Shape Of Relative Permeability Curves Research Articles

Impact of Wettability Alteration on the Front Instability of Immiscible Displacement in Porous Media

AbstractWettability alteration that occurs as a result of changing the brine composition or using chemicals that lower the interfacial tension can significantly alter the mobility of nonaqueous liquid (NAPL)/water phases. Here, we show that including dynamic wettability alternation (moving from non‐water‐wet to water‐wet) or interpolating between two sets of relative permeability curves may create an unstable displacement of the residence‐fluid by the injected fluid. The instability occurs due to not only the viscosity ratio but also the new shape of relative permeability curves and their end‐point values. We perform a full factorial design on Corey relative permeability parameters to determine the most destabilizing factors when the viscosity ratio is one. The observations indicate that instability proliferates when the end‐point relative permeability to the NAPL phase of modified salinity brine increases, and their corresponding exponents decrease compared with high salinity brine (seawater or formation water). Besides, numerical simulations of such a displacement demonstrate that modified salinity water (MSW)'s breakthrough is accelerated by wettability change toward water‐wet compared with a non‐fingering analytical solution. This may result in a delayed mobilization of the NAPL phase in porous media. We also discuss the role of capillary pressure, heterogeneity, and secondary and tertiary injection of MSW in stabilizing the shock front.

Experimental investigation of the displacement flow mechanism and oil recovery in primary polymer flood operations

Polymer flooding is a mature chemical enhanced oil recovery method employed in oilfields at pilot testing and field scales. Although results from these applications empirically demonstrate the higher displacement efficiency of polymer flooding over waterflooding operations, the fact remains that not all the oil will be recovered. Thus, continued research attention is needed to further understand the displacement flow mechanism of the immiscible process and the rock–fluid interaction propagated by the multiphase flow during polymer flooding operations. In this study, displacement sequence experiments were conducted to investigate the viscosifying effect of polymer solutions on oil recovery in sandpack systems. The history matching technique was employed to estimate relative permeability, fractional flow and saturation profile through the implementation of a Corey-type function. Experimental results showed that in the case of the motor oil being the displaced fluid, the XG 2500 ppm polymer achieved a 47.0% increase in oil recovery compared with the waterflood case, while the XG 1000 ppm polymer achieved a 38.6% increase in oil recovery compared with the waterflood case. Testing with the motor oil being the displaced fluid, the viscosity ratio was 136 for the waterflood case, 18 for the polymer flood case with XG 1000 ppm polymer and 9 for the polymer flood case with XG 2500 ppm polymer. Findings also revealed that for the waterflood cases, the porous media exhibited oil-wet characteristics, while the polymer flood cases demonstrated water-wet characteristics. This paper provides theoretical support for the application of polymer to improve oil recovery by providing insights into the mechanism behind oil displacement.Graphic abstractHighlightsThe difference in shape of relative permeability curves are indicative of the effect of mobility control of each polymer concentration.The water-oil systems exhibited oil-wet characteristics, while the polymer-oil systems demonstrated water-wet characteristics.A large contrast in displacing and displaced fluid viscosities led to viscous fingering and early water breakthrough.

Unravelling Effects of the Pore‐Size Correlation Length on the Two‐Phase Flow and Solute Transport Properties: GPU‐based Pore‐Network Modeling

AbstractContinuum‐scale models for two‐phase flow and transport in porous media are based on the empirical constitutive relations that highly depend on the porous medium heterogeneity at multiple scales including the microscale pore‐size correlation length. The pore‐size correlation length determines the representative elementary volume and controls the immiscible two‐phase invasion pattern and fluids occupancy. The fluids occupancy controls not only the shape of relative permeability curves but also the transport zonation under two‐phase flow conditions, which results in the non‐Fickian transport. This study aims to quantify the signature of the pore‐size correlation length on two‐phase flow and solute transport properties such as the capillary pressure‐ and relative permeability‐saturation, dispersivity, stagnant saturation, and mass transfer rate. Given the capability of pore‐scale models in capturing the pore morphology and detailed physics of flow and transport, a novel graphics processing unit (GPU)‐based pore‐network model has been developed. This GPU‐based model allows us to simulate flow and transport in networks with multimillions pores, equivalent to the centimeter length scale. The impact of the pore‐size correlation length on all aforementioned properties was studied and quantified. Moreover, by classification of the pore space to flowing and stagnant regions, a simple semianalytical relation for the mass transfer between the flowing and stagnant regions was derived, which showed a very good agreement with pore‐network simulation results. Results indicate that the characterization of the topology of the stagnant regions as a function of pore‐size correlation length is essential for a better estimation of the two‐phase flow and solute transport properties.

Gas Relative Permeability and its Evolution During Water Imbibition in Unconventional Reservoir Rocks: Direct Laboratory Measurement and a Conceptual Model

SummaryRelative permeability has a significant impact on gas or oil and water production, and is one of the most complicated properties in unconventional reservoirs. Current understanding of relative permeability for unconventional reservoir rocks is limited, mainly because of a lack of direct measurement of relative permeability for rocks that have a matrix permeability at the submicrodarcy level. Because of the difficulties related to direct measurement, most studies on relative permeability in unconventional reservoirs are based on indirect or modeling methods. In this paper, a modified gas–expansion method for shale matrix–permeability measurement (Peng et al. 2019) was adopted to measure gas relative permeability directly under the scenario of water imbibition for samples from different unconventional reservoir formations. Evolution of gas permeability, along with gas porosity and fracture/matrix interaction, during the process of water redistribution (which mimics what occurs in the shut–in period in real production) was also closely measured. Results show that gas relative permeability in the matrix decreases during water redistribution because of water imbibition from fractures to the matrix coupled with a water–block effect. The water–block effect is more significant at low water saturations than at higher water saturations, leading to a rapid–to–gradual drop of gas relative permeability with increasing water saturation.A conceptual model on water redistribution in a fracture/matrix system and the change of gas and water relative permeability is proposed on the basis of experimental results and observations. Influencing factors including pore size, shape, connectivity, and wettability are taken into account in this conceptual model. The combined effect of these four influencing factors determines the level of residual gas saturation, which is the most important parameter in defining the shape of relative permeability curves. Water relative permeability is predicted on the basis of the conceptual model and the measured gas relative permeability using modified Brooks–Corey equations. Deducing the oil/water relative permeability is also discussed. The implications of relative permeability for gas or oil and water production and potential strategies for optimal production are also discussed in the paper. The hysteresis effect is not included in this study but will be addressed in future work.

The Characteristics and Impacts Factors of Relative Permeability Curves in High Temperature and Low-Permeability Limestone Reservoirs

To improve the understanding of the influence of effective permeability, reservoir temperature and oil-water viscosity on relative permeability and oil recovery factor, core displacement experiments had been performed under several experimental conditions. Core samples used in every test were natural cores that came from Halfaya oilfield while formation fluids were simulated oil and water prepared based on analyze data of actual oil and productive water. Results from the experiments indicated that the shape of relative permeability curves, irreducible water saturation, residual oil saturation, width of two-phase region and position of isotonic point were all affected by these factors. Besides, oil recovery and water cut were also related closely to permeability, temperature and viscosity ratio.

Measuring Oil and Water Relative Permeability in a Single Fracture and Researching Its Impacting Factors

For the research of oil and water relative permeability in single fracture it is important to study the law of flow in fractured-vuggy reservoirs. Base on the wetting property of the field, single-fracture acrylic models with different fracture apertures are created. Using these models, oil and water relative permeability with different water-oil viscosity ratio, different fracture aperture, different fracture dip, and different displacing velocity are measured by the steady-state method. How the relative permeability is influenced by these factors is further studied. The results show that: when the water-oil viscosity ratio is close to 1, the shape of relative permeability curve is similar to X. Relative permeability of oil and water decreases with increasing water-oil viscosity ratio and decreasing fracture aperture and increasing displacing velocity. Fracture dip has little effect on the shape of the relative permeability curve. Residual oil saturation decreases with decreasing water-oil viscosity ratio, increasing fracture aperture, increasing fracture dip, and increasing displacing velocity.

Effect of Temperature on Two-Phase Relative Permeabilities of Heavy Oil, Water, Carbon Dioxide, and Methane Determined by Displacement Technique

Two coreflood setups were used to measure heavy oil–water, heavy oil–carbon dioxide, and heavy oil–methane relative permeabilities. Using fractional effluents measured with precision meters and differential pressure data records, the Johnson–Bossler–Naumann technique was applied to calculate two-phase relative permeability in a consolidated sandstone core. In order to investigate the effect of temperature on the shape of relative permeability curves, a series of coreflood tests was conducted at three different temperatures (28, 40, and 52 °C) for each fluid pair. Analysis of the data obtained for the heavy oil–water system showed a linear increase of about 65% and 50% in water relative permeabilities when temperature ranged from 28 to 40 °C and 40 to 52 °C, respectively. However, although the oil relative permeability curve showed an increase of about 70% when temperature increased from 28 to 40 °C, it was dramatically decreased by about 30% when temperature was increased from 40 to 52 °C. In the case of heavy oil–gas a different effect was observed for methane and carbon dioxide. Although both methane and carbon dioxide relative permeabilities increased nonlinearly at higher temperatures, oil relative permeability in the presence of carbon dioxide decreased when temperature increased. In contrast, in the presence of methane, oil relative permeability experienced a reduction of 80% from 28 to 40 °C followed by a considerable increase of 15-fold from 40 to 52 °C.

Investigating the Effect of Capillary Number on Performance Prediction of an Iranian Fractured Gas Condensate Reservoir

Gas condensate reservoirs are one of the most complicated reservoirs in which the special thermodynamic behavior of reservoir fluid leads to condensate buildup instead of gas expansion, when the reservoir pressure drops below dew point pressure. To justify the phase behavior of such reservoirs, several models have been proposed. One of the models is a capillary number model that has a considerable effect on the shape of relative permeability curves. Taking account of capillary number is shown to improve the performance prediction of gas condensate reservoirs that otherwise is poorly predicted. In pressures below dew point pressure, velocity and surface tension between gas and oil increases more rapidly in the vicinity of the well compared with other parts of the reservoir, which results in condensate saturation reduction and gas relative permeability improvement. The authors model a fractured gas condensate reservoir with and without taking capillary number into consideration; the performance prediction results are compared to the actual results. The model with capillary number included is shown to be able to predict the performance with a greater accuracy than the case without capillary number.

Modeling Low-Salinity Waterflooding

Summary Low-salinity waterflooding is an emerging enhanced-oil-recovery (EOR) technique in which the salinity of the injected water is controlled to improve oil recovery vs. conventional, higher-salinity waterflooding. Corefloods and single-well chemical-tracer tests have shown that low-salinity waterflooding can improve basic waterflood performance by 5 to 38%. This paper describes a model of low-salinity flooding that can be used to evaluate projects; shows the implications of that model and demonstrates its use to represent corefloods, single-well tests, and field-scale simulations; and gives insight into the reservoir engineering of low-salinity floods. The model represents low-salinity flooding using salinity-dependent oil/water relative permeability functions resulting from wettability change. This is similar to other EOR modeling, and conventional fractional-flow theory can be adapted to describe the process in 1D for secondary and tertiary low-salinity waterflooding. This simple analysis shows that while some degree of connate-water banking occurs, it need not hinder the process. Mixing of injected water with in-situ water delays the attainment of low salinity, potentially preventing attainment of low salinity all together if very small slugs of low-salinity water are used. This paper demonstrates the importance of mixing to modeling of low-salinity flooding and suggests addressing it in engineering calculations. Care must be taken in representing mixing appropriately in interpreting data and in constructing models. The use of numerical dispersion to represent physical dispersion in 1D, radial, and pattern simulations of this process is demonstrated (i.e., coarse-grid simulations are shown to give the same result as fine-grid simulations with an appropriately large physical dispersion). In many applications, the fine-grid simulation necessary to represent appropriate levels of dispersion is not practical, and pseudoization is necessary. We demonstrate that this can be achieved by changing the salinity dependence and shapes of relative permeability curves.

Effect of Fracture Compressibility on Oil Recovery From Stress-Sensitive Naturally Fractured Reservoirs

Abstract The tank material balance (MB) equation for undersaturated and saturated reservoirs has been written taking into account the effective compressibility of matrix and fractures. The solution is presented in finite difference form to achieve a quick convergence of the iteration process. Historically, compressibility has been neglected when carrying out MB calculations of conventional reservoirs producing below the bubble point. This assumes that the reservoir strata are static. It is shown however, that under some conditions, fracture compressibility can have a significant impact on oil rates and recoveries of naturally fractured reservoirs (NFRs) performing below the bubble point, as the fracture permeability and fracture porosity are stress-dependant. Other stress-sensitive properties discussed in this paper include the partitioning coefficient and the exponent for the shape of relative permeability curves. The use of the MB finite difference equations is illustrated with an example. Introduction Forecasting the performance of naturally fractured reservoirs (NFRs) is a major challenge. Various authors have tackled the problem throughout the years using MB calculations. To the best of my knowledge, the effect of fracture compressibility below the bubble point has been usually ignored in MB equations for saturated reservoirs. The work presented in this paper is not meant to replace a detailed reservoir simulation, which is the best way to try to solve the problem provided that reservoir characterization and quality of the pressure and production data is good. The objective is to have a tool that can provide a quick indication with respect to potential oil recoveries from stress-sensitive NFRs. Pirson(1) pioneered efforts to try to explain the high GOR associated with many NFRs once the bubble point is reached. He considered the reservoir to be made of two porosity and permeability systems in parallel and visualized production as a succession of equilibrium stages. Jones-Parra and Seijas-Reytor(2) studied the effect of gas-oil ratio on the behaviour of fractured limestone reservoirs using a two-porosity model. They assumed that gravity segregation took place freely and resistance to fluid flow was very small in the fracture network. In the matrix or fine porosity system, there was high resistance to flow and no segregation. Aguilera(3, 4) used combined log analyses and MB to try to explain the high gasoil ratios observed in many NFRs. More recently, Penuela et al.(5) presented a MB for calculating oil-in-place in matrix and fractures taking into account the compressibility difference between matrix and fractures. This paper presents MB equations for predicting oil recovery and rates of undersaturated and saturated reservoirs. The equations are written taking into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, partitioning coefficient, and exponent for shape of relative permeabilities are taken into account. The solution is presented in finite difference form to achieve a quick convergence of the iteration process.

Simultaneous Estimation of Absolute and Relative Permeability by Automatic History Matching of Three-Phase Flow Production Data

Abstract This paper focuses on the simultaneous estimation of the absolute permeability field and relative permeability curves from three-phase flow production data. Irreducible water saturation, critical gas saturation, and residual oil saturations are assumed to be known. The two-phase relative permeability curves for an oil-gas system and the two-phase relative permeability curves for an oil-water system are represented by power law models. The three-phase oil relative permeability curve is calculated from the two sets of two-phase curves using Stone's Model II. The adjoint method is applied to three-phase flow problems to calculate the sensitivity of production data to the absolute permeability field and the parameters defining the relative permeability functions. Using the calculated sensitivity coefficients, absolute permeability, and relative permeability fields are estimated by automatic history matching of production data. Introduction The main objective of this paper is to consider the feasibility of estimating absolute permeability fields and parameters that define relative permeability functions by automatic history matching of production data obtained under multiphase flow conditions. While the topic is not new, to the best of our knowledge, no paper in the petroleum engineering literature has considered this problemunder three-phase flow conditions. It appears that Archer and Wong(1) were the first authors to consider the estimation of relative permeability curves by applying a reservoir simulator to history match laboratory core flood data. They estimated only parameters that define the shape of relative permeability curves for simple empirical relative permeability models and adjusted relative permeabilities by a trial and error method during the history matching. Sigmund and McCaffery(2) were the first to apply nonlinear regression to the problem of history matching laboratory core flood data. They used power law expressions to model relative permeability curves and estimated only the two exponential parameters in these formulas. Kerig and Watson(3) considered a similar problem. They calculated predicted data from the Buckley- Leverett model, used cubic splines to parameterize relative permeability curves and compared relative permeability estimates obtained with such a representation to those obtained using a power law functional form. They showed that, in general, power law models do not contain enough degrees of freedom to represent the truth well, whereas cubic splines with a small number of knots appear to be sufficiently flexible to yield more accurate estimates of true relative permeability curves. In their results, they assume absolute permeability is known. Lee and Seinfeld(4) considered the simultaneous estimation of the absolute permeability field and relative permeabilities for a two-dimensional, two-phase flow oil-water system. They assumed power law relative permeability curves and assumed that the end point values of relative permeabilities were known. Thus, only the two exponents in the power law relative permeability functions were estimated. They modelled the two-dimensional isotropic heterogeneousermeability field using bi-cubic B-splines. In the specific xamples considered, they matched pressure and water cut data at wells producing from an oil reservoir under waterflood. Tikhonov(5) regularization was used to stabilize the nonlinear least squares problem.

Effect of Flow Rate on Imbibition Three-Phase Permeabilities and Capillary Pressures

Effects of displacement pressure, pressure gradient, and flow rate on the shape of relative permeability curves have long been a controversial subject in petroleum literature. For drainage experiments it has been reported that the relative permeabilities are independent of flow rate. However, for imbibition experiments the rare literature, mainly concerned with oil-water phases, does not agree on this point. Three-phase, unsteady state CT scanned displacement tests were conducted using fired Berea sandstone to obtain relative permeability and capillary pressure data. Eight percent Potassium Bromide doped brine, hexane, and nitrogen gas was used. Relative permeabilities and capillary pressures were then estimated simultaneously after minimizing a least squares objective function containing all available and reliable experimental data obtained from three phase imbibition experiments using an automated history matching code where simulated annealing was utilized. It has been found that brine and hexane relative permeability curves were affected much more compared to the gas relative permeability curve, especially near the endpoints. Moreover, gas relative permeabilities decreased with increase in flow rate. Capillary pressure curves were affected in a similar manner.Finally, in order to confirm the above results an approach consisting of matching, at the same time, the fastest, the slowest, and a medium rate experimental data were tested. The algorithm failed to find a set of flow function curves which could fit both experimental data; therefore the conclusion was that for three-phase imbibition the flow functions depend on the flow rate.

Practical Procedure To Predict Cresting Behavior of Horizontal Wells

Summary Water and gas cresting in horizontal wells are important phenomena in reservoirs that have an aquifer or a gas cap. In practical situations, many reservoirs are produced under supercritical rates, and a breakthrough of the displacing phase becomes inevitable. At the beginning of a reservoir simulation study, it is desirable to make an estimate of the breakthrough time and the post-breakthrough behavior. Grid sensitivity runs are also required to obtain the appropriate gridblock sizes. An accurate representation of cresting behavior requires a very fine grid, which is not always practical. In this work, a procedure was developed to obtain accurate breakthrough times by use of just coarse grid simulations. The flow equations were written in dimensionless form, and important parameters affecting multiphase flow were identified. Simple correlations for a quick estimate of breakthrough time, maximum oil rate, and post-breakthrough behavior were derived on the basis of an appropriate set of dimensionless variables and an extensive number of simulation runs. The effects of gridblock size and grid pattern were investigated in detail. Effects of rate, mobility ratio, well drainage area, well height, and endpoints and shapes of relative permeability curves were also included. A procedure to derive pseudofunctions, either by numerical correlations or coarse grid simulations, is also presented. These pseudofunctions can be used to improve the performance of coarse grid simulations. An optimum grid pattern to start a reservoir simulation study is proposed. An application with real data shows that the correlations and procedures derived are reliable and accurate and can be used for quick estimates before starting a reservoir simulation study.

Micellar Flooding - Compositional Effects on Oil Displacement

Abstract Key variables that govern oil displacement in a micellar flood are capillary number (velocity x viscosity/interfacial tension) and chemical loss. At high capillary numbers, oil displacement is very efficient if various phases propagate at the same velocity. Chemical loss, however, is not always low when oil displacement efficiency is high. Compositions developed in situ often alter the ability of the micellar fluid to displace oil. Oil recovery can be predicted from static equilibrium fluid properties, providing the in situ compositions are known.The displacement of the wetting phase requires a capillary number of 10 times higher than that required to displace the nonwetting phase. This implies less efficient oil displacement in oil-wet systems. The correlation of oil recovery vs capillary number also varies with rock structure and wettability. Hence, for field application, immiscible oil displacement with micellar fluids should be determined in reservoir rocks. The decrease in final oil saturation with increase in capillary number indicates that relative permeability changes with capillary number. A numerically study showed that both the end-points and the shape of the relative permeability curves affect oil recovery at high permeability curves affect oil recovery at high capillary number in a slug process. The shape of the relative-permeability curves also affects the design of micellar slug viscosity. Thus, for field application, it is important to know the shape of relative-permeability curves at anticipated capillary numbers. Introduction In a micellar flood, the injected fluid banks interact with one another and with the reservoir brine, crude oil, and reservoir rock. This places stringent requirements on the design of the micellar flood. Initially, the micellar fluid may be miscible with crude oil and reservoir brine. However, because of dilution and surfactant adsorption, the flood can degenerate to an immiscible displacement. If low interfacial tension (IFT), or more specifically, high capillary number (velocity x viscosity/IFT) is maintained between all the phases, the displacement efficiency is good.There are many phenomena that can decrease oil recovery efficiency. The most important are chemical (surfactant or sulfonate) losses from adsorption by the rock, precipitation by high-salinity and high-hardness brines, interaction with polymer, partitioning into an immobile phase, and trapping of partitioning into an immobile phase, and trapping of the surfactant-rich phase. Recovery efficiency also can be poor when unfavorable in situ compositions develop. This occurs when the micellar fluid is diluted, develops undesirable salinity and hardness environment, experiences selective adsorption of surfactant, or undergoes selective partitioning of components into phases moving at different velocities.A micellar phase (or microemulsion) can exist in equilibrium with excess oil, water, or both. Winsor designated such phase behavior as Type I, II, and III, respectively. More recently, Healy et al. identified this behavior as lower phase (where the micellar phase is in equilibrium with excess oil), upper phase (where the micellar phase is in equilibrium with excess water), and middle phase (where the micellar phase is in equilibrium with excess oil and water). The importance of phase behavior has been the subject of considerable discussion in the literature.Since the function of the micellar fluid is to displace crude oil, not water, it would be desirable if the micellar fluid remained miscible with oil and immiscible with water during the immiscible displacement portion of a flood. This is achieved with upper-phase micellar systems. Since only a small bank of micellar fluid is injected, it must be displaced effectively by the succeeding polymer water bank. However, the upper-phase micellar fluid is not miscible with the polymer water; therefore, some of the micellar phase may be trapped as an immobile saturation (much as residual oil is trapped). SPEJ p. 116

Factors Affecting Liquid-Liquid Relative Permeabilities of a Consolidated Porous Medium

Abstract Many laboratory displacement tests have been performed to study factors affecting relative performed to study factors affecting relative permeability curves, residual saturations, and shape permeability curves, residual saturations, and shape of recovery curves. Three sintered artificial porous materials and pure fluid mixtures have been used for this systematic study. The factors were interfacial tension, the viscosity and the velocity of the fluids (in the dimensionless group σ/µv), the wettability, and the viscosity ratio. The results can be used as guidelines for research on recovery processes. Introduction Waterflooding is by far the most common secondary recovery technique. Several processes (polymer injection, surfactant injection, hot water injection, etc.) attempt to improve sweep efficiency by affecting some of the factors involved in the displacement process. For orienting research on these processes, process. For orienting research on these processes, a good knowledge of how these parameters affect local displacement efficiency and over-all sweep efficiency in the reservoir is required. We present here an attempt to understand the effects of such parameters: (1) at the microscopic level on the shape of relative permeability curves and the values of final saturations obtained by flooding, and (2) at the macroscopic level, on the behavior of one-dimensional displacement. Effects of the morphology of the porous medium were not included in this study. We mainly examined the effects of fluid properties on fluid displacement in only three specific porous media. These three artificial sintered media were made of Teflon, stainless steel and alumina. For the following reasons they were very well suited to the systematic investigation undertaken: (1) they are homogeneous and so the results are not subject to macroscopic heterogeneity effects; (2) they are identical in the same series, thus permitting the results to be compared from one experiment to another (3) their constant and well-defined chemical composition makes it possible to perform wettability measurements outside the porous medium; (4) they are consolidated like most of reservoir rocks; (5) they have good mechanical properties and so can be washed successively without being altered and (6) the three media used correspond to three possible cases of wettability, i.e., Teflon is strongly oil-wet, alumina is strongly water wet, and stainless steel may have intermediate wettability depending on the fluids considered. Some of our results reported here (concerning experiments with Teflon at a viscosity ratio of one) were presented earlier.