Estimation of Three-Phase Relative Permeability Isoperms in Heavy Oil/Water/Carbon Dioxide and Heavy Oil/Water/Methane Systems

In-situ recovery of heavy oils and bitumen's often involves simultaneous flow of oil, water and gas in the oil sands. Such multi-phase flow in porous media is a complex process. Mathematical simulation of such recovery processes requires a knowledge of the three-phase relative permeability characteristics of the system. Experimentally measured three-phase relative permeability data for heavy oil reservoirs are not available in the literature. This lack of data is primarily due to the tedious nature of such measurements and shows a need for developing less time consuming methods. In this study, an unsteady-state technique similar to the Johnson-Bossler-Naumann (JBN) method for two-phase flow was developed and used to estimate three-phase relative permeability data. The method was validated by comparing the oil isoperms with those obtained using the steady-state method. A reasonably good agreement was obtained which suggests that the proposed unsteady-state method could be employed as a faster alternative to obtain three-phase relative permeability data. Introduction Petroleum production often involves simultaneous flow of three immiscible fluids through subterranean porous rock formations. Examples of recovery processes involving such three-phase flow include alternating gas and water injection, steam drive, in-situ combustion, and immiscible gas injection in presence of mobile water. Thorough analysis of these processes is impossible without reliable three-phase relative permeability data. Reservoir simulation programs incorporate one or several techniques for estimating three-phase relative permeabilities, which permit three-phase simulation studies m be carried out with input of only two-phase relative permeabilities. However such simulation studies may be no more reliable than me techniques for estimating three-phase relative permeabilites employed in them. Unfortunately, the reliability of these estimation techniques cannot be tested without availability of extensive experimental data on three-phase relative permeabilities. Compared to the wealth of information available in the literature on two-phase relative permeabilities, there is a dearth of experimental studies on three-phase flow through porous media. Virtually no information is available on three-phase relative permeabilities in intermediately-wet or oil-wet systems. Effects of variables such as contact angles, viscosity ratios, interfacial tension, flood velocity and temperature on three-phase relative permeability have not been investigated. There is an obvious need for more experimental investigations of three-phase relative permeabilities to resolve some of the uncertainties concerning the effects of variables mentioned above. The reason for this scarcity of experimental dam on three-phase relative permeabilities appears to be the effort and time required for such measurements. The only well accepted technique for such measurements is the steady-state method. Between 50 to 100 steady-state measurements are required to fully define the relative permeability characteristics of a given system for one direction of saturation change. It often takes 24 hours or more to reach steady state conditions for each such measurements. Combined with the time involved in core preparation and periodic extractions to overcome the problem of error accumulation the total effort involved is indeed formidable. If the hysteresis effects corresponding to various possible directions of saturation change are also to be evaluated, the task becomes even more onerous.

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady-state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady-state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two-phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-phase relative permeability as it does in two-phase flow. Introduction In the light of increasing demand for three-phase, relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between 1/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. Proposed Method The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three-phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

A method is described for measuring two- and three-phase relative permeabilities in sandstones or sand packs using a nuclear magnetic resonance (NMR) technique to determine fluid saturations Two- and three-phase relative permeabilities have been determined on Boise sandstone using the NMR technique of saturation measurement. Three- phase relative permeability to water was found to depend only on the water saturation, whereas three-phase permeability to oil depended on both the water and oil saturations. Relative permeability to gas in three-phase flow was found to depend only on the total liquid saturation. Introduction Three-phase relative permeabilities are extremely useful in calculating field performance for reservoirs being produced by simultaneous water and gas drives. Three-phase relative permeability data are also needed for analyzing solution gas-drive reservoirs which are partially depleted and are being produced by water drive. Some thermal recovery processes involve three-phase flow which require three-phase relative permeability data for predicting reservoir-behavior. Unfortunately three-phase relative permeability measurements have rarely been made. Also, because of the scarcity of three-phase data, it has not been possible to date to relate other measured rock characteristics to the relative permeabilities with a great certainty. Leverett and Lewis, Reid and Snells have reported three-phase relative permeability data on unconsolidated sands. Leverett and Lewis used ring electrodes spaced along the length of the sand sample to -measure the resistivity of the sample which was assumed to be monotonically related to brine saturation. Gas saturation was determined from pressure-volume measurements. Oil saturation was obtained by material balance on the cell containing the sand sample. This method is involved and time consuming. Another difficulty arises from the fact that the resistivity of the sand is a function not only of saturation of brine but also of the distribution and saturation history of the brine in the pore spaces. Reid used a gamma ray absorption technique for measuring liquid saturation. This method has the disadvantage that total liquid saturation rather than oil or brine saturation is all that can be measured and still another method is required to determine the saturations of individual components. Snells used a neutron bombardment method which also required a separate determination of the individual component saturations. Caudle et al. measured three-phase relative permeability on consolidated sandstones using vacuum distillation for determining fluid saturations. Distillation after each reading makes this technique very lengthy and time consuming. Corey et al and Naar and Wygal measured three-phase relative permeability on sandstones by the capillary- pressure method. Semipermeable diaphragm assemblies were used at each end of the core specimen to keep the water base in the core. Gravimetric methods were used to determine fluid saturations. Sarem recently repeated an unsteady-state method for measuring three-phase relative permeability on sandstones. This method is an extension of Weige's methods for measuring two-phase relative permeability. Although Sarem's method is simple and comparatively fast, the assumptions involved may oversimplify the problem. Sarem's assumption, that in all rocks relative permeability to each fluid will depend only on the saturation of that fluid, seems to be rather unrealistic. Neglecting capillary effects at the end of the core is also a weak assumption Donaldson and Deans measured three-phase relative permeability using a method similar to Sarem's.

In situ recovery of heavy oil and bitumen from oil sands often involves simultaneous flow of oil, water and gas in the oil sands. Such multi-phase flow in porous media is a complex process. Mathematical simulation of such recovery processes requires a knowledge of the threephase relative permeability characteristics of the system. Experimentally measured three-phase relative permeability data for heavy oil reservoirs are not available ill the literature. This lack of data is primarily due to the tedious nature of such measurements and shows a need for developing less time consuming methods. In this study, an unsteady-state technique similar to the JBN method for two-phase flow was developed and used to estimate three-phase relative permeability data. The method was validated by comparing the oil isoperms with those obtained using the steady-state method. A reasonably good agreement was obtained which suggests that the proposed unsteady-state method could be employed as a faster alternative to obtain three-phase relative permeability data. Introduction Petroleum production often involves simultaneous flow of three immiscible fluids through subterranean porous rock formations. Examples of recovery processes involving such three-phase flow include; alternating gas and water injection, steam drive, in-situ combustion, and immiscible gas injection in presence of mobile water. Thorough analysis of these processes is impossible without reliable three-phase relative permeability data. Reservoir simulation programs incorporate one or several techniques for estimating three-phase relative permeabilities, which permit three-phase simulation studies to be carried out with input of only two-phase relative permeabilities. However such simulation studies may be no more reliable than the techniques for estimating three-phase relative permeabilities employed in them. Unfortunately, the reliability of these estimation techniques can not be tested without availability of extensive experimental data on three-phase relative permeabilities Compared to the wealth of information available in the literature on two-phase relative permeabilities, there is a dearth of experimental studies on three-phase flow through porous media. Virtually no information is available on three-phase relative permeabilities in intennediately-wet or oil-wet systems. Effects of variables such as: contact angles, viscosity ratios. interfacial tension, flood velocity and temperature on three-phase relative permeability have not been investigated. There is an obvious need for more experimental investigations of threephase relative permeabilities to resolve some of the uncertainties concerning the effects of variables mentioned above. The reason for this scarcity of experimental data on three-phase relative permeabilities appears to be the effort and time required for such measurements. The only well accepted technique for such measurements is the steady-state method. Between 50 to 100 steady-stale measurements are required to fully define the relative permeability characteristics of a given system for one direction of saturation change. It often takes 24 hours or more to reach steady state conditions for each such measurements. Combined with the time involved in core preparation and periodic extractions to overcome the problem of error accumulation the total effort involved is indeed formidable. If the hysteresis effects corresponding to various possible directions of saturation change are also to be evaluated, the task becomes even more onerous.

The main difficulties to overcome in dynamic displacement relative permeability measurements are capillary end effects and viscous fingering. The latter problem is particularly severe in three-phase systems which include gas. Both of these problems are greatly mitigated in the three liquid system presented here. Water, benzyl alcohol, and decane are the three immiscible liquids which play the role of water, oil, and gas in the conventional three-phase system. The interfacial tensions in this system are about a factor of ten smaller than the comparable tensions for the conventional system, so the capillary end effect is less. Furthermore, viscosity contrasts are diminished, thus lowering the chance of fingering. An extension of the Welge-JBN method to three phases is derived. Each displacement experiment follows a saturation trajectory across the ternary diagram. The method is used to calculate three-phase relative permeabilities along each trajectory. Finally, the data from all trajectories are combined to provide isoperms over a large portion of the ternary diagram. Also included are the two sets of two-phase relative permeabilities needed to apply the interpolative three-phase relative permeability model of Stone. The measured isoperms indicate the model over-predict the relative permeability to oil: oil flows at lower rates than predicted.

Modeling three-phase flow in gas-condensate systems requires the relative permeability of each fluid as a function of the fluid saturation. The Coreflood laboratory and experimental measurement of three-phase relative permeability (3-PRP) data is much complicated, more time consuming and relatively expensive when compared to forecasting two-phase relative permeability data.Owing to this, many three-phase relative permeability correlations have been proposed in the petroleum industry for estimating three-phase relative permeability using geometric or arithmetic summation and interpolation of two-phase relative permeability data. After comparing results of most of the existing three-phase models to Oaks experiment, we realized that most of the existing three-phase models fail to incorporate the physical mechanisms underlying multiphase flow in gas-condensate systems.This paper aims to fill this knowledge gap by proposing a novel 3-PRP model to forecast three-phase relative permeability in gas-condensate systems. Three-phase interactions between fluids and fluid saturations are fully incorporated in this model by introducing three-phase characteristic coefficients. Using these coefficients, the total two-phase oil saturation relative to water is not only a function of the three-phase oil saturation relative to water but it is expressed as a function of the three-phase oil saturation with respect to both water and gas.The proposed 3-PRP model is successfully validated against experimentally measured three-phase relative permeability data.

The objective of this work is to improve determination of two-phase and three-phase relative permeabilities by the use of saturation imaging techniques. The first part of the paper reports on steady-state and unsteady-state relative permeability experiments performed on restored-state carbonate reservoir cores. The aim was to study how relative pemeability test methodology impacts relative permeability curves, hysteresis and residual oil saturations in these intermediate-wet cores. Refined oil was used. Significant hysteresis was observed in both the unsteady-state water and oil relative permeabilities. The characteristics of the unsteady-state water relative permeabilities imply that viscous instabilities were present during the waterflood. Centrifuge capillary pressure-wettability tests performed on companion core plugs both before and after the relative permeability tests showed good agreement with the unsteady-state results, but indicated change towards less oil-wetness during the steady-state tests. The main conclusion of this work is that extensive flushing of a restored-state core with refined oil may lead to a non representative relative permeability data and should therefore be avoided. The second part of the paper presents a summary of results obtained from three-phase unsteady-state flow in water-wet sandstone (Berea and Clashach) cores. In-situ saturation measurements show that the water relative permeability is dependent on water saturation alone, and that there is no change in water relative permeability due to three-phase flow. The waterflood residual oil saturation was found reduced in the presence of a gas phase, and may depend on the phase (oil or gas) injected prior to waterflooding.

Summary Varieties of enhanced oil recovery (EOR) processes involve simultaneous flow of two or three immiscible fluids (i.e., water, oil, and gas) in reservoirs. Proper quantification of multi-phase flow processes has considerable economic and scientific importance in management and development of oil- and gas-bearing geologic formations. Relative permeabilities are key rock-fluid properties required for continuous-scale modeling of multiphase flow dynamics in porous and fractured media. A reliable characterization of these quantities, including uncertainty quantification, enables reservoir engineers to assess reservoir performance, forecast ultimate oil recovery, and investigate the efficiency of enhanced oil recovery techniques. In this work, we report the results of a suite of laboratory-scale experimental investigations of multi-phase (water/oil/gas) relative permeabilities on reservoir core sample. Two (water/oil) - and three-phase (water/oil/gas) relative permeability data are obtained at high temperature of the reservoir by way of a Steady-State (SS) technique. Our laboratory methodology allows improved relative permeability acquisition through a joint use of traditional flow-through investigations and direct X-Ray measurement of the core local saturation distribution. The latter renders detailed distributions of (section-averaged) fluid phases along the core, which can then be employed for the characterization of relative permeabilities. The three-phase Steady-State relative permeability experiments have been conducted by resorting to a dual energy X-Ray methodology. The experimental setup also includes a closed loop system to validate and support saturation measurements/estimates. The SS three-phase experiments are performed by following diverse saturation paths including CDI, DDI, IID and some cycle injection of WAG, where, C, D and I denote as Constant, Increasing and Decreasing (i.e., CDI means Constant water, Decreasing oil and Increasing Gas). Several different flow rate ratios have been selected to cover the saturation ternary diagram extension as completely as possible. The use of in-situ X-Ray scanning technology enables us to accurately measure depth-averaged fluid displacement during the core-flooding test. We observe in most of the tests, three-phase water relative permeabilities display an approximately linear dependence on its saturation when the latter is subject to a logarithmic transformation. The three-phase oil and gas relative permeabilities, when plotted versus their saturations are scattered by apparently quasi-linear trends, compared to the behavior of water relative permeabilities. We provide the experimental data set to demonstrate the possible three-phase region and eventually investigate the hysteretic effects on three-phase relative permeabilities. As only a limited quantity of three-phase data are available, this study stands as a reliable reference for further model development and testing.

Experimental investigation of temperature effect on three-phase relative permeability isoperms in heavy oil systems

With the method described here, three-phase relative permeability data may be estimated from two sets of more easily measured two-phase data - water displacing oil, and gas displacing oil. The resulting data compare favorably with the limited experimental data available in the literature, so that they may be used to estimate three-phase data for combination-drive reservoir calculations. Introduction Although thorough analysis of combination gas- and water-drive reservoirs requires three-phase relative permeability data, the effort involved in determining permeability data, the effort involved in determining these data experimentally generally rules out such a direct approach. Refs. 1 through 4 suggest, however, that more easily measured two-phase data can be used to predict the relative permeability to both the wetting and nonwetting fluids in three-phase flow. This report describes a method of using two sets of two-phase data to predict the relative permeability of the intermediate wettability phase in a three-phase system. Use is made of probability concepts and appropriate empirical definitions. This technique may be regarded as a means of interpolating between the two sets of two-phase data to obtain the three-phase relative permeability. In many reservoirs that involve three-phase flow, only gas and oil are mobile in the upper portion of the reservoir; in the lower portion, water and oil are the phases of high mobility. The probability model is phases of high mobility. The probability model is such that it will yield the correct two-phase data when only two phases are flowing, and will provide interpolated data for three-phase flow that are consistent and continuous functions of the phase saturations. It will be shown later that these interpolated values agree with the available three-phase data within experimental uncertainty. Although the method applies to either a preferentially water-wet or a preferentially oil-wet system, preferentially water-wet or a preferentially oil-wet system, this discussion will be limited to a water-wet system. Extension of the method to a preferentially oil-wet system is straightforward; here, water becomes the fluid of intermediate wettability. Estimation of Three-Phase Relative Permeability Data Permeability Data This section presents the data required to predict three-phase relative permeability data, the equations used, and the definitions and assumptions on which the method is based. The next section describes a reasonable physical model that is consistent with these assumptions, and the final section presents an empirical evaluation of the model: Data Required Data required for the estimation of three-phase relative permeability are two sets of two-phase data water-oil and gas-oil. From the water-oil data we obtain both krw and krow, as a function of water saturation, where krow is defined as the relative permeability to oil in the oil-water two-phase system. Similarly, we obtain krg and krog as a function of gas saturation. Hysteresis effects are taken into consideration, as far as possible, by employing the appropriate two-phase data. For example, consider a water-wet system in which oil saturation is decreasing and gas and water saturations are increasing. Imbibition data should be used for the water-oil data, and drainage data should be used for the oil-gas data. JPT P. 214

Anomalous trends have been observed in laboratory-derived relative permeability data especially in rock samples that contain mobile (siliceous/micaceous/ kaolinitic) fines and/or water sensitive clays. Water-oil relative permeability data determined for such rocks by the unsteady-state technique have at times exhibited the following characteristics:Non-monotonic trends with saturationSlightly S-shaped relative water permeability with a ‘bend-over’ at high water saturationsRebound in relative water permeability at residual oil saturation with reversal in flow direction These characteristics are indicative of adverse physicochemical interactions between the flowing phases and the rock, which invalidate the relative permeability concept. This paper presents the results of laboratory studies conducted to elucidate the role of formation damage processes in the determination of relative permeability data. Experimental data generated on rocks with fine particulates, indicate that mechanically induced damage can occur if the displacing fluid velocity, increased to overcome capillary end effect, exceeds the critical velocity for mobilization of resident mineral fines. Chemically induced damage was found to accompany the mechanical damage if the injected brine was not in ionic equilibrium with the rock. Most friable samples containing micas, feldspars and illite/kaolinite, which have potassium ions in their interlayer sites, were damaged by the flow of sodium and/or calcium chloride brines during brine permeability tests. Critical velocities for entrainment of fines were determined to be higher for KCl brines than for NaCl/CaCl2 brines in water-wet Berea samples. Laboratory protocols which eliminate formation damage processes during relative permeability measurement have been developed and are presented in this paper. These include: (a) use of velocities less than critical for floods on butted cores with lengths sufficient to reduce capillary end effects, (b) addition of trace ions such as K+ ions in simulated formation brines, (c) equilibration of the fluids with the rock and the use of aged fluids for dynamic displacement. Unsteady-state imbibition tests performed on short core plugs at flowrates greater than critical for fines mobilization, are discouraged. Rather, low rate floods should be conducted and the data analyzed by numerical techniques which include the capillary pressure term in deriving relative permeability curves.

Three-phase relative permeabilities have an important role in numerical simulation of oil recovery processes. Thermal methods for heavy oil recovery, such as steam injection and in situ combustion, involve simultaneous flow of oil, water and gas at high temperatures. A knowledge of three-phase relative permeabilities at elevated temperatures is required to predict performance of these processes by reservoir simulation studies. Measurements of three-phase relative permeabilities for heavy oil systems at elevated temperatures have been unavailable due to experimental difficulties.The objectives of this work were to develop an experimental apparatus for measuring three-phase relative permeabilities at elevated temperatures and pressures and to carry out such measurements in a model system. The rock-fluid system used in these measurements comprised Ottawa sand - refined mineral oil - distilled water - nitrogen gas. A high viscosity mineral oil (405 mPa.s at 23°C) was selected to simulate heavy oil behaviour. The measurements were carried out at 100°C temperature and 3.5 MPa pressure. Two-and three-phase relative permeability measurements were obtained using the steady-state technique. A large number of steady-state tests were carried out to completely define the three-phase relative permeability characteristics in two types of saturation histories; (1) water and gas saturations increasing and oil saturation decreasing, (2) water and gas saturation decreasing, oil saturation increasing.The three-phase water relative permeability was found to be a function of water saturation only and did not change with the direction of saturation change. The gas relative permeability was also a function of its own saturation only. It was lower in the direction of decreasing gas saturation. The oil relative permeability was found to vary with saturations of the other fluids. Oil isoperms were concave towards the oil apex.

Three-phase relative permeability characteristics applicable to various oil displacement processes in the reservoir such as combustion and alternate gas-water injection were determined on both outcrop and reservoir core samples. Steady-state and nonsteady-state tests were performed on a variety of sandstone and carbonate core samples having different wetting properties. Some of the tests were performed on preserved samples. Some of the three-phase tests were performed on samples that contained two flowing phases and a third nonflowing phase, either gas or oil. These were classed as three-phase flow tests because the third phase played an important role in the flow behavior which was determined. The three-phase relative permeability test results are directly compared with the results of two-phase gas-oil and water-oil test. Wetting-phase relative permeability was found to be primarily dependent on its own saturation, i.e., relative permeability to the wetting phase during three-phase flow was in agreement with and could be predicted from the tow-phase data. Nonwetting-phase relative permeability-saturation relationships were found to be more complex and to depend in some cases on the saturation history of both nonwetting phases and on the saturation ratio of the second nonwetting phase and the wetting phases. Trapping of a given nonwetting phase or mutual flow interference between the two nonwetting phases when both are flowing accounts for most of the low relative permeabilities observed for three-phase flow tests. However, in special cases nonwetting-phase relative permeabilities at a given saturation are higher than those given by two-phase flow data. Despite these complexities some types of three-phase flow behavior can be predicted from two-phase flow data. Through its effect on the spatial distribution of the phases, wettability is shown to be a controlling factor in determining three-phase relative permeability characteristics. however, despite the importance of wettability the present data shown that for both water-wet and oil-wet systems oil recovery can be improved by several different injection processes, but the additional oil recovery is accompanied by lower fluid mobility. Introduction The increasing emphasis on optimizing recovery and the rapid and extensive development and use of mathematical modes for predicting reservoir performance are together creating a widespread need for reliable basic data on rock flow behavior. The two-phase imbibition or drainage flow relationships common to conventional oil recovery processes (depletion, gas or water injection, gravity drainage) are not applicable to some of the newer secondary and tertiary recovery techniques. This is because the reservoir displacement process may differ from that easily simulated in laboratory relative permeability studies. in some situations, data are needed fro a three-phase system where almost any combination of two fluids or even all three fluids may be flowing. In other, however, only two flowing phases are present, but the saturation history of the system is unique. Leverett and Lewis were the first to collect experimental relative permeability data on a three-phase system. Corey et al. were similarly leaders in efforts to define three-phase flow relationships using empirical approaches. Space does not permit a critical review of these earlier works. For those interested, a recent article by Saraf and Fatt provides a brief discussion of the experimental techniques used by earlier investigators. Suffice it to say that both experimental and empirical approaches have been used, but the applicability of both has been limited because in only one case have three-phase relative permeability data been obtained on reservoir rock material. SPEJ P. 75ˆ

Users of thermal simulators usually provide data in terms of two sets of two phase relative permeability functions: (1) krow and krw in a water-oil system, and (2) krog and krg in an oil-gas system. Within the thermal simulator two-phase relative permeabilities are used to predict effective permeability of each phase when all three phases are flowing simultaneously in a block. The most frequently used models for making these predictions are due to Stone (Model I and Model II) and their modifications. The literature does not provide clear guidance on the selection of a relative permeability model for a given problem. In this paper we present theoretical and numerical analyses of three-phase relative permeability models for steamflood problems. Our analysis shows that relatively high krw and krg (from two-phase data) lead to higher kro from Model I than Model II, and the reverse is true when krw and krg are relatively low. The differences in predicted kro by the two models are greatest in the range of low oil saturations. We have selected three sets of relative permeability data from the literature that have been previously used for the modelling of steamfloods. Data Sets 1, 2 and 3 are characterized by moderate, low and high values of krw and krg, respectively. The oil relative permeability (kro) predicted for Data Set 1 by the Stone's two models is about the same. As expected from our theoretical analysis, Stone's two models yield quite different kro's for Data Sets 2 and 3. However, oil production predictions with Model I and Model II for Data Set 3 are not too different, but these two models show significant differences in the simulation results for Data Set 2. Investigation of saturation profiles near production and injection wells show that low krw and krg values (Data Set 2) tend to drive saturations into the range where Stone's two models give different results, and high krw and krg values (Data Set 3) tend to keep saturations in the range where the two models give similar results. The results of this study should be of value in selecting three-phase relative permeability models for steamflood simulations.

This paper describes an automatic relative permeameter. Problems which are encountered in operating unsteady state relative permeameters are first identified. Solutions are then offered, by describing a fully-automated relative permeameter which employs a pseudo-constant pressure flow system, a unique production mandrel design, and an innovative fractionmeter / flowmeter system. The new apparatus offers a fast and accurate method of obtaining displacement data, with direct input into a computer for data analysis. Introduction The relative permeabilities of a porousmedia to simultaneous flow of two different fluids are fundamental parameters of major importance to the study of flow in petroleum reservoirs. They are also the most difficult properties to measure in the laboratory. Superficially, the determination of relative permeabilities is straightforward. With two phases flowing through a rock sample, the pressure drop and flow rates of each phase are measured. Darcy's law in the form Equation (Available In Full Paper) where Qa is the flow rate of the Han phase, k is the absolute permeability, kar, is the relative permeability, µa is the viscosity, A is the cross-sectional area, Pa is the pressure and x is the spatial coordinate, is then used to determine kar,. The relative permeability is a function of saturation; therefore, the saturations of both phases are required for each set of flow rates. The difficulty in experimentally determining relative permeabilities lies not in the basic concept, but in the simultaneous measurement of flow rate, pressure drop and saturation. There are two methods of obtaining relative permeability data: steady state and unsteady state. Only the unsteady state method is considered in this paper. The unsteady state method is based on interpreting an immiscible displacement process. The interpretation of this displacement process to obtain relative permeability data is performed by one of two analysis techniques: application of Buckley-Leverett frontal advance theory(l) or direct computer simulation. Application of Buckley-Leverett theory requires a number of experimental restrictions. For example, the pressure drop across the sample must be sufficiently large so that capillary effects, particularly at the outlet end of the core, are negligible. This method of calculation is based on estimating the saturation of the flooding phase, and measuring the fractional flow of this phase at the outlet face of the core. In this way the relative permeability can be related to the saturation. Because the experiment is performed rapidly, these measurements are not always easy to obtain. For this reason, actual reservoir fluids are not generally used; instead, fluids with viscosities which facilitate interpretation of the experiment are employed. Direct computer simulation is a more sophisticated and more meaningful method of extracting relative permeability data from displacement experiments, particularly' for vuggy samples(2). The method is applied by assuming that relative permeability is related to saturation by means of the following expressions (for a two-phase system, a and b): Equation (Available In Full Paper) where kir is the relative permeability, kire is the end point relative permeability (kare at Sbr and kbre at Sar), Si is the saturation, Sir is the residual saturation and ni is the saturation exponent.