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Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*25 (05): 704–710.

Paper Number: SPE-12724-PA

Published: 01 October 1985

..., and for studying oilfield drill cores. Comments in the literature and our own experiments suggest that simple approaches to the leaching process may yield accuracies of 10 to 20% for chlorides in rocks with a significant PV

**fraction**. As water contents decrease to 1%, however, an uncontrolled system...
Abstract

We have devised a technique for determining chloride in interstitial water of consolidated rocks. Samples of rocks ranging from 5 to 10 g are crushed and sieved under controlled conditions and then ground with distilled water to submicron size in a closed mechanical mill. After ultra-centrifugation, chloride content is determined by coulometric titration. The chloride concentrations and total pore-water concentrations, obtained earlier from the same pore-water concentrations, obtained earlier from the same samples by low-temperature vacuum desiccation, are used to arrive at the "original" pore-water chloride concentrations by a simple iteration procedure. Interstitial chlorinity results obtained from Cretaceous and Jurassic strata in the Gulf of Mexico coastal areas ranged from 20 to 100 g/kg Cl with reproducibility approaching +/- 1%. We have also applied the technique to igneous and metamorphic bedrocks as well as ocean basalts containing 1 % water or less. Chloride values ranging from 6.7 to 20 g/kg with a reproducibility of about 5% were obtained. Introduction This paper outlines a technique for precision analysis of interstitial chloride and water content (porosity) of shales and other consolidated rocks from deep-earth strata. Nearly all the literature on the composition of interstitial water (formation fluid) of deep-earth strata refers to fluids from reservoir rocks or permeable horizons. In many areas, shales or other nonreservoir rocks constitute the bulk of sedimentary sequences. These rocks contain interstitial fluids of generally unknown composition. The paucity of data is caused partly by the lack of access to fresh cores and partly by analytical difficulties in obtaining interstitial water from such materials. Until the late 1960's, much of the analytical literature dealing with pore fluids from deep sedimentary nonreservoir rocks was published in the Soviet Union and in references cited by those authors. Since then, interest in several hydrochemical phenomena relating to nonreservoir rocks has increased among phenomena relating to nonreservoir rocks has increased among scientists in the U.S. and other Western countries: interest in hydrocarbon resources in overpressured strata dominated by undercompacted shales that may have anomalous chloride content; need for knowledge of the proportion of bound water (electrolyte-poor) in porosity proportion of bound water (electrolyte-poor) in porosity during quantitative interpretation of electrical logs for oil and gas saturation in shaly sands; need for better understanding of nonreservoir rocks as sealing beds for deep waste disposal; and, finally, a desire to understand better the hydrochemical history of deeper sedimentary basins. However, only a relatively few field studies are available on the topics in question. Many of these are student theses or work based on them. The basic procedure underlying the studies of interstitial water composition of shales is simply crushing and grinding a rock sample, leaching it with distilled water, and analyzing the leachate. The salt content of the solid is then related to an independent determination of total pore fluid or porosity. Techniques based on this principle were used for shallow groundwater studies, for general rocks, and for studying oilfield drill cores. Comments in the literature and our own experiments suggest that simple approaches to the leaching process may yield accuracies of 10 to 20% for chlorides in rocks with a significant PV fraction. As water contents decrease to 1%, however, an uncontrolled system may easily yield errors of several hundred percent and uncertainties associated with the bound water (see the section called Discussion). Most of the studies of interstitial chlorinity of water composition in deep oilfield strata have been performed on stored, dried, or partly dried materials and/or have used insufficiently documented or quantified techniques. The goal of this study has been to approach a reproducibility and relative accuracy of I % in the values of interstitial chloride, given our definition of mobile water discussed later. Sampling and Handling of Drilling-Core Samples A potential source of error in interstitial fluid analysis is the contamination of cores by drilling fluid. However, experience in the Deep Sea Drilling Project and other drilling studies 11–15 show that, if external contaminated layers are cut or chipped away from undeformed normal, non-fractured silty-clay cores soon after recovery, virtually unaffected inner sections can be obtained. Even permeable (reservoir-type) rocks sometimes may be sampled successfully for pore-fluid study. During wireline coring by the AMCOR project with the drilling vessel Glomar Conception on the Atlantic Continental Shelf, virtually identical pore-fluid chloride profiles were obtained in repeated drillings performed with seawater and freshwater drilling fluids (Fig. 1). SPEJ P. 704

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*25 (05): 693–703.

Paper Number: SPE-12586-PA

Published: 01 October 1985

... branching. SPEJ P. 693 1 10 1985 1 10 1985 1985. Society of Petroleum Engineers cosurfactant concentration pseudocomponent phase behavior amphiphilic species

**fraction**material balance salinity pseudophase chemical flooding methods pvt measurement artificial intelligence...
Abstract

A thermodynamic model is presented for modeling the partitioning of amphiphilic species between the different partitioning of amphiphilic species between the different phases of systems typically used for chemical flooding. phases of systems typically used for chemical flooding. The model, an extension of the pseudophase model by Biais et al. that can analyze only a four-component system, can work with five-component systems, including two partitioning amphiphilic species (e.g., two alcohols or one alcohol and a partitioning cosurfactant species). The self-association of alcohol in the organic phases, which results in a variable alcohol partition coefficient, is considered. Experiments to determine thermodynamic constants (which are entered into the model) are described for four-component systems, including one alcohol. The salinity dependence of these parameters is also studied. Brine/decane/isobutanol/TRS 10–410 as well as brine/nonane/ isopropanol/TRS 10–80 systems are considered. Some computations of pseudophase compositions for the five-component model and for various overall compositions are included. This partitioning model has been included in the chemical-flooding simulator developed at the U. of Texas; the results of this model have been presented in another paper. The model used for the presented in another paper. The model used for the binodal surface that is required to calculate phase compositions from pseudophase compositions is presented in this paper, as well as comparisons with experimental data for both four- and five-component systems. Reservoir simulation results are presented in Ref. 3. Introduction The possibility of reaching very low interfacial tensions (IFT) during the displacement of oil by surfactant solutions has been the subject of intense interest for some time. Because the decrease in IFT can be as much as several orders of magnitude, almost all the contacted oil can be mobilized by this process. However, the recovery rate has proved to be very sensitive to many parameters, and the process has to be designed carefully to achieve a good oil recovery. It is commonly recognized that the phase behavior is one of the most critical features for the phase behavior is one of the most critical features for the design of chemical oil-recovery processes. Many investigators have studied phase behavior of systems with various combinations of brine, oil, surfactants, and cosurfactants. Winsor introduced a very convenient classification of phase behavior for such systems. Type I is a lower-phase microemulsion (surfactant-rich phase) in equilibrium with an oleic phase; Type II is an phase) in equilibrium with an oleic phase; Type II is an upper-phase microemulsion in equilibrium with an aqueous phase, and Type III corresponds to a middle-phase microemulsion in equilibrium with both aqueous lower phase and oleic upper phase. The number of phases and their composition determined IFT's, viscosity, relative permeabilities and other hydrodynamic parameters on permeabilities and other hydrodynamic parameters on which the efficiency of the process is directly dependent. Components present in the reservoir during chemical flooding include water, electrolytes, oil, polymer, and the amphiphilic species surfactant and cosurfactant. From the viewpoint of chemical thermodynamics, the number of chemical species is very large if we consider every species of which oil, surfactant, and cosurfactant are made. Fortunately, some of these species behave collectively, so they can be considered a single pseudocomponent in the phase behavior description, thereby pseudocomponent in the phase behavior description, thereby making the study more tractable. For example, Vinatieri and Fleming considered brine a good pseudocomponent, which means that the ratio of salt to water is about the same in each phase. McQuigg et al.'s experiments yield similar conclusions. Even crude oil has been shown to be a good pseudocomponent with a fairly acceptable accuracy. Dealing with amphiphilic species is far more difficult. In some laboratory studies, surfactant can be a chemically pure component, but for field applications it is usually a complex blend, such as petroleum sulfonates. In the case of petroleum sulfonates, different monosulfonated or polysulfonated species are present with varied carbon polysulfonated species are present with varied carbon tails. Commercial nonionic surfactants, which generally are ethoxylated alcohols, show a broad distribution of ethylene oxide number (EON). In both cases, investigators have shown that these commercially available surfactants do not behave collectively but in some situations partition selectively between the phases. The cosurfactant generally is an alcohol or an ethoxylated alcohol. Although many research programs currently are devoted to the design of alcohol-free systems to avoid some of the drawbacks induced by its presence (lower solubilization parameters, higher IFT's), most of the commonly used systems include alcohol or even a blend of alcohols with different carbon chain lengths and/or branching. SPEJ P. 693

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*25 (02): 303–312.

Paper Number: SPE-11689-PA

Published: 01 April 1985

... for the modeling of idealized fractured reservoirs. Simulations are carried out for a five-spot well pattern with various well spacings, fracture spacings, and pattern with various well spacings, fracture spacings, and injection

**fractions**. The production rates from the wells are calculated using a...
Abstract

Numerical studies of the effects of injection on the behavior of production wells completed in fractured two-phase geothermal reservoirs are presented. In these studies the multiple-interacting-continua (MINC) method is employed for the modeling of idealized fractured reservoirs. Simulations are carried out for a five-spot well pattern with various well spacings, fracture spacings, and pattern with various well spacings, fracture spacings, and injection fractions. The production rates from the wells are calculated using a deliverability model. The results of the studies show that injection into two-phase fractured reservoirs increases flow rates and decreases enthalpies of producing wells. These two effects offset each other so that injection tends to have small effects on the usable energy output of production wells in the short term. However, if a sufficiently large fraction of the produced fluids is injected, the fracture system may become liquid-filled and an increased steam rate is obtained. Our studies show that injection greatly increases the long-term energy output from wells because it helps extract heat from the reservoir rocks. If a high fraction of the produced fluids is injected, the ultimate energy recovery will increase many-fold. Introduction At present, reinjection of geothermal brines is employed or being considered at most high-temperature geothermal fields under development. At many geothermal fields, primarily those in the U.S. or Japan, reinjection is a primarily those in the U.S. or Japan, reinjection is a necessity because environmental considerations do not permit surface disposal of the brines (unacceptable permit surface disposal of the brines (unacceptable concentrations of toxic minerals). At other fields (e.g., The Geysers, CA) reinjection is used for reservoir management to help maintain reservoir pressures and to enhance energy recovery from the reservoir rocks. The effectiveness of injection in maintaining reservoir pressures has been illustrated at the Ahuachapan geothermal field in El Salvador. During the last decade various investigators have studied the effects of injection on pressures and overall energy recovery from geothermal fields. Theoretical studies have been carried out by Kasameyer and Schroeder, Lippmann et al., O'Sullivan wad Pruess, Schroeder et al., and Pruess, among others. Site-specific studies were reported by Morris and Campbell on East Mesa, CA; Schroeder et al. and Giovannoni et al. on Larderello, Italy; Bodvarsson et al. on Baca, NM; Tsang et al. on Cerro Prieto, Mexico; and Jonsson and Pruess et al. on Krafla, Iceland. These studies have given valuable insight into physical processes and reservoir response during injection. However, there is limited understanding of injection effects in fractured reservoirs, especially high-temperature, two-phase systems. Fundamental studies and quantitative results for the design of injection programs in such systems are greedy needed. The objectives of the present work are to investigate the effects of injection on the behavior of fractured two-phase reservoirs. Several questions will be addressed. How will injection affect flow rates and enthalpies of the production wans? Can injection increase the short-term usable energy output of well? What are the long-term effects of injection? How is the efficiency of injection dependent on factors such as well spacing and fracture spacing? Reliable answers to these questions should be valuable for field operators in the design of injection systems for two-phase fractured reservoirs. Approach In the present work we consider wells arranged in a five-spot pattern (Fig. 1). Because of symmetry we only need to model one-eighth of a basic element as shown in Fig. 1; however, our results always are presented for the full five spot. The "primary" (porous medium) mesh shown in Fig. 1 consists of 38 elements; some of the smaller ones close to the wells are not shown. The mesh has a single layer, so that gravity effects are neglected. The fractured reservoir calculations are carried out by the MINC method, which is a generalization of the double-porosity concept introduced by Barenblatt et al. and Warren and Root. The basic reservoir model consists of rectangular matrix blocks bounded by three sets of orthogonal infinite fractures of equal aperture b and spacing D (Fig. 2a. M the mathematical formulation the fractures with high transport and low storage capacity are combined into one continuum and the low-permeability, high storativity matrix blocks into another. The MINC method treats transient flow of fluid (steam and/or water) and heat between the two continua by means of numerical methods. Resolution of the pressure and temperature gradients at the matrix/fracture interface is achieved by partitioning of the matrix blocks into a series of interacting partitioning of the matrix blocks into a series of interacting continua. SPEJ P. 303

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*25 (02): 202–214.

Paper Number: SPE-11713-PA

Published: 01 April 1985

... method factorization saturation heat capacity

**fraction**reaction computer calculation constraint well flow equation enhanced recovery artificial intelligence A General Purpose Thermal Model Barry Rubin, * SPE, Computer Modelling Group W. Lloyd Buchanan, SPE, Computer Modelling Group Abstract...
Abstract

This paper describes a fully implicit four-phase (oil, water, gas, solid fuel) numerical reservoir model for simulating hot water injection, steam injection, dry combustion, and wet combustion in one, two, or three dimensions and in either a Cartesian, radial, or curvilinear geometry. The simulator rigorously models fluid flow, heat transfer (convective and conductive), heat loss to formation, fluid vaporization/condensation, and chemical reactions. Any number of oil or gas phase components may be specified, along with any number of solid phase components (fuel and catalysts). The simulator employs either D4 Gaussian elimination or powerful incomplete factorization methods to solve the often poorly conditioned matrix problems. An implicit well model is coupled to the simulator, where reservoir unknowns and well block pressures are primary variables. This paper includes comparisons of the numerical model's results with previously reported laboratory physical models' results for steam and combustion and physical models' results for steam and combustion and analytical solutions to a hot waterflood problem. In addition, an actual field-scale history match is presented for a single-well steam stimulation problem. Introduction Recent papers by Crookston et al., Youngren Rubin and Vinsome, and Coats have outlined the current trend in thermal process simulation. The trend has been the development of more implicit, more comprehensive finite-difference simulators. Youngren describes a model based on a highly implicit steam model. The components representing air and combustion gases are treated explicitly. Burning reactions are handled not through rates but through the assumption of 100% oxygen utilization at the combustion front. Crookston et al. describe a linearized implicit combustion model that can describe the reaction of a predetermined set of gases and oils. Both of these models are predetermined set of gases and oils. Both of these models are multidimensional and do not handle wellbore-reservoir coupling fully implicitly. Rubin and Vinsome describe a fully implicit one-dimensional (ID) combustion tube simulator. Coats 4 describes a fully implicit four-phase multicomponent multidimensional combustion simulator. This model is general in nature except for the wellbore-reservoir coupling. This work describes a general, fully implicit, four-phase, multicomponent, multidimensional steam and combustion simulator that includes a fully implicit well model and a suite of powerful iterative techniques that can be used for the solution of large-scale thermal problems. The following sections of this paper describe the model's fluid and energy flow equations, property package, powerful iterative techniques capable of reliable package, powerful iterative techniques capable of reliable use with steam and combustion problems, fully implicit well model, and equation substitution formulation. Further, a section considering the applications of the model is presented. Mathematical Model The simulator ISCOM rigorously models fluid flow, vaporization/condensation phenomena, and heat transfer and is efficient enough to allow the simulation of realistically large reservoir problems. The formulation allows for any number of chemical components and reactions. The components can exist in any of four phases: oil, water, gas, or solid. A reaction also can occur in any of the above phases. Furthermore, water and any of the oil components can vaporize. The simulator development is based on the following assumptions. The model can operate in one, two, or three dimensions (1D, 2D, or 3D) with variable grid spacing. Cartesian, radial, non-Cartesian (variable-thickness grids), and specific curvilinear grids corresponding to the commonly used well patterns can be used. patterns can be used. The number of components existing in each phase is variable, and the components can be distributed among four phases. The number and type of chemical reactions can be varied. Each layer, well, or block in the reservoir can exhibit different properties (e.g., viscosities, relative permeabilities, and properties (e.g., viscosities, relative permeabilities, and compressibilities) at different times. Wells can operate under specified fluid rates or flowing pressures and are subject to a hierarchy of user-specified constraints. The simulator must be reasonably efficient to handle field-scale simulation economically, without sacrificing accuracy. Grid Generation The model defines a block-centered grid system in 1-, 2-, or 3D, normally based on Cartesian xyz coordinates. Radial geometries are accommodated by internal modification of the gridblock volumes and interblock transmissibilities. For rectangular grids with variable thickness layers, the interblock transmissibilities and gravity head terms are derived from gridblock dimensions and depth from reference. Curvilinear grids are generated by the method of conformal transformation, which yields analytical formulae for potential and stream functions. Two simple patterns are considered: one-eighth of a five-spot and one-eighth of a nine-spot. SPEJ P. 202

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*25 (02): 268–274.

Paper Number: SPE-11959-PA

Published: 01 April 1985

... temperature, oil C 5+ molecular weight, volatile oil

**fraction**, intermediate oil**fraction**, and composition of the CO 2 stream. The effects of temperature and oil C 5+ molecular weight on pure CO 2 MMP have been well documented. However, CO 2 sources are rarely pure, and solution gas usually is present in...
Abstract

This paper presents an empirically derived correlation for estimating the minimum pressure required for multicontact miscible (MCM) displacement of live oil systems by pure or impure CO 2 streams. Minimum miscibility pressure (MMP) has been correlated with temperature, oil C 5+ molecular weight, volatile oil fraction, intermediate oil fraction, and composition of the CO 2 stream. The effects of temperature and oil C 5+ molecular weight on pure CO 2 MMP have been well documented. However, CO 2 sources are rarely pure, and solution gas usually is present in reservoir oils. The correlation presented in this paper accounts for the additional effects on MMP caused by the presence of volatile components (methane, C 1 ; and N 2 ) and intermediate components (ethane, C 2 ; propane, C 3 ; butane, C 4 ; hydrogen sulfide, H 2 S; and CO 2 ) in the reservoir oil. This correlation also is capable of estimating MMP for a contaminated or enriched CO 2 stream on the basis of the pure CO 2 MMP. Introduction Miscible displacements using hydrocarbon solvents have been described in the literature by many authors. 1–6 The use of a slim tube apparatus for the establishment of MMP requirements for enriched or vaporizing gas drives was presented by Deffrenne et al. 5 and Yarborough and Smith. 7 Rutherford 8 referred to these systems as conditionally miscible processes. The initial work of Rathmell et al . 9 and Ballard and Smith 10 illustrated that the mechanisms of CO 2 displacements are similar to those of high-pressure MCM vaporizing gas drives. Since the high solubility of CO 2 in reservoir oils diminishes the pressure required for miscibility to occur, a CO 2 vaporizing gas drive can operate in the same manner as a lean-gas injection process, but at significantly lower pressures. Correlations for the prediction of MMP requirements for CO 2 flooding are extremely helpful in the screening of candidate reservoirs for CO 2 floods. Holm and Josendal 11 were the first to introduce a method for estimating the MMP required for CO 2 displacing oil. Other correlations for CO 2 MMP have been introduced by the Natl. Petroleum Council, 12 Yellig and Metcalfe, 13 and Johnson and Pollin, 14 as well as a new correlation from Holm and Josendal. 15,16 This paper presents an empirical approach to MMP estimation. Included in this study are the effects of solution gas (live oil systems) and the effects of impure CO 2 sources. Concepts of Miscible Displacement Miscible displacement is represented most easily by a ternary diagram. A pseudoternary diagram for a hypothetical hydrocarbon system is shown in Fig. 1. This is a pseudoternary representation since the apexes do not consist of pure components, but it can be used to qualitatively describe the process of miscible displacement. Fig. 1 has been divided into three areas: Zone 1, Zone 2, and Zone 3. Zone 1 represents the area of first-contact miscibility. Any solvent falling within this region can be mixed with the reservoir oil shown, such that any and all mixtures will fall outside of the two-phase region. Zone 2 represents the region of multicontact miscibility. Solvents within this area, while not initially miscible in all proportions with the reservoir oil, eventually will achieve miscibility through the repeated contacts of the reservoir oil and equilibrium fluids. There are two types of MCM processes: vaporizing gas drive, where the solvent is enriched by components vaporized from the reservoir oil, and condensing or enriched gas drive, where the solvent contributes to the enrichment of the reservoir fluid. 17 Commercially viable CO 2 -miscible EOR processes are usually of the MCM type, because reservoir pressure requirements for this process are significantly lower than required for first contact miscibility. Zone 3 represents the area of immiscible displacement. Displacement of the reservoir oil by an fluid falling within Zone 3 will result in multiphase flow. The mass transfer between the oil and displacing fluid is such that miscibility cannot be achieved.

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (06): 685–696.

Paper Number: SPE-11200-PA

Published: 01 December 1984

... reservoir fluids with extended C 7+ analysis have been chosen, representing a broad range of compositions and PVT data. First, the study deals with methods for estimating specific gravities and boiling points of petroleum

**fractions**, two properties usually required by critical property correlations. EOS...
Abstract

Summary This work studies the effect of heptanes-plus (C 7+ ) characterization on equation-of-state (EOS) predictions. Both the Peng-Robinson EOS (PREOS) and a modified Redlich-Kwong EOS are used. Several characterization schemes found in the literature are used in the study. Six reservoir fluids with extended C 7+ analysis have been chosen, representing a broad range of compositions and PVT data. First, the study deals with methods for estimating specific gravities and boiling points of petroleum fractions, two properties usually required by critical property correlations. EOS predictions are made by using critical properties based on specific gravities and boiling points measured experimentally and estimated with correlations. Next, a review of critical-property correlations is given, including a review of commonly used correlations. Four correlations are chosen to study the effect of critical properties on EOS predictions. Results indicate that relatively small differences in critical properties and acentric factor can result in significant differences in EOS predictions. Finally, a study is made of the effect that adjustments in C 7+ critical properties have on EOS predictions; adjustments of EOS constants (O a and O b ) and binary interaction coefficients also are studied. The influence of individual and combined adjustments to C 7+ properties are illustrated graphically. They provide qualitative guidelines that can be used when matching experimental PVT data with an EOS. Introduction Recently there has been an increasing interest in EOR methods. One result has been the need to develop numerical models for simulating EOR processes involving complex phase behavior. Most of these models use an EOS to predict vapor/liquid equilibrium (VLE) and volumetric phase behavior. A typical problem with using an EOS is the difficulty in describing petroleum fractions constituting C 7+ . These fractions significantly affect EOS predictions, as has been reported in the literature. Usually only limited C 7+ data are available to describe C 7+ fractions. Even so, estimates of critical properties - critical pressure, critical temperature, and acentric factor - are required by most EOS's. Several correlations exist for estimating critical properties of petroleum fractions. Most are empirical equations giving a best fit of graphical correlations based on experimental data. Boiling point and specific gravity usually are required by critical property correlations. Several methods exist for estimating specific gravity and boiling point of petroleum fractions when only C 7+ properties are known. Four of these have been used in our study. Several methods have been tried to improve C 7+ characterization by approximating the chemical makeup of petroleum fractions. The most common approach assumes that petroleum fractions are composed of three hydrocarbon groups: paraffins (P), naphthenes (N), and aromatics (A). Several methods exist for estimating PNA content of petroleum fractions. 1–3 Three aspects of C 7+ characterization have been studied: methods for estimating specific gravity and boiling point of petroleum fractions, correlations for estimating critical pressure, critical temperature, and acentric factor, and manual adjustment of critical properties, EOS constants (O a and O b ), and binary interaction coefficients (particularly between methane/CO 2 and C 7+ fractions). Reservoir fluids used in this study were chosen on the basis of availability of distillation data for C 7+ fractions and the type of PVT measurements reported. Six fluids have been chosen from the literature, including fluids ranging from a lean gas to a black oil. PVT measurements have been reported at more than one temperature for some of the mixtures, which allows the study of temperature dependence of binary interaction coefficients between methane and C 7+ fractions. Two cubic EOS's are used to make PVT predictions. PREOS 4 was chosen because it is widely accepted in the industry and it generally yields better liquid-density estimates than the comparable Soave-Redlich-Kwong 5 (SRK) equation. As a representative of the Redlich-Kwong 6 family, Yarborough's 7 version of the modified Zudkevich-Joffe-Redlich-Kwong 8 (ZJRK) equation was chosen. Results from this work suggest that C 7+ characterization has a significant influence on EOS predictions of reservoir fluid behavior. It is difficult to make objective conclusions about which C 7+ characterization schemes are best. A different approach to characterization is needed. One possible alternative would be to calculate critical properties of petroleum fractions such that measured values of specific gravity and boiling point are force-fit by the EOS.

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (06): 617–627.

Paper Number: SPE-9009-PA

Published: 01 December 1984

.../polymer process is designed to produce residual oil trapped by capillary forces. Papers pro-posing numerical models of the process have been documented. Most neglect the unsteady-state flow of fluids and the capillary pressure between phases by employing a

**fractional**flow formula combined with Darcy's law...
Abstract

A highly implicit, multidimensional, multicomponent, multiphase, unsteady-state flow model has been for-mulated to simulate a micellar/polymer process. Unlike most compositional approaches, the proposed model ac- counts for capillary pressure. In addition, the model describes the unsteady-state flow of fluids and accounts for additional pressure- and concentration-dependent variables such as average mass velocity, effective disper- sivity, and FVF that most compositional models do not. Numerical solutions to this model are obtained by a finite-difference method. For a one-dimensional (1D) case, the system is treated in terms of five pseudocomponents and two mobile phases. The proposed model is represented by a system of nonlinear partial differential equations in the dependent variables, component concentrations, and phase pressures. The model incorporates the process variables. These include those mentioned above plus in-terfacial tension (IFT), relative permeability, partition coefficient, adsorption concentration, and viscosity. The model was validated by history-matching with a laboratory core displacement test. The agreement of the numerical results and laboratory results shows the model's reliability and gives a realistic insight into its usefulness as a multidimensional, multicomponent, multiphase simulator. After testing, the model was used to investigate the effect of variations in the input parameters on the production history. Introduction The micellar/polymer process is designed to produce residual oil trapped by capillary forces. Papers pro-posing numerical models of the process have been documented. Most neglect the unsteady-state flow of fluids and the capillary pressure between phases by employing a fractional flow formula combined with Darcy's law to represent individual phase transport. They also approximate the physical dispersion by numerical dispersion with appropriate choice of timestep and spacestep. On the other hand, these models deal with the compositional effects and provide design criteria for chemical flooding. The purpose of this paper is to present a new set of micellar/polymer process model equations and methods to model process variables while requiring no restrictions for implicit formulation. This approach is presented as the first step for multidimensional simulation of reservoir flow systems where the proposed process variables govern. The proposed numerical model consists of a system of equations derived from the combination of mass balance, Darcy's law, Fick's first law, and the consideration of various forces. This system of equations was solved simultaneously for a 1D case by a finite-difference method. Included in this paper are solution methods, numerical techniques, verification of model by history-matching with a core displacement test, treatment of proc-ess variables, and effects of variations in the input parameters on the production performance. Model Equations General assumptions of a multidimensional, multicompo-nent, multiphase system are: the displacement process is carried out under isothermal conditions and the total volume does not change with mixing of individual com-ponents. Based on these assumptions, the generalized model equations may be expressed for n components within in phases as ......................(1) SPEJ P. 617^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (05): 536–544.

Paper Number: SPE-11210-PA

Published: 01 October 1984

... pressure range; selected high-pressure data indicate how the compressibility deviates at much higher pressures. To within the resolution of the data, the composition dependence is linear in volume-

**fraction**composition; moreover, the effective compressibilities of oil and water in solution appear to be near...
Abstract

Compression to reservoir pressures can alter microemulsion phase behavior, on which the success of microemulsion-based phase behavior, on which the success of microemulsion-based EOR processes depends. For convenience, however, phase behavior studies usually are conducted at atmospheric pressure. Extrapolating phase behavior data from atmospheric to reservoir pressures requires the volumetric properties of each phase pressures requires the volumetric properties of each phase under compression, including the isothermal compressibility as a function of pressure and composition. Two topics are addressed here. First, compressibility data up to 16 MPa [2,300 psi] are presented for several systems of oil and water with surfactants and proto surfactants and the data are fit to simple models for pressure and composition dependence. The pressure dependence fits the Tait equation in this pressure range; selected high-pressure data indicate how the compressibility deviates at much higher pressures. To within the resolution of the data, the composition dependence is linear in volume-fraction composition; moreover, the effective compressibilities of oil and water in solution appear to be near their pure-component values. More data are needed to verify and determine the exact dependence. Second, a simple compressibility cell is described that allows both rapid determination of compressibility and direct determination of the phase boundary in pressure. Both phase separation and coalescence of distinct phases with increasing pressure was observed in microemulsion systems, although the phase boundaries in pressure for these systems were not mapped out systematically. The effect of dissolved gases such as methane, which can affect microemulsion phase behavior at high pressures, is not addressed here. Introduction The phase behavior of mixtures of oil and water with surfactant is crucial to the analysis and design of microemulsion flooding processes for EOR. Phase behavior governs the local compositions and saturations of the various fluid phases, which, through fractional flow relations, determine microscopic displacement. Moreover, phase behavior influences the fractional flow relations phase behavior influences the fractional flow relations themselves through its influence on interfacial tension, wettability, and fluid properties. The importance of phase behavior to process design has prompted a wide phase behavior to process design has prompted a wide range of laboratory studies of microemulsion phase behavior. However, compression to reservoir pressure distorts phase behavior from that observed in the laboratory. A phase behavior from that observed in the laboratory. A familiar example of the effect of pressure is described by the Clausius-Clapeyron equation for the change in freezing point of a pure liquid. More generally, in multicomponent point of a pure liquid. More generally, in multicomponent mixtures equilibrium conditions derive from the required equality of chemical potentials ...............(1) between phases A and B. Any intensive variable influences phase behavior through its effect on chemical potentials; that of pressure acts through the partial potentials; that of pressure acts through the partial molar volumes: .......(2) where is partial molar volume and p is a fixed reference pressure such as 100 kPa [14.5 psi]. Because for each component the molar volume can differ between phases, a change in pressure can upset the equality of phases, a change in pressure can upset the equality of chemical potentials unless phase compositions change to restore equilibrium. Thus the shift in phase boundaries under compression results from the dependence of chemical potentials on pressure and composition. Phase behavior in microemulsion systems is especially sensitive to intensive variables like temperature and salinity. Recent reports disagree on its sensitivity to pressure. O'Connell and Walker and Good found that pressure significantly altered the phase behavior of pressure significantly altered the phase behavior of microemulsion systems made with several synthetic oils. Nelson, on the other hand, observed a negligible pressure effect on two microemulsion systems, one made with a crude oil and one with a synthetic oil. Evidently the thermodynamic properties that govern the effect of pressure can differ among microemulsion systems. To extrapolate phase behavior from atmospheric to reservoir pressures by using Eq. 2 requires knowledge of volumetric properties of the phases involved; specifically, the partial molar volume, vi, of all components in each phase must be known as functions of pressure and phase must be known as functions of pressure and composition. These may be derived from the partial molar volumes at atmospheric pressure, more easily measured in the laboratory, and a correlation for the compressibility of the mixture as a function of pressure and composition, . An example of the correction of chemical potentials for pressure effects is given in Ref. 18. SPEJ p. 536

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (04): 435–446.

Paper Number: SPE-10200-PA

Published: 01 August 1984

...Albert F. Chan; Surendra P. Gupta This paper presents a novel method of characterizing the broad equivalent-weight (BEW) sulfonates composed of two pseudosulfonate

**fractions**that behave as the oil-moving and the sulfonate-solubilizing components. The terms quasi-monosulfonate and quasi-disulfonate...
Abstract

This paper presents a novel method of characterizing the broad equivalent-weight (BEW) sulfonates composed of two pseudosulfonate fractions that behave as the oil-moving and the sulfonate-solubilizing components. The terms quasi-monosulfonate and quasi-disulfonate are used to characterize these oil-moving and solubilizing components, respectively. Such a description of BEW sulfonates allows determination of sulfonate concentration in the flowing phases as well as the quantity adsorbed on the porous medium, and permits modeling of the sulfonate retention and transport behavior. Furthermore, the paper shows that the performance of a BEW sulfonate system in which a lower-phase microemulsion environment is predominant can be predicted by using independently measured input data, which include interfacial tension (IFT), fluid viscosity, and sulfonate retention isotherm. Introduction The BEW sulfonates commonly have a broad range of equivalent weights and a significant percentage of di- and polysulfonated components, and exhibit unique properties and phase behavior compared with the relatively narrow-equivalent-weight or pure sulfonates. They usually are fractionated during the oil displacement process. This paper introduces a method to calibrate the fractionated sulfonates by using two pseudosulfonate fractions obtained from a polarity partitioning technique. This technique, in conjunction with the high-performance liquid chromatography (HPLC) analysis, allows an artificial separation of BEW sulfonates into two major fractions, which simulate the oil-moving and the solubilizing components of sulfonate. The terms quasi-monosulfonate and quasi-disulfonate are used to characterize these oil-moving and sulfonate-solubilizing components, respectively. This calibration method was used successfully to determine sulfonate concentrations in the oil and aqueous phase effluents as well as the sulfonate retained on the rock surfaces. This has been valuable for interpreting the sulfonate retention and transport behavior. The retention measurements of quasi-monosulfonate were found to depend on micellar slug size, core length, and contact time. These results suggest that the effect of contact time may become significant in laboratory short-core tests with a small slug and should be an important consideration when interpreting the data. This paper also discusses the sulfonate propagation and displacement behavior of micellar systems with a BEW sulfonate in which the lower-phase microemulsion environment is predominant. It is shown that such a system can give effective oil displacement through the generation of low IFT, favorable phase behavior, and good mobility control. Furthermore, the performance of such a lower-phase system can be simulated easily by using independently measured input data, which include IFT, fluid viscosity, and sulfonate retention isotherm. This simulation provides a means to estimate sulfonate retention and also to optimize sulfonate use in micellar flooding. Micellar Fluid Systems and Experimental Details The primary surfactant used in all the formulations is a BEW vacuum gas oil (VGO) sulfonate. Table 1 lists the major components of the bulk sulfonate. The equivalent-weight distributions of VGO sulfonate components in this study range between 300 and 700. The cosurfactant was either isopropyl alcohol or an ethoxylated hexanol. A micellar formulation containing a VGO sulfonate and isopropyl alcohol is given in Table 2. The oil was a 4-cp [4-MPa's] field crude, and the in-place brine consisted of 0.25 N NaCl solution. Xanflood biopolymer was used as the mobility control agent. All tests were conducted at 110 degrees F [43.3 degrees C]. Oil displacement tests for the sulfonate propagation and retention studies were conducted in 2- and 6-ft [0.61- and 1.83-m] Berea cores at 2.3-ft/D [0.70-m/D] frontal advance rate. Sulfonate retention measurements in the absence of crude oil were conducted in 8-in. [20-cm] Berea cores. Details of these tests are given in Tables 3 through 5. Analyses of the core effluent components were accomplished by using HPLC, gas chromatography, and gel permeation chromatography. The fluid viscosity was measured by using a Brookfield viscometer with a UL adaptor. The IFT's were measured by using a spinning-drop interfacial tensiometer. SPEJ P. 435^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (04): 447–457.

Paper Number: SPE-10976-PA

Published: 01 August 1984

... events. This paper describes a shale management procedure that handles sampling of the empirical statistics, generates shale coordinates, and maintains control such that conditioning at the wells is achieved. Conditioning means that the

**fraction**of shale and the vertical succession of sand and shale...
Abstract

Virtually every sandstone reservoir contains significant amounts of shale. Although the sand/shale sequence in the wells may be known, a reliable reservoir description must define quantitatively the lateral continuity of the shale, the shale distribution in unsampled areas, and the effects of the shales on transport properties. This paper presents statistical techniques by which the lateral continuity and spatial disposition of shales can be estimated. These techniques rely on shale statistics from the wells and outcrop statistics from appropriate depositional environments. The resulting shale description can be conditioned to conform with the observations of the wells. The subsequent discretizing of the reservoir into gridblocks for numerical simulation yields large elemental units that usually contain both sand and shale. The paper concludes by showing how the permeability and paper concludes by showing how the permeability and porosity may be estimated from the disposition of shales porosity may be estimated from the disposition of shales within each block. Introduction Shales either divide reservoirs into separate hydraulic units, or, if the shales are discontinuous, set a tortuous environment in which fluid transport occurs. While continuous correlatable shales are handled with ease in reservoir simulation models, discontinuous shales present a problem. This study is concerned with such present a problem. This study is concerned with such uncorrelatable discontinuous shales in sandstone reservoirs. The primary source of information about shales is, as with virtually all reservoir properties, the wells. An empirical distribution of shale thicknesses can he inferred from an observed sand/shale sequence. Unless the well spacing is extremely dense, nothing is revealed about the shale's lateral dimensions. A secondary source of information is visual studies on shale dimensions in outcrops of ancient sediments. Once the depositional environment is identified by the geologist, outcrop statistics from a depositional environment similar to the one to be simulated are used for the assignment of lateral shale dimensions. Since we are concerned here with uncorrelatable or stochastic shales, the shales are assumed to be randomly distributed in space. This means that the shale dimensions and the coordinates of the shale centers are random, independent statistical events. This paper describes a shale management procedure that handles sampling of the empirical statistics, generates shale coordinates, and maintains control such that conditioning at the wells is achieved. Conditioning means that the fraction of shale and the vertical succession of sand and shale observed in a well are identical to that in a synthetic description. Finally, when a user-defined grid system is superimposed on the resulting description, the procedure calculates effective porosities and permeabilities for each gridblock. Definition Four scales of averaging volume can be recognized for porous media averages: microscopic (the scale of only a porous media averages: microscopic (the scale of only a few pores), macroscopic (the size of conventional core plugs), megascopic (the size of large gridblocks in field plugs), megascopic (the size of large gridblocks in field models), and gigascopic (total formation or regional scale). These concepts are illustrated in Fig. 1a. As discussed by Bear, porous-media transport equations usually are based on the continuum approach. This means that the actual porous medium is replaced by a fictitious continuum. Physical properties and dependent variables are averages over elemental physical volumes constituting the continuum. The suggested distinction among four scales is necessary because measurements on one scale are not necessarily applicable on another scale (Fig. 1b). In particular, measurements on cores, by which intrinsic sand properties are found, cannot be used readily for megascopic blocks, which include gross textural differences such as sand and shales. This discrepancy is particularly noticeable in numerical reservoir simulation particularly noticeable in numerical reservoir simulation where fluid flow equations are formulated on a macroscale but are frequently solved on a megascale. Shales are generally recognized by geologists as fine-grained, indurated sedimentary rocks with finely laminated structure. They are believed to be a lithification product of muddy sediment, of any origin, and the finely laminated texture is related to orientation of micaceous clay mineral constituents. For our purposes, the term "shale" includes shale laminae, shale streaks, and massive shales. Two shale types are distinguished. The definitions are based on whether the dimensions and spatial disposition of the shales are known. Stochastic shales cannot be correlated between wells and appear to be scattered randomly within the sand matrix (Fig. 2a). Deterministic shales are continuous between observation points. There is no uncertainty associated with their existence and lateral continuity (Fig. 2b). Most reservoirs are hybrid with respect to shales in that both deterministic and stochastic shales coexist; however, the occurrence of stochastic shales clearly becomes more prevalent with large well spacings. SPEJ P. 447

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (03): 283–293.

Paper Number: SPE-11202-PA

Published: 01 June 1984

.... 2 and propane. Possible improvements of the model are also discussed. Finally, the model is used to predict field conditions favorable to asphalt and asphaltene precipitation. Asphaltenes, Resins, and Asphalt. Asphaltenes are defined as the n-heptane insoluble

**fraction**of crude oil obtained...
Abstract

A thermodynamic liquid model has been developed to describe the behavior of asphalt and asphaltenes in reservoir crudes upon changes in pressure, temperature, or composition. Asphaltene solubility properties used as input to the model may be obtained from titration experiments on tank oil. High-pressure flocculation experiments confirm the potential of the model. The model appears to be well applicable to conditions at which asphaltenes are associated with resins. The model may be used to identify field conditions where asphalt or asphaltene precipitation will occur. Introduction Scope of study. Miscible flooding with enriched gas or CO has the potential of recovering a significantly larger volume of oil more economically than conventional water flooding. One of the problems in gas drives is asphaltene instability, which might result in plugging or wettability reversal. Asphalt or asphaltenes precipitation may also affect production in the course of precipitation may also affect production in the course of reservoir development by natural depletion. The parameters that govern precipitation appear to be composition of the crude, pressure, temperature, and properties of asphaltenes. For a specific project one can properties of asphaltenes. For a specific project one can investigate the flocculation process experimentally. This proposition is usually impractical because it requires a proposition is usually impractical because it requires a large number of experiments at reservoir conditions of pressure and temperature. Hence, there is a need for a pressure and temperature. Hence, there is a need for a theoretical description using only a limited amount of experimental data to predict precipitation. The search for such a model has been hampered by the widely held notion that asphaltene precipitation is not a (fully) reversible process. Re-examination of experimental information indicates that reversibility of asphaltene precipitation should be considered an open question. If reversible, the process can be described with a thermodynamic model. The aim of the present paper is to demonstrate that flocculation of asphalt and asphaltenes in light crudes (formation of a bituminous phase) can be described with a simple molecular thermodynamic model. The key concepts of asphalt, asphaltenes, and resins are defined in the next section. The model proposed is described in the following section, in which we also review previous studies. We then discuss field experiences. Experimental data are presented on the phase behavior of two light crudes: an Iranian crude oil with an n-heptane asphaltene content of 1.9 wt% (of tank oil) and a North Sea crude with a low (0.3 wt%) asphaltene content (see PVT properties in Tables 1 and 2). We first use the proposed model (Appendix A) to determine the solubility properties of asphaltenes in Crude No. 1, from a series of titration experiments on tank oil. Using, these results, we compare the measured and predicted amounts of asphaltenes precipitated on mixing recombined Crude No. 1 with three potential injection gases (Table 3). We discuss the pressure dependence of asphalt precipitation and compare measured and predicted pressure dependence of the amount of asphalt precipitated from a mixture of crude No. 2 and propane. Possible improvements of the model are also discussed. Finally, the model is used to predict field conditions favorable to asphalt and asphaltene precipitation. Asphaltenes, Resins, and Asphalt. Asphaltenes are defined as the n-heptane insoluble fraction of crude oil obtained following the Inst. of Petroleum (IP) Method Test 143. Resins can be defined as the fraction of crude oil not soluble in ethylacetate but soluble in n-heptane, toluene, and benzene at room temperature. Asphalt is used here as a general term to designate the combination of asphaltenes and resins. Asphalt precipitated by propane can be molten. n-heptane asphaltenes are solid and decompose upon heating. Asphaltenes and resins are heterocompounds and form the most polar fraction of crude oil. Recent studies on asphaltene structure show that the basic asphaltene "molecule" (asphaltene sheet ) has a molecular weight of the same order of magnitude as that of resins (5 × 10 to 10 3 ). Depending on "purity" and concentration asphaltenes form aggregates with a molecular weight of the order of magnitude of 10 to 10 (asphaltene particles ). Resins have a strong tendency to associate with particles ). Resins have a strong tendency to associate with asphaltenes. This reduces the aggregation of asphaltenes, which determines to a large extent their solubility in crude oil. The most common model for asphaltene/resin interaction is the colloidal model. Asphaltene micelles (aggregates) are assumed to be kept in solution (stabilized or peptized) by a layer of resins ("onion-skin model"). peptized) by a layer of resins ("onion-skin model"). However, the studies of Yen, Speight, and Briant provide a basis for developing a molecular model for provide a basis for developing a molecular model for asphaltene/resin interaction. SPEJ P. 283

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (03): 277–282.

Paper Number: SPE-11280-PA

Published: 01 June 1984

... viscosities. This paper documents the development of a simple but generalized correlation for predicting viscosities of binary mixtures of heavy oil, bitumen, and petroleum

**fractions**, with particular emphasis on heavy-oil/solvent systems. Background Previous Work. Viscosity of liquid mixtures has been...
Abstract

High viscosity is a major constraint in the recovery and transportation of heavy crudes and tar sand bitumens. Viscosity reduction may be achieved by mixing the crude with a light petroleum solvent. This paper presents a generalized correlation for calculating viscosities of such mixtures. A power-law mixing rule was generalized by use of the Einstein-type relationship for the viscosities of infinitely dilute solutions. Literature and in-house data were compiled to establish the con-elation. The final correlation requires only density and viscosity of the two fluids to predict blending viscosity at any mixture composition. The correlation is tested with heavy-oil/solvent blending data and gives an excellent prediction of the blending viscosities. Introduction To reduce viscosity, solvents frequently are used to dilute heavy crudes. This is one of the most efficient methods of pipeline transportation of heavy oils. Solvents also are injected into the reservoir for well cleaning, stimulation, fracturing and, less frequently, for miscible displacement. Engineering application of these processes often requires calculation of mixture processes often requires calculation of mixture viscosities. This paper documents the development of a simple but generalized correlation for predicting viscosities of binary mixtures of heavy oil, bitumen, and petroleum fractions, with particular emphasis on heavy-oil/solvent systems. Background Previous Work. Viscosity of liquid mixtures has been Previous Work. Viscosity of liquid mixtures has been studied extensively. Ref. 1 gives a brief review of the object. In general, the mixture viscosity as a function of composition is extremely complex. Theoretical considerations have offered little help in explaining these behaviors. Attempts such as McAllister's to derive a generalized expression for viscosities of all mixtures inevitably resulted in equations with many undetermined constants. There is no reliable method at present to allow an a priori prediction of these constants. These methods, therefore, can be classified only as descriptive. Literature reports few predictive methods, and those are mostly empirical and often specific to a particular group of mixtures. For mixtures of liquid hydrocarbons, including petroleum oils and fractions, the viscosity-composition petroleum oils and fractions, the viscosity-composition curve is generally a monotonic, concave-upward function, and rarely goes through a minimum. Regardless of the function's simplicity, a review by API showed that no single correlation would represent the viscosities of all hydrocarbon mixtures. Some of the reviewed correlations include Arrhenius (Eq. 1), Bingham (Eq. 2), and Kendal and Monroe (Eq. 3). ............(1) ............(2) ............(3) In these equations, VA and VB are volume fractions, MA and MB are mole fractions, and A, B, and are the viscosities of components A and B and their mixture, respectively. API recommended Eq. 3 for the blending of pure hydrocarbons and a graphical Wright method for mixtures of petroleum liquids. The latter calls for the use of the ASTM D341 viscosity-temperature charts. The procedure is to plot the viscosity-temperature lines of the oils and then to "blend" by linear proportioning along the log T axis. A hand-held calculator program, is now available to replace this tedious graphical manipulation. The viscosity ratios associated with the API data are mostly in the range of 1 to 100, where the ratio is calculated as the viscosity of the more viscous component divided by that of the less viscous one. In application to heavy-oil systems, we are interested in mixtures with viscosity ratio of 10(3) and higher. The only published method intended for blending heavy-oil systems was reported by Cragoe. Cragoe defined a function L such that .........(4) and proposed to calculate from the mixing rule ......................(5) SPEJ p. 277

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (02): 169–179.

Paper Number: SPE-10069-PA

Published: 01 April 1984

...

**fraction**shock front fluid dynamics simple wave correspond injection gas flow rate characteristic tie line An Analytical Model for One-Dimensional, Three-Component Condensing and Vaporizing Gas Drives 1.M. Dumon~, Koninklijke/Shell E&P 1. Hagoort, * Koninklijke/Shcll E&P A.S. Risseeuw...
Abstract

An analytical model based on the method of characteristics is presented for the calculation of one- dimensional (1D), three-component condensing and vaporizing gas dives. The model describes (1) mass transfer between oil and gas, (2) swelling and shrinkage, (3) viscosity and density changes, (4) gravity stabilization, and (5) rock/fluid interaction. The main assumptions of the model are local thermodynamic equilibrium and the absence of dispersion, diffusion, and capillarity. Example calculations are presented that bring out the main features of both condensing and vaporizing gas drives and also indicate the importance of mass transfer between the phases. In the special case of "developed miscibility," the model predicts a piston-like displacement having a complete recovery at gas breakthrough. The main applications of the model are in (1) conceptual studies of gas drives in which mass transfer plays an important role and (2) the calibration and checking of numerical reservoir simulators for multicomponent, multiphase flow. Introduction Gas injection is increasingly being applied as a secondary or tertiary recovery technique. In many applications injection gas is not directly miscible and is not in thermodynamic equilibrium with reservoir oil. As a consequence, component transfer takes place between gas and oil, which has a direct bearing on the displacement efficiency of the gas-injection process. Depending on the component transfer, two different processes are commonly distinguished: condensing and vaporizing gas drives. In condensing gas drives, the composition of the gas phase becomes progressively leaner on contact with the reservoir oil; the heavier components in the injection gas "condense" in the oil phase. Condensing gas drives occur when relatively rich gas is injected and are therefore called "rich" or "enriched" gas drives. In vaporizing gas drives, the reverse process occurs: the gas phase becomes progressively richer owing to vaporization of the middle components of the reservoir oil. Vaporizing gas drives occur when relatively lean gas is injected and are therefore called "lean" gas drives. A mechanistic understanding of oil displacement by immiscible, nonequilibrium gases is no simple matter. In these processes the flow of the two phases--gas and oil--is strongly influenced by the phase behavior of the multicomponent gas/oil mixture. This is compounded by the nonconstant physical properties of gas and oil resulting from compositional changes during the displacement. To investigate multicomponent gas drives theoretically, two approaches can be taken. First, the numerical approach: the basic differential equations are directly cast in a difference form and subsequently solved. In principle, this approach can handle many components and three dimensions. The drawback of the numerical approach is that possible sharp fronts are smeared out by numerical dispersion, which may obscure the results and make interpretation rather difficult. The second approach is the analytical one: the basic differential equations are simplified such that they become amenable to analytical mathematical analysis, notably the method of characteristics. This approach is less versatile in that it generally will be restricted to one dimension and a small number of components. Analytical models, however, are very helpful in obtaining a mechanistic understanding of the process. In addition, these models can accommodate sharp fronts and can therefore be used to calibrate and check numerical models. The first successful attempt to describe the coupling of two-phase flow and phase behavior in gas drives analytically was made by Welge et al. They investigated a 1D, three-component condensing gas drive and developed a calculation method essentially based on the method of characteristics. The problem of coupled multiphase flow and phase behavior also occurs in alcohol and surfactant flooding. Here the problems also can be formulated such that they can be solved by the method of characteristics. Wachmann presented a theory for alcohol flooding along these lines. Larson and Hirasaki and Larson applied the theory of characteristics to surfactant flooding. Recently Helfferich presented a general theory on 1D multiphase, multicomponent fluid flow in porous media. based on concepts developed in the area of theoretical multicomponent chromatography. Hirasaki applied these concepts to surfactant flooding. SPEJ P. 169^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (02): 121–128.

Paper Number: SPE-11061-PA

Published: 01 April 1984

... bit design geothermal reservoir heat flux rotational speed heat-transfer coefficient coefficient production logging bit selection contract production monitoring wearflat convective cooling polycrystalline diamond drag tool

**fraction**production control frictional heating friction...
Abstract

A numerical-analytical model is developed to predict temperatures in stud-mounted polycrystalline diamond compact (PDC) drag tools during rock cutting. Experimental measurements of the convective heat-transfer coefficient for PDC cutters are used in the model to predict temperatures under typical drilling conditions with fluid flow. The analysis compares favorably with measurements of frictional temperatures in controlled cutting tests on Tennessee marble. An equation incorporating several drilling parameters is developed to predict the mean operating temperature across the cutter wearflat, defined as that portion of the cutter surface that wears against the rock formation. It is shown that mean wearflat temperatures can be maintained below a maximum safe value of 750C [1,382F] only under conditions of low friction at the cutter/rock interface, regardless of the level of convective cooling. The ability of liquid drilling fluids to reduce interface friction is thus shown to be far more important in preventing excessive temperatures than their ability to provide cutter cooling. Because of the relatively high interface friction provide cutter cooling. Because of the relatively high interface friction developed under typical air drilling conditions, it is doubtful that temperatures can be kept subcritical at high rotary speeds in some formations when air is employed as the drilling fluid. Introduction Over the past several years, considerable interest has been focused on drag-type drill bits employing PDC elements. Although these bits have been most successful in drilling relatively soft formations, work has been under way at Sandia Natl. Laboratories to investigate the potential of PDC bits in the more severe environments typical of geothermal drilling. Unsealed roller bits have limited lives in such environments, and conventional sealed roller bits cannot be used in many geothermal reservoirs because of temperature limitations on seals and lubricants. Because PDC bits require no bearings or seals, they are particularly attractive for geothermal drilling, especially at the high rotational speeds typical of downhole motors. The high penetration rates and long lives achieved with PDC bits in certain formations further suggest that geothermal drilling costs might be reduced if PDC bits can be developed for this application. The inherent characteristics of drag bits impose high frictional heating on PDC cutters. The purpose of our study was to investigate the thermal characteristics of PDC elements mounted on tungsten carbide (WC) studs to understand the driving parameters behind the thermal response of these cutter. The incentive for understanding these parameter, is to permit action to keep cutter operating temperatures as low as possible. permit action to keep cutter operating temperatures as low as possible. The need for achieving this goal is illustrated by an examination of the wear characteristics of PDC cutters at various operating temperatures. Below 750C [1,382F], the primary mode of wear of PDC cutters is microchipping of the sintered diamond. It has been shown 3 that the intensity of this wear increases with sliding speed, presumably a result of the increased temperatures associated with higher speeds. Evidence indicates that this increased wear rate is caused by a decrease in the hot hardness of individual diamond crystals with increasing temperature. Above750C [1,382F], the wear mode changes from microchipping of individual diamond grains to a more severe form in which entire grains are pulled from the compact. This is caused by stresses resulting from differential thermal expansion between the diamond and residual metal inclusions along the diamond grain boundaries, which lead to intergranular cracking and grain boundary failure. By 800C [1,472F], the hot hardness of the WC stud is severely degraded, leading to accelerated wear of the stud itself, which even at low temperatures has a wear rate greater than that of sintered diamond. For temperatures above 950C [1,742F], WC is susceptible to plastic deformation and flow under applied surface shear. In this study, we therefore establish 750C [1,382F] as the maximum safe operating temperature of PDC/WC cutters but recognize that even below this temperature, wear rate can be significantly reduced by maintaining operating temperatures as low as possible. The major objective of our study was to identify parameters that can be controlled to achieve this goal. Approach. Numerical modeling of PDC cutters was performed to compute local temperatures for assumed frictional heating and convective cooling rates. Referring to Fig. 1, the assumptions used in this thermal modeling are the following. SPEJ p. 121

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (02): 153–168.

Paper Number: SPE-6859-PA

Published: 01 April 1984

... conductivity terms to a particular type of water, each occupying a representative volume of the total porosity. This approach has been named the "dual-water" (DW) model because of these two water types - the conductivity and volume

**fraction**of each being predicted by the model. The DW model has been tested on...
Abstract

A simple petrophysical model proposed by Waxman and Smits (WS) 1 in 1968 and Waxman and Thomas (WT)2 in 1972 accounts for the results of an extensive experimental study on the effects of clays on the resistivity of shaly sands. This model has been well accepted by the industry despite a few inconsistencies with experimental results. It is proposed that these inconsistencies resulted from the unaccounted presence of salt-free water at the clay/water interface. Electrochemistry indicates that this water should exist, but is there enough to influence the results? Both a theoretical study and reinterpretation of Waxman-Smits-Thomas data show that there is. The corresponding new model starts from the Waxman and Smits concept of supplementing the water conductivity with a conductivity from the clay counterions. The crucial step, however, is equating each of these conductivity terms to a particular type of water, each occupying a representative volume of the total porosity. This approach has been named the "dual-water" (DW) model because of these two water types - the conductivity and volume fraction of each being predicted by the model. The DW model has been tested on most of the core data reported in Refs. 1 and 2. The DW concept is also supported by log data 3 and has been successfully applied to the interpretation of thousands of wells. However, the scope of this paper remains limited to the theoretical and experimental bases of the DW model. The Petrophysical DW Model The purpose of this model is to account for the resistivity behavior of clayey sands. For petrophysical considerations, a clayey formation is characterized by its total porosity, f t ; its formation factor, F 0 ; its water saturation, S wT ; its bulk conductivity, C t ; and its concentration per unit PV of clay counterions, Q v . The formation behaves like a clean formation with identical parameters f t , F 0 , and S wt but containing a water whose conductivity, C we , differs from the bulk formation water. Neither the type of clays nor their distribution influences the results. Since the formation obeys Archie's laws, Equation 1 The clayey sand equivalent water conductivity, C we , can be considered a mixture of two waters. 1. A clay water surrounds the clay particles but has a conductivity independent of the type and amount of clay. Its conductivity, C cw , comes exclusively from the clay counterions. The volume fraction of clay water, V cw , is directly proportional to the counterion concentration, Q v Equation 2 where v Q is the amount of clay water associated with 1 unit (meq) of clay counterions. 2. The water further away from the clay is called far water . Its conductivity, C w , and ionic concentration correspond to the salinity of bulk-formation water. The volume fraction of this water, V fw , is the balance between the total water content and the clay water. Equation 3 The implicit assumption is that the far water is displaced preferentially by hydrocarbons.

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*24 (01): 87–96.

Paper Number: SPE-11126-PA

Published: 01 February 1984

... tested explicitly, and the sets of equilibrium constants are developed phase by phase before all phases are handled simultaneously. SPEJ P. 87^ 1 2 1984 1 2 1984 1984. Society of Petroleum Engineers water phase liquid phase phase behavior

**fraction**pvt measurement equation...
Abstract

Modeling of reservoir processes like gas miscible flooding may require consideration of phase equilibrium between multiple liquid phases. Under certain conditions two hydrocarbon liquid phases may form; one may also want to account for mass transfer between the hydrocarbon and the aqueous phases. This paper describes a refined successive substitution (SS) method for calculating multiphase flash equilibrium. The phase behavior procedure proceeds in a stepwise manner, and additional phases are introduced by a special testing scheme based on phase fugacities. This is to avoid trivial solutions and to ensure continuity across phase boundaries. The method has been tested on various three- and four-phase systems, and examples of application show that the method performs well. Introduction Fluid phase behavior constitutes a very important aspect of more sophisticated oil recovery processes such as gas miscue flooding. In such processes mixtures of the reservoir fluids and the injected gas typically may approach critical conditions, and laboratory experiments have shown that the oil phase may in some cases split into two or more coexisting hydrocarbon liquid phases. In addition, interaction with the water phase may become important as the dissolution of gas components in water may affect the overall process performance significantly. The complexity of phase behavior during gas miscible flooding makes modeling and predictions a demanding task. Cubic Redlich-Kwong type EOS's have proved applicable for both gaseous and liquid phases. Thus, because of their simplicity, their reasonable accuracy, and their consistency near critical points, they have received much recent attention as a tool for describing compositional hydrocarbon reservoir phenomena. Various schemes for flash equilibrium calculations based on an EOS have been proposed. Broadly, they may be categorized as variants of the widely applied SS method or as second-order Newton-type methods. Most applications deal with two-phase problems, but extensions to multiphase problems have been reported. A basic solution scheme for multiphase cases was presented by Peng and Robinson. In addition, an extension of the minimum variable Newton technique was described by Fussell, and a combination of both first- and second-order methods was considered by Mehra and Mehra et al. One main problem with flash equilibrium calculations band on EOS's convergence toward trivial solutions and a proper delineation of phase boundaries. This is so for two-phase problems but even more so for multiphase problems, where phase boundaries may be very close to each other and good estimates of equilibrium K-values are more difficult to obtain. The work described here is part of a research project aimed at development of numerical modeling tools for EOR processes. The method for multiphase equilibrium calculations presented is an extension of the refined SS method previously developed for two-phase problems. The method has been incorporated into a fluid phase behavior package (COPEC). In developing the method, special emphasis has been put on computational efficiency and continuity across phase boundaries. Calculation Steps of Multiphase Flash The basis for our approach to the multiphase flash equilibrium problem is the SS method, which consists of the following steps.1. Assume equilibrium K-values.2. Calculate the phase distribution and compositions corresponding to the given K-values.3. Calculate component fugacities in each phase and check forequality.4. If equality is not achieved. correct the K-values on the basis of the fugacities and repeat from Step 2. We assume that fugacities are given from a cubic EOS (Redlich-Kwong, Peng-Robinson), but the problem of selecting suitable parameters, especially for lumped and/or heavy components, is considered beyond the scope of this paper. If the initial K-value estimates are sufficient, simultaneous handling of mi phases is probably the most efficient method. Frequently this is not the case, however, and the method then easily, becomes unstable and leads to trivial solutions. We have found it advantageous, therefore, to develop a more stepwise approach. Existence of the different phases is tested explicitly, and the sets of equilibrium constants are developed phase by phase before all phases are handled simultaneously. SPEJ P. 87^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*23 (05): 727–742.

Paper Number: SPE-10516-PA

Published: 01 October 1983

... property correlation

**fraction**compositional model composition hydrocarbon phase displacement timestep reservoir simulation gridpoint enhanced recovery gas condensate pvt measurement procedure A Generalized Compositional Approach for ReseIVoir Simulation Larry C. Young, SPE, Amoco Production...
Abstract

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered are a conventional waterflood problem, displacement of oil by CO, and the displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*23 (04): 657–668.

Paper Number: SPE-8995-PA

Published: 01 August 1983

... convenient to define equivalent

**fractions**of calcium ions in each phase by dividing the calcium con- centration by the total cation concentration of each phase. The**fraction**of calcium ions in solution is defined as Ix == C Ca / C s while the**fraction**of calcium sites on the solid is/y==Zca/Z(. When...
Abstract

Exchange of hardness ions is important in EOR with chemical additives. In both micellar/polymer and caustic flooding processes, multivalent ions released from rock surfaces can interact with anionic surfactants, rendering them preferentially oil soluble and/or insoluble in water. Because hardness cations are sparingly soluble and precipitate in alkaline solutions, such solutions may be more efficient as surfactant-flood preflushes than are softened brines. Multivalent ion precipitation may also occur in alkaline water flooding. To permit design of such processes, this paper presents a chromatographic theory for simultaneous ion exchange with precipitation of divalent ions. Theoretical effluent histories and concentration profiles are presented for the cases of finite pulses and continuous injection of hydroxide ions into linear cores. Complete capture of the insoluble salt particles is assumed. Results are given for the case of instantaneous equilibration of the solution with the precipitate, as well as for the case of complete nonequilibration in which the solid precipitate does not redissolve. These two physical extremes predict field performance and laboratory results, respectively. Data for Berea sandstone and an argillaceous sand compare favorably with the proposed theory. The efficiency of alkaline preflushing is shown to depend on the exchange isotherm, initial divalent loading of the rock, injected pH and salinity, the solubility product of the precipitated salt, and pulse size. The effect of pulse size on complete equilibrium removal of hardness ions is reduced efficiency with increasing size until a critical volume approximating continuous injection is reached. Increasing injected pH and salinity provides a more favorable response. The theoretical model, when applied to field conditions, predicts redissolution zones that have not been previously recognized because solution residence times in laboratory columns are too short. Calculations show that precipitate redissolution by the low-pH solutions following alkaline pulses may introduce high concentrations of calcium behind the preflush where interference with micellar or polymer solutions is likely. These results suggest that reservoir preflush design from laboratory tests, while possible, must be made carefully. Introduction The presence of multivalent cations in reservoir brines can profoundly affect the oil-recovery efficiency of micellar or polymer slugs. These chemicals can react with hardness cations present to produce water-insoluble constituents. Removal of divalent cations, such as magnesium or calcium, with softened brines has been studied extensively. Problems with reservoir heterogeneities and incomplete sweep are legion. Equally important, however, is the strong preference of most reservoir rock for calcium, which means that large volumes of preflush are required even in the swept zones to obtain the desired low concentrations of hardness ions. Campbell and Holm and Robertson have proposed using chemicals such as sodium hydroxide or sodium orthosilicate in a preflush to react with multivalent cations by precipitation. Currently, a field test of this idea is under way. SPEJ P. 657^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*23 (04): 683–694.

Paper Number: SPE-12233-PA

Published: 01 August 1983

...Curtis H. Whitson Whitson, Curtis H., SPE, U. of Trondheim Abstract Methods are developed for characterizing the molar distribution (mole

**fraction**/molecular weight relation) and physical properties of petroleum**fractions**such as heptanes-plus (C7 +). These methods should enhance equation-of-state...
Abstract

Whitson, Curtis H., SPE, U. of Trondheim Abstract Methods are developed for characterizing the molar distribution (mole fraction/molecular weight relation) and physical properties of petroleum fractions such as heptanes-plus (C7 +). These methods should enhance equation-of-state (EOS) predictions when experimental data are lacking. predictions when experimental data are lacking. The three-parameter gamma probability function is used to characterize the molar distribution, as well as to fit experimental weight and molar distributions and to generate synthetic distributions of heptanes-plus fractions. Equations are provided for calculating physical properties such as critical pressure and temperature properties such as critical pressure and temperature of single-carbon-number (SCN) groups. A simple three-parameter equation is also presented for calculating the Watson characterization factor from molecular weight and specific gravity. Finally, a regrouping scheme is developed to reduce extended analyses to only a few multiple-carbon-number (MCN) groups. Two sets of mixing rules are considered, giving essentially the same results when used with the proposed regrouping procedure. Introduction During the development of the application of EOS's to naturally occurring hydrocarbon mixtures, it has become clear that insufficient description of heavier hydrocarbons (e.g., heptanes and heavier) reduces the accuracy of PVT predictions. Volatile oil and gas-condensate volumetric phase behavior is particularly sensitive to composition and properties of the heaviest components. properties of the heaviest components. Until recently there has not been published in technical journals a comprehensive method for characterizing compositional variation, which we call "molar distribution." Several authors have given lucid descriptions of petroleum fraction characterization, though they deal mainly with physical property estimation. Usually, only physical property estimation. Usually, only a single heptanes-plus (C7 + ) fraction lumps together thousands of compounds with a carbon number higher than six. Molecular weight and specific gravity (or density) of the C7 + fraction may be the only measured data available. Preferably, a complete true-boiling-point (TBP) analysis should be performed on fluids to be matched by an EOS. Distillation experiments yield boiling points, specific gravities, and molecular weights, from which molar distribution is found directly. Special analyses of TBP data can also provide estimates of the paraffin/napthene/ aromatic (PNA) content of SCN groups, which are useful in some property correlations. Unfortunately, such high-quality data are seldom available for fluids being matched or predicted by an EOS. If data other than lumped C7+ properties are available, they might include a partial component analysis (weight distribution) from chromatographic measurements. In this case. only weight fractions of SCN groups are reported; normal boiling points, specific gravities, and molecular weights (needed to convert to a molar basis) simply are not available. Compositional simulation based on an EOS involves two major problems: how to "split" a C7 + fraction into SCN groups with mole fractions. molecular weights, and specific gravities that match measured C7+ properties, and if a partial extended analysis (e.g., C 11 + ) is available, how to extend it to higher carbon numbers. The first step in addressing these problems is to find a versatile, easy-to-use probability function for describing molar distribution. The distribution function should allow consistent matching and reasonable extension of partial analyses. Also, it should not contain too many unknown or difficult-to-determine parameters. This paper presents such a probabilistic model and describes its application to several reservoir fluids under "Molar Distribution."The second step in characterizing plus fractions involves estimating SCN group specific gravities, which, together with estimated molecular weights (from the probabilistic model), could be used to estimate critical properties required by EOS's. We address this problem and suggest a simple method for specific gravity estimation under "Physical Properties Estimation." SPEJ p. 683

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*Society of Petroleum Engineers Journal*23 (03): 461–474.

Paper Number: SPE-10202-PA

Published: 01 June 1983

... oil & gas microemulsion dispersion slug equation composition artificial intelligence coefficient

**fraction**simulation oil recovery chemical flooding methods aqueous phase experiment enhanced recovery mechanism time step surfactant viscosity saturation polymer A Numerical...
Abstract

This paper describes an enhanced oil recovery (EOR) model involving use of chemical additives. The model is as general as possible in light of present phenomenological knowledge. It takes into consideration diffusion, exchanges between fluid phases. exchanges between fluids and solids, and convection (including gravity, relative permeabilities, viscosities, interfacial tensions (IFT's), and mobility reduction by polymers). Its main properties are three-phase flow (aqueous, oleic, and microemulsion); that each phase can be represented by a mixture of seven components: overall flow is one dimensional (ID), but the sections of space considered may be constant or variable; and the porous medium may be heterogeneous. In addition to its compositional nature. which is required for describing changes in phase properties, the model must also account for ionic environment, loss of chemicals, and capillary number distribution. For these reasons, it differs from conventional multicomponent models. It is designed for simulating any EOR problem involving the addition of suitable chemicals to fluids to be injected continuously or in successive slugs. The model has been tested successfully by two-phase flow, four components (water, oil, polymer, and surfactant plus alcohol), and Winsor Type I environment experiments. It can be adapted to more and more complex phenomenological situations, depending on availability of data. Introduction Of the new techniques leading to increased oil production, EOR using chemical additives is one of the most promising. It involves adding sufficient amounts of chemical species to injected fluids to change phase properties, thereby enhancing oil flow. These changes occur in a highly complex way because of the superposition of several mass-transfer phenomena. The difficulties are increased because some of these phenomena, such as exchange between fluid phases and between fluids and solids, are not yet fully understood. A great deal of experimental research is being done to clarify this situation. However, no matter what experimental progress is made, it will never be easy to analyze all the mechanisms that occur simultaneously and to predict the behavior of the recovery process by pure reasoning or by intuition. A mathematical approach becomes necessary, and the first numerical studies of the problem can be found in the literature. Our contribution to this effort is described in this paper. It concerns developing a numerical model that is as general as possible within the scope of current phenomenological knowledge. The model is necessarily multicomponent and multiphase. However, it differs from ordinary compositional models by the number of new problems to be investigated. The principal problems include suitable ionic environment, loss of chemical additives, and capillary number distribution in space and time. SPEJ P. 461^