Residual Non-wetting Phase Saturation Research Articles

Immiscible imbibition in fractured media: A dual-porosity microfluidics study

We use dual porosity microfluidics and fluorescence microscopy to investigate immiscible imbibition in the pore networks formed in fractured rocks, and to identify emergent pore-scale events that arise as a result of the interplay between advection-dominant flow in fractures (F) and capillary-driven matrix imbibition (M). The dimensionless ratio between the two time scales T = tF/tM defines the various displacement patterns: fracture-dominant advective invasion at low Τ-values leaves a higher residual non-wetting phase saturation; compact invasion is observed at intermediate T-values, and fractures act as capillary barriers during matrix-dominant capillary imbibition at high Τ-values. Experiments and analyses show effective capillary-driven corner flow during immiscible imbibition; in particular, corner flow imbibition displaces non-wetting fluids that were initially trapped in the matrix during fast advective invasion. In contrast to wetting fluid invasion and imbibition, injected non-wetting fluids invade and flow along fractures as soon as the capillary pressure reaches the fracture entry pressure, and there is no matrix invasion and drainage. The capillary pressure versus saturation curve for the fractured rock mass assumes that fractures and matrix blocks share the same capillary pressure at equilibrium; then, the combined pressure-saturation response is a function of their relative contributions to the total porosity. In the absence of gouge or precipitates, fractures determine the entry pressure while the matrix controls storativity.

Microscale Investigation of the Impact of Surfactant Structure on the Residual Trapping in Natural Porous Media

Residual trapping of a nonwetting phase in a porous medium is directly impacted by the relative magnitude of capillary, viscous, and gravity forces. Ratios of these forces control the sequence by which different pore-scale displacement mechanisms take place, which in turn govern the pore fluid occupancy and the residual nonwetting phase saturation. Parameters such as pore geometry, rock surface wettability, fluid–fluid interfacial tension, and fluids’ viscosities, densities, and flow rates determine the magnitude of the above-mentioned forces. In this study, we show that there is an additional set of factors that directly contributes to the distribution of fluids at the pore scale. We demonstrate that, under similar rock and fluid properties, interfacial repulsive and attractive interactions, caused by the adsorption of surface-active chemicals on fluid–fluid interfaces, can significantly alter pore-scale fluid occupancies. Using the microcomputed tomography (micro-CT) imaging technique integrated with a miniature core-flooding apparatus, we investigate the impact of surfactant structure on pore-scale fluid distributions in a limestone core sample subjected to injection of different wetting fluid solutions. Poly(ethylene oxide) (PEO), a nonionic surfactant, and ammonium alkyl ether sulfate, an anionic surfactant, are utilized as surface-active agents providing similar oil–brine interfacial tension (IFT) and contact angle (CA) values. Oil cluster analyses along with three-dimensional (3D) visualization of fluid distributions indicate that using the nonionic surfactant instead of the anionic surfactant results in the breaking up of the large and medium oil clusters into smaller and scattered ones. We propose a mechanism relating the stability of oil–brine interface to surfactant structure that is responsible for the breakup and/or coalescence of oil clusters inside the pore space. The suggested mechanism is confirmed by the micro-CT images and associated oil cluster analyses. This phenomenon affects the competition between the frequency of displacement mechanisms causing variations in remaining oil saturations.

Capillary pressure‐saturation relations in quartz and carbonate sands: Limitations for correlating capillary and wettability influences on air, oil, and supercritical CO2 trapping

AbstractCapillary pressure (Pc)‐saturation (Sw) relations are essential for predicting equilibrium and flow of immiscible fluid pairs in soils and deeper geologic formations. In systems that are difficult to measure, behavior is often estimated based on capillary scaling of easily measured Pc–Sw relations (e.g., air‐water, and oil‐water), yet the reliability of such approximations needs to be examined. In this study, 17 sets of brine drainage and imbibition curves were measured with air‐brine, decane‐brine, and supercritical (sc) CO2‐brine in homogeneous quartz and carbonate sands, using porous plate systems under ambient (0.1 MPa, 23°C) and reservoir (12.0 MPa, 45°C) conditions. Comparisons between these measurements showed significant differences in residual nonwetting phase saturation, Snw,r. Through applying capillary scaling, changes in interfacial properties were indicated, particularly wettability. With respect to the residual trapping of the nonwetting phases, Snwr, CO2 > Snwr, decane > Snwr, air. Decane‐brine and scCO2‐brine Pc–Sw curves deviated significantly from predictions assuming hydrophilic interactions. Moreover, neither the scaled capillary behavior nor Snw,r for scCO2‐brine were well represented by decane‐brine, apparently because of differences in wettability and viscosities, indicating limitations for using decane (and other organic liquids) as a surrogate fluid in studies intended to apply to geological carbon sequestration. Thus, challenges remain in applying scaling for predicting capillary trapping and multiphase displacement processes across such diverse fields as vadose zone hydrology, enhanced oil recovery, and geologic carbon sequestration.

History effects on nonwetting fluid residuals during desaturation flow through disordered porous media.

We investigate experimentally the sweeping of a nonwetting fluid by a wetting one in a quasi-two-dimensional porous medium consisting of random obstacles. We focus primarily on the resulting phase distributions and the residual nonwetting phase saturation as a function of the normalized wetting fluid flow rate-the capillary number Ca-at steady state. The wetting liquid is then flowing in the medium partially saturated by immobile nonwetting liquid blobs. The decrease of the nonwetting saturation is an irreversible process that depends strongly on flow history and more specifically on the highest value of Ca reached in the past. At lower Ca values, when capillary forces are dominant, the residual steady state saturation depends significantly on the initial phase configuration. However, at higher Ca, the saturation becomes independent of the history and thus follows a master curve that converges to an asymptotic residual value. Blob sizes range over four orders of magnitude in our experimental domain, following a probability distribution function P that scales with the blob size s as P(s)∝s(-2) for blob sizes larger than the typical pore size. It also exhibits a maximum size cutoff s(max), that decreases as s(max)∝Ca(-1). To determine the flow properties, we have measured the pressure drop (B) versus the flow rate (Ca). In the ranges of low and high Ca values, the relationship between Ca and B is found to be linear, following Darcy's law (B∝Ca). In the intermediate regime, the progressive mobilization of blobs leads to a nonlinear dependence B∝Ca(0.65), due to an increase of the available flow paths.

Capillary-Trapping Capacity of Sandstones and Sandpacks

This paper (SPE 120960) was accepted for presentation at the EUROPEC/EAGE Conference and Exhibition, Amsterdam, 8–11 June 2009, and revised for publication. Original manuscript received for review 23 February 2009. Revised manuscript received for review 3 December 2010. Paper peer approved 15 April 2011. Summary We quantify the influence of the initial nonwetting-phase saturation and porosity on the residual nonwetting-phase saturation using data in the literature and our own experimental results on sandpacks and consolidated sandstones. These experiments were conducted at ambient or elevated pressure and temperature (ETP) conditions. The principal application of this work is for carbon capture and storage (CCS) where capillary trapping is a rapid and effective way to render the injected CO2 immobile, guaranteeing safe storage. We introduce the concept of capillary-trapping capacity (Ctrap) which is the product of residual saturation and porosity that represents the fraction of the rock volume that can be occupied by a trapped nonwetting phase. We show that the measured trapping capacity reaches a maximum of approximately 11% for porosities of 22%, which suggests an optimal porosity for CO2 storage.

Measurements of the capillary trapping of super-critical carbon dioxide in Berea sandstone

[1] We measure primary drainage capillary pressure and the relationship between initial and residual non-wetting phase saturation for a supercritical carbon dioxide (CO2)-brine system in Berea sandstone. We use the semi-permeable disk (porous-plate) coreflood method. Brine and CO2 were equilibrated prior to injection to ensure immiscible displacement. A maximum CO2 saturation of 85% was measured for an applied capillary pressure of 296 kPa. After injection of brine the CO2 saturation dropped to 35%; this is less than the maximum trapped saturation of 48% measured in an equivalent n-decane (oil)-brine experiment. The dimensionless capillary pressure is the same to within experimental error for supercritical CO2-brine, n-decane-brine and a mercury-air system. CO2 is the non-wetting phase and significant quantities can be trapped by capillary forces. We discuss the implications for CO2 storage.

Immiscible Displacements and Capillary Trapping in CO2 Storage

Abstract We measure the residual non-wetting phase saturation of super-critical carbon dioxide in a Berea sandstone core. We use the porous plate method while a stirred reactor ensures equilibrium between the carbon dioxide and brine. We also measure carbon dioxide-brine contact angles on the porous plate to understand wetting behavior in the experiment. The application of the work is for carbon dioxide storage in aquifers, where capillary trapping is a rapid and effective mechanism to render the injected fluid immobile. The experiment was performed at temperature and pressure representative of potential subsurface storage formations. The measured residual saturation is 37% which is lower than the measured residual for an oil-brine system on a similar core (48%), but higher than measured by other authors for super-critical CO 2 in Berea sandstone. We suggest that super-critical CO 2 is still non-wetting in sandstones with considerable trapping and discuss the implications for CO 2 storage in aquifers.

NONWETTING PHASE RESIDUAL SATURATION IN SAND PACKS

We measure residual nonwetting phase saturation in six unconsolidated sands of different average grain sizes. We also analyze the pore structure using three-dimensional images from which topologically equivalent pore networks are extracted. The residual saturations range from 10.8% to 13.1%, which is lower than for most consolidated media. Higher porosity is associated with lower residual saturations, while there is little correlation between grain and pore shape and the degree of trapping. We also study layered packs: the residual saturations are reduced compared to comparable homogeneous systems. We discuss the results in the context of capillary trapping during carbon storage in aquifers.

Experimental and visual analysis of co- and counter-current spontaneous imbibition for different viscosity ratios, interfacial tensions, and wettabilities

We analyzed the dynamics of spontaneous imbibition using core and sand pack (made of transparent glass beads) visualization experiments. The effects of the critical factors such as temperature, wettability, gravity, oil viscosity, interfacial tension (IFT), and matrix boundary conditions on the process were studied. First, data were collected through experiments conducted on Berea sandstone samples for air–water and oil–water pairs. The samples were coated to ensure co-current and counter-current type interaction. To support the observations obtained through the core scale experiments, visual data obtained from 2-D sand pack models were used. This was helpful in depicting the phase distribution in the matrix and defining the causes of the residual non-wetting phase saturation. Significant differences were observed between oil–water and air–water capillary imbibition dynamics and phase distribution in the matrix. For the air–water pair, it was noticed that more fingering occurs as the temperature is increased. For horizontal orientation, in the absence of gravity effect, the wetting phase invasion developed from a single point as a “single finger” and displacement was achieved by the growth of this finger, which was much thicker in case of mineral oil compared to the kerosene case. The same was observed for the aged (less water-wet case). For co-current interaction, when the two (bottom and top parts) sides are in contact with the wetting phase, fingering was remarkable for the high viscosity oil. Finally, a quantitative analysis was performed by testing different dimensionless groups. Modifications to them were suggested to have a robust dimensionless group that covers all the parameters considered and to be used further in the scaling applications.

Oil recovery by counter-current spontaneous imbibition: Effects of matrix shape factor, gravity, IFT, oil viscosity, wettability, and rock type

The effects of the matrix shape factor, wettability, gravity, rock type, oil viscosity, and interfacial tension on the rate of capillary imbibition and development of residual non-wetting phase saturation were studied experimentally in this paper. Experiments were conducted on Berea sandstone and Indiana limestone samples. Cylindrical samples with different shape factors were obtained by cutting the plugs 1/2, 1 and 2 in. in diameter and 2, 4, and 6 in. in length. All sides were coated with epoxy except one end to ensure counter-current interaction. Static imbibition experiments were conducted on vertically and laterally situated samples to incorporate the effect of gravity where the imbibition took place upward and lateral directions, respectively. Brine-kerosene, brine-mineral oil and surfactant solution-mineral oil pairs were used as fluids. The rate of imbibition was evaluated for different matrix size, shape factor, wetting/non-wetting phase types and IFT. Conditions at which the shape factor controls the residual oil development were identified. It was observed that the residual oil after capillary imbibition is influenced by the matrix shape factor for the vertically positioned samples (unlike horizontal samples). In the low IFT experiments, surfactant was found to play a strong role on the rate of imbibition and the development of residual oil saturation. Scaling analyses were performed testing and comparing four different scaling groups. The equations were modified to take wettability and gravity effects into account. A new empirically correlated-gravity sensitive characteristic length was introduced.

Effects of Snap-Off in Imbibition in Porous Media with Different Spatial Correlations

Quasi-static imbibition was simulated using random and correlated stochastic network models. Using the snap-off pore-scale displacement observed by Lernormand et al. (1983) the effects of many parameters on relative permeabilities and residual saturation reported in the literature were reproduced and explained. Increased relative permeabilities and decreased residual non-wetting phase saturation were the results of an increased contact angle (Li and Wardlaw, 1986b; Gauglitz and Radke, 1990; Blunt et al., 1992; Mogensen and Stenby, 1998) a decreased pore–throat aspect ratio, the presence of long-range pore-pore size correlations (Iaonnidis and Chatzis, 1993; Blunt, 1997a), or local pore–throat correlations (Jerauld and Salter, 1990; Iaonnidis and Chatzis, 1993). By modifying the level of snap-off, or its spatial distribution, these parameters varied the efficiency of the displacement patterns and ultimately affect relative permeabilities and residual saturations. Mani and Mohanty (1999) performed simulations on networks with infinite-ranged fractional Brownian motion (fBm) correlations and reported trends of relative permeabilities and residual saturations that were opposite to others’ results (Ioannidis and Chatzis, 1993; Blunt, 1997a). Applying a cut-off length to the fBm correlations reversed Mani and Mohanty’s trends to conform with the common observations.

Field determination of mechanical aperture, entry pressure and relative permeability of fractures using NAPL injection

An in situ field technique has been developed and implemented to measure non-aqueous phase liquid (NAPL) entry pressure and subsequently estimate mechanical aperture variability in an undisturbed, water-saturated rock fracture. The field experiment also provided the opportunity to measure wetting phase relative permeability at residual non-wetting phase saturation, kw,r(Snw,r). The radial aperture determination by the injection of oil (RADIO) method employs a constant-rate injection of a non-toxic NAPL into a fracture isolated by a double packer array. Injection pressures are recorded to provide a characteristic signature that is interpreted to reveal aperture enlargements and constrictions several metres from the borehole. Fracture aperture values are calculated by reverse modelling of the pressure signatures using the FRACAS fully compositional two-phase flow model. Pre-NAPL injection hydraulic testing established a baseline dataset of hydraulic apertures ranging from 26 μm to 259 μm with a mean value of 86 μm. Post-NAPL injection hydraulic testing gave kw,r(Snw,r) values ranging from 0·04 to 0·39 with a mean value of 0·15. Numerical modelling calculated fracture mechanical apertures vary from 36 μm to >1000 μm in test 1, and from 46 μm to >1000 μm in test 2. Single-value approximations of volume-averaged fracture apertures are two to three times larger than the respective hydraulic apertures, suggesting that volume balance calculations using the hydraulic aperture may overpredict NAPL penetration distances.

Assessing Risk from DNAPLs in Fractured Aquifers

Chlorinated solvents are among the most widespread pollutants of groundwater. As DNAPLs (dense nonaqueous phase liquids), they can move rapidly and in complex patterns through fractures to reach and contaminate large volumes of aquifer, and then dissolve to cause significant pollution of groundwater. However, clean-up of DNAPLs in fractured rocks is virtually impossible and certainly expensive. Risk assessment should be used to decide whether the pollution is serious enough to justify major expenditure on clean-up or containment. A key aspect of risk assessment for DNAPLs in fractured aquifers is to understand how deep they are likely to have penetrated through the fracture network. This paper addresses two aspects of such predictions: measuring fracture apertures in situ and the connectivity of fracture networks with respect to DNAPLs. Fracture aperture is an in-situ field technique that has been developed and implemented to measure aperture variability and NAPL entry pressure in an undisturbed, water-saturated rock fracture. The field experiment also provided the opportunity to measure the wetting phase relative permeability at residual non-wetting phase saturation. The RADIO (Radial Aperture Determination by the Injection of Oil) method employs a constant rate injection of a non-toxic NAPL into a fracture isolated by a double packer array. The method was applied at the field site in Scotland, and measured apertures out to ~5m from the borehole. It showed that hydraulic aperture (from packer tests) was a poor estimator of the controlling aperture for DNAPL movement. This is the first time such large-scale aperture measurements have been made, and the technique is the first which can provide useful aperture estimates for risk analysis of DNAPL movement.Network connectivity is a fundamental property of the fracture system. DNAPL connectivity extends the concept to take account of the fluid properties.

Wall-Effect/Gel-Droplet Model of Disproportionate Permeability Reduction

Summary Many polymers and gels can reduce the permeability to water more than they can the permeability to oil or gas. However, the mechanism of this disproportionate permeability reduction is not clear. This paper considers a promising potential explanation that is based on a combined "wall-effect" and "gel-droplet" model. Many aspects of the disproportionate permeability reduction can be explained by a wall-effect model if the gelant is prepared from or matches the wetting phase, and by a gel-droplet model if the gelant is prepared from or matches the nonwetting phase. The combined model predicts that disproportionate permeability reduction should increase with increasing residual nonwetting-phase saturation. New experimental results support this prediction.

Effect of pore-space spatial correlations on two-phase flow in porous media

The pore space in naturally occurring porous media is often spatially correlated. This work is aimed at developing an understanding of the effect of these correlations on multiphase transport properties. Three different correlation structures, namely, spatially uncorrelated, spherical and fractional Brownian motion (fBm) are used to construct the pore space. Two-phase primary drainage and imbibition capillary pressure and relative permeability curves are calculated from pore-level network simulations. Capillary pressure and relative permeability curves for uncorrelated and spherically correlated media are realization-independent, i.e., variations in these properties from realization to realization tend to vanish for large lattices. This is not true for porous networks based on fBm; variability increases with the Hurst exponent for both primary drainage and imbibition. The percolating cluster during primary drainage for uncorrelated and spherically correlated media is fractal, displaying decreasing density with increase in the system size. The percolating cluster is dense for fBm media studied, displaying scale-invariance. Spatial pore-space correlation has a large impact on imbibition capillary pressure and relative permeability curves. Moreover, the effects of these correlations on the imbibition process are quite different from those observed for primary drainage. The imbibition process for correlated systems is characterized by an increased probability for snap-off with a corresponding decreased probability for piston-like displacement. These mechanisms dictate the residual nonwetting-phase saturation, which generally increases with increasing degrees of pore-size spatial correlation.

Effects of Heterogeneity and Wetting on Relative Permeability Using Pore Level Modeling

AbstractWe present a three-dimensional, capillary equilibrium based, pore level network model that computes relative permeability and capillary pressure for drainage and imbibition cycles. The model accounts for wetting layers in crevices of the pore space, cooperative pore filling and different contact angles. Arbitrary distributions of pore size with different spatial correlations are studied. We show that relative permeabilities for unconsolidated media can be represented in the model using spatially uncorrelated distributions of pore size, but that curves typical of consolidated rock can only be explained by allowing spatial correlation in the pore structure. We also study the effects of flow in wetting layers and different types of cooperative pore filling. This represents changes in contact angle from a completely water-wet system to a neutrally-wet rock. Relative permeability can be extremely sensitive to small changes in contact angle. In general, the residual non-wetting phase saturation decreases as the system becomes less strongly water-wet.

Waterflooding Increases Gas Recovery

Summary Injecting water into a low-pressure gas reservoir nearing abandonment will displace gas and increase ultimate recovery. This paper examines the theory and reports the results of a case history. Water was injected into a southern Louisiana gas reservoir for more than 10 years, successfully increasing recovery by 25 Bcf [710×106 m3]. This paper also discusses the importance of considering all possible producing mechanisms early in a reservoir's life to predict future performance properly and shows that straight-line p/z performance does not necessarily indicate that a gas reservoir has a depletion drive, as is frequently assumed in practice. Introduction Natural gas is a major source of energy production and consumption in the U.S. As reserves decline, investigators are studying the potential of increased supplies from several unconventional sources1 and from waterdrive reservoirs with high production rates in the gas zones2,3 and the aquifers.4 Production at high rates from a waterdrive reservoir is an attempt to reduce reservoir pressure to a low value, thereby minimizing the actual gas volume occupying residual pore space. A reservoir with little water influx that depletes to low pressure has the opposite problem because all the pore space is still filled with gas. This paper shows that increased recovery can be obtained by waterflooding a low-pressure gas reservoir and discusses an actual field case. The Discorbis 1 reservoir (Reservoir D-1) in the Duck Lake field of southern Louisiana (St. Martin Parish) initially produced by limited aquifer influx. Water injection was initiated after reservoir pressure had fallen below 1,000 psi [6.9 MPa] and continued for 11 years. An incremental recovery of 25 Bcf [710×106 m3] was attributed to water injection. This project was primarily a low-cost expansion of the field's existing saltwater disposal system, providing a unique opportunity for an economic project at the gas prices of the 1970's, which were about 15% of current prices. Analysis of Reservoir D-1 also provides the opportunity to show that straight-line p/z performance does not necessarily mean that a gas reservoir has a depletion drive. Theory showing that depletion-drive gas reservoirs will exhibit a straight-line p/z plot has been developed. The corollary - that a straight-line p/z plot proves the existence of a depletion drive - has not been proven, although it is frequently assumed in practice. Theory If a gas reservoir produces strictly by pressure depletion, hydrocarbon pore space at abandonment pressure should be equal to that at initial pressure. A significant amount of gas, however, can remain in the reservoir. Injecting water at abandonment pressure displaces a fraction of the PV to production wells, leaving a residual gas saturation that contains a minimal standard volume because of the low trapping pressure. Thus, the good features of pressure depletion and water displacement are combined in a controlled production mechanism to maximize recovery. Craft and Hawkins5 showed that recovery for a waterdrive reservoir can be expressed asEquation 1 and that recovery for a depletion-drive reservoir can be expressed asEquation 2 For imbibition fluid displacements, Naar and Henderson6 concluded that residual nonwetting-phase saturation should be about one-half the initial nonwetting-phase saturation, so thatEquation 3 Substituting Eq. 3 into Eq. 1 and subtracting Eq. 2 yieldsEquation 4 Eq. 4 presents a simple means to calculate a theoretical incremental recovery, as a percentage of original gas in place (OGIP), that results from waterflooding a gas reservoir that is pressure depleting. This recovery factor is representative of a homogeneous reservoir where permeability is uniform areally and vertically, and water coning is neglected.

Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties

Abstract Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water-wet rocks for both two- and three-phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. Introduction Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. and by Osaba et al. Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems. Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by Snell as II, ID, DI and DD. I refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis published three-phase curves for unconsolidated sand, and Snell reported results of several English authors for both drainage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et al. for increasing water and gas saturations (ID). Corey et al. reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean and Sarem calculated three- phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three - phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (II) are those of Naar and Wygal. These curves are based on at theoretical study of the model of Wyllie and Gardner as modified by Naar and Henderson. Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids. Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term. SPEJ P. 149ˆ

Application of Air-Mercury and Oil-Air Capillary Pressure Data In the Study of Pore Structure and Fluid Distribution

Abstract Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquid interfacial tension and liquid-solid wetting conditions. The capillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent surface conditions. Investigations indicate that residual non-wetting-phase saturations following the imbibition process (i.e., wetting phase displacing non-wetting phase) are dependent upon both pore structure and initial non-wetting phase saturation and suggest that residual fluid is distributed to discontinuous globules, one to a few pore sizes in dimension, through the entire range of pore sizes originally occupied. It appears that air-mercury capillary pressure data adequately reflect the distribution of fluids in a water-oil system when strong wetting conditions prevail. An oil-air counter-current imbibition technique has also been found to provide a rapid means of obtaining residual-initial saturation data. In a majority of cases, residual saturations determined from the oil-air or air-mercury process reasonably approximate residual oil and saturation following water drive of a strongly water-wet medium. Introduction A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measurements of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in the distribution of fluids and that viscous forces in the range normally of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are described. Although air-mercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, heptane, octane or toluene is the wetting phase. Interfacial Tension and Capillary Pressure Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighboring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions mLt-2 and are numerically equal.

The Importance of Water Influx in Gas Reservoirs

Abstract Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited information on the subject has been available until recently. This study was performed to show the quantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appears to depend in an important way on:the production rate and manner of production;the residual gas saturation;aquifer properties; andthe volumetric displacement efficiency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state method, the Hurst modified steady-state method, and various unsteady-state methods such as those of van Everdingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should be investigated early to permit adequate planning to optimize the gas reserves. Introduction In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.1–3 Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,4 the Hurst modified steady-state method,5 and various unsteady-state methods such as those of van Everdingen-Hurst,6 Hurst,7 and Carter-Tracy.8 Interesting applications of these solutions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,18 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high.9 A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation.10 The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reservoir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive, gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.8 However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions.