Showing papers on "Multiphase flow published in 1987"
TL;DR: In this article, a parametric model is developed to describe relative permeability-saturation-fluid pressure functional relationships in two- or threefluid phase porous media systems subject to monotonic saturation paths.
Abstract: A parametric model is developed to describe relative permeability-saturation-fluid pressure functional relationships in two- or three-fluid phase porous media systems subject to monotonic saturation paths. All functions are obtained as simple closed-form expressions convenient for implementation in numerical multiphase flow models. Model calibration requires only relatively simple determinations of saturation-pressure relations in two-phase systems. A scaling procedure is employed to simplify the description of two-phase saturation-capillary head relations for arbitrary fluid pairs and experimental results for two porous media are presented to demonstrate its applicability. Extension of two-phase relations to three- phase systems is obtained under the assumption that fluid wettability follows the sequence water > nonaqueous phase liquid > air. Expressions for fluid relative permeabilities are derived from the scaled saturation-capillary head function using a flow channel distribution model to estimate effective mean fluid-conducting pore dimensions. Constraints on model application are discussed.
710 citations
TL;DR: In this paper, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two-or three-phase porous media systems subject to arbitrary saturation paths.
Abstract: In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two-or three-phase (e.g., air-water or air-oil-water) porous media systems subject to arbitrary saturation paths. A parametric description of hysteretic S-P relations is developed in paper 1 which includes effects of air and oil phase occlusion or “entrapment” during imbibition. Entrapped nonwetting fluid saturations at a given point along a saturation path are linearly interpolated between endpoints of primary imbibition scanning curves using maximum trapped saturations estimated by extension of the method of Land (1968). Arbitrary order scanning curves are predicted using an empirical interpolation scheme coupled with a scaling procedure which simplifies computations and minimizes the parametric complexity of the model. All model parameters are defined in terms of measurements which may be obtained from two-phase systems (air-water, air-oil, oil-water). Extension to three-phase systems is based on the assumption that fluid entrapment processes in three phase systems are similar to those in two-phase systems and that wettability decreases in the order: water to oil to air.
451 citations
Book•
01 Jan 1987
TL;DR: In this article, the governing equations of multiphase flow in a Deforming Porous Medium (DPM) secondary consolidation program are used to validate Elastic and Elasto-plastic Consolidation Programs.
Abstract: Introduction The Governing Equations of Multiphase Flow in a Deforming Porous Medium Numerical Solutions of the Governing Equations Constitutive Relationships and Variable Permeabilities Validation of Elastic and Elasto-plastic Consolidation Programs Modelling of Subsidence Heat and Fluid Flow in Deforming Porous Media Secondary Consolidation Two- dimensional, Non-linear Thermoelastoplastic Consolidation Program Plascon.
396 citations
TL;DR: Parker et al. as discussed by the authors presented a theoretical model for the prediction of relative permeability-saturation (k-S) relations in two-phase and three-phase porous media systems subject to arbitrary saturation paths.
Abstract: A theoretical model is described for the prediction of relative permeability-saturation (k-S) relations in two-phase (air-water) and three-phase (air-oil-water) porous media systems subject to arbitrary saturation paths Integral expressions for air, water, and oil realtive permeabilities are presented which extend the nonhysteretic relative permeability model of Parker et al (1987) to accomodate effects of pore blockage by air trapped in water and oil phases and oil trapped in the water phase The parametric model for saturation-pressure (S-P) relations and fluid entrapment of paper 1 (Parker and Lenhard, this issue) is employed in the integral equations to enable derivation of closed-form expressions for air, water, and oil relative permeabilities as functions of current fluid saturations and saturation history Three-phase k-S relations are calculated for main drainage and imbibition paths for a hypothetical soil to illustrate usage of the model and to evaluate the magnitude of fluid entrapment effects on relative permeabilities Water permeability-saturation relations are predicted to exhibit mild hysteretic effects except at high saturations, while hysteresis in air permeability-saturation relations is much more pronounced Predicted hysteresis in oil permeability is low at low water saturations but becomes quite marked as water saturation increases Predictions of k-S-P relations for a hypothetical NAPL contamination scenario are presented using model parameters determined for a sandy soil by two methods in paper 1 (Parker and Lenhard, this issue) The results indicate that hysteresis and nonwetting fluid entrapment effects on k-S-P relations may be quite substantial Sensitivity to calibration method is found to be rather small
296 citations
TL;DR: In this article, the authors describe how CT is used to measure the volume fraction of pore space occupied by up to three discrete phases, such as oil, water, and gas.
Abstract: The medical x‐ray computerized tomography (CT) scanner has proved to be a useful tool for studies of fluid flow in porous media, with particular applications in reservoir engineering and enhanced oil recovery. This paper explains how CT is used to measure the volume fraction of pore space occupied by up to three discrete phases, such as oil, water, and gas. The image processing system, x‐ray transparent high‐pressure flow equipment, choice of fluid dopants, and x‐ray energies are described for scanning of core flood experiments. Examples are given of tertiary miscible carbon dioxide displacements in Berea sandstone.
232 citations
TL;DR: In this paper, the authors review the historical development of design tools used to address multiphase flow features and present state-of-the-art technology for multihase flow analysis.
Abstract: Multiphase flow can occur throughout the production system. The fluids involved in multiphase flow in the petroleum industry are multicomponent mixtures with complex phase behavior. Petroleum engineers are faced with the need to predict the relationships between flow rates, pressure drop, and piping geometry for reservoir fluids produced during the life of a field. This paper reviews the historical development of design tools used to address these unique multiphase-flow features. State-of-the-art technology is also presented.
230 citations
TL;DR: In this article, scaled multiphase versions of the Brooks-Corey and van Genuchten retention functions were used to describe saturation-capillary pressure curves measured in air-water, air-organic liquid and organic liquid-water systems in a sandy porous medium for four organic liquids during monotonic wetting phase drainage.
200 citations
TL;DR: In this paper, a macroscopic description of a two-phase flow in a porous medium is given by writing, firstly, mass and momentum-balance equations and, secondly, phenomenological equations derived from the theory of irreversible thermodynamic processes.
Abstract: A macroscopic description of a two-phase flow in a porous medium is given by writing, firstly, mass and momentum-balance equations and, secondly, phenomenological equations derived from the theory of irreversible thermodynamic processes. The main results are as follows: (i) the law of capillary pressure is extended to dynamic conditions, (ii) an extended formulation of Darcy's law is established for each fluid phase and also for fluid/fluid interface which is considered as a phase of the system, and (iii) a coupling may appear between fluid phases.
133 citations
TL;DR: In this article, a finite-element model is developed for multiphase flow through soil involving three immiscible fluids: air, water, and a nonaqueous phase liquid (NAPL).
Abstract: A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equations governing flow in a three-fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures, which are derived in a companion paper by J. C. Parker et al. (this issue) and which may be calibrated from two-phase laboratory measurements, are employed in the finite-element program. The solution procedure uses backward time integration with iteration by a modified Picard method to handle the nonlinear properties. Laboratory experiments involving water displacement from soil columns by p cymene (a benzene-derivative hydrocarbon) under constant pressure were simulated by the finite-element program to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured saturation-capillary head data agreed with observed outflow data within the limits of precision of the predictions as estimated by a first-order Taylor series approximation considering parameter uncertainty due to experimental reproducability and constitutive model accuracy. Two-dimensional simulations are presented for a hypothetical field case involving introduction of NAPL near the soil surface due to leakage from an underground storage tank. Subsequent transport of NAPL in the variably saturated vadose and groundwater zones is analyzed.
102 citations
Book•
01 Jan 1987
TL;DR: In this paper, a systematic, rigorous and unified treatment to provide a general understanding of the phenomena involved in thermal flows in porous media is presented. But the treatment is basically mathematical, specific physical problems are also dealt with.
Abstract: Thermal flows in porous media are important in a wide range of areas: oil recovery, geothermal development, chemical and nuclear industry, civil engineering, energy storage and energy conversion. This book uses a systematic, rigorous and unified treatment to provide a general understanding of the phenomena involved. General equations for single- or multiphase flows (including an arbitrary number of components inside each phase), diffusion and chemical reactions are presented. The boundary conditions which may be imposed, the non-dimensional para meters, the structures of the solutions, the stability of the finite amplitude solutions and many other related topics ae also studied. Although the treatment is basically mathematical, specific physical problems are also dealt with. There are two major fields of applications: natural convection and underground combustion. Both are discussed in detail. Various examples with exact or numerical solutions, for the case of bounded or unbounded domains, are presented, accompanied by extensive comment.
102 citations
01 Jan 1987
TL;DR: In this paper, the concept and size of a representative elementary volume (REV) was introduced and a model of Pore Scale Physical Modeling of Transport Phenomena in Porous Media was presented.
Abstract: 1. Heat and Mass Transport in Single and Multiphase Systems.- On the Concept and Size of a Representative Elementary Volume (REV).- Advective and Diffusive Fluxes in Porous Media.- Pore Scale Physical Modeling of Transport Phenomena in Porous Media.- Natural Convection in Porous Media.- Heat and Mass Transport in Geothermal Reservoirs.- Thermohydraulics of an Aquifer Thermal Energy Storage System.- Mechanics of Fluids in Layered Soils.- 2. Particle Transport in Porous Media.- Governing Equations for Particle Transport in Porous Media.- Theory of Filtration.- 3. Transport Phenomena in Fractured Rocks.- Transport Equations for Fractured Porous Media.- Chemical Transport in Fractured Rock.- Multiphase Flow in Fractured Reservoirs.- 4. Uncertainty and the Stochastic Approach to Transport in Porous Media.- Non Stationary Geostatistics.- Stochastic Analysis of Solute Transport in Saturated and Unsaturated Porous Media.- Uncertainty Assessment for Fluid Flow and Contaminant Transport Modeling in Heterogeneous Groundwater Systems.- An Overview of the Stochastic Modeling of Dispersion in Fractured Media.- Sensitivity Analysis of Ground-water Models.- 5. Advances in Numerical Methods.- Mathematical Modeling of the Behavior of Hydrocarbon Reservoirs - The Present and the Future.- Numerical Modeling of Multiphase Flow in Porous Media.- Advection-Dispersion with Adaptive Eulerian-Lagrangian Finite Elements.- Moving Point Techniques.- Table of Contents of "Fundamentals of Transport Phenomena in Porous Media, 1984".
TL;DR: In this paper, a finite-element technique that uses double nodes along the interface has been implemented to analyze stratified multiphase flow fields, where the position of the interface is unknown a priori.
Abstract: The analysis of stratified multiphase flow fields is difficult because the position of the interface is unknown a priori and there is a discontinuity in the normal viscous stress and/or pressure at the interface. A finite-element technique that uses double nodes along the interface has been implemented. The immiscible liquid displacement in a capillary tube was examined in detail. Fountain flow in the advancing fluid, reverse fountain flow in the receding fluid, and a recirculating flow region in the less viscous fluid were determined. In Newtonian flat film coextrusion the entry region, where the two immiscible fluids form an interface, and the characteristic swelling and bending of the extrudate at the die exit were studied. The computational results compare favorably with available experimental observations.
TL;DR: In this article, an algebraic slip model (ASM) is used to represent the relative migration of particles and air in the liquid mixture, which yields field values of velocity, pressure, particle and air concentrations, as well as the overall performance parameters more familiar to cyclone operators.
01 Jan 1987
TL;DR: The scope of the chapter is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.
Abstract: The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation offers the only viable approach to the mathematical modeling of multiphase flows. This chapter provides an overview of the types of models that are used in this field and highlights some of the numerical techniques that have appeared recently. The exposition includes discusssions of multiphase, multispecies flows in which chemical transport and interphase mass transfers play important roles. This chapter also examines some of the outstanding physical and mathematical problems in multiphase flow simulation. The scope of the chapter is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.
Patent•
ARCO1
TL;DR: In this article, the total mass flow rate of a multiphase fluid flow stream such as a water, oil and gas mixture being produced from underground wells is determined by passing the flowstream through an apparatus which forces a substantial change in direction of the fluid flowstream and wherein a pressure differential is measured across flow paths of known cross-sectional flow area.
Abstract: The total mass flowrate of a multiphase fluid flowstream such as a water, oil and gas mixture being produced from subterranean wells is determined by passing the flowstream through an apparatus which forces a substantial change in direction of the fluid flowstream and wherein a pressure differential is measured across flow paths of known cross-sectional flow area. The total mass flow is determined from the cross-sectional flow areas, the measured total density of the flowstream and the differential pressure. A sample of the flowstream is withdrawn from the flow path, gas is separated from liquid and the liquid fraction of water is measured by passing the liquid mixture through a device which measures the dielectric constant of the liquid mixture using microwave radiation transmissivity or differential pressure between columns of the liquid mixture and a column of water of equal height is compared. Total density of the flowstream may be obtained by measuring differential pressures across changes in elevation of the flowstream.
Book•
01 Jan 1987
TL;DR: In this article, a three-volume set provides information in particulate and multiphase processes, including contamination analysis and control, suspensions and slurry transport, and fine particle powder science and technology.
Abstract: This three-volume set provides information in particulate and multiphase processes. Authorities investigate four key areas of current scientific and engineering interest: aerosol science and technology; contamination analysis and control; suspensions and slurry transport; and fine particle powder science and technology.
TL;DR: In this article, a statistical pattern recognition method was applied to the analysis of the signals of a cross-sectional mean void fraction for discriminating gas-liquid two-phase flow regimes based on six key flow patterns: bubble, cap-bubble, plug, froth (FI and FII), and annular flow.
Abstract: A statistical pattern recognition method was applied to the analysis of the signals of a cross-sectional mean void fraction for discriminating gas-liquid two-phase flow regimes. The analysis and discrimination were carried out based on six key flow patterns: bubble, cap-bubble, plug, froth (FI and FII), and annular flow. For each flow condition, 100 void signals with a recording dimension of 1 second were used and transferred to discrete data, the sampling frequency of which was selected as 100 Hz by comparison with correct recognition rates obtained from different frequencies. The magnitude of the time-averaged void fraction was partly employed supplementary to the pattern recognition method. The boundaries between the six flow regimes were determined corresponding to a correct recognition rate of 80% and were drawn on a superficial gas-liquid velocities diagram. These flow boundaries were also compared with those available in the literature.
01 Jan 1987
TL;DR: In this article, the authors studied the multiphase flow in naturally fractured reservoirs and found that the complexity of multi-phase flow in such reservoirs adds to the complexity and has been extensively studied over the last few years.
Abstract: Naturally fractured reservoirs represent a complex class of reservoirs. Multiphase flow in such reservoirs adds to the complexity and has been studied extensively over the last few years.
TL;DR: In this paper, it was shown that the two problems are mathematically equivalent, regardless of the dimensionality of the flow system and the presence of dissipative effects, and an extension to multiphase immiscible displacement and multicomponent miscible displacement is also briefly discussed.
Abstract: Displacement processes in porous media share several common characteristics. Fundamental among them is the representation of the momentum balance via Darcy’s law and its multiphase extension (Bear, 1972). Such description leads to systems of equations the solution of which parallels the behavior of the solution of processes in multicomponent chromatography. For instance, it has been recognized that noncapillary, multiphase displacement in one-dimensional (rectilinear or radial) porous media can be solved by techniques identical to those used in chromatographic transport (Helfferich, I98 I; Rhee et al., 1986, and references therein). This similarity arises naturally for the case of one-dimensional flow geometries and in the absence of dissipative terms (diffusion, dispersion, or capillarity), where both multiphase and multicomponent chromatography processes are formulated by systems of first-order hyperbolic equations. In this note we pursue further this relationship in mathematical representation between multiphase flow and chromatographic processes in porous media. Specifically, we consider two-phase, immiscible displacement and single-phase, miscible displacement in the presence of equilibrium adsorption. It is demonstrated that the two problems are mathematically equivalent, regardless of the dimensionality of the flow system and the presence of dissipative effects. Such an analogy is of practical importance in the analysis of various process characteristics, for instance in describing the evolution of unstable two-dimensional disturbances during viscous fingering. The latter is a topic of active current investigations (Homsy, 1987, and references therein), and of fundamental importance in process performance. Any similarities between seemingly different processes would be of considerable help in an effort to reduce complexity and to uncover common mechanisms. An extension to multiphase immiscible displacement and multicomponent miscible displacement is also briefly discussed. Mathematical Description
TL;DR: The IVA2/001 as discussed by the authors is a computer code for simulating transient, threedimensional, three-phase, threecomponent nonhomogeneous (three velocity fields), nonequilibrium flow in a cylindrical porous body.
Abstract: IVA2/001 is a computer code for simulating transient, three-dimensional, three-phase, three-component nonhomogeneous (three velocity fields), nonequilibrium flow in a cylindrical porous body (including nuclear reactor cores if desired) Each velocity field consists of an inert and a noninert component A separated equation of field mass, inert mass concentration in each of the fields, and entropy of the fields together with mixture momentum equations for the flow are solved by a semi-implicit numerical method with an analytical reduction to the pressure or pressure velocity problem and backward substitution The flexibility of the method in describing three velocity fields of arbitrary direction is demonstrated The solution procedure of the hydrodynamic problem is described Finally, a numerical example and a comparison with experimental data demonstrate that the IVA2 method is a powerful tool for numerical multiphase flow simulation
01 Jan 1987
TL;DR: In this article, a volume fraction measuring device (IVFM) was used to measure the velocities of small amplitude kinematic waves in both air-water and solids-water flows using a cross-correlation technique.
Abstract: Friction pressure drop measurements were made in vertical bubbly and particulate flows, and friction factors up to two orders of magnitude higher than pure liquid values were obtained. The two-phase friction multiplier for air-water flows was shown to attain values up to 15 times higher than the predictions given by the Lockhart and Martinelli correlations (1949). These findings exemplify the lack of detailed understanding of multi-component flow phenomena. The lack of understanding of the flow kinematics and the small amount of information available on the topic has been primarily due to the primitive stage of development of flow measuring instrumentation. A shielded, temperature compensated and non-intrusive Impedance Volume Fraction Meter (IVFM) was built and shown to have good spatial and temporal resolution. The dynamic calibration of the device demonstrated that the volume fraction measuring device could also be used to measure both the dispersed medium velocity and concentration. This device enabled us to carry out measurements of small and large amplitude kinematic stability and wave propagation in two-component and three-component flows. The velocities of small amplitude kinematic waves in both air-water and solids-water flows were measured using a cross-correlation technique and these were shown to be non-dispersive. The persistence of flow structure was quantified using the coherence of the IVFM noise at two locations. The structure in solids-water flows was found to be more persistent than in air-water flows, and the most coherent wave length was measured to be of the order of .5 m, or five pipe diameters in both flows. The statistical properties in the inherent noise in the IVFM output was shown to contain valuable information on two- and three-component flow quantities and regime. In this thesis, we show that much can be learned about the complex nature of multi-component flows with adequate instrumentation, and we emphasize the need for further development of critical flow measuring techniques for use not only in fundamental investigations but also in the monitoring and control of practical multiphase flow processes.
TL;DR: Etude des difficultes numeriques rencontrees for des deplacements de fluides miscible en milieu poreux and for des fluides non miscibles egalement in MILPoreux.
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TL;DR: In this article, a comprehensive review describes both the experimental and modeling studies of the fundamental characteristics of gas-liquid-solid three phase flow, including hydrodynamics, heat and mass transfer.
Abstract: The optimum design and operation of a gas liquid solid flow system depend on the ability to accurately predict the fundamental properies of the hydrodynamics, heat and mass transfer and so on. Identification of the flow regimes is also needed to understand the overall system performance. This comprehensive review describes both the experimental and modeling studies of the fundamental characteristics of gas-liquid-solid three phase flow.
TL;DR: In this paper, the authors measured the unsteady fluctuations due to turbulent flow which occur at points on the image plane of a shadowgraph visualisation system using a small photodetector and found that the signals are related in magnitude to the difference in density between the mixing air jet flow and the ambient air surrounding the turbulent mixing flow.
Abstract: The unsteady fluctuations due to turbulent flow which occur at points on the image plane of a shadowgraph visualisation system are measured using a small photodetector. The characteristics of the output signal have been investigated to determine when it has linear response to the turbulent fluctuations, and to verify that it has the expected spectral composition. It has been found that the signals are related in magnitude to the difference in density between the mixing air jet flow and the ambient air surrounding the turbulent mixing flow. Distributions of the optical shadowgraph fluctuations have been transformed by an Abel integral method to yield radial distributions of the turbulent density fluctuations within the mixing region.