Showing papers on "Multiphase flow published in 1990"

Introduction to modeling of transport phenomena in porous media.

Abstract: A General Theory.- 1 The Porous Medium.- 1.1 Definition and Classification of Porous Media.- 1.1.1 Definition of a porous medium.- 1.1.2 Classification of porous media.- 1.1.3 Some geometrical characteristics of porous media.- 1.1.4 Homogeneity and isotropy of a porous medium.- 1.2 The Continuum Model of a Porous Medium.- 1.2.1 The need for a continuum approach.- 1.2.2 Representative Elementary Volume (REV).- 1.2.3 Selection of REV.- 1.2.4 Representative Elementary Area (REA).- 1.3 Macroscopic Values.- 1.3.1 Volume and mass averages.- 1.3.2 Areal averages.- 1.3.3 Relationship between volume and areal averages.- 1.4 Higher-Order Averaging.- 1.4.1 Smoothing out macroscopic heterogeneity.- 1.4.2 The hydraulic approach.- 1.4.3 Compartmental models.- 1.5 Multicontinuum Models.- 1.5.1 Fractured porous media.- 1.5.2 Multilayer systems.- 2 Macroscopic Description of Transport Phenomena in Porous Media.- 2.1 Elements of Kinematics of Continua.- 2.1.1 Points and particles.- 2.1.2 Coordinates.- 2.1.3 Displacement and strain.- 2.1.4 Processes.- 2.1.5 Material derivative.- 2.1.6 Velocities.- 2.1.7 Flux and discharge.- 2.1.8 Gauss' theorem.- 2.1.9 Reynolds' transport theorem.- 2.1.10 Green's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed' domain.- 2.7.7 Boundary with fluid phase change.- 2.7.8 Boundary between a porous medium and an overlying body of flowing fluid.- 3 Mathematical Statement of a Transport Problem.- 3.1 Standard Content of a Problem Statement.- 3.1.1 Conceptual model.- 3.1.2 Mathematical model.- 3.2 Multicontinuum Models.- 3.3 Deletion of Nondominant Effects.- 3.3.1 Methodology.- 3.3.2 Examples.- 3.3.3 Concluding remarks.- B Application.- 4 Mass Transport of a Single Fluid Phase Under Isothermal Conditions.- 4.1 Mass Balance Equations.- 4.1.1 The basic equation.- 4.1.2 Stationary rigid porous medium.- 4.1.3 Deformable porous medium.- 4.2 Boundary Conditions.- 4.2.1 Boundary of prescribed pressure or head.- 4.2.2 Boundary of prescribed mass flux.- 4.2.3 Semipervious boundary.- 4.2.4 Discontinuity in solid matrix properties.- 4.2.5 Sharp interface between two fluids.- 4.2.6 Phreatic surface.- 4.2.7 Seepage face.- 4.3 Complete Mathematical Model.- 4.4 Inertial Effects.- 5 Mass Transport of Multiple Fluid Phases Under Isothermal Conditions.- 5.1 Hydrostatics of a Multiphase System.- 5.1.1 Interfacial tension and capillary pressure.- 5.1.2 Capillary pressure curves.- 5.1.3 Three fluid phases.- 5.1.4 Saturation at medium discontinuity.- 5.2 Advective Fluxes.- 5.2.1 Two fluids.- 5.2.2 Two-phase effective permeability.- 5.2.3 Three-phase effective permeability.- 5.3 Mass Balance Equations.- 5.3.1 Basic equations.- 5.3.2 Nondeformable porous medium.- 5.3.3 Deformable porous medium.- 5.3.4 Buckley-Leverett approximation.- 5.3.5 Flow with interphase mass transfer.- 5.3.6 Immobile fluid phase.- 5.4 Complete Model of Multiphase Flow.- 5.4.1 Boundary and initial conditions.- 5.4.2 Complete model.- 5.4.3 Saturated-unsaturated flow domain.- 6 Transport of a Component in a Fluid Phase Under Isothermal Conditions.- 6.1 Balance Equation for a Component of a Phase.- 6.1.1 The dispersive flux.- 6.1.2 Diffusive flux.- 6.1.3 Sources and sinks at the solid-fluid interface.- 6.1.4 Sources and sinks within the liquid phase.- 6.1.5 Mass balance equation for a single component.- 6.1.6 Variable fluid density and deformable porous medium.- 6.1.7 Balance equations with immobile liquid.- 6.1.8 Fractured porous media.- 6.2 Boundary Conditions.- 6.2.1 Boundary of prescribed concentration.- 6.2.2 Boundary of prescribed flux.- 6.2.3 Boundary between two porous media.- 6.2.4 Boundary with a body of fluid.- 6.2.5 Boundary between two fluids.- 6.2.6 Phreatic surface.- 6.2.7 Seepage face.- 6.3 Complete Mathematical Model.- 6.4 Multicomponent systems.- 6.4.1 Radionuclide and other decay chains.- 6.4.2 Two multicomponent phases.- 6.4.3 Three multicomponent phases.- 7 Heat and Mass Transport.- 7.1 Fluxes.- 7.1.1 Advective flux.- 7.1.2 Dispersive flux.- 7.1.3 Diffusive flux.- 7.2 Balance Equations.- 7.2.1 Single fluid phase.- 7.2.2 Multiple fluid phases.- 7.2.3 Deformable porous medium.- 7.3 Initial and Boundary Conditions.- 7.3.1 Boundary of prescribed temperature.- 7.3.2 Boundary of prescribed flux.- 7.3.3 Boundary between two porous media.- 7.3.4 Boundary with a 'well mixed' domain.- 7.3.5 Boundary with phase change.- 7.4 Complete Mathematical Model.- 7.5 Natural Convection.- 8 Hydraulic Approach to Transport in Aquifers.- 8.1 Essentially Horizontal Flow Approximation.- 8.2 Integration Along Thickness.- 8.3 Conditions on the Top and Bottom Surfaces.- 8.3.1 General flux condition on a boundary.- 8.3.2 Conditions for mass transport of a single fluid phase.- 8.3.3 Conditions for a component of a fluid phase.- 8.3.4 Heat.- 8.3.5 Conditions for stress.- 8.4 Particular Balance Equations for an Aquifer.- 8.4.1 Single fluid phase.- 8.4.2 Component of a phase.- 8.4.3 Fluids separated by an abrupt interface.- 8.5 Aquifer Compaction.- 8.5.1 Integrated flow equation.- 8.5.2 Integrated equilibrium equation.- 8.6 Complete Statement of a Problem of Transport in an Aquifer.- 8.6.1 Mass of a single fluid phase.- 8.6.2 Mass of a component of a fluid phase.- 8.6.3 Saturated-unsaturated mass and component transport.- References.- Problems.

On Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Rock Fractures

Abstract: This paper presents a conceptual and numerical model of multiphase flow in fractures. The void space of real rough-walled rock fractures is conceptualized as a two-dimensional heterogeneous porous medium, characterized by aperture as a function of position in the fracture plane. Portions of a fracture are occupied by wetting and nonwetting phase, respectively, according to local capillary pressure and accessibility criteria. Phase occupancy and permeability are derived by assuming a parallel-plate approximation for suitably small subregions in the fracture plane. For log-normal aperture distributions, a simple approximation to fracture capillary pressure is obtained in closed form; it is found to resemble the typical shape of Leverett's j-function. Wetting and non-wetting phase relative permeabilities are calculated by numerically simulating single phase flows separately in the wetted and non-wetted pore spaces. Illustrative examples indicate that relative permeabilities depend sensitively on the nature and range of spatial correlation between apertures. It is also observed that interference between fluid phases flowing in a fracture tends to be strong, with the sum of wetting and nonwetting phase relative permeabilities being considerably less than 1 at intermediate saturations.

Advances in thermodynamics

Abstract: This book covers the following: heat transfer during freezing of biological materials; condensation of azeotropic and nonazeotropic binary vapor mixtures; interface in film condensation; thermal phenomena in High-T{sub c} thin-film superconductors; a comparative analysis of multiphase transport models in porous media; a comparison of convective heat transfer in packed beds and granular flows; and microscales and scales in heat transfer.

Vertical integration of three-phase flow equations for analysis of light hydrocarbon plume movement

Abstract: A mathematical model is derived for areal flow of water and light hydrocarbon in the presence of gas at atmospheric pressure. Vertical integration of the governing three-dimensional, three-phase flow equations is performed under the assumption of local vertical equilibrium to reduce the dimensionality of the problem to two orthogonal horizontal directions. Independent variables in the coupled water and hydrocarbon areal flow equations are specified as the elevation of zero gauge hydrocarbon pressure (air-oil table) and the elevation of zero gauge water pressure (air-water table). Constitutive relations required in the areal flow model are vertically integrated fluid saturations and vertically integrated fluid conductivities as functions of air-oil and air-water table elevations. Closed-form expressions for the vertically integrated constitutive relations are derived based on a three-phase extension of the Brooks-Corey saturation-capillary pressure function. Closed-form Brooks-Corey relations are compared with numerically computed analogs based on the Van Genuchten retention function. Close agreement between the two constitutive models is observed except at low oil volumes when the Brooks-Corey model predicts lower oil volumes and transmissivities owing to the assumption of a distinct fluid entry pressure. Nonlinearity in the vertically integrated constitutive relations is much less severe than in the unintegrated relations. Reduction in dimensionality combined with diminished nonlinearity, makes the vertically integrated water and hydrocarbon model an efficient formulation for analyzing field-scale problems involving hydrocarbon spreading or recovery under conditions for which the vertical equilibrium assumption is expected to be a satisfactory approximation.

Nonlinear evolution equations that change type

Abstract: This volume should be of interest to applied mathematicians, to researchers in partial differential equations, and to those involved in fluid dynamics and numerical analysis examining models for viscoelastic flows, porous medium and granular flows, and flows exhibiting phase transitions. As papers in this volume indicate, physical processes whose simplest models may involve change of type occur also in other dynamic contexts, such as in the simulation of oil reservoirs, involving multiphase flow in a porous medium, and in granular flow.

Characterization of non-Darcy multiphase flow in petroleum bearing formations

Abstract: The objectives of this research are: Develop a proper theoretical model for characterizing non-Darcy multi-phase flow in petroleum bearing formations. Develop an experimental technique for measuring non-Darcy flow coefficients under multiphase flow at insitu reservoir conditions. Develop dimensional consistent correlations to express the non-Darcy flow coefficient as a function of rock and fluid properties for consolidated and unconsolidated porous media. The research accomplished during the period May 1991--May 1992 focused upon theoretical and experimental studies of multiphase non-Darcy flow in porous media.

Sixth SPE comparative solution project : dual-porosity simulators

Abstract: Two problems are used to compare fractured reservoir models: 1) a simple single-block example, and 2) a more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. In selection of the problems for this Comparative Solution Project, some aspects of the physics of multiphase flow in fractured porous media were considered. The influence of fracture capillary pressure on reservoir performance has been addressed by cases with zero and nonzero gas/oil capillary pressure in the fractures

Estimation of Multiphase Flow Functions From Displacement Experiments

Abstract: A method to obtain accurate estimates of relative permeability functions from low flood rate dynamic displacement data is presented. The simultaneous estimation of the capillary pressure function from this data is also discussed. These functions are estimated using a regression-based approach by parameter estimation with a numerical coreflood simulator. Pressure drop and production data are matched with the coreflood simulator. This estimation problem is solved through minimization of the appropriate weighted least-square objective function. Careful consideration is given to the functional representation of the relative permeability and capillary pressure functions so that the most accurate estimates of those properties can be obtained.

A review of interaction mechanisms in fluid-solid flows

Abstract: Multiphase flows have become the subject of considerable attention because of their importance in many industrial applications, such as fluidized beds, pneumatic transport of solids, coal combustion, etc. Fundamental research into the nature of pneumatic transport has made significant progress in identifying key parameters controlling the characteristics of these processes. The emphasis of this study is on a mixture composed of spherical particles of uniform size and a linearly viscous fluid. Section 1 introduces our approach and the importance of this study. In Section 2, the dynamics of a single particle as studied in classical hydrodynamics and fluid dynamics is presented. This has been a subject of study for more than 200 years. In Section 3, we review the literature for the constitutive relations as given in multiphase studies, i.e., generalization of single particle and as given in literature concerning the continuum theories of mixtures or multicomponent systems. In Section 4, a comparison between these representations and the earlier approach, i.e., forces acting on a single particle will be made. The importance of flow regimes, particle concentration, particle size and shape, rotation of the particle, effect of solid walls, etc. are discussed. 141 refs.

Sixth SPE Comparative Solution Project: Dual-Porosity Simulators

Abstract: Two problems are used to compare fractured reservoir models: 1) a simple single-block example, and 2) a more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. In selection of the problems for this Comparative Solution Project, some aspects of the physics of multiphase flow in fractured porous media were considered. The influence of fracture capillary pressure on reservoir performance has been addressed by cases with zero and nonzero gas/oil capillary pressure in the fractures

Discontinuous and mixed finite elements for two-phase incompressible flow

Abstract: The simulation of multiphase flow presents several difficulties, including the occurrence of sharp moving fronts when convection is dominating, the need for a good approximation of velocities to calculate the convective terms of the equation, and flow singularities around wells. To handle the first difficulty, the authors propose a Godunov-type higher-order scheme based on a piecewise linear approximation of the saturation associated with a multidimensional slope limiter. With respect to the second, the pressure equation is approximated by means of a mixed-hybrid formulation equivalent to the classic mixed formulation but yielding a positive-definite linear system. To solve the third difficulty, the authors introduce macroelements around wells. Numerical experiments illustrate the capabilities of the method.

Discontinuous and mixed finite elements for two-phase incompressible flow

Abstract: Presentation of a new method to solve the difficulties presented by the simulation of multiphase flow. The problem of occurence of sharp moving fronts when convection is dominating, is handled by use of a Godunov-type higher -order scheme. The need for good approximation of velocities, to calculate the convective term of the equation is met by mixed-hybrid formulation. To solve the third difficulty, flow singularities around wells, macroelements around wells are introduced.

Numerical modeling of microscopic fluid distribution in porous media

Abstract: Three numerical methods have been developed to model the equilibrium distribution of fluid phases in a multiphase saturated porous medium. The basic assumption made is that the distribution of phases is governed by the static interfacial free energy of the system, such that the equilibrium phase distribution corresponds to a minimum in the total interfacial free energy of the system. The example of determining the distribution of water vapor and liquid water in 2D numerical models of the pore space in a rock is considered. Starting with a numerical model of the pore space, the objective of each method is to obtain the minimum energy configuration of water vapor and liquid water in the pore space for some set level of water saturation. Two of the methods are simple and computationally fast methods that can produce fluid distributions close to, or matching, the equilibrium configuration. These methods can, however, produce metastable configurations due to the simplistic nature of the algorithms. The third method applied to this problem is a simulated annealing method. This method consistently produced the lowest possible energy configuration. It is concluded that simulated annealing can be successfully used to numerically model fluid distribution in multiphase saturated porous media.

Method for determining dynamic flow characteristics of multiphase flows

Abstract: A method for determining at least one dynamic flow characteristic of a multiphase flow circulating in a pipe, the flow being composed of a lighter dispersed-phase and a heavier continuous-phase. A tracer is discharged (or activated) into the flow at a chosen first location in the pipe by mixing (or activating) a portion of the tracer with the continuous-phase therein. The tracer concentration at a chosen second location in the pipe is measured with a detector as a function of time t, so as to obtain a signal S(t). Then a relationship is fitted to the signal S(t) so as to derive the values of the velocity U of the continuous phase and/or of a dispersion coefficient k. The slip velocity v s of the dispersed phase relative to the velocity of the continuous phase is also advantageously determined. From the values of velocities U and v s and from the volume fraction y 1 of the continuous phase in the pipe (obtained by an ancillary measurement), the volumetric flow rates of the continuous and dispersed phases are determined.

Improved Prediction of Wet-Gas-Well Performance

Abstract: A series of field tests on liquid loading of gas wells demonstrated that various types of behavior could be encountered in such wells. On the basis of the test results, an improved model for predicting the performance of gas wells producing liquids was formulated. This model takes into account multiphase reservoir performance and the vertical flow performance of the tubings for wet gas. It provides improved estimates for gas deliverability and the remaining life of watering-out gas wells, compared with common methods that calculate critical conditions at a single point (usually the wellhead) in the tubing string.

A fluid‐dynamically based model of bubble column reactors

Abstract: A heterogeneous fluid dynamic model has been developed to describe the complex flow structure of two-phase in bubble columns. The equation of continuity and momentum balances form the basis of the model. Coupling of the two phases occurs via an interaction force, deduced by a force balance around a single rising bubble. Multiphase flow mixing processes are taken into consideration by introducing turbulent viscosities of the two phases involved. The Simulation program was extended to reactive system, taking into account the mass balances of a second order gas-liquid chemical reaction as well as the different absorption/reaction regimes. The gas phase concentration profiles show pronounced axial and radial dependences, while the liquid phase can be regarded as a CSTR with respect to the liquid component. With reference to the gaseous component, which is being absorbed in the liquid phase, the degree of back mixing does not show CSTR behaviour as the influence of different absorption conditions in different axial and radial reactor positions is superposed on that of turbulent motion of the liquid carrier of the dissolved gaseous component.

Use of Nuclear Magnetic Resonance as an Experimental Probe in Multiphase Systems: Determination of the Instrument Weight Function for Measurements of Liquid-Phase Volume Fractions

Abstract: The relativist approach (Baveye and Sposito (1984)) to the interpretation of measurements in multiphase systems was proposed in order to incorporate the details of measurements into theoretical analyses of multiphase transport processes. To help establish the utility of this approach, the weight functions for actual experimental probes must be determined. In this paper we analyze the measurement of liquid-phase porosity in a model system by nuclear magnetic resonance imaging. We show how both nuclear magnetic resonance (NMR) physics and experimental technique combine to determine the weight function for the spin-warp spin-echo sequence. The analysis shows clearly what aspects of the weight function are determined by the experimental method and what aspects are determined by the system being studied. The results will help establish the utility of the relativist approach as well as improve understanding NMR measurements in multiphase systems.

Toward a unified theory of well testing for nonlinear-radial-flow problems with application to interference tests

Abstract: This work presents an analytical solution for the pseudopressure function that represents the reservoir and wellbore responses resulting from production at a constant oil rate in a solution-gas-drive reservoir. The solution can also be reduced to obtain the analytical solution for the corresponding single-phase-flow problem. The general analytical solution suggests a new definition for the dimensionless flow rate. The analytical solutionis used to construct new type curves for analysis of interference tests conducted under multiphase-flow conditions. It is shown that if one ignores multiphase-flow effects and analyze interference data with the line-source-solution type curve, then the estimates of the permeability and porosity-compressibility product obtained may be in error by 20 to 40%.

Laboratory setup and results of experiments on two-dimensional multiphase flow in porous media

Abstract: In the event of an accidental release into earth's subsurface of an immiscible organic liquid, such as a petroleum hydrocarbon or chlorinated organic solvent, the spatial and temporal distribution of the organic liquid is of great interest when considering efforts to prevent groundwater contamination or restore contaminated groundwater. An accurate prediction of immiscible organic liquid migration requires the incorporation of relevant physical principles in models of multiphase flow in porous media; these physical principles must be determined from physical experiments. This report presents a series of such experiments performed during the 1970s at the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland. The experiments were designed to study the transient, two-dimensional displacement of three immiscible fluids in a porous medium. This experimental study appears to be the most detailed published to date. The data obtained from these experiments are suitable for the validation and test calibration of multiphase flow codes. 73 refs., 140 figs.

Theoretical studies of non-Newtonian and Newtonian fluid flow through porous media

Abstract: A comprehensive theoretical study has been carried out on the flow behavior of both single and multiple phase non-Newtonian fluids in porous media This work is divided into three parts: (1) development of numerical and analytical solutions; (2) theoretical studies of transient flow of non-Newtonian fluids in porous media; and (3) applications of well test analysis and displacement efficiency evaluation to field problems A fully implicit, integral finite difference model has been developed for simulation of non-Newtonian and Newtonian fluid flow through porous media Several commonly-used rheological models of power-law and Bingham plastic non-Newtonian fluids have been incorporated in the simulator A Buckley-Leverett type analytical solution for one-dimensional, immiscible displacement involving non-Newtonian fluids in porous media has been developed Based on this solution, a graphic approach for evaluating non-Newtonian displacement efficiency has been developed The Buckley-Leverett-Welge theory is extended to flow problems with non-Newtonian fluids An integral method is also presented for the study of transient flow of Bingham fluids in porous media In addition, two well test analysis methods have been developed for analyzing pressure transient tests of power-law and Bingham fluids, respectively Applications are included to demonstrate this new technology The physical mechanisms involved in immiscible displacement withmore » non-Newtonian fluids in porous media have been studied using the Buckley-Leverett type analytical solution The results show that this kind of displacement is a complicated process and is determined by the rheological properties of the non-Newtonian fluids and the flow conditions, in addition to relative permeability data In another study, an idealized fracture model has been used to obtain some insights into the flow of a power-law fluid in a double-porosity medium For flow at a constant rate, non-Newtonian flow behavior in a fractured medium is characterized by two-parallel straight lines on a log-log plot of injection pressure versus time Transient flow of a general pseudoplastic fluid has been studied numerically and it has been found that the long time pressure responses tend to be equivalent to that of a Newtonian system« less