Three-phase Relative Permeability Data Research Articles

Coupled Capillary-Pressure and Three-Phase Flash Models Simulate Liquid Blockage

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 190242, “Simulation of Water and Condensate Blockage and Solvent Treatments in Tight Formations Using Coupled Three-Phase Flash and Capillary-Pressure Models,” by Sajjad S. Neshat, SPE, Ryosuke Okuno, SPE, and Gary A. Pope, SPE, The University of Texas at Austin, prepared for the 2018 SPE Improved Oil Recovery Conference, Tulsa, 14–18 April. The paper has not been peer reviewed. Water and condensate blockage near production wells in unconventional reservoirs can reduce oil- and gas-production rates significantly. This paper presents a new approach for more-accurate modeling of liquid blockage in tight oil and gas reservoirs and investigates the use of solvents for blockage removal. Introduction In this paper, coupled three-phase flash and capillary-pressure models are presented for simulation of tight oil and gas reservoirs. The capillary pressure between each phase pair (e.g., oil/gas or oil/aqueous) is calculated with a general three-phase capillary-pressure model that integrates the effect of important petrophysical properties including pore-size distribution, phase saturations, and different wettability conditions. The capillary-pressure function is integrated with three-phase flash calculations to define the equilibrium state between oil, gas, and aqueous phases under reservoir conditions. The criterion for selection of cubic equation-of-state (EOS) roots is extended for three-phase mixtures. This method minimizes the global Gibbs free energy (GFE) of the whole mixture instead of minimizing the free energy of each phase separately. The models are then used for simulation of primary production and solvent enhanced-oil-recovery (EOR) processes in tight formations. Using rock and fluid properties for tight oil and gas reservoirs, the effect of water and condensate blockage and capillary pressure on production is simulated. The use of solvents to remove liquid blockage and to increase production rates is extended to tight formations with high capillary pressure. Coupled Three-Phase Flash and Capillary-Pressure Models At three-phase equilibrium conditions, the chemical potential of each component must be equal in all three phases. In the presence of capillary pressure, the chemical potentials are calculated at corresponding phase pressures. Capillary pressure across a two-phase interface is a function of the surface curvature and interfacial tension (IFT). The variation in pore size and interfacial curvature can be accounted for by saturation-dependent functions. In the presence of a third phase, the interface between any two phase pairs would shift toward either larger or smaller pores depending on wettability conditions. A general three-phase model that can be used to define the capillary pressure between any phase pairs under the entire range of wettability conditions has been coupled with a three-phase relative permeability model with three-phase hysteresis and compositional consistency and was validated through measured three-phase relative permeability data. For the applications discussed in this study, it is assumed that the gas phase is always the most nonwetting phase, while a mixed wetting condition for oil and aqueous phases is assumed.

A New Three-Phase Microemulsion Relative Permeability Model

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 187369, “A New Three-Phase Microemulsion Relative Permeability Model for Chemical-Flooding Reservoir Simulators,” by Hamid R. Lashgari, Gary A. Pope, Mohsen Tagavifar, Haishan Luo, and Kamy Sepehrnoori, The University of Texas at Austin, and Zhitao Li and Mojdeh Delshad, Ultimate EOR Services, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–11 October. The paper has not been peer reviewed. The complete paper presents a new three-phase relative permeability model for use in chemical-flooding simulators. A model that has been widely used in chemical-flooding simulators for decades has numerical discontinuities that are not physical in nature and that can lead to oscillations in the numerical simulations. The proposed model is simpler, has fewer parameters, and requires fewer experimental data to determine the relative permeability parameters compared with the original model. Background Two- and three-phase relative permeability measurements at low interfacial tension (IFT) have been published previously, and microemulsion relative permeability models have been proposed in the literature as well. But none of these can model the microemulsion phase across different phase-behavior environments, from oil-in-water, to the middle phase, to water-in-oil emulsions. Desirable features should include agreement between two- and three-phase micro emulsion relative permeability and oil-recovery data, and relative simplicity for use in reservoir simulators with a minimum number of model parameters that can be estimated from experimental data in a straightforward way. Satisfying these requirements has turned out to be an extremely challenging task. The objective of this study was to develop a simple, continuous two- and three-phase microemulsion relative permeability model with relatively few parameters that is practical for use in chemical-flooding simulators. Discontinuities in relative permeability cause numerical problems that can cause severe reductions in the size of the timesteps. Discontinuities also cause errors in the physical predictions of important phenomena such as phase trapping and surfactant retention. The need for a continuous model has been well-known, but it was a challenging task to develop a continuous model because of the complexity of three-phase microemulsion phase behavior.

A mechanistic model for prediction of three-phase flow in petroleum reservoirs

Multiphase flow in the porous media is of great interest for many engineering fields such as underground oil and gas reservoirs, environmental process (e.g. carbon dioxide (CO2) geological storage) and underground water resources remediation. Modelling of these process requires relative permeability (kr) of each fluid as a function of the fluid saturation. The experimental measurement of the three-phase relative permeability is much more complex and time consuming process than the two-phase relative permeability. Hence, many correlations have been proposed in the oil industry for the calculation of the three-phase relative permeability using two-phase kr data. However, most of the existing three-phase models ignore the physical mechanism underlying the multiphase flow in the porous media.In this study, a novel mechanistic model is proposed to predict the three-phase relative permeability of the oil, water and gas in the petroleum reservoir (i.e. porous rock). The new idea is that the interaction between various fluids (i.e. oil, water and gas) and also the fluid saturation distribution are somehow considered in the estimation of the relative permeability. For this purpose, a new parameter named characteristic coefficient is introduced in the model. This parameter reflects the contribution of each fluid in controlling the flow of the other fluids. In other words, this factor is net impact of the various rock and fluid parameters (e.g. surface tension between fluids, wettability and saturation distribution) that all influence the flow in the porous media. This idea is taken from the glass-micro-model experiment that visualises the mechanism underlying the flow at the pore scale. Another feature of this method is that, at least one set of experimental three-phase kr data is required to tune the characteristic coefficients. The estimated characteristic factors can then be employed to predict the three-phase relative permeability for the other saturation path.The model is successfully validated against the experimentally measured three-phase relative permeability data.

Modeling of Cyclic Hysteresis of Three-Phase Relative Permeability During Water-Alternating-Gas Injection

Summary Multiphase flow takes place in many petroleum reservoirs—in particular, mature fields and reservoirs under fluid [e.g., gas, water-alternating-gas (WAG)] injection. The numerical simulation of such reservoirs requires knowledge of flow functions (i.e., relative permeability and capillary pressure). Because experimental measurement of fluid permeabilities (in particular) under three-phase-flow conditions is very time-consuming and difficult, many correlations and models were developed and these are widely used instead of measured data. In this study, we have used the results of a comprehensive set of WAG-injection coreflood experiments performed under different wettability conditions and core-permeability values to obtain relative permeabilites of oil, water, and gas under reservoir pressure and temperature. Three-phase relative permeability of each phase was obtained by history matching the measured production and differential pressure obtained in the laboratory. The results of the experiments revealed significant cyclic hysteresis effects in gas and oil relative permeability. We proposed new formulations and methodology for the modeling of cyclic hysteresis of three-phase relative permeability during WAG injection. This technique is a direct method that uses measured three-phase kr data obtained from the first cycle of WAG injection to predict the relative permeability of the subsequent cycles. The integrity of this technique was validated against the three-phase kr data obtained from our WAG experiments. We also assess the validity of the WAG-injection hysteresis model available in reservoir simulators against our three-phase relative permeability data to evaluate its performance.

Multiscale Simulation of WAG Flooding in Naturally Fractured Reservoirs

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 164837, ’Multiscale Simulation of WAG Flooding in Naturally Fractured Reservoirs,’ by Mohamed Ahmed Elfeel, Adnan Al-Dhahli, Sebastian Geiger, SPE, and Marinus I.J. van Dijke, Heriot-Watt University, prepared for the 2013 EAGE Annual Conference and Exhibition/SPE Europec, London, 10-13 June. The paper has not been peer reviewed. Naturally fractured reservoirs (NFRs) contain a significant amount of remaining petroleum reserves and are now being considered for water-alternating-gas (WAG) flooding as secondary or tertiary recovery. The authors face the challenge of reservoir simulation of WAG by building models at various scales, starting with pore scale and expanding to an intermediate scale and then to reservoir scale. They show how pore-network modeling and fine-grid modeling where the fractures and matrix are represented explicitly can be used to increase the accuracy of numerical simulations at field scale. Introduction A significant portion of the world’s remaining petroleum resources is located in NFRs, including supergiant fields in the Middle East. A detailed understanding of the recovery processes involved in extracting hydrocarbons from NFRs by use of enhanced-oil-recovery techniques is key to increasing ultimate recovery for such reservoirs. Waterflooding has been used with various degrees of success in NFRs. For unfavorable (i.e., mixed- to oil-wet) matrix wettability, however, waterflooding can be ineffective. Gas/oil gravity drainage (GOGD) provides an important drive mechanism that can be effective irrespective of the rock wettability. In NFRs, fractures increase the exposure of the injected gas to oil in reservoir rock, which renders GOGD more effective than it is in unfractured reservoirs. Consequently, gas injection has been applied in many NFRs. However, because the gas mobility is very high compared with that of water and oil, so is the risk of bypassed oil and gravity override, which can lead to very early gas breakthrough. This is particularly true for NFRs. WAG flooding combines the merits of the two injection fluids on macroscopic and microscopic scales while stabilizing the injection front, delaying breakthroughs, and, therefore, leading to increased oil recovery compared with continuous water or gas injection. Reservoir simulation of WAG injection is very challenging because a representative three-phase saturation model is required to predict relative permeability and capillary pressure as water and gas saturations increase and decrease alternately. Three-phase relative permeability and capillary pressure data are extremely difficult to measure experimentally. Even if experimental evaluation becomes feasible, an infinite number of saturation paths can occur in the reservoir. This necessitates the use of empirical, or interpolation, models to predict three-phase relative permeability and capillary pressure from two-phase experiments. In NFRs, capillary pressure and relative permeability functions have a major effect on fluid exchange between matrix blocks and fractures. Predicting the effects of the interplay of viscous, capillary, and gravity forces is challenging because fluid flow is viscous-dominated in the fractures while transfer between fractures and matrix blocks is dominated by capillary and gravity forces. Because most of the oil is contained inside the matrix, capillary and gravity forces can be more important in NFRs than in conventional reservoirs.

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

This study reports effect of temperature on the estimated relative permeability isoperms for a fluid system of heavy oil, water, and CO2. An experimental/numerical technique was utilized to estimate relative permeability isoperms for a three-phase fluid system. Two-phase displacement tests were separately carried out in order to measure residual saturations. Three-phase displacements were conducted in the form of CO2 injection into a consolidated Berea core saturated with heavy oil and water at temperatures 28, 40, and 52°C. A three-phase one-dimensional numerical simulator (able to use three-phase relative permeability data in explicit form) was developed to simulate the displacement experiments. The procedure was validated using steady state experiment as well as sensitivity analysis. The results of this study demonstrate that limited three-phase flow zone exists for heavy oil fluid systems due to high values of residual oil saturation. Different curvatures are observed for each of the phases. These curvatures are more complicated for oil and water than in the gas phase. Although temperature is found to change the position of the three-phase flow zone in ternary diagrams, however, no significant change in the size of the three-phase flow zone is observed. The effect of an increase in temperature on the relative permeability isoperms is very different in each phase. This process decreases the relative permeability of oil. In an opposite way, the relative permeability of the gas phase increases at elevated temperatures. When it comes to water, reversal behavior is observed as it increases from 28°C to 40°C and, then, decreases as temperature further rises to 52°C.

Experimental Investigation of Near-Miscible Water-Alternating-Gas Injection Performance in Water-Wet and Mixed-Wet Systems

Summary Laboratory data on water-alternating-gas (WAG) injection for non-water-wet systems are very limited, especially for near-miscible (very low IFT) gas/oil systems, which represent injection scenarios involving high-pressure hydrocarbon gas or CO2 injection. Simulation of these processes requires three-phase relative permeability (kr) data. Most of the existing three-phase relative permeability correlations have been developed for water-wet conditions. However, a majority of oil reservoirs are believed to be mixed-wet and, hence, prediction of the performance of WAG injection in these reservoirs is associated with significant uncertainties. Reliable simulation of WAG injection, therefore, requires improved relative permeability and hysteresis models validated by reliable measured data. In this paper, we report the results of a comprehensive series of coreflood experiments carried out in a core under natural water-wet conditions. These included water injection, gas injection, and also WAG injection. Then, to investigate the impact of wettability on the performance of these injection strategies, the wettability of the same core was changed to mixed-wet (by aging the core in an appropriate crude oil) and a similar set of experiments were performed in the mixed-wet core. WAG experiments under both wettability conditions started with water injection (I) followed by gas injection (D), and this cyclic injection of water and gas was repeated (IDIDID). The results show that in both the water-wet and mixed-wet cores, WAG injection performs better than water injection or gas injection alone. Changing the rock wettability from water-wet to mixed-wet significantly improves the performance of water injection. Under both wettability conditions (water-wet and mixed-wet), the breakthrough (BT) of the gas during gas injection happens sooner than the BT of water in water injection. Ultimate oil recovery by gas injection is considerably higher than that obtained by water injection in the water-wet system, while in the mixed-wet system, gas injection recovers considerably less oil.

Three-phase relative permeability and hysteresis effect during WAG process in mixed wet and low IFT systems

There is significant uncertainty associated with the selection of three-phase relative permeability in particular for the numerical simulations of water-alternating-gas (WAG) injection. Generally, three-phase relative permeabilities are calculated from empirical correlations, which are based on two-phase relative permeabilities. Water alternating gas injection involves drainage and imbibition processes taking place sequentially. Therefore, accurate prediction of the relative permeability ( k r) functions and their hysteresis effects applicable to WAG are extremely complex. The problem of 3-phase k r selection becomes even more difficult for three-phase systems involving mixed-wet rocks and low gas–oil IFT (interfacial tension) fluids (nearly-miscible fluids). We use the results of coreflood experiments carried out on two different cores (one water-wet and one mixed-wet) using a low IFT gas–oil system to generate two-phase and three-phase relative permeability data by using an in-house three-phase coreflood simulator. The results show that water and gas three-phase k r values depend on two independent saturations, contrary to the inherent assumption in most of the existing empirical k r models. Three-phase water, oil and gas k r values were all significantly lower than their corresponding two-phase values. This reduction in k r was more profound for the gas where the three-phase k rg was an order of magnitude lower than its corresponding two-phase k rg. Using the laboratory derived three-phase k r data, the performance of some of the existing three-phase k r models was evaluated by comparing the results of the WAG experiments with predictions made by a commercial reservoir simulator. In general, considerable discrepancies between the measured and the predicted k r values were observed. Some models performed better than others but no single model was capable of matching all experimental results adequately.

Impact of relative permeability hysteresis on the numerical simulation of WAG injection

Pore-scale physics, laboratory investigations, and field experience, dictate that three-phase relative permeabilities exhibit strong dependence on the saturation path and the saturation history. Such dependence is especially relevant in immiscible water-alternating-gas (WAG) processes, which are characterized by a sequence of three-phase drainage and imbibition cycles. In this paper, we study the influence of relative permeability hysteresis on the field-scale predictions of WAG injection. Because their measurement is difficult and time-consuming, three-phase relative permeabilities are usually interpolated from two-phase data. The errors associated with this procedure have been investigated by Oak (SPE 20183), who reported that interpolated values might differ significantly from experimental ones. The effect of using different interpolation models in field-scale simulations has been illustrated by a number of authors, who found that recovery predictions could be significantly different depending on the three-phase relative permeability model. Here, we study the impact of using history-dependent saturation functions in reservoir simulations. First, we investigate the degree of accuracy with which different hysteretic models reproduce Oak's three-phase relative permeability data. In doing so, we assess the validity of existing models, and we identify the model parameters subject to most uncertainty. Our analysis suggests that current models account for some of the hysteretic behavior observed experimentally, but do not reproduce experimental measurements adequately during cyclic water/gas injection. Second, we illustrate how the use of a hysteretic relative permeability model affects reservoir simulations. We use a synthetic model of a quarter five-spot pattern in a homogenous reservoir, and a more realistic heterogeneous reservoir modified from the PUNQ-S3 model. We find that there is striking disparity in the simulation results depending on whether a hysteretic or a nonhysteretic model is employed. Therefore, we conclude that (1) it is essential to incorporate hysteresis in the relative permeabilities in order to obtain accurate predictions of realistic immiscible WAG processes; and (2) enhancements are needed to improve the predictive capabilities of current relative permeability hysteresis models.

An Unsteady-state Technique For Three-phase Relative Permeability Measurements

Abstract 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.

An Improved Model For Estimating Three-Phase Oil-Water-Gas Relative Permeabilities From Two-Phase Oil-Water And Oil-Gas Data

Abstract Laboratory measurements of three-phase relative permeabilities are extremely time-consuming and are rarely obtained for reservoir systems. Therefore, computer simulations of reservoir processes involving three-phase flow have to rely on predictive techniques for supplying the three-phase relative permeability data. The empirical models developed by Stone(8,9) have been used extensively. As discussed by Aziz and Settari(15) the Stone models must be normalized to obtain a good match of the oil relative permeabilities at the oil-water and oil-gas two-phase ends for systems in which the relative permeability to oil at connate water saturation in an oil-water system and at zero gas saturation in an oil-gas system is not unity. Even after incorporating the normalization suggested by Aziz and Settari(15), the Stone models do not provide a satisfactory match of available three-phase data. This paper presents a new method for normalizing Stone's first model. The method was tested against six different sets of experimental data reported in the literature as well as with a new set of experimental data. Considerably improved matches were obtained with this version of the normalization scheme compared to the conventional Stone's Methods I and II results. The new fits are excellent at the highest oil isoperms and deviate slightly as the residual oil saturation is approached. Introduction Displacement of oil in reservoirs generally involves the flow of oil, water and gas. Enhanced oil recovery methods such as wAG solvent flooding, steamflooding and in situ combustion involve multiphase flow. To simulate such processes by numerical modelling requires experimental data or prediction methods for threephase relative permeabilities. There are only a limited number of studies which deal with threephase relative permeability measurements and correlations in the literature. The first study was conducted by Leverett and Lewis(1) in 1941. They measured the three-phase relative permeability of a water-oil-gas system in unconsolidated sands. Since their work in 1941 several other studies have been reported. Numerous review articles on three-phase relative permeability correlations and experimental studies have also appeared in the literature. Some of these are the work of Saraf and McCaffery(2), Honarpour et al.(3), Bakerter(4) Manjnath and Honarpour(5), Parmeswar and Maerfat(6), Maini et al(7). The interested reader is referred to these studies for an up-to-date literature review of three-phase relative permeabilities. Measurement of three-phase relative permeability in the laboratory is a difficult and time-consuming task due to the complicationsof three-phase flow through porous media. Relative permeabilities are function of fluid saturation history which makes their measurement complicated. A detailed description of the methods and the problems involved in the measurement of threephase relative permeability is given by Saraf and McCaffery(2) and Honarpour et at.(3). Due to the problems associated with threephase flow experiments and the amount of time and effort needed for obtaining experimental data on three-phase relative permeabilities, use of a predictive model is an attractive alternative. Stone Models The models of Stone(8,9), designated as Methods I and II, have been used extensively in reservoir simulation studies in the absence of three-phase data.

Estimation of Three-Phase Relative Permeability And Residual Oil Data

Abstract The probability model presented in an earlier paper has been revised to yield improved estimates of three phase relative permeabilities. Both the old and the new models use two sets of two-phase data ? water-oil and gas-oil – as a basis for estimating the more difficult-to measure three-phase data. The relative permeabilities predicted by the new model compare favorably with the experimental data available in the literature, including data on the dependence of waterflood residual oil saturations on trapped gas saturations. Introduction A PROBABILITY MODEL for the estimation of threephase relative permeability data, which was described in an earlier paper,(2) has been revised and improved. The revised model uses two sets of two-phase data water displacing oil and gas displacing oil – as the basis for making such estimates. Hysteresis is taken into consideration by employing the appropriate two-phase data, as discussed in the section titled "Data Required." Relative permeabilities predic.ted by this model are in better agreement with experimental data than those resulting from the earlier model, especially in the region of low oil saturations. In fact, the new approach is capable of providing estimates of residual oil data in the three-phase region which are needed, for example, to determine the effect on oil recovery of an initial free gas saturation during a water-flood. In theprevious model, these residual oil data had to be provided as input to supplement the two sets of two-phase data. Both the old and the new model have a desirable property in that they yield the correct two-phase data when only two phases are flowing and yet provide interpolated data for three-phase flow that are consistent and continuous functions of the phase saturations. As will be shown later, these interpolated values agree with the available three-phase data within experimental uncertainty. The method can be used to estimate the relative permeability to oil in a preferentially water-wet system in which water and gas relative permeabilities depend on only the water and gas saturations, respectively. Its applicability to preferentially oil-wet and mixed-wettability systems is a matter of conjecture, because the data used to evaluate it were measured on cores or sand packs which the experimenters attempted to keep fully waterwet. However, the probabilistic basis of the model suggests that it should be useful for estimating the relative permeability of one phase if the relative permeability of the other twophases is a function only of their respective phase saturations. Thus, in a fully oil-wet system where oil relative permeability is a function of oil saturation and gas relative permeability a function of gas saturation, one would expect the probability model to be effective in predicting the water relative permeability. For systems in which mixed wettability is caused by a fraction of the pore spaces ?being strongly oil wet while the remainder are strongly water wet, a reasonable, but not proven, hypothesis is that in one saturation range equations applicable to a water-wet system can be used, whereas elsewhere the oil-wet equations will apply.

Sandstone and Carbonate Two- and Three-Phase Relative Permeability Characteristics

Abstract 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

Probability Model for Estimating Three-Phase Relative Permeability

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

Three-Phase Relative Permeability Measurement Using a Nuclear Magnetic Resonance Technique for Estimating Fluid Saturation

Abstract 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. SPEJ P. 235ˆ

Three-Phase Relative Permeability Measurements by Unsteady-State Method

Abstract 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.