The Effect of Interfacial Tensions on Relative Oil/Water Permeabilities of Consolidated Porous Media

1982 ◽  
Vol 22 (03) ◽  
pp. 371-381 ◽  
Author(s):  
Jude O. Amaefule ◽  
Lyman L. Handy
Keyword(s):  
Porous Media ◽  
Interfacial Tension ◽  
Relative Permeability ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Interfacial Tensions ◽  
Oil Displacement ◽  
Oil Water ◽  
Relative Permeability Curves ◽  
Low Tension

Abstract Relative permeabilities of systems containing low- tension additives are needed to develop mechanistic insights as to how injected aqueous chemicals affect fluid distribution and flow behavior. This paper presents results of an experimental investigation of the effect of low interfacial tensions (IFT's) on relative oil/water permeabilities of consolidated porous media. The steady- and unsteady-state displacement methods were used to generate relative permeability curves. Aqueous low-concentration surfactant systems were used to vary IFT levels. Empirical correlations were developed that relate the imbibition relative permeabilities, apparent viscosity, residual oil, and water saturations to the interfacial tension through the capillary number (Nc=v mu / sigma). They require two empirical, experimentally generated coefficients. The experimental results show that the relative oil/water permeabilities at any given saturation are affected substantially by IFT values lower than 10-1 mN/m. Relative oil/water permeabilities increased with decreasing IFT (increasing N ). The residual oil and residual water saturations (S, and S) decreased, while the total relative mobilities increased with decreasing IFT. The correlations predict values of relative oil/water permeability ratios, fractional flow, and residual saturations that agree with our experimental data. Apparent mobility design viscosities decreased exponentially with the capillary number. The results of this study can be used with simulators to predict process performance and efficiency for enhanced oil-recovery projects in which chemicals are considered for use either as waterflood or steamflood additives. However, the combined effect of decreased interfacial tension and increased temperature on relative permeabilities has not yet been studied. Introduction Oil displacement with an aqueous low-concentration surfactant solution is primarily dependent on the effectiveness of the solutions in reducing the IFT between the aqueous phase and the reservoir oil. With the attainment of ultralow IFT's (10 mN/m) and with adequate mobility controls, all the oil contacted can conceivably be displaced. When the interfacial tension is reduced to near zero values, the process tends to approach miscible displacement. However, most high-concentration soluble oil systems revert to immiscible displacement processes as the injected chemical traverses the reservoir. This is a result of the continual depletion of the surfactant by adsorption on the rock and by precipitation with divalent cations in the reservoir brine. The mechanism by which residual oil is mobilized by low-tension displacing fluids cannot be explained solely by the application of Darcy's law to both the aqueous and the oleic phases. On the other hand, in those reservoir regions in which water and oil are flowing concurrently as continuous phases, Darcy's law would be expected to apply and the relative permeability concept would be valid. If a low-tension aqueous phase were to invade a region in which the oil had not as yet been reduced to a discontinuous irreducible saturation, one would expect, also, that the relative permeability concept would be applicable. Under circumstances for which these conditions apply, relative permeabilities at low interfacial tensions would be required, The effect of IFT's on relative permeability curves has received limited treatment in the petroleum literature. Leverett reported a small but definite tendency for a water/oil system in unconsolidated rocks to exhibit 20 to 30% higher relative permeabilities if the IFT was decreased from 24 to 5 mN/m. Mungan studied interfacial effects on oil displacement in Teflons cores. The interfacial tension values varied from 5 to 40 mN/m. SPEJ P. 371^

Influence of Very Low Interfacial Tensions on Relative Permeability

1980 ◽  
Vol 20 (05) ◽  
pp. 391-401 ◽  
Author(s):  
D.G. Longeron
Keyword(s):  
High Pressure ◽  
Interfacial Tension ◽  
Relative Permeability ◽  
Capillary Number ◽  
Capillary Forces ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Oil Saturation ◽  
Interfacial Tensions ◽  
Liquid And Vapor Phases

Abstract Laboratory studies have been conducted to determine the influence of the composition of gas and oil phases on the parameters involved in the description of two-phase flow in porous media when the compositions of the phases vary over a wide range. Relative permeabilities to gas and oil were determined under high pressure and temperature for binary systems (methane/n-heptane, methane/n-decane, etc.), leading to very wide variations of the interfacial tensions values. Investigations were focused specifically on mixtures involving low interfacial tensions, down to 0.001 mN/m. This study has shown that residual oil saturations and relative permeabilities determined from the displacement tests with a filtration velocity of about 20 cm/hr are affected strongly by interfacial tension, especially when it is lower than 10-2 mN/m. Introduction This study deals with the influence of the compositions of the liquid and vapor phases in equilibrium on displacements of oil by gas in porous media. One of the goals of high-pressure or enriched-gas injection is to obtain low interfacial tensions between the in-place oil and injected gas. During the displacement of gas in oil-bearing formations, multiple exchanges may take place between the liquid and vapor phases so that complete miscibility may be achieved. This phenomenon generally is called thermodynamic miscibility. During this process the interfacial tension is reduced progressively to zero. The resulting reduction in capillary forces makes it possible to decrease the residual oil saturation considerably. The same goal also is sought by other enhanced recovery techniques not examined here i.e., surfactant flooding or microemulsion flooding. The purpose of this study is to examine the influence of the thermodynamic conditions on the relative permeabilities in displacements of a liquid phase by a vapor phase when both phases are at equilibrium. The Problem The general equations describing the flows of two phases are the relative permeability equations. They show, for each phase, that the flow rate in a porous medium is a function of the absolute permeability, relative permeability to the fluid involved, fluid viscosity, pressure gradient in this phase, and gravity. In fact, relative permeabilities depend on a greater number of parameters.1 Some of them are the ratio of viscosities, µ2/µ1; the ratio of gravity to capillary forces (Bond number), (?2-?1)gk]/s; the ratio of the inertia forces to the viscosity forces (Reynolds number), (?1·u·k)/µ1; the ratio of the viscosity forces to the capillary forces (capillary number), (µ1·u)/s; and wettability. When they exist, exchanges between the phases can modify the physical and chemical properties of the fluids, especially at the interfaces. Under such conditions the influence of the capillary number (µ1·u)/s is by no means negligible, with the decrease in interfacial tension causing an increase in oil recovery.2 It may be thought that relative permeability to oil is closely dependent on this capillary number,3 especially when the value of s is small, and that this influence is principally apparent with low oil-saturation levels.

Displacement Studies in Dolomite With Wettability Control by Octanoic Acid

1973 ◽  
Vol 13 (04) ◽  
pp. 221-232 ◽  
Author(s):  
N.R. Morrow ◽  
P.J. Cram ◽  
F.G. McCaffery
Keyword(s):  
Contact Angle ◽  
Interfacial Tension ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Significant Influence ◽  
Octanoic Acid ◽  
Contact Angles ◽  
Wettability Alteration ◽  
Residual Oil ◽  
Relative Permeability Curves

Abstract Various nitrogen-, oxygen- and sulfur-containing compounds native to crude oils were screened for their effect on wettability as measured by contact angle. Solid substrates of quartz, calcite, and dolomite crystals were used to represent reservoir rock surfaces. With water and decane as liquids, contact angles were measured after a given polar compound was added to the oil phase. Contact angles measured at the two types of carbonate surfaces were generally similar. None of the nitrogen or sulfur compounds studied gave contact angles greater than 66 degrees on either quartz or carbonates. Of the oxygen-containing compounds, octanoic acid gave the widest range of contact angle - 0 degrees to 145 degrees on dolomite - over a molar concentration range up to 0.1. Capillary - pressure and relative-permeability curves were obtained for water and solutions of octanoic acid in oil, using packings of powdered dolomite as the porous medium. Because of a slow reaction between dolomite and octanoic acid, which was not revealed by standard contact angle studies, special precautions were needed to ensure satisfactory wettability control during displacement tests. Capillary-pressure drainage curves were measured at six contact angles, ranging from 0 degrees to 140 degrees. Drainage-imbibition cycles for three packings of distinctly different particle size were measured at contact angles of 0 degrees and 49 degrees. The effect of contact angle on imbibition capillary pressures was close to that found previously for porous polytetra-fluoroethylene, whereas there was comparatively polytetra-fluoroethylene, whereas there was comparatively less effect on drainage behavior-steady-state relative permeability curves exhibited distinct differences for contact angles of 15 degrees, 100 degrees and 155 degrees. Introduction Waterflooding is the most successful and widely applied improved recovery technique. Its application in Alberta has, on the average, more than doubled the recovery obtained by primary depletion. However, even after waterflooding, it is estimated that two-thirds of the discovered oil remains unrecovered. Interfacial forces acting during waterflooding lead to the entrapment of large quantities of residual oil in the swept zones. Considerable attention has been paid to recovering this oil through new recovery methods in which the interface is eliminated as in miscible processes, or the interfacial tension is drastically lowered, as in surfactant floods. Such processes involve a high initial cost for an injected solvent or surfactant bank. Recently released information on a variety of such improved recovery techniques has not been altogether encouraging with regard to developing economical processes. A distinct alternative to eliminating the interface is to understand it and learn how it can be manipulated to give increased waterflood recoveries. A prospect for improved recovery at interfacial tensions of the order normally encountered in reservoirs lies in a favorable adjustment of wettability by incorporating small amounts of low-cost additives in the floodwater. A first step in developing the technology of improved recovery by wettability alteration is to determine the effect of wettability alteration on displacement in systems of uniform wettability. It has been shown that, even in the "near miscible" surfactant processes, wettability can still have a significant influence on the extent to which interfacial tension must be lowered in order to mobilize residual oil. At the time when waterflooding first found widespread use, wettability was recognized as a variable that might well have a significant influence on recovery performance. Reservoir wettability and the role of wettability in displacement has been the subject of some 50 or so publications. Even so, many aspects of wettability are not well understood and there is no general agreement on a satisfactory method of characterizing it. Opinions as to the optimum wettability condition for recovery cover the spectrum from strongly water-wet through weakly water-wet or intermediately wet to strongly oil-wet. It has recently been suggested that a mixed wettability condition can give high ultimate recoveries. SPEJ P. 221

Issue with Stone-II Three Phase Permeability Model, and A Novel Robust Fundamentals-Based Alternative to It

2021 ◽  
Author(s):  
Subodh Gupta
Keyword(s):  
Relative Permeability ◽  
Phase Flow ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Phase Permeability ◽  
Permeability Model ◽  
Oil Saturation ◽  
Three Phase ◽  
Three Phase Flow ◽  
Relative Permeability Curves

Abstract The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase flow model that avoids the pitfalls of conventional models such as Stone-II or Baker's three-phase permeability models. While investigating the myth of residual oil saturation in SAGD with comparing model generated results against field data, Gupta et al. (2020) highlighted the difficulty in matching observed residual oil saturation in steamed reservoir with Stone-II and Baker's linear models. Though the use of Stone-II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears to counter-intuitively limit the flow of oil when water is present near its irreducible saturation. The current work begins with describing the problem with existing combinatorial methods such as Stone-II, which in turn combine the water-oil, and gas-oil relative permeability curves to yield the oil relative permeability curve in presence of water and gas. Then starting with the fundamentals of laminar flow in capillaries and with successive analogical formulations, it develops expressions that directly yield the relative permeabilities for all three phases. In this it assumes a pore size distribution approximated by functions used earlier in the literature for deriving two-phase relative permeability curves. The outlined approach by-passes the need for having combinatorial functions such as prescribed by Stone or Baker. The model so developed is simple to use, and it avoids the unnatural phenomenon or discrepancy due to a mathematical artefact described in the context of Stone-II above. The model also explains why in the past some researchers have found relative permeability to be a function of temperature. The new model is also amenable to be determined experimentally, instead of being based on an assumed pore-size distribution. In that context it serves as a set of skeletal functions of known dependencies on various saturations, leaving constants to be determined experimentally. The novelty of the work is in development of a three-phase relative permeability model that is based on fundamentals of flow in fine channels and which explains the observed results in the context of flow in porous media better. The significance of the work includes, aside from predicting results more in line with expectations and an explanation of temperature dependent relative permeabilities of oil, a more reliable time dependent residual oleic-phase saturation in the context of gravity-based oil recovery methods.

Evaluation of Normalized Stone's Methods for Estimating Three-Phase Relative Permeabilities

1984 ◽  
Vol 24 (02) ◽  
pp. 224-232 ◽  
Author(s):  
F.J. Fayers ◽  
J.D. Matthews
Keyword(s):  
Relative Permeability ◽  
Gas Oil ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Mobile Water ◽  
Oil Displacement ◽  
Three Phase ◽  
Phase Data ◽  
Definition Of

Abstract This paper examines normalized forms of Stone's two methods for predicting three-phase relative permeabilities. Recommendations are made on selection of the residual oil parameter, S om, in Method I. The methods are tested against selected published three-phase experimental data, using the plotting program called CPS-1 to infer improved data fitting. It is concluded that the normalized Method I with the recommended form for S om, is superior to Method II. Introduction Stone has produced two methods for estimating three-phase relative permeability from two-phase data. Both models assume a dominant wetting phase (usually water), a dominant nonwetting phase (gas), and an intermediate wetting phase (usually oil). The relative permeabilities for the water and gas are assumed to permeabilities for the water and gas are assumed to depend entirely on their individual saturations because they occupy the smallest and largest pores, respectively. The oil occupies the intermediate-size pores so that the oil relative permeability is an unknown function of water and gas saturation. For his first method, Stone proposed a formula for oil relative, permeability that was a product of oil relative permeability in the absence of gas, oil relative permeability in the absence of gas, oil relative permeability in the absence of mobile water, and some permeability in the absence of mobile water, and some variable scaling factors. He compared this formula with the experimental results of Corey et al., Dalton et al., and Saraf and Fatt. The formula is likely to be most in error at low oil relative permeability where more data are needed that show the behavior of residual oil saturation as a function of mixed gas and water saturations. In particular, the best value for the parameter S om that occurs in the model is not well resolved. In his second method, Stone developed a new formula and compared it against the data of Corey et al., Dalton et al., Saraf And Fatt, and some residual oil data from Holmgren and Morse. Stone suggested that his second method gave reasonable agreement with experiments without the need to include the parameter S om. If in the absence of residual oil data, S om = 0 is used in the first method, the second method is then better than the first method, although it tends to under predict relative permeability. Dietrich and Bondor later showed that Stone's second method did not adequately approximate the two-phase data unless the oil relative permeability at connate water saturation, k rocw, was close to unity. Dietrich and Bondor suggested a normalization that achieved consistency with the two-phase data when k rocw, was not unity. This normalization can be unsatisfactory because k roc an exceed unity in some saturation ranges if k rocw is small. More recently this objection has been overcome by the normalization of Method II introduced by Aziz and Settari. Aziz and Settari also pointed out a similar normalization problem with Stone's first method and suggested an alternative to overcome the deficiency. However, no attempt was made to investigate the accuracy of these normalized formulas with respect to experimental data. In the next section of the paper we review the principal forms of Stone's formulas, and introduce some new ideas on the use and choice of the parameter S om. Later we examine the first of Stone's assumptions that water and gas relative permeabilities are functions only of their respective saturations for a water-wet system. This involves a critical review of all the published experimental measurements. Earlier reviews did not take into account some of the available data. Last, we examine the predictions of normalized Stone's methods for oil relative permeability against the more reliable experimental results. It is concluded that the normalized Stone's Method I with the improved definition of S om is more accurate than the normalized Method II. Mathematical Definition of Three-Phase Relative Permeabilities We briefly review the principal forms of the Stone's formulas that use the two-phase relative permeabilities defined by water/oil displacement in the absence of gas, k rw = k rw (S w) and k row = k row (S w) and gas/oil displacement in the presence of connate water, k rg = k rg (S g) and k rog = k rog (S g). SPEJ p. 224

Vesicular Dispersion Delivery Systems and Surfactant Waterflooding

1982 ◽  
Vol 22 (01) ◽  
pp. 37-52 ◽  
Author(s):  
Jorge E. Puig ◽  
Elias I. Franses ◽  
Yeshayahu Talmon ◽  
H. Ted Davis ◽  
Wilmer G. Miller ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Oil Recovery ◽  
Liquid Crystalline ◽  
Capillary Forces ◽  
Residual Oil ◽  
Interfacial Tensions ◽  
Low Concentration ◽  
Tertiary Oil Recovery ◽  
Oil Water ◽  
Recovery Methods

Abstract Surfactant waterflooding processes that rely on ultralow interfacial tensions suffer from surfactant retention by reservoir rock and from the need to avoid injectivity problems. New findings reported here open the possibility that by delivering the surfactant in vesicle form, more successful low-concentration, alcohol-free surfactant waterflooding processes can be designed. Basic studies of low concentration (less than 2 wt %) aqueous dispersions of lamellar liquid crystals of a model surfactant, Texas No. 1, have established the role of dispersed liquid crystallites in the achievement of ultralow tensions between oil and water. Recent work, including fast-freeze, cold-stage transmission electron microscopy (TEM), reveals that sonication both in the absence and the presence of sodium chloride converts particulate dispersions of Texas No. 1 into dispersions of vesicles, which are spheroidal bilayers or multilayers, less than 0.1 mum in diameter filled with aqueous phase. Vesicles ordinarily revert only very slowly to the bulk liquid crystalline state. We find, however, that their stability depends on their preparation and salinity history, and that contact with oil can accelerate greatly the reversion of a vesiculated dispersion and enable it to produce low tensions between oil and water. Tests with Berea cores show that surfactant retention and attendant pressure buildup can be reduced greatly by sonicating Texas No. 1 dispersions to convert liquid crystallites to vesicles. In simple core-flooding experiments both the unsonicated liquid crystalline dispersions and the sonicated vesicle dispersions are able to produce substantial amounts of residual oil. We point out implications and directions for further investigation. Introduction Methods of enhancing, petroleum recovery, especially tertiary recovery, following the primary and secondary stages, are under intense research and development. Among these are at least two classes of surfactant-based recovery methods-surfactant waterflooding and so-called micellar or microemulsion flooding. Gilliland and Conley suggest that of the various enhanced-recovery methods, surfactant waterflooding has the potential for the widest application in the U.S. Residual oil is trapped as blobs in porous rock by capillary forces. The number of mechanisms is limited both for reducing entrapment and for mobilizing that residual oil remaining entrapped, there by improving the microscopic displacement efficiency of a petroleum recovery process. Taber and Melrose and Brandner established that tertiary oil recovery by an immiscible flooding process is possible by increasing the capillary number, which measures the ratio of Darcy flow forces of mobilization to capillary forces of entrapment. In practice this can be achieved by lowering the oil-water interfacial tension to about 10 mN/m or less. That this is feasible in the surfactant waterflooding range-i.e. at surfactant concentration less than those characterizing the microemulsion flooding range-and in the absence of cosurfactants or cosolvents that typify microemulsions is well established. Gale and Sandvik suggested four criteria for selecting a surfactant for a tertiary oil-recovery process:low oil-water interfacial tension,low adsorption.compatibility with reservoir fluids, andlow cost. For a given oil and type of surfactant, it has been shown that the interfacial tensions are extremely sensitive to surfactant molecular weight. SPEJ P. 37^

scholarly journals Variations in Permeability and Porosity of Synthetic Oil Reservoir Rock-Methods of Control

1965 ◽  
Vol 5 (04) ◽  
pp. 329-332 ◽  
Author(s):  
Larman J. Heath
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Reservoir Rock ◽  
Oil Reservoir ◽  
Natural Reservoir ◽  
Natural Rock ◽  
Unconsolidated Sand ◽  
Synthetic Rock ◽  
Porosity And Permeability ◽  
Relative Permeability Curves

Abstract Synthetic rock with predictable porosity and permeability bas been prepared from mixtures of sand, cement and water. Three series of mixes were investigated primarily for the relation between porosity and permeability for certain grain sizes and proportions. Synthetic rock prepared of 65 per cent large grains, 27 per cent small grains and 8 per cent Portland cement, gave measurable results ranging in porosity from 22.5 to 40 per cent and in permeability from 0.1 darcies to 6 darcies. This variation in porosity and permeability was caused by varying the amount of blending water. Drainage- cycle relative permeability characteristics of the synthetic rock were similar to those of natural reservoir rock. Introduction The fundamental behavior characteristics of fluids flowing through porous media have been described in the literature. Practical application of these flow characteristics to field conditions is too complicated except where assumptions are overly simplified. The use of dimensionally scaled models to simulate oil reservoirs has been described in the literature. These and other papers have presented the theoretical and experimental justification for model design. Others have presented elements of model construction and their operation. In most investigations the porous media have consisted of either unconsolidated sand, glass beads, broken glass or plastic-impregnated granular substances-materials in which the flow behavior is not identical to that in natural reservoir rock. The relative permeability curves for unconsolidated sands differ from those for consolidated sandstone. The effect of saturation history on relative permeability measurements A discussed by Geffen, et al. Wygal has shown quite conclusively that a process of artificial cementation can be used to render unconsolidated packs into synthetic sandstones having properties similar to those of natural rock. Many theoretical and experimental studies have been made in attempts to determine the structure and properties of unconsolidated sand, the most notable being by Naar and Wygal. Others have theorized and experimented with the fundamental characteristics of reservoir rocks. This study was conducted to determine if some general relationship could be established between the size of sand grains and the porosity and permeability in consolidated binary packs. This paper presents the results obtained by changing some of the factors which affect the porosity and permeability of synthetically prepared sandstone. In addition, drainage relative permeability curves are presented. EXPERIMENTAL PROCEDURE Mixtures of Portland cement with water and aggregate generally are designed to have certain characteristics, but essentially all are planned to be impervious to water or other liquids. Synthetic sandstone simulating oil reservoir rock, however, must be designed to have a given permeability (sometimes several darcies), a porosity which is primarily the effective porosity but quantitatively similar to natural rock, and other characteristics comparable to reservoir rock, such as wettability, pore geometry, tortuosity, etc. Unconsolidated ternary mixtures of spheres gave both a theoretically computed and an experimentally observed minimum porosity of about 25 per cent. By using a particle-distribution system, one-size particle packs had reproducible porosities in the reproducible range of 35 to 37 per cent. For model reservoir studies of the prototype system, a synthetic rock having a porosity of 25 per cent or less and a permeability of 2 darcies was required. The rock bad to be uniform and competent enough to handle. Synthetic sandstone cores mere prepared utilizing the technique developed by Wygal. Some tight variations in the procedure were incorporated. The sand was sieved through U.S. Standard sieves. SPEJ P. 329ˆ

Cocurrent Spontaneous Imbibition In Porous Media With the Dynamics of Viscous Coupling and Capillary Backpressure

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 158-177 ◽  
Author(s):  
Pål Østebø Andersen ◽  
Yangyang Qiao ◽  
Dag Chun Standnes ◽  
Steinar Evje
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Flow Regimes ◽  
Spontaneous Imbibition ◽  
The Other ◽  
Countercurrent Flow ◽  
Relative Permeabilities ◽  
Viscous Coupling ◽  
Generalized Model ◽  
Matrix Block

Summary This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature. We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

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