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The Flow Mechanism of Dilute, Stable Emulsions in Porous Media Hwalll Soot and Clayton J. Radke' Chemical Englneerlng Lbpartment, Unlversiv of California, Berkeley, California 94 720
This work establishes the flow mechanism of dilute, stable emulsions in fine grained porous medii. Oil-in-water emulsions of mean drop sizes ranging from 1 to 10 pm are studied In sandpacks of 0.57 and 1.15 pm2 permeability at a superficial velocity of 0.07 "1s. Low viscosity oil drops cause permeabillty reductions of up to 80%, with 4 to 5 pm size drops being the most effective. By examining drop sizes and pores sizes,as well as transient effluent emulsion concentration and transient pressure data, we find that Permeability reductions during emulsion flow are caused by droplet capture mechanisms similar to those found for solid particle deep-bed filtration. The proposed filtration mechanism is verified by a micromodel study.
Introduction Emulsion flow in porous media may be broadly classified according to the stability of the emulsion and to the drop size of the dispersed phase and the pore size of the medium. Because of the need to renovate oily wastewaters, considerable effort has been devoted toward the class of dilute, relatively unstable emulsions flowing in fibrous or granular media where the average drop-size to pore-size ratio is very small (Spielman and Goren, 1970; Su and Spielman, 1977). In this class of emulsions, Spielman and Goren (1970) demonstrate that two regimes of oil flow exist in the porous medium. One regime consists of oil droplets dispersed in water and the other regime consists of continuous oil that has coalesced and transports according to its relative permeability (Scheidegger, 1974). No major change of absolute permeability occurs during, or due to, the flow. A second class of emulsion flow in porous media arises when emulsions are externally injected or formed in situ to improve oil recovery from petroleum reservoirs (McAuliffe, 1973) or tar sands (Doscher, 1967). Here the emulsions may be quite stable, the drop-size to pore-size ratio may be of order unity, and large reductions in the permeability of the porous medium may take place. The few studies of thistype of emulsion flow, as outlined below, conflict both as the nature of the flow behavior and the underlying physical mechanisms. Uzoigwe (1970) and later Alvarado and Marsden (1979) investigated the flow of surfactant-stabilized, oil-in-water emulsions through both synthetic and natural porous media. Non-Darcy flow is found only when the dispersed-phase concentration reaches about 50 vol %, at which concentration the bulk emulsion exhibits nonNewtonian behavior. These workers view the emulsionflow process as that of a continuum liquid, with drop size influencing only the bulk emulsion viscosity. Uzoigwe (1970) and Alvarado and Marsden (1979) focus on the steady state; they successfully correlate their resulh using porous-medium scaling procedures appropriate to nonNewtonian flow of homogeneous liquids (Savins, 1969). However, transient permeability reduction is observed in all experiments, and in some cases, depending on drop size and permeability, reductions of up to 40% are reported. Cartmill and Dickey (1979), with the aim of investigating the mechanism of oil migration through reservoir sandstones, carry out experiments with stable, crude oil-inUnion Carbide Corp., South Charleston, WV 25303. 0196-4313/84/1023-0342$01.50/0
water emulsions flowing through glass bead packs having differing serial permeability zones. They find considerable amounts of oil drops retained at the junction between two different permeability zones, with maximum retention at the front portion of the low permeability zone. Large permeability reductions are also found. For example, a permeability lowering of 80% is detected for a 1-pm drop-size emulsion flowing in a 5-pm2permeability zone, sandwiched between two 53-pm2regions. McAuliffe (1973) is apparently the first person to propose using dilute, stable emulsions as mobility control agents for oil recovery processes and to study their transient permeability behavior. In his work, an oil-in-water emulsion is obtained by reacting acidic crude oil with a caustic solution. Emulsions of various drop sizes are injected into consolidated Berea sandstone under a constant pressure. The emulsions drastically reduce water permeability of the sandstone (i-e.,sometimes by up to 90%)with the larger reductions observed for larger drop-ske to initial permeability ratios. Further, McAuliffe observes that the rate and amount of permeability reduction decreases with increasing injection pressure. He denotes this behavior as "pseudo" non-Newtonian, although the rheology of the dilute, bulk emulsion is Newtonian. The offered explanation is that oil droplets must overcome capillary retarding forces (Jamin, 1860; Gardescu, 1930) to squeeze through pore constrictions; higher imposed pressure drops overpower these capillary resistances. Unfortunately, this explanation is not satisfactory because McAuliff s results show that important permeability reduction occurs even when the emulsion drop sizes are very much s m d e r than the mean size of the pore constrictions. In view of the conflicting ideas of how emulsions are transported in porous media, this work attempts to establish experimentally the flow mechanism. We study stable, oil-in-water emulsions with average drop diameters of 2, 3, 5, 7, and 10 pm flowing in quartz sandpacks of permeabilities of 0.57 and 1.15 pm2with mean pore-throat diameters of 17.3 and 29.5 pm, and at a superficial velocity of 0.07 mm/s. In contrast to the earlier work, we determine not only transient permeabilities but also the poresize distribution of the porous medium and the inlet and effluent drop concentrations and size distributions. The permeability experiments are augmented by micromodel studies to provide visual information on oil-droplet migration in the porous medium. The main finding of this work is that dilute, stable oil-in-water emulsions do not flow in porous media as a continuum viscous liquid, nor by squeezing through pore constrictions, but rather by 0 1984 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 23, ,S.S.ENTRANCE
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PRESSURE
P
GAUGE
DISTRIBUTION RING
U
45 cm
SbMFLE WLECTION
EMULSION RESERVOIR
1
Figure 2. Schematic of the flow apparatus. DISTRIBUTION RING
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DISTRIBUTION RING
Figure 1. Schematic of the sandpack.
capture of the disperse phase with subsequent permeability reduction to the continuous phase. Experimental Procedures : from ao Oil-in-water emulsions employed : are prepared refined mineral oil (Chevron 410H), which has a viscosity of 1.5 mPa.s, or Chevron white oil no. 3, which has a viscosity of 23 mPa.8, and a distilled water (conductivity 4 0 - 6 S/cm) sodium hydroxide (Mallinckrodt, analytic) solution. They are stabilized by sodium oleate and oleic acid. Carbon tetrachloride is mixed with the oil phase to render it neutrally buoyant. This prevents the accumulation of the drops in the supply line to the porous medium and reduces any droplet gravity segregation within the medium. mol/dm3 of oleic acid (U.S.P.) is Oil containing 5 X contacted with lo4 M sodium hydroxide in a 1:lOO volume ratio and mixed in a Waring blender. The resulting emulsion is then diluted with a pH 10 caustic solution to the desked oil content of 0.5 vol % . Dropsize distributions of the emulsions are controlled by blender speed and are determined by manual counting (Zeiss particle counter) from photomicrographs. At the dilute droplet concentration, the bulk emulsion viscosity is that of water. The [ potential of the emulsion droplets is approximately -80 mV, as determined by microelectrophoresis (Rank, Mark 11). Thus, significant electrical double-layer repulsion exists between drops (Kruyt, 1952). The interfacial tension of the emulsion oil-water interface is about 15 mN/m, as obtained with a spinning-drop tensiometer. Emulsions prepared in the described manner are highly stable, always lasting for the duration of the flow experiment (Le., up to 8 h) with no observable change in drop-size distribution. Fine Ottawa sand of known grain-size distribution (Le., measured from screen sieves) is packed into a stainless steel cylinder, 2.5 cm in diameter and 5 cm long, and serves as the porous medium. The cylindrical core, which is shown in Figure 1, is specially designed to fit into a large centrifuge holder so that water-drainage capillary pressure curves can be measured directly, and pore-throat size distributions can be calculated (Hassler and Brunner, 1945; Slobod et al., 1951). The permeability of the porous medium is varied by carefully adjusting the sand grain-size distribution. To ensure that the core is completely water saturated, water imbibition proceeds slowly in a vacuum chamber at a pressure below 100 pm of mercury. Nitrogen and water permeabilities must agree to within 10% before the sandpack is considered usable. The Ottawa sand used is thoroughly cleaned by repeated washing with dilute acid and base to establish a strongly water-wet, reproducible surface. Microelectrophoresisstudies with the smaller sand grains demonstrate a -70 mV [ potential in the alkaline aqueous phase.
:5.3pm
i
: IOpm
0
10 DROP DIAMETER, O d . pm
15
20
Figure 3. Droplet-size distributions of the emulsions. The oil viscosity is 1.5 mPa-e.
Figure 2 shows a schematic of the experimental flow system. Dilute emulsion of known drop-size distribution is supplied from a slowly stirred reservoir to the sandpack of known initial pore-size distribution and permeability by a positive displacement pump (FMI). The volumetric flow rate is kept constant at 0.02 cm3/s and checked periodically by weight. Overall pressure drop is continuously monitored with a transducer (Validyne). Emulsion samples are routinely taken at the outlet of the core and analyzed photographically for drop-size distribution and drop-volume concentration. Experimental error in the flow experiment mainly arises from the emulsion volume-concentration measurement. Extreme care must be taken when photographing the droplets. In general, the error in the concentration measurement is about f5%. Further, because of the difficulty in reproducing precisely the same initial drop-size distribution, the flow experiments are not easy to replicate exactly. (Figure 11discussed later gives some indication of the reproducibility of the flow results.) Considerable care is taken to ensure that no appreciable oil accumulation occurs at the core entry and that the inlet oil fraction remains constant throughout the duration of the experiment. Routine examination of the drop concentration and size distribution at the front surface of the sandpack after each flow run confirms the lack of any face plugging. After each experiment the core is flushed successively with distilled water, 2-propanol, and distilled water, and then is vacuum-oven dried. After water saturation, the same core is reused, but only if its permeability is within 5% of the original value. A detailed discussion of the experimental procedures is available in the thesis of So0 (1983).
Results and Discussion Drop-Size Distribution. The volume-average mean drop diameters of the emulsions employed in this study range from 2 to 10 pm, while the minimum drop diameter is around 1pm and the maximum is approximately 30 pm. Figure 3 presents three typical drop-size distributions expressed in volume frequency. Solid lines are the corresponding besbfit log-normal distributions. Note that the
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IO 20 30 PORE T H R O A T DIAMETER, D p , p m
40
Figure 4. Pore-size distributions of the sand-packed cores at two different permeabilities (0.57 and 1.15 pm').
I
I
0
0 05
I
I
0 10
T c , , PORE VOLUME
0 I5
1
020
OIL
Figure 6. Experimental permeability-reduction (filled symbols) and breakthrough-concentration histories (open symbols) for varying drop sizes (2.1, 3.1, 4.5, and 6.1 pm) in the 1.15-pm2 permeability core. The oil viscosity is 1.5 mPa-s.
K 3 = 0 57 u m z
1
INITIAL
AFTER
PORE THROAT DIAMETER, Dp,
pm
Figure 5. Comparison between the initial pore-size distribution and the pore-size distribution after 8 successive flow experiments (0.57pm2 core).
smaller the drop size, the narrower is the distribution. This is characteristic of emulsions prepared with a blender. Porous Media. Two different grain-size-distribution sandpacks are used in this study. Figure 4 reports their pore-entry diameter distributions, determined from capillary pressure data of air-water centrifugal displacement experiments. Procedures for reducing the capillary pressure data to a pore-size distribution are outlined by So0 (1983). The mean pore-entry diameter of the 1.15-pm2 sandpack is 29.5 pm while that of the 0.57-pm2sandpack is 17.3 pm. These are in good agreement with an empirical correlation listed by Alvarado and Marsden (1979). The porosity of the sandpacks, as determined by the weighing method, is 0.34 for the 1.15-pm2sandpack and is 0.31 for the 0.57-pm2sandpack. To ascertain whether the poreentry diameter distribution alters after successive cleaning and flow experiments, a centrifugal ail-water displacement experiment was conducted on the 0.57-pm2 sandpack at the completion of 8 runs. Comparison of the initial pore-entry size distribution with the final distribution is given in Figure 5. This figure indicates an increase in the pore-entry size distribution after the repeated flushing of the sandpack. The shift is most likely caused by fines loss or migration during cleaning. The permeability of the used sandpack, however, was measured to be 0.6 pm2 and the flow behavior of similar drop-size emulsions was reproducible. The number of cleaning and reuse treatments in Figure 5 is severe. Usually a given sandpack is discarded after about four runs. Flow Experiments. Figure 6 portrays typical results for the transient, reduced, overall permeability, K/Ko,as determined from the measured pressure drops and the reduced drop effluent volume concentration, cL/ci. The symbol r denotes the pore volumes of injected fluid so that the abscissa, cir, corresponds to the pore volumes of injected emulsified oil. Filled symbols and solid lines in this
D R O P D I A M E T E R , Dd, pm
Figure 7. Comparison between effluent drop-size distributions and the inlet distribution. A 4.5-gm mean drop-diameter emulsion of oil viscosity equal to 1.5 mPa.s flows through the 1.15+m2 core; the exit drop-size distribution is shown after injection of 7 and 15 pore volumes.
figure (and in following corresponding figures) refer to the permeability, while open symbols and dashed lines refer to the effluent drop concentration. The solid and dashed lines corresponding to each experiment are not simply best fit but rather are predicted according to a flow theory (Soo, 1983; So0 and Radke, 1984). The flow model relies on deep-bed filtration principles (Herzig et al., 1970) and is guided by the experimental findings reported below. In Figure 6, the initial permeability is 1.15 pm2 and the mean drop size ranges from 2 to 6 pm. Several important features are revealed in Figure 6. The core permeability falls over many injected fluid pore volumes, r , and eventually levels off. Oil droplets do not appear in the effluent immediately at one pore volume. Rather, they are delayed, and after elution, their concentration slowly rises over several injected emulsion pore volumes to the inlet value of ci = 0.5 vol % . At the time for which the droplets approach their inlet concentration, the permeability stops changing. Figure 6 confirms establishing permeability reductions reported by McAulZfe (1973). He did not measure effluent drop concentrations and so was unable to observe drop holdup. The results in Figure 6 also partly confirm the experiments of Uzoigwe (1970) and Aivarado and Marsden (1979) in that apparently a steady state is attained. These authors employ high emulsion concentrations so that steady flow is achieved rapidly. Also, their porous media are preflushed with large quantities of emulsion and all flow behavior is recorded in the steady regime. The question of establishing of steady state is examined further in Figure 7. Here the effluent drop-size distribution is given for the 4.5-pm, mean drop-size emulsion of Figure 6 after 7 and 15 fluid pore volumes of injection. Drops eluting early are generally smaller than the injected
Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984 345
As c
1
I
WATER i INJECTION I
io
0 0
I
&
1
~r
0 05 010'0 TCL, PORE VOLUME O I L
f
I
n~
I
I
2 4 6 8 T , PORE VOLUME WATER
Figure 8. Experimental permeability-reduction(filled symbols)and breakthrough-concentrationhistories (open symbols) of a 20 porevolume pulse of a 3.1-pm, mean drop-size emulsion (droplet oil viscosity is 1.5 mPa.s) in the 1.15-pm2core. The pulse is followed by pH 10 solution.
distribution; as time proceeds the effluent drops shift to larger diameters until, eventually, the inlet drop-size distribution is matched. Thus, the steady-state flow suggeated in Figure 6 is consistent for pressure drop, effluent concentration, and effluent drop size. Additionally, the drop-size shift of Figure 7, which shows no larger drops eluting than are injected, indicates little if any, drop coalescence in the packed bed. Because the injection concentration in Figures 6 and 7 is so low that the bulk emulsion viscosity is that of water, the experimental findings of these two figures clearly discredit the model of continuum liquid flow in the porous medium. Indeed, when drop and pore sizes are comparable, the bulk liquid viscosity likely cannot describe flow in a tortuous pore space. Droplet retardation, however, can account for the effects seen in Figures 6 and 7. If droplet squeezing in constrictions is the source of the flow resistance, then injection of water behind the emulsion should displace the droplets over several pore volumes, while the permeability should rise to its initial value. Figure 8 presents results for this experiment. A 20 pore-volume pulse of a 3.1-pm, mean drop-size emulsion flows through the 1.15-pm2sandpack and is followed by pH 10 water. After emulsion injection, a permeability reduction of about 50% is recorded. Once water injection commences, the effluent drop concentration falls to zero after about one pore volume, whereas the permeability is unaltered. Therefore, droplet retardation does not appear to be the main source of the flow restriction. The physical picture that emerges from Figures 6 through 8 is one of drops sticking in the porous medium and blocking or restricting flow paths. Drops are retained even under the circumstance that their diameters are considerably smaller than the pore-entry diameters. By comparing the drop-size distribution in Figure 3 to the pore-entry size distribution in Figure 4, we find that only a small fraction of the pore constrictions have sizes smaller than the drop sizes. Nevertheless, emulsion breakthrough is delayed and appreciable permeability reduction occurs. This implies that drops occluding pore constrictions is not the only capture mechanism. Other capture mechanisms, such as drops trapped in recirculation eddies and on sand surfaces, are also operative. Figure 8 demonstrates that the drops, once captured, do not reenter the flow stream, at least at the flow velocity of this work. Hence, steady flow is not a dynamic balance between drop capture and re-entrainment. The physical interpretation for a steady state is proposed as follows. Initially, drops preferentially capture in small size pores.
emulsion injection proceeds, more and more small pores become blocked. Flow is diverted mostly to the large size pores and drop capture rate decreases. Eventually, when the drop capture sites in the large pores are fiied, capture ceases and steady state is reached. This explanation implies that the stabilized drops do not capture on top of themselves and that the larger pores of the sandpack form a contiguous path through the medium. We thus adopt the view that dilute, stable emulsions flow in porous media according to filtration principles (Herzig et al., 1970). It is now possible to explore the drop-size trends accentuated in Figure 6. As the drop size increases, the effluent concentration data show that overall emulsion retention increases. This is because capture probability is higher for the larger drops, and a smaller fraction of pores remain open to flow as steady state is approached. The higher capture probabilities for the larger drops also explain why they elute later than the smaller drops in Figure 7. For emulsions of small mean drop diameters and consequent narrower size distributions (e.g., the 2.1-pm emulsion of Figure 6), we do not find the transient dropsize shift portrayed in Figure 7. The emulsion drops are delayed, but they emerge with essentially their inlet size distribution. Presumably, the capture probabilities are not significantly different between the largest and the smallest drops in these smaller drop-size emulsions. The effect of drop size on the absolute permeability in Figure 6 is not so straightforward to explain. Permeability reduction increases as the drop size increases from 2.1 to 4.5 pm. Initially, however, transient permeabilities decrease less rapidly as the drop size changes from 4.5 to 6.1 pm. Apparently, not only the amount of the drops retained but also their distribution among the pores influences the overall permeability reduction. At identical volume retentions (e.g., before drop breakthrough), the number of drops captured is larger for the smaller drop-size emulsion. Therefore, the retained oil must be more finely and evenly dispersed in the pore space, and smaller drops reduce the permeability more effectively than larger ones at equivalent capture volumes. Thus, we conclude that two factors control the permeability reduction: the total volume of drops retained and the effectiveness of those drops in restricting flow. In Figure 6, for the emulsions of drop size smaller than 4.5 pm, the effect of drop size on retention outweighs the effect of drop size on their obstructing ability. Consequently, the larger drop size results in a greater permeability reduction. When the drop size increases from 4.5 to 6.1pm, the effect of drop size on restriction effectiveness dominates. Before breakthrough of either the 4.5-pm or 6.1-pm drops, oil retention in the sandpack is identical for both drop-size emulsions. Therefore, the 4.5-pm emulsion reduces transient permeability more because the 4.5-pm drops restrict flow more effectively than the 6.1-pm drops a t equivalent volume amounts retained, as explained above. Eventually at steady state, larger drop-size emulsions should reduce permeability more than smaller drop-size emulsions. A similar drop-size effect on transient permeability reduction is depicted in Figure 9, which gives the results of injecting emulsions of 3.3,5.3, and 10-wm mean drop sizes into the 0.57-pm2sandpack at a superficial velocity of 0.07 "/e. Breakthrough of the two larger drop-size emulsions is not achieved for up to 100 pore volumes of emulsion injected, and steady state was never reached. Hence, the effluent concentration profiles are not available. Note that injecting 100 pore volumes of a 0.5% volume concentration emulsion without breakthrough implies an oil saturation
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Figure 9. Experimental permeability reduction (filled symbols) and breakthrough concentration histories (open symbols) for varying drop-sizes (3.3,5.3,and 10 pm) in the 0.57-pm2core. The oil viscosity is 1.5 mPa.s.
1
0
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Figure 11. Experimental permeability reduction (filled symbols) and breakthrough concentration histories (open symbols) for two viscosities of the oil phase (1.5 mPa.s and 23 mPa-a) with a 3-pm drop-size emulsion.
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Figure 10. Experimental permeability reduction (filled symbols) and breakthrough concentration histories (open symbols) for two initial permeabilities (0.57 and 1.15 pm2) with the 3.3-pm drop-size emulsion. The oil viscosity is 1.5 mPa-s.
of at least 50% in the sandpack. This is way above the usual residual oil saturation (Scheidegger, 1974). If the drops were unstable and coalescing, a continuous flowing oil phase should be formed. This confirms the results of Figure 7 that the emulsions employed here are highly stable; no coalescence occurs in the sandpack. Figure 10 depicts the effects of the 3.3-pm drop-size emulsion on the two different permeability sandpacks. As anticipated, the low permeability sandpack exhibits later emulsion breakthrough indicating higher drop retention, which gives larger permeability reduction at steady state. A projection of the filtration picture is that drop viscosity should have little effect on flow behavior. Drop sizes, pore sizes, and drop and sand-grain surface chemistry dominate the capture probability. With the continuum and retardation models, however, the viscosity of the oil phase is expected to have some effect on the emulsion flow rate. Figure 11 demonstrates the role of viscosity of the oil droplets on emulsion flow behavior. Experimental results are compared for injecting 3.1- and 3.4-pm drop-size emulsions with oil-phase viscosities of 1.5 and 23 mPa.s, respectively, into the 1.15-pm2sandpack. Both effluent concentration and transient permeability histories do not vary significantly as the oil-phase viscosity increases by 15 times. The slight differences seen in Figure 11 are undoubtedly due to our inability to inject exactly the same inlet drop-size distribution and to restore the core perfectly. Figure 11provides further evidence that oil drops are not simply retarded as they percolate through a porous medium. Rather, they are retained in the medium so that a filtration model more correctly reflects the physics of emulsion flow in porous media.
CENTER FRAME
W D R O W LINE
Figure 12. Schematic of the micromodel.
Micromodel Study To gain further understanding of the physical mechanisms of emulsion flow in porous media, a visual micromodel study was conducted. In this study, oil-in-water emulsions of drop sizes ranging from 1 to 50 pm are injected into a micromodel of Ottawa sand sandwiched between two glass plates. The flow behavior is observed under a microscope. A schematic of the micromodel is shown in Figure 12. A stainless steel frame 5.7 cm wide and 11.4 cm long is machined out for two glass plates. The gap between the glass plates is 0.16 cm. One end of the frame is removable so that the sand can be tightly packed. The glass plates are held in place by stainless steel retainer frames that are attached to the center frame. Much effort was directed toward obtaining low enough permeabilities for representative drop-size to pore-size ratios. With appropriate sand grain-sizedistributions, water permeabilities as low as 4 pm2 (Le., approximately a 50-pm, average pore-entry size) can be attained. Production of an emulsion with good visual contrast against the continuous fluid phase, and with controllable drop sizes, presented an elusive technical problem. After a series of tests, it was found that emulsions of acidic crude
Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984 347
oil (Wilmington, CA) dispersed in caustic solution provide high visibility under a microscope. Therefore, in the micromodel work the emulsions are made by blending crude oil alone with an NaOH solution. Crude oil-in-water emulsions of known drop sizes are injected into the water-saturated micromodel of known permeability with Sage syringe pump at superficial velocities of between 0.02 to 0.12 mm/s. These velocities are on the same order as the velocity of the sandpack experiments, which is set at 0.07 mm/s. The flow behavior is observed under a Nikon microscope, which has three objectives equipped for Hoffman Modulation contrast, and hence can better display the three-dimensional nature of the porous matrix. The behavior of the emulsions of large 20-pm drop-size is obvious: they simply lodge in the pores. Drops following behind are then diverted to other nearby pores. When the flow rate, and hence the pressure drop, is increased abruptly lodged drops slip through the pores to flow downstream. They do not adhere to the surface of the sand grains. For the smaller drops, a different type of flow behavior is seen. Though the drops are considerably smaller than the average pore diameter, many are collected in the porous medium. Most of them are retained in the pockets or crevices formed by the sand grains. After several of the small drops capture in a pocket, enough flow restriction occurs so that ensuing drops flow through adjacent larger pores. Some of the smaller drops are also retained on the surface of the sand grains. Direct interception seems to be responsible for bringing the drops into contact with the surface of the sand grains. Usually these drops reenter the flow immediately after apparent contact, but a few, after sliding along the surface for a while, adhere permanently to the surface. Eventually, the sand grains become almost “coated”with small drops with the result that the available volume for flow in the sandpack decreases. In the time frame of the visual experiments, drops are never seen captured by the previously retained drops. Clusters of drops exist only in the pockets formed by the sand grains. The micromodel study reveals that the transient permeability reduction during emulsion flow mainly arises from retention of drops in pores. Drops are not only captured in the pores of constriction sizes smaller than their own, but also, they are captured in crevices or pockets formed by the sand grains and sometimes on the surface of the sand grains. The details of these visual observations are obviously sensitive to the surface chemistry of the drops and the porous matrix, in particular to the pH and ionic strength of the aqueous phase. Nevertheless, the micromodel experiments provide convincing evidence for the filtration viewpoint of emulsion flow in porous media.
Conclusions The flow mechanism of dilute, stable emulsions in porous media is established by analyzing experimental effluent emulsion concentration and transient permeability histories for mean drop sizes between 2 and 10 pm, initial core permeabilities of 0.57 and 1.15 pm2, and oil-phase viscosities of 1.5 and 23 mPa.s. Flow of dilute, stable emulsions is physically very similar to a filtration process. When emulsions are injected into porous media, drops are retained in the pores and permeability decreases. The drops not only block pores of throat sizes smaller than their
own, but they also capture on pore walls and in crevices. The larger the size of the drops the higher is their capture probability. A steady state is reached where all capture sites are occupied, and where local flow diverts to contiguous large channels. This physical picture is confirmed by a visual micromodel study. Twofactors determine the overall permeability reduction: the volume of drops retained and how effective those drops are in restricting the flow. As the drop size of the emulsion increases, the drop retention increases. However, at identical volume retentions, smaller sized drops are more effective in restricting flow. For the systems of smaller I0.2 in this work), dropsize emulsions (i.e., for (Dd)/(D,) the effect of drop size on the retention dominates, and increasing the drop size results in an increased permeability reduction. For systems of larger drop-size emulsions, the effect of drop size on restriction effectiveness dominates, and increasing the drop-size results in less transient permeability reduction. In concert with the filtration picture, the viscosity of the oil phase has little effect on both effluent concentration and transient permeability histories. Acknowledgment The author wishes to thank B. J. Larkin for designing the micromodel and R. R. Waterhouse for conducting the micromodel experiments. This research was supported by the U.S.Department of Energy under Grant W-7405ENG-48to the Lawrence Berkeley Laboratory. Partial support to H. So0 was provided by Chevron Oil Company. Nomenclature ci = injection volume concentration of oil drops in emulsion, volume of drops/flowing volume CL = effluent volume concentration of oil drops in emulsion, volume of drops/flowing volume (Da)= mean drop diameter, pm (D,)= mean pore-entry diameter, pm K = overall permeability, pm2 KO= initial permeability, pm2 L = core length, m t = time, s u = superficial velocity, m/s Greek Letters to = bed porosity, void volume/bed volume T = injected fluid pore volumes, ut/c&, dimensionless p = viscosity, mPa.s Literature Cited Alvarado, D. A.; Marsden, S. S. Soc.Pet. €ng. 1979, 10, 369-377. Cartmill, J. C.; Dickey, P. A. Am. Assoc. Pet. W/og/stBull. 1979. 54. 2438. Doscher, T. M. Roc. 7th WorMPet. Congr. 1967, 3 , 628. Gerdescu, I. I. Trans. A I M 1930, 86, 348. Hassler, G. L.; Brunner, E. Trans. A I M 1945, 160, 114-123. Herzig, J. P.; Leclerc, D. M.; LeGoff. P. Ind. €ng. Chem. 1970, 62(5), 8. Jamln, J. Phll. M g . 4th Ser. 1860, 19, 204. Kruyt, H. R. “Colloid Science”; Elsevier: New York, 1952. McAullffe, C. D. J . Pet. Techno/. June 1973, 727. Savlns, J. 0. Ind. €178.Chem. 1969, 61, 18. Scheldegger, A. E. “The Physics of Flow through Porous Media”, 3rd ed.; University of Toronto Press: Toronto, 1974. Slobod, R. L.; Chambers, A,; Prehn, W. L., Jr. Trans. A I M 1951, 192, 127. Soo, H. PhD. Thesls, University of California, Berkeley, CA, 1983. Soo,H.; Radke, C. J. In preparation, 1984. Spielman, L. A.; Goren, S. L. Ind. Eng. C h m . 1970, 62, 10. Su, Y. P.;Spielman, L. A. Ind. Eng. Chem. Fundam. 1977, 16, 272. Uzolgwe, A. C. Ph.D. Dissertation, Stanford University, Stanford, CA, 1970.
Received for review July 1, 1983 Accepted February 2, 1984
