax and Kyte developed equations for scaling up imbibition effects. Parsons and Chaney used these equations to study imbibition effects in carbonate rocks. Iffly et al., in addition to experimental work, used a one-dimensional, two-phase, semi-implicit mathematical model to match oil recoveries from the matrix. A similar mathematical model in two dimensions was used by Kleppe and Morse to match the results of their imbibition experiments. While the last two papers show that imbibition oil recovery can be simulated numerically, the total concept of fluid flow in fracture-matrix systems has not been investigated adequately either numerically or experimentally. Mathematical Model The porous media used here were cylindrical cores or rectangular blocks cut along the long axis. The flow experiments were conducted so that the fracture plane and the entire core were horizontal. Therefore, the fractured cores were simulated by a layered two-dimensional simulator. The core halves were simulated as two matrix layers having the properties of the original core. The fracture was simulated as a very thin, high-permeability, and high-flow-capacity layer, where capillary pressure was essentially zero. The basic flow equations, assuming imcompressible flow, are w w----- wx ------ + ----- wz --------x x x zax az Sw+ qw Bw (X - Xo) = -------................(1)at t o o------ ox------ + ------ oz -------qoBo (X-Xo)x x z z So= ---------..................................(2)t Sw + So = 1.....................................(3) Pc(Sw) = po - pw....................................(4) kxkrwwx = 0.006328 -----------,......................(5)w SPEJ P. 175

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PERSISTENCE MEASURES FOR 2D SOAP FROTH

International Journal of Modern Physics C ◽

10.1142/s0129183103005285 ◽

2003 ◽

Vol 14 (09) ◽

pp. 1163-1170

Author(s):

Y. FENG ◽

H. J. RUSKIN ◽

B. ZHU

Keyword(s):

Temporal Evolution ◽

Simulation Method ◽

The Other ◽

Area Fraction ◽

Cellular Structures ◽

Phase System ◽

Direct Simulation ◽

Topological Properties ◽

Two Phase ◽

Independent Measure

Soap froths as typical disordered cellular structures, exhibiting spatial and temporal evolution, have been studied through their distributions and topological properties. Recently, persistence measures, which permit representation of the froth as a two-phase system, have been introduced to study froth dynamics at different length scales. Several aspects of the dynamics may be considered and cluster persistence has been observed through froth experiment. Using a direct simulation method, we have investigated persistent properties in 2D froth both by monitoring the persistence of survivor cells, a topologically independent measure, and in terms of cluster persistence. It appears that the area fraction behavior for both survivor and cluster persistence is similar for Voronoi froth and uniform froth (with defects). Survivor and cluster persistent fractions are also similar for a uniform froth, particularly when geometries are constrained, but differences observed for the Voronoi case appear to be attributable to the strong topological dependency inherent in cluster persistence. Survivor persistence, on the other hand, depends on the number rather than size and position of remaining bubbles and does not exhibit the characteristic decay to zero.

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