Influence of Viscous and Capillary Forces on Immiscible Fluid

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Influence of Viscous and Capillary Forces on Immiscible Fluid Displacement: Pore-Scale Experimental Study in a Water-Wet Micromodel Demonstrating Viscous and Capillary Fingering Changyong Zhang,* Mart Oostrom, Thomas W. Wietsma, Jay W. Grate, and Marvin G. Warner Pacific Northwest National Laboratory, 902 Battelle Boulevard, Post Office Box 999, MSIN K8 96, Richland, Washington 99352, United States ABSTRACT: Unstable immiscible fluid displacement in porous media affects geological carbon sequestration, enhanced oil recovery, and groundwater contamination by non-aqueous phase liquids. Characterization of immiscible displacement processes at the pore scale is important to better understand macroscopic processes at the continuum scale. A series of displacement experiments was conducted to investigate the impacts of viscous and capillary forces on displacement stability and fluid saturation distributions in a homogeneous water-wet pore network micromodel with precisely microfabricated pore structures. Displacements were studied using seven wetting
non-wetting fluid pairs with viscosity ratios M (viscosity of the advancing non-wetting fluid divided by the viscosity of the displaced wetting fluid) ranging 4 orders of magnitude from log M =
1.95 to 1.88. The micromodel was initially saturated with either polyethylene glycol 200 (PEG200) or water as the wetting fluid, which was then displaced by a non-wetting alkane fluid under different flow rates. Capillary numbers (Ca) ranged over 4 orders of magnitude for the reported experiments, from log Ca =
5.88 to
1.02. Fluorescent microscopy was used to visualize displacement and measure non-wetting fluid saturations and interfacial area. In the experiments initially saturated with PEG200, a viscous wetting fluid, unstable displacement occurred by viscous fingering over the whole range of imposed capillary numbers. For the experiments initially saturated with water, unstable displacement occurred by capillary fingering at low capillary numbers. When the viscous forces were increased by increasing the injection rate, crossover into stable displacement was observed for the fluid pairs with log M > 0. For unstable displacement experiments applying the same capillary number for the seven fluid pairs, non-wetting fluid saturations were higher when capillary fingering was the dominant fingering process compared to viscous fingering. These experiments extend the fundamental work by Lenormand et al. (Lenormand, R.; Touboul, E.; Zarcone, C. Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 1988, 189, 165
187) using precision-fabricated water-wet micromodels and enhanced image analysis of the saturation distributions. Our saturation distributions are consistent with other published experimental work and confirm the numerical results obtained by Lenormand et al.

1. INTRODUCTION Immiscible fluid displacement in porous media impacts several subsurface processes, including geological carbon sequestration, enhanced oil and gas recovery, and non-aqueous phase liquid (NAPL) contamination of groundwater. For two-phase flow, these processes include drainage, when a wetting fluid is displaced by a non-wetting fluid, and imbibition, when a nonwetting fluid is displaced by a wetting fluid. Unstable displacement resulting in fingering is one of the major reasons for inefficiency in subsurface two-phase flow. For instance, during enhanced oil recovery using water flooding, water typically displaces less than half of the oil in any given formation.2 In CO2 sequestration, fingering of low-viscosity supercritical CO2 limits the available storage capacity, so that only a fraction of the reservoir is occupied with the injected gas.3 Remediation of dense NAPL (DNAPL) with standard pump-and-treat remediation methods is often ineffective because water flushing bypasses zones containing DNAPL.4
7 A solid understanding of displacement stability, fluid flow pathways, and pore-saturation levels are of critical importance to evaluate the impacts and efficiencies of these displacement processes. However, such an understanding is complicated by the large number of factors influencing flow in porous systems, r 2011 American Chemical Society

such as fluid viscosity and density, interfacial tension, wetting properties and heterogeneity of the porous media, fluid flow rates, and the considered length scales.8 Pore-scale multi-phase displacement phenomena can be experimentally observed in micromodels, which are two-dimensional (2D) pore network patterns etched into materials, such as silicon,9,10 glass,2 polydimethylsiloxane (PDMS),8 and polyester resin.1,11
13 Pore sizes are typically on the order of tens of micrometers but can be configured to be both smaller and larger. Micromodels are advantageous because any 2D heterogeneous pore structure can be created and fluid flow and effluent flux can be directly controlled and/or monitored. Although recent advances in microfabrication allow for precise manufacturing of a wide variety of pore structures,9,14,15 most micromodels used to date in multi-fluid displacement experiments have rectangular pore bodies and throats.1,2,8,11,12,16
18 Micromodels typically enable direct visualization using cameras with or without fluorescent microscopy, and subsequent quantitative evaluation of fluid saturation and interfacial area may lead to a better understanding Received: December 21, 2010 Revised: June 13, 2011 Published: June 16, 2011 3493

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21 Although generally accepted as 2D systems, micromodel studies may provide insights and implications for processes occurring at the continuum scale. Primarily driven by an interest in enhanced oil recovery using an aqueous phase, the majority of the micromodel two-phase displacement studies have been conducted for imbibition conditions.12,22,23 Recently, an increased emphasis on subsurface injection of low-viscosity supercritical CO2 has renewed interest in pore-scale research for drainage systems.2,8,24 The descriptions of pore-scale displacement mechanisms under drainage conditions mostly originate from Lenormand et al.,11 who based their theory on the behavior of capillary pressure in pore bodies and throats. In the absence of viscous forces, horizontal displacement of a wetting fluid by a non-wetting fluid is governed by capillary forces and a non-wetting fluid is not able to enter a porous medium spontaneously. The non-wetting fluid can only enter a pore throat with a radius r when the capillary pressure, i.e., the difference between the non-wetting and wetting fluid pressure, exceeds the entry value Pe = 2σnw/r, where σnw is the interfacial tension between the non-wetting (subscript n) and wetting fluid (subscript w). Under these conditions, pressure distributions in both fluids are uniform and pore size distributions control displacement. A displacement front advances by invading the largest available pore bodies and throats available that have the lowest capillary resistance. When viscous forces also become important, the pressure distributions become non-uniform and pressure differences may force the non-wetting fluid into smaller pore throats. Two-phase displacement in horizontal micromodels, in the absence of gravitational forces, can be characterized by two dimensionless numbers: the capillary number (Ca) and the viscosity ratio (M). The capillary number relates viscous to capillary forces and is defined as Ca = μnun/σnw cos θ, where μn and un are the viscosity and velocity of the advancing nonwetting fluid, respectively, and θ is the fluid
fluid contact angle. The viscosity ratio, M, is defined as the ratio of the advancing non-wetting fluid viscosity and the displaced wetting fluid viscosity: M = μn/μw. Using simple models of two-phase flow, Lenormand et al.1 and Fernandez et al.25 showed that the invasion percolation (IP) modeling technique could be used for systems where capillary forces were dominant and the diffusion limited aggregation (DLA) technique for modeling was more appropriate for conditions where viscous forces were dominant. Lenormand et al.1 completed a large number of displacement experiments for several fluid pairs in an oil-wet micromodel constructed of a polymer resin. They observed that, for M > 1 at low capillary numbers, displacement occurred in the form of capillary fingers. For larger capillary numbers, the displacement gradually became stable. For M < 1 at low capillary numbers, capillary fingers were again observed. However, because of the lower viscosity of the invading non-wetting fluid, viscous fingering dominated at higher capillary numbers, while for moderate capillary number values, both capillary and viscous fingers were observed. The zone where the type of unstable fingers change from capillary to viscous is typically denoted as the crossover zone.2,8 Ferer et al.2 combined experiments where air was injected into a glass micromodel with pore-scale modeling to relate a system-dependent crossover length to the capillary number using fractal theory. In their work, they were also able to experimentally verify predictions by Fernandez et al.25 for the

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injection of a zero-viscosity fluid in an initially water-saturated micromodel. More recently, quantitative image analysis techniques allow for the determination of fluid saturations19,26,27 and interfacial areas19,21 in micromodel displacement experiments. Characterization of the interfacial area (L2) between immiscible fluids is important because many processes occur at the fluid
fluid interfaces, such as interfacial mass transfer that affects dissolution and solubility trapping of CO2,28 mineral dissolution and precipitation related to carbon sequestration10 and enhanced oil recovery,29 as well as NAPL dissolution and contamination of groundwater.30,31 The experiments conducted by Lenormand et al.1 using oil-wet micromodels have been the only micromodel study thus far where a large number of fluid pairs have been tested for a variety of flow conditions. Although Ferer et al.,2 Cottin et al.,8 and Lovoll et al.32 also conducted drainage displacement experiments investigating the formation of capillary and viscous instabilities, the ranges in imposed capillary number and viscosity ratio were limited. In this paper, we present results of a series of drainage experiments in water-wet micromodels over a large range in capillary number and viscosity ratio. Specifically, displacement of seven immiscible fluid pairs with viscosity ratios ranging 4 orders of magnitude (from log M =
1.95 to 1.88) were studied in a pore network micromodel etched into a silicon wafer, for injection rates ranging 3 orders of magnitude, leading to capillary numbers ranging over 4 orders of magnitude (from log Ca =
5.88 to
1.02). This research not only complements the work by Lenormand et al.1,11,33 using water-wet micromodels, it also represents considerable improvements in microfabrication, fluid saturation visualization, and image analysis. As noted by Chang et al.,12 the pore shapes in the micromodels used by Lenormand et al.1,33 were, primarily as a result of the etching technique, quite irregular and inconsistent with the theoretical displacement mechanisms developed for perfectly rectangular pores by Lenormand et al.11 Recent advances in microfabrication methods allowed us to construct well-defined porous systems with circular posts and consistently shaped pore bodies and throats using dry-etching techniques.10,14,20 Lenormand et al.1 were also not able to quantitatively analyze fluid saturation distributions because of the quality of the obtained images. In this work, we were able to take advantage of techniques, such as fluorescent microscopy27 and automated image processing, to generate saturation distribution as a function of the capillary number and viscosity ratio. The results of the displacement experiments are compared to results of other micromodel drainage studies,1,2,8 where ranges in capillary number and viscosity ratio were also considered.

2. MATERIALS AND METHODS 2.1. Chemicals and Properties. Two wetting fluids, polyethylene glycol 200 (PEG200) and water, and four non-wetting fluids (alkanes), hexane (HA), dodecane (DD), hexadecane (HD), and heavy mineral oil (MO), were used in the displacement study. A fluorescent dye, Nile Red, was added to the non-wetting fluid to distinguish the non-wetting phase from the wetting phase. All chemicals are ACS-reagent-grade (SigmaAldrich). When PEG200 is the wetting phase, a fraction of the Nile Red partitions into PEG200 and displays a different fluorescence color than it had in the alkane, because the fluorescence emission spectrum is sensitive to the solvent environment. This phenomenon is known as solvatochromism and was used to selectively visualize both immiscible fluids as well as wetting fluid structures in a pore network micromodel as 3494

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Table 1. Summary of Fluid Properties viscosity (cP) wetting (w)

non-wetting (nw)

μw

μnw

log M

σnw (mN/m)

contact angle (deg)

PEG200

HA

29.2

0.33


1.95

12.35

26.49

PEG200

DD

29.2

1.35


1.34

13.87

37.66

29.2

PEG200

HD

3.34


0.94

14.27

19.23

water

HA

1.02

0.33


0.49

49.71

14.82

water

DD

1.02

1.35

0.12

51.21

24.91

water

HD

1.02

3.34

0.52

52.00

16.79

water

MO

1.02

1.88

36.32

18.25

77.6

Figure 1. Schematic of the micromodel and displacement experimental setup. reported by Grate et al.20 In this study, this feature enabled the selective observation of residual PEG200 wetting structures and their dependence upon capillarity. Nile Red emission in the alkane phase decreases with extended light exposure, and the half-life (t1/2) of Nile Red can be determined by measuring fluorescence signal intensity over time. The photosensitivity of the dye was used to distinguish stagnant and mobile portions of the non-wetting phase when unstable displacement occurred. For non-wetting fluid in an active flowpath, emission decreases were insignificant relative to dye replenishment by flow. However, when a finger became stagnant, the signal intensity decreased. Seven wetting
non-wetting fluid pairs were selected with viscosity ratios ranging 4 orders of magnitude. Table 1 summarizes physical properties of the seven fluid pairs used in each displacement experiment. Viscosity was measured using a low shear falling ball viscometer (Gilmont 100), which was precalibrated with water. Interfacial tensions were measured by the pendant drop method using a drop shape analysis system (Kruss DSA 100). A total of five measurements were performed for each fluid pair, and average values were reported in Table 1. All measurements were carried out at room temperature (∼20 °C) and with dissolved Nile Red in both phases. 2.2. Micromodels and Experimental Setup. Micromodels were fabricated in silicon wafer using standard photolithography and inductively coupled plasma
deep reactive ion etching (ICP
DRIE) techniques. Details of the microfabrication process can be found in, among others, the studies by Chomsurin and Werth19 and Willingham et al.9 The micromodel used in this study consists of one inlet channel, connected to a pore network (30  15 mm; length  width), and one outlet channel (Figure 1). The pore network contains a uniform distribution of cylindrical posts 300 μm in diameter, with 180 μm pore bodies, 40 μm pore throats, and a porosity of 0.39. The average depth of the etched pore network is ∼53 μm (measured by a profilometer), with a variation of (1 μm because of the non-uniformity (3%) associated with the plasma-etching technique. To render the silicon surface hydrophilic, the fabricated micromodels were heated to 1100 °C under oxygen for 1 h to grow a thin oxide layer (∼0.1 μm).

Finally, a cover sheet of Pyrex glass was anodically bonded to the etched silicon micromodel to seal the flow channels. Prior to each experiment, the micromodel was first flushed with CO2 gas to facilitate subsequent saturation by the wetting fluid, followed by a sufficient amount of degassed wetting fluid. Non-wetting fluid was introduced through the inlet using a Harvard syringe pump at a volumetric flow rate (q), which was sequentially increased from 5 to 7500 μL/h, corresponding to Darcy velocity between 0.39 and 580.55 m/day. The corresponding maximum Reynolds number is less than 1 for all experiments. The outlet is open to the atmosphere. At each flow rate, the non-wetting fluid was allowed to displace wetting fluid until saturation of the non-wetting fluid reached quasi-steady state (i.e., the number of pixels occupied by the non-wetting fluid in the micromodel was constant over time). For each experiment, this stage occurred after greater than 10 pore volumes of non-wetting fluid were transported through the pore network. After each experiment, the micromodel was thoroughly cleaned using a rigorous cleaning procedure in the following order: isopropanol, deionized (DI) water, 2 M HCl solution, DI water, and a basic solution (DI water/NH4OH/H2O2 at 5:1:1). All displacement experiments were performed in the same micromodel with three replicates for each fluid pair, starting again at the lowest flow rate and sequentially increasing the flow rate, recording images, and measuring saturation at each step. The capillary numbers associated with each fluid pair for the different flow rates are listed in Table 2. It is worth noting that density and buoyancy effects were negligible in this study because of the horizontal 2D nature of the displacement process in the micromodel and the limited vertical depth of the micromodels.

2.3. Microscope Imaging and Quantitative Image Analysis. The micromodel was placed horizontally on an automated microscope stage (Prior Scientific Instrument), and all micromodel images were acquired with a Nikon Eclipse-2000TE (Nikon, Melville, NY) epifluorescent microscope using a 4 inverted objective at 3.23 μm spatial resolution. The microscope is equipped with a monochrome digital charge-coupled device (CCD) camera, both connected to a computer and controlled by NIS-Elements imaging software (Nikon, 3495

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Table 2. Summary of Log Ca Values as a Function of the Flow Rate q for Seven Fluid Pairs qa (μL/h) 5 wetting (w)

20

100

250

500

2500

5000

7500

log Ca

non-wetting (nw)

PEG200

HA


5.87


5.27


4.57


4.17


3.87


3.17


2.87


2.70

PEG200

DD


5.26


4.66


3.96


3.56


3.26


2.56


2.26


2.08

PEG200

HD


4.95

water

HA





4.35


3.65


3.25


2.95


2.25


1.95


1.78


5.91


5.21


4.81


4.51


3.81


3.51


3.33

water

DD


5.88


5.28


4.58


4.19


3.88


3.19


2.88


2.71

water

HD


5.52


4.92


4.22


3.82


3.52


2.82


2.52


2.35

water

MO


4.00


3.39


2.69


2.30


2.00


1.30


1.00




Additional experiments were conducted at flow rates that correspond to log Ca =
4.57 and
3.35 for all fluid pairs;
Indicates no experiments were performed. a

Figure 2. Selected images of the non-wetting phase (green) in the micromodel with PEG200 as the initial wetting phase (the flow direction of the displacing non-wetting fluid is from left to right). Melville, NY). Epifluorescent images of alkanes were obtained through a B-2E/C filter (λex = 485
495 nm, λem = 520 nm), and epifluorescent images of PEG200 were obtained through a TR-Cy3.5 filter (λex = 541
551 nm, λem = 610 nm). To form a single image that captured the entire pore network, a total of 160 (20  8) separate images were taken at the observed stage of the displacement process and were montaged. Montaged images of micromodels were analyzed using image segmentation and edge detection algorithms previously reported by Chomsurin and Werth19 and Baumann and Niessner26 to quantitatively evaluate the non-wetting fluid saturation (Snw) and interfacial area in the micromodel. The image intensity of non-wetting fluid containing Nile Red is much higher than that for the silicon posts and pore spaces filled with wetting fluid, with an average signal-to-noise ratio (the ratio of the

fluorescent intensity of pixels with non-wetting fluid to the intensity of pixels with wetting fluid or silicon) greater than 10. A threshold intensity value can be unambiguously determined for each image to distinguish pixels with non-wetting fluid from silicon posts and pore space filled with wetting fluid, and the area (i.e., number of pixels) and saturation corresponding to the non-wetting fluid can be determined, as well as the surface area of non-wetting fluid (i.e., perimeter), which is used as a measure for interfacial area. In selected experiments with PEG200 as the wetting phase, the filter cube was changed to selectively visualize the fluorescence emission from residual PEG200 in the micromodel after displacement. We validated the image segmentation method by comparing (i) the measured porosity from fluorescent images and computed from the micromodel design and (ii) the measured circumference of the silicon 3496

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Figure 3. Selected images of the non-wetting phase (green) in the micromodel with water as the initial wetting phase (the flow direction of the displacing non-wetting fluid is from left to right). posts and the design value. Both of the comparisons showed good agreement with errors 0 (except for water by HA) an increase in the capillary number resulted in newly developed flow paths that are connected to the initial finger and resulted in an increase in the flow path width (Figure 3). At the highest capillary number, especially at a high viscosity ratio (displacement of water by mineral oil), the final saturations are very high, as would be expected for stable or near-stable displacement of a less viscous fluid by a much more viscous fluid at a high flow rate.1 Figure 4 illustrates the observed displacement regimes (predominantly stable displacement, viscous fingering, and capillary fingering) for the experiments listed in Table 2, as plotted on a log M
log Ca stability phase diagram. The shape of the three regions was discussed in detail by Lenormand et al.1 The position of each of the region boundaries was derived using a simple force balance relating viscous to capillary forces. It was also explained that the location of the each of the region boundaries was systemdependent and had to be estimated by studying experimental and/or numerical results.1 The PEG200 displacement experiments, except for the ones conducted at the lowest Ca, primarily showed viscous fingering, where the principal force is due to the viscosity of the wetting fluid, leading to pressure drops across the length of this fluid in the pore network, and where the capillary effects and pressure drop in the alkanes are negligible. The finger growth is clearly toward the outlet, and no back loops are formed. Once formed, an alkane finger reaching into the more viscous PEG200 zone encounters a region of lower pressure and, hence, keeps moving forward. The PEG200 experiments at the lowest imposed Ca for each fluid pair also showed some features associated with capillary fingers (some spreading through the network and some back loops) to place these three experiments in the crossover zone. Several of the water displacement experiments at low Ca showed considerable capillary fingering to locate them into that region. In these displacements, the viscous forces and, hence, the pressure drops are small in both fluids and the principal force is related to strong capillarity. These fingers show spreading across considerable parts of the micromodel, and growth is seen in all directions, even backward toward the inlet. When capillary fingering occurs, some wetting fluid becomes entrapped because of the complex displacement patterns.2 Stable displacement was observed for several experiments where water was displaced by mineral oil and a few where HD was the nonwetting fluid. For these displacements, the principal force is due to the viscosity of the more viscous oils; i.e., the pressure drop occurs across the length of the viscous displacing fluid, and the capillary effects and pressure drop in the water are negligible. If a finger were to develop, the end of the finger would have a lower pressure than the main fluid front, and hence, the front would catch up; the displacement front can be regarded as “selfcorrecting”. In such cases, entrapment of wetting fluid is minor and in the order of a few pores.

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Figure 5. Non-wetting fluid saturation versus capillary number relations for (a) PEG200 and (b) water displacements. Error bars represent the standard deviation of three replicates for each fluid pair.

For reference, the plot also indicates the three regions of immiscible displacement as shown in the phase diagram by Lenormand et al.,1 which was developed on the basis of results of numerical displacement simulations and related experiments. In comparison to our experimental observations, each of their dominant regions was considerably smaller than the size of our regions. Consequently, the crossover zones from capillary fingering to viscous fingering, for systems where log M < 0, and from capillary fingering to stable displacement, for systems where log M < 0, were smaller in our experiments. The main reason for these differences was that, in our work, an almost homogeneous, isotropic micromodel was used, limiting the size of the zones where multiple displacement processes could coexist. Lenormand et al.1 used a micromodel with a considerable range in pore-throat size, resulting in larger zones where neither of the displacement processes would clearly dominate. Another apparent difference between the Lenormand et al.1 results and the experiments presented in this paper is the observed range in Ca. The combination of (1) using a relatively thick micromodel (∼1 mm), (2) the use of low-viscosity air as the injected fluid in some experiments, and (3) the use of mercury in other experiments (which provided high interfacial tensions with some of the oils) led to Ca values that were up to 3 orders of magnitude smaller in Lenormand et al.1 work than what could be achieved in our work. Because of the non-wetting fluid imaging method using dyes, we could not use air as a non-wetting fluid, while the use of mercury was not considered because of safety concerns. Despite the more 3498

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Figure 6. Images of non-wetting phase distribution (green) at two capillary numbers for displacement of PEG200.

Figure 7. Images of non-wetting phase distribution (green) at two capillary numbers for displacement of water.

limited range in Ca, clear evidence of capillary fingering and stable displacement regimes was obtained for the water displacements, while experiments could be conducted in the crossover zone for the log M < 0 displacement. In this context, one should be cautious in trying to extend the applicability of Ca beyond the system for which they are obtained. Although the numbers in this and other studies1,2,8 are computed using the same expression (see the Introduction), the pore geometry and topology of the various micromodels also have to be considered when Ca is related to the displacement behavior. For instance, if the same Ca was imposed on our micromodel and a similar micromodel with different post and pore-throat sizes, the dominant displacement mechanism (viscous versus capillary fingering and unstable versus stable displacement) would not necessarily be the same. Non-wetting fluid saturations in the pore network were determined through quantitative analysis of fluorescence images acquired from displacements at different flow rates. The observed quasi-steady state saturations of the non-wetting fluid (Snw) are plotted as a function of log Ca in Figure 5 for both the PEG200 and water displacements. When viscous and capillary fingering occurred at a low capillary number (i.e., log Ca <
4.6), the rate of increase in non-wetting fluid saturation (i.e., slope of the Snw
log Ca curve) is small for both the PEG200 and water displacements. The rate of increase is fairly constant for the PEG200 displacements (Figure 5a) with less viscous non-wetting fluids, because of the formation of additional viscous fingers with an increasing flow rate (Figure 2). As more viscous fingers are formed with an increasing flow rate, the micromodel fills up with these fingers and the saturation increases to a value close to 1. The same near linear increase in saturation of the non-wetting

fluid during drainage as a function of Ca was reported by Cottin et al.8 when dodecane was displaced with water in an oil-wet micromodel. For water displacements, the rate of increase is more variable. The greatest increase is observed between log Ca =
4.6 and
3.6 (Figure 5b), indicating a rapid transition from capillary fingering toward stable displacement, which is consistent with visual observations (Figure 3). The rate of increase in non-wetting fluid saturation is minimal at higher capillary numbers (log Ca >
3.6) for water displacement with more viscous non-wetting fluids. For the associated flow rates, the non-wetting fluid saturation is close to 1 in that region, suggesting that stable displacements have taken place and that only limited amounts of wetting fluids are still available for subsequent displacement. The variable rate in saturation increases for displacement of wetting fluid by more viscous nonwetting fluids was also demonstrated using a numerical model by Lenormand et al.1 Over a similar range in Ca as for our experiments, the shape of their curve looks similar to the experimentally determined Figure 5b. Additional experiments at two constant capillary numbers (log Ca =
4.57 and
3.35) were conducted for all seven immiscible fluid pairs in the same micromodel. Flow rates were adjusted for each fluid pair, because of the dependence of Ca upon both μnw and σnw, to obtain the constant capillary numbers. Images of the non-wetting fluid distribution in the pore network are shown in Figures 6 and 7 for PEG200 and water displacements, respectively, while Figure 8 shows the non-wetting fluid saturation as a function of the viscosity ratio. At log Ca =
4.57 (lower row of Figures 6 and 7), displacement is unstable for all fluid pairs, with viscous fingering dominating for all displacements of PEG200 and capillary fingering as the main displacement process for 3499

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Figure 8. Non-wetting fluid saturation versus viscosity ratio for all seven fluid pairs at two capillary numbers. Error bars represent the standard deviation of three replicates for each fluid pair.

Figure 10. Development of viscous fingering for HA (green) displacing PEG200 (left panels) and capillary fingering for HD (green) displacing water (right panels).

Figure 9. Fluorescent emission signal for Nile Red dissolved in HA and HD versus time.

displacements of water. For the same Ca, non-wetting fluid saturations during capillary fingering for water displacements are approximately 20% higher than when viscous fingering takes place during PEG200 displacement (Figure 8). At log Ca =
3.35, displacement of PEG200 is still in the viscous fingering regime, whereas displacement of water is approaching the stable regime, as was also indicated by the small increase in Snw shown in Figure 5. Non-wetting fluid saturations are again approximately 20% higher for water displacement than for PEG200 displacement for this Ca. The pore network modeling results shown by Lenormand et al.1 showed a similar rapid increase in saturation for log M values near 0. Their numerically obtained saturation range was larger because a log Ca value of 0 was used, which was not possible for our experimental conditions. Viscous and capillary fingering demonstrated different characteristics during the initial stages of the displacement, before quasi-steady-state conditions were obtained, which could be identified using the photosensitive properties of Nile Red. It was observed that its emission in the alkane phases decreases with extended light exposure with, for instance, a half-life of 120 s in HA and 30 s in HD. Examples of the fluorescence emission signal as a function of time are shown in Figure 9. To illustrate the

Figure 11. Fluorescence intensity of (a) viscous fingers (A
A0 transect in the left panels of Figure 10) and (b) capillary fingers (B
B0 transect in the right panels of Figure 10).

different characteristics during initial finger development, images of HA displacement of PEG200 and HD displacement of water at various pore volumes (PV) of injected non-wetting fluid are 3500

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Figure 12. Volume fractions of non-wetting fluid as mobile (active flowpaths) and immobile large and small blobs for PEG200 (left panels) and water (right panels) displacements.

shown in Figure 10. The non-wetting fluids for each displacement were injected at low but comparable flow rates, resulting in a log Ca =
5.27 for HA and log Ca =
5.52 for HD. Fluorescent signal intensity profiles corresponding to the A
A0 and B
B0 transects in Figure 10 are shown in Figure 11. As is shown in the bottom left panel of Figure 10, viscous fingers of HA initially developed from the top left corner. A second finger branched out from the first one after approximately 1 /10 of the pore network length and later split into two branches after reaching approximately 1/5 of the pore network length. The third finger through the middle of the pore network reached the outlet channel after 0.36 PV of HA was injected. Next, the first finger that originated near the top broke through after 0.91 PV, as can be seen in the middle left-hand panel of Figure 10. The second finger that started in the middle of the model terminated after approximately 2/3 of the pore network length. All three viscous fingers of HA were actively flowing during the early stages of the development (0.36 PV), as reflected by the uniform signal intensity across A
A0 . Over time, the second and third fingers became less mobile (0.91 PV) and nearly stagnant (1.52 PV), resulting a decrease in the signal (Figure 11a). For the upper

finger, the intensity increased to a constant value over time, indicating that this finger became the major fluid conduit for this particular displacement velocity. The capillary finger developing when HD displaced water did not initiate from a single point but from the top half of the micromodel (right panels of Figure 10). After 0.28 PV, the finger occupied approximately half of the pore network cross-sectional area and broke through into the outlet channel near the top boundary after 0.83 PV. After this breakthrough, the HD distribution remained largely unchanged, as can be seen by comparing the distributions after 0.83 and 1.21 PV. In contrast with what was observed for the PEG200 displacement by HA, the signal intensity for the capillary finger remained constant over time (Figure 11b), indicating the entire width of the finger as an active flowpath for the duration of the experiment. Because the capillary numbers for both sets of experiments shown in Figure 10 are fairly similar, the differences in intensity behavior are primarily related to the viscosity ratios. On the basis of image segmentation results, the non-wetting fluid distributions at quasi-steady state were classified into three groups: (i) mobile fraction of the non-wetting fluid that occupy active flowpaths (finger), (ii) immobile large blobs of 3501

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Figure 14. Specific interfacial length (cm
1) versus non-wetting fluid saturation. The data are fitted separately for the PEG200 and water displacement experiments.

Figure 13. Residual PEG200 in the micromodel during displacement of PEG200 by HD (log M =
0.94) at (a) log Ca =
2.95 and (b) log Ca =
1.95.

non-wetting fluid that occupy greater than five pore bodies, and (iii) immobile small blobs of non-wetting fluid that occupy less than five pore bodies. Such classifications may be important for better understanding of the efficiency of displacement in multiphase systems, such as oil production and supercritical CO2. Volume fractions for six fluid pairs are shown in Figure 12. For the PEG200 displacements, more than 90% of the non-wetting fluids are mobile at log Ca <
4 and the mobile fraction decreases to below 75% at log Ca >
4. The fraction of small blobs increased to 10
25%, with a small fraction (90%) of the non-wetting fluid occupied the active flowpaths, with a small fraction ( 0 except for water by HA) as the initial wetting fluids. The results were also consistent with experimental findings by Cottin et al.5 for displacement in an oil-wet micromodel. The experimental confirmation of the numerical results by Lenormand et al.1 indicates that the displacement physics implemented in their numerical model are probably correct. During the transient stages of the displacements, viscous and capillary fingering characteristics could be identified using the photosensitive properties of the Nile Red dye. At low flow rates

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and capillary numbers, each of the viscous fingers develop from a single point at the micromodel boundary and branch out into two or three other narrow viscous fingers at some distance from the inlet. Over time, only one of these fingers is able to continuously transport the non-wetting fluid across the micromodel to the outlet channel. At higher flow rates, many viscous fingers form and displace the majority of the wetting fluid. Capillary fingers typically initiate over a much larger part of the inlet boundary and grow inside the micromodel without obvious signs of photobleaching, indicating that, once pores are part of a capillary finger, they keep on conducting non-wetting fluids for the duration of the experiment. The use of Nile Red as a solvatochromic dye allowed for visualization of wetting fluid distributions when PEG200 was the wetting phase.20 Under quasi-steady-state conditions, the wetting phase is found to be present in pools that occupy multiple pore bodies, thin films surrounding the silicon posts, bridges between pore throats, and cones on the downgradient side of the posts. For both wetting fluids, the specific interfacial length between the immiscible fluids and non-wetting fluid saturation is linearly correlated for the entire imposed flow rate range. The slope for the PEG200 displacements is slightly higher (∼5%) than that for the water displacements, and this may be attributed to the formation of smaller blobs with a larger interfacial length during PEG200 displacements. The linear relationships between non-wetting fluid saturation and interfacial length in the 2D micromodels are consistent with experimental drainage results from a 1D column filled with a variety of porous media.30,35,39 Although the reported experiments were conducted at the pore scale, some of the results may be extrapolated to immiscible displacements at larger scales. For instance, displacement of brine by supercritical CO2 in the field typically occurs at low viscosity ratios with log M between approximately
1.6 and
0.7.40 It is possible that, under these conditions, non-uniform CO2 distributions develop as a result of unstable displacement, which may affect short-term trapping mechanisms as well as long-term mineral trapping. Likewise, enhanced oil recovery generally occurs over a wide range of viscosity ratios depending upon the fluid being used.41
44 Both viscous and capillary fingering could potentially impact the recovery efficiency under unfavorable conditions (i.e., low capillary numbers).

’ AUTHOR INFORMATION Corresponding Author

*Telephone: 1-509-371-6659. Fax: 1-509-371-6354. E-mail: [email protected].

’ ACKNOWLEDGMENT This research is supported by the Pacific Northwest National Laboratory (PNNL) Directed Research and Development Program under PNNL’s Carbon Sequestration Initiative. The experiments were conducted in the William R. Wiley Environmental Molecular Sciences Laboratory, a United States Department of Energy (DOE) scientific user facility operated for the DOE by PNNL. We thank Professor Charles J. Werth in the Department of Civil and Environmental Engineering, University of Illinois at Urbana
Champaign for his help with micromodel fabrication. ’ REFERENCES (1) Lenormand, R.; Touboul, E.; Zarcone, C. Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 1988, 189, 165–187. 3503

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