Environ. Sci. Technol. 1999, 33, 2447-2455
Effects of Capillary Pressure and Use of Polymer Solutions on Dense, Non-Aqueous-Phase Liquid Retention and Mobilization in a Rough-Walled Fracture BETTINA L. LONGINO† AND BERNARD H. KUEPER* Department of Civil Engineering, Queen’s University, Kingston, Ontario, Canada K7L 3N6
In this laboratory study, perchloroethylene (PCE) was permitted to migrate through a horizontal rough-walled limestone fracture under controlled conditions to assess fracture retention capacity. Retention of immiscible-phase PCE in the absence of an applied wetting-phase hydraulic gradient varied between 11% and 26% of the fracture volume. A portion of this residual could be removed through water flooding; however, even at the maximum applied hydraulic gradient of 1.0, residual PCE remained in the fracture. The observed correlation of reduced residual saturation with capillary number (NC) demonstrated that this rough-walled fracture exhibited behavior similar to that of a porous medium under water-flooding conditions. For a given hydraulic gradient, polymer-enhanced floods (using xanthan gum) were not as successful as conventional water flooding at removing residual from the fracture. The traditional form of the capillary number became an increasingly poor predictor of mobilization behavior as the viscosity of the displacing phase was increased. Incorporation of (µW/µNW)-0.5 into the traditional capillary number provided a more appropriate dimensionless group with which to correlate residual PCE saturation in the fracture as µW increased.
Introduction Concern regarding groundwater contamination by dense, non-aqueous-phase liquids (DNAPLs) such as chlorinated solvents and PCB oils has been increasing in recent years. A DNAPL released in an unconsolidated medium will migrate until the entire release volume is immobilized both as discontinuous blobs and ganglia of organic liquid referred to as residual and as continuous distributions referred to as pools. While DNAPL saturations are higher within pools than within zones of residual, the volume of subsurface impacted by residual DNAPL generally far exceeds that impacted by pooled DNAPL. Residual saturations vary depending on the specific properties of the medium, the physical characteristics of the fluids present, and the in situ conditions that preceded residual formation. Thus, residual DNAPL saturations will vary widely, not only from site to site but also along a single migration pathway. * Corresponding author: phone: (613) 545-6834; fax: (613) 5452128; e-mail:
[email protected]. † Present address: Geomatrix Consultants, Oakland, CA. 10.1021/es980752h CCC: $18.00 Published on Web 06/11/1999
1999 American Chemical Society
Recent investigations have attempted to quantify the volume of NAPL residual that can be anticipated in porous media. In an extensive literature review, Mercer and Cohen (1) reported overall NAPL saturations in water-saturated, unconsolidated media that varied between 15% and 50% of the medium pore volume, with saturation increasing with increased aspect ratio and pore size heterogeneity. Similar results are reported in a comprehensive study presented by Wilson et al. (2). In one of the only reported field studies, Kueper et al. (3) measured residual perchloroethylene (PCE) saturations below the water table of 1-15% of pore space in an unconfined sand aquifer. Morrow and Songkran (4) and Chatzis et al. (5) both present discussions of residual NAPL formation from the petroleum industry perspective. Fractures at sites underlain by bedrock provide primary pathways for DNAPL movement in the subsurface (6, 7). Since matrix permeabilities in rock are typically quite low (8), DNAPL which enters a fracture network is often restricted to the open fractures and has the potential to migrate significant distances from the initial release location (9). DNAPL will tend to move vertically downward in response to gravitational forces but will flow laterally in a fracture network if fracture closure with depth prevents downward migration or if vertical pathways are unable to accept the total DNAPL flux (6, 10). Once formed, the ultimate fate of residual DNAPL in a fractured rock mass may be governed by matrix diffusion for the case of high DNAPL solubility and high matrix porosity (11). The amount of mass available to diffuse into the matrix is dictated primarily by the amount of residual formed during the initial migration. To the authors’ knowledge, a measure of the amount of NAPL residual retained in a natural rock fracture has never been published. These data are necessary to understand DNAPL distribution at sites underlain by fractured bedrock and to design appropriate, workable remediation strategies. The specific objective of this study was to assess the DNAPL retention capacity of a water-saturated, rough-walled fracture under the influence of a range of applied hydraulic gradients and the use of polymer solutions. Varying volumes of PCE were introduced to a fractured limestone sample under a number of capillary pressure conditions, and the PCE retention volume was measured. Investigation of retention capacity was followed by water and polymer floods under a series of applied hydraulic gradients designed to quantify the potential for residual mobilization using aqueous fluid injection. To minimize buoyancy forces, all experiments were performed with the fracture oriented horizontally. Results are presented in terms of capillary number curves relating mobilization behavior to a measure of the ratio of viscous to capillary forces existing during displacement.
Theoretical Development Immobilization of disconnected DNAPL blobs along the migration pathway in a rough-walled fracture results from capillary forces acting within the pore structure of the medium. The “blob” designation was introduced in the porous media literature to describe a residual non-wetting phase that occupies one or more pore bodies. Residual organic liquid trapped in a water-saturated medium is typically observed to be the non-wetting phase (3, 9, 12-15). Discussion of the non-wetting phase throughout this paper refers to the NAPL phase. NAPL-water interfacial tension results in a pressure difference across a curved NAPL-water interface referred to as the capillary pressure, defined as the difference between VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. x-y Cartesian coordinate system in a horizontal, variable aperture fracture plane. the non-wetting (PNW) and wetting (PW) fluid pressures:
PC ) PNW - PW
(1)
For a NAPL blob trapped in a variable aperture fracture where the local aperture is smaller than the radius of curvature of the blob in the plane of the fracture, the local entry pressure can be approximated by (10, 16):
PC )
2σ cos θ e
(2)
where θ is the wetting contact angle, σ is the interfacial tension between the NAPL and water phases, and e is the local parallel plate fracture aperture. The assumption that the local aperture is smaller than the radius of curvature of the blob in the plane of the fracture is justified by the fact that a fracture is a quasi-planar medium, much unlike a porous medium which is fully three-dimensional at the pore scale. The application of a hydraulic gradient creates a difference in capillary pressures across a NAPL blob situated in a roughwalled fracture:
∆PC ) 2σ
(
)
cos θr cos θa ed ei
(3)
where θr is the trailing contact angle, θa is the advancing contact angle, ed is the fracture aperture at the trailing end of the blob, and ei is the fracture aperture at the advancing end of the blob. To mobilize a residual blob trapped in a rough-walled fracture, the viscous and gravitational forces must exceed the resisting capillary force. For a horizontal fracture plane, the gravitational force component will be zero. Since capillary and viscous forces both act on blob area normal to the direction of movement, a force balance reduces to:
(
)
∆PW 2σ cos θr cos θa ) l ed ei l
(4)
where PW is the wetting-phase pressure and l is defined as the blob length in the direction of eventual movement. If ed and ei were known, the local pressure gradient required to mobilize a blob of given length, interfacial tension, and wetting characteristics could be calculated. However, local estimations of fracture aperture have traditionally eluded researchers due to the difficulty of measuring such quantities at the pore scale. This is especially true for natural fractures, where observation of pore scale dynamics is impossible without opening or casting the fracture, possibly altering the integrity of the natural fracture plane. Thus, more easily measured macroscopic scale parameters are often used for mathematical approximation of residual NAPL mobilization behavior. Figure 1 illustrates an x-y Cartesian coordinate system 2448
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in the plane of a horizontal, variable aperture fracture. A wetting-phase gradient (∇h) applied across the fracture plane makes an angle (β - ν) with the preferred mobilization direction m. Since the blob will move through the largest aperture openings in the anisotropic fracture plane, mobilization will not necessarily occur in the direction of -∇h. In an anisotropic medium, a functional relationship likely exists between medium hydraulic conductivity and mobilization direction. Knowledge of the anisotropic hydraulic conductivity tensor components and the direction of applied hydraulic gradient (ν) allows determination of the direction of wetting-phase flux. Whether this coincides with the direction of mobilization, m, is not clear. A hydraulic gradient imposed across the entire fracture plane (∇h) will result in a wetting-phase pressure drop across a trapped blob that can be approximated as:
∆PW ) FWg∇h cos(β - ν) l
(5)
where FW is the wetting-phase density and g is the acceleration due to gravity. Substituting in eq 4 and adopting the simplifying assumption that the advancing and trailing contact angles are the same give:
(
)
2σ cos θ 1 1 ) FWg∇h cos(β - ν) l ed ei
(6)
Substituting λ ) ei/ed, stable horizontal blob length can be expressed as:
l)
1 2σ cos θ 1λ edFWg∇h cos(β - ν)
(
)
(7)
The capillary number, NC, is a dimensionless parameter which represents a ratio of the viscous to capillary forces acting on the blob and can be written for the fracture of interest as:
NC )
kkrWFWg∇h cos (β - ν) σ cos θ
(8)
The terms k and krW represent intrinsic medium permeability and relative wetting-phase permeability, respectively. Substitution of NC in eq 7 gives:
l)
2kkrW 1 1NCed λ
(
)
(9)
Equation 9 demonstrates that stable horizontal blob length is inversely proportional to capillary number. Therefore, as the ratio of viscous to capillary forces in a medium increases, the length of blob that can become or remain trapped within the medium decreases. This relationship provides a basis for predicting the utility of water flooding as a remediation technology. If isotropic conditions exist within the fracture plane, β ) ν and eq 8 becomes:
NC )
kkrWFWg∇h σ cos θ
(10)
Darcy’s law can be used to relate the wetting-phase flux to the applied hydraulic gradient, resulting in a second form of eq 10:
NC )
µW q σ cos θ
(11)
where q is the Darcy flux and µW is the viscosity of the wetting phase. Note that the anisotropic form of eq 11 requires
TABLE 2. Physicochemical Properties of PCE property
value
density (FNW)a absolute viscosity (µNW)b aqueous solubility (Cs)c vapor pressure (p°)c partition coefficient to organic carbon (Koc)b PCE-water interfacial tension (dyed) (σ)d
1.62 g/cm3 (at 20 °C) 0.9 cP (at 25 °C) 150 mg/L (at 25 °C) 14 mmHg (at 20 °C) 364 mL/g 0.0279 N/m
a Reference 17. b Reference 18. c Reference 19. d Measured in the laboratory using a platinum ring tensiometer (ASTM D971) at 22 °C.
FIGURE 2. Schematic illustrations of the fractured rock sample.
TABLE 1. Rock Fracture and Matrix Properties property fracture length in the direction of flow (L) fracture width perpendicular to flow (w) sample thickness perpendicular to fracture plane (tf) projected fracture area (Af) fracture hydraulic aperture (eh)a estimated fracture volume (Vf)b matrix porosity (φ)c matrix fraction organic carbon (foc)d matrix dry bulk density (Fb)c
value 25.7 cm 30.8 cm 10.0 cm 792 cm2 374 µm 29.6 mL 1.9% 3.7% 2.65 g/cm3
a Calculated using results of constant-headwater permeability tests. Calculated as a product of projected fracture area and hydraulic aperture. c Measured by Core Laboratories using API RP40. d Measured by Core Laboratories using ASTM D2974. b
substitution of qi ) -Kij∇h into eq 8, where Kij represents the components of the anisotropic hydraulic conductivity tensor for the fracture. Even if these components were known, the functional relationship between hydraulic conductivity and blob mobilization direction (m) in an anisotropic fracture plane is unclear.
Materials A natural limestone sample obtained in the Kingston, Ontario, area was prepared in the laboratory by fracturing along a single existing plane of weakness using the uniaxial compression technique previously presented by Reitsma and Kueper (9). The rectangular block sample was wrapped in high-tension strapping prior to fracturing to ensure that the fracture remained aligned and did not open during the procedure. One pair of opposite sides was then sealed with plastic steel epoxy (Devcon), and glass end-plates were attached to the remaining two sides which intersected the fracture plane to facilitate fluid flow through the fracture (see Figure 2). Fracture and medium properties are presented in Table 1. Analytical grade PCE was used for this set of experiments. Fluid properties are listed in Table 2. PCE is a common groundwater contaminant due to its widespread use as a dry-cleaning fluid and metal degreaser. PCE was also selected for its low solubility in water, which minimized losses due to dissolution in the aqueous phase. Sudan IV (Fisher Scientific), a hydrophobic, non-volatile, non-partitioning red
dye, was added to the PCE at a concentration of 0.1 g/L to increase the visibility of PCE. To assess fracture wettability, droplets of PCE were placed on an open fracture surface, cut from the same matrix block as the fracture sample described above, and immersed in water. Visual observation over a period of several days confirmed that PCE was non-wetting with respect to water on the fracture walls. De-aired tap water was used for the water floods. Xanthan gum, a food grade biopolymer used extensively in enhanced oil recovery processes, was added to increase the aqueousphase viscosity for some runs. Laboratory testing verified that the aqueous-phase density and interfacial tension with PCE were not affected by the addition of polymer. Aqueous phase was exposed to PCE for a minimum of 24 h before use to minimize dissolution of residual PCE during aqueous flooding of the fracture. Pre-equilibration of the phases to limit mass transfer during mobilization experiments has been previously reported (20, 21).
Methodology The laboratory setup is illustrated in Figure 3. Both aqueous and NAPL phase flows through the fracture were controlled by constant-head reservoirs attached to the inlet and outlet end-plates. Approximately 1500 pore volumes of de-aired water (pre-equilibrated with PCE) were flowed through the fracture initially to ensure that the fracture was completely water-saturated and to allow dissolved phase PCE to diffuse into the matrix prior to the introduction of DNAPL. A carbon dioxide pre-flood was not used due to the potential for chemical reaction with the limestone matrix. Prior to the introduction of DNAPL to the fracture, a series of constant-head permeability tests were performed. A fracture hydraulic aperture (eh) of 374 µm was estimated from the data using the cubic law (22):
Q)-
eh3wFg (∇h) 12µ
(12)
where Q is the volumetric flow rate, w is the fracture width perpendicular to flow, F is the density of the flowing fluid, and ∇h is the hydraulic gradient. Although the hydraulic aperture determined from eq 12 represents the equivalent separation of two parallel plates required to produce the observed flow rate for the given pressure drop, it is acknowledged here that the fracture of interest is characterized by a spatially variable aperture distribution with local apertures likely ranging from near zero (closure points) to values significantly greater than eh. Residual PCE saturation was established in the initially water-saturated fracture under a prescribed initial capillary pressure condition along the inlet face (determined by the relative heights of the PCE inlet and water outlet reservoirs). PCE was allowed to flow through the fracture until a specified volume had accumulated in the outlet collection system. The inlet and outlet reservoir heights remained constant during emplacement, however they were varied between runs VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Schematic of laboratory setup. to generate emplacement capillary pressures ranging from 147 to 1957 Pa. The volume of PCE remaining in the fracture after flow was stopped (VPCE) was used to define the initial residual saturation, S*NWr:
S*NWr )
VPCE Vf
(13)
where Vf is the fracture volume as defined in Table 1. Initial residual saturation is often measured gravimetrically in porous media systems (4, 5, 23). This was not practical for this fracture sample, however, because of the large mass of the rock relative to the small mass of residual contained in the fracture. In this case, the cumulative amount of displaced non-wetting phase was collected throughout each experiment and measured volumetrically in order to calculate S*NWr. PCE exiting the fracture under each hydraulic gradient was collected in the outlet collection system (Figure 3) under a water head. Before moving to the next gradient, PCE was removed from the collection system and its volume determined gravimetrically. Measurement error in measured PCE volume was approximately (0.01 mL. The reader is referred to ref 24 for further details of the methodology. Following PCE emplacement, the system was allowed to equilibrate for a minimum of 1 h. During this period, the inlet and outlet ends of the sample were exposed to a constant head of water (resulting in no hydraulic gradient across the fracture). Water was therefore allowed to imbibe into the inlet and outlet ends of the sample, displacing PCE from the fracture plane. After establishing the initial saturation of PCE in this manner, the fracture was water-flooded at a series of hydraulic gradients (0.025, 0.05, 0.1, 0.5, and 1.0). PCE exiting the fracture under each hydraulic gradient was collected from the outlet end-plate and the volume measured. Reduced residual saturation is represented by SNWr, where SNWr is always less than S*NWr. Following the last aqueous flood for each series of applied gradients, approximately 15 pore volumes of 1-propanol were flowed through the fracture to remove any remaining PCE residual. Alcohol flooding to remove residual NAPL has been used by previous researchers (25, 26) without any cited effects on wettability in subsequent water floods. Sample analysis was performed on a Hewlett-Packard 5890 series II gas chromatograph equipped with a flame ionization detector 2450
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(FID) and a Porpak S column (Chromatographic Specialties). The fracture was reconditioned by water flooding until alcohol concentration in the effluent dropped below 50 ppm, well below the concentration at which the PCE-water interfacial tension was affected (27). Approximately 675 pore volumes of de-aired water (pre-equilibrated with PCE) were flowed through the fracture between experiments to ensure that the fracture was free of alcohol prior to beginning the subsequent run. The integrity of the fracture was verified by remeasuring the hydraulic aperture at the completion of each run. Xanthan gum polymer solutions were created by adding powdered polymer (Xanvis, Kelco Oil Field Group, Inc.) to 500-mL volumes of tap water already under agitation in a Hamilton Beach mixer. The mixer provided an adequate shear rate to disperse the polymer and prevent gel formation. Each 500-mL aliquot of solution was mixed for 5 min and filtered (Whatman #1). The aqueous solution was then de-aired under vacuum for 24 h and equilibrated with pure phase PCE for a further 24 h prior to use in the displacement experiments. No preservatives were added to the polymer solution. For the polymer runs, PCE was emplaced in an initially watersaturated fracture, which was then flooded with polymer solution at the same incremental hydraulic gradients as those used for the water floods.
Experimental Results and Discussion PCE was emplaced in the fracture under four initial capillary pressures and three approximate emplacement volumes. This experimental design ensured that comparisons could be made between runs in which the fracture was exposed to the same volume of NAPL during emplacement. Emplacement volume represents the volume of PCE that was allowed to flow through the fracture into the outlet collection system during the emplacement stage. The initial retention data (prior to application of a wetting-phase hydraulic gradient) are summarized in Table 3. Effect of Emplacement Capillary Pressure. During emplacement, PCE exited the fracture not as a continuous “sheet” of DNAPL but as individual droplets at specific points along the fracture face. The formation of droplets resulted from PCE encountering the water-filled end-plate; the existence of flow and no-flow areas along the exit face clearly indicated a heterogeneous distribution of flow paths within the fracture plane.
TABLE 3. PCE Retention Capacity of Horizontal Rough-Walled Fracture run F1-H1 F1-H2 F1-H3 F1-H4 F1-H5 F1-H6 F1-H7 F1-H8 F1-H9 F1-H10 F1-H11 F1-H12
emplacement PCE retained in fracture capillary emplacement pressure (Pa) volume (mL) VPCE (mL) S*NWr (% of PV) 1957 1957 1957 1957 979 979 979 489 489 489 147 147
400 400 850 1170 400 660 1080 450 750 1260 425 800
3.226 3.355 3.875 3.320 5.317 6.193 5.900 3.643 6.174 5.932 5.844 7.558
11.0 11.3 13.1 11.2 18.0 21.0 20.0 12.3 20.9 20.1 19.8 25.6
As emplacement capillary pressure was increased, nonwetting phase penetrated the fracture more quickly. At 147 Pa (runs F1-H11 and F1-H12), there was a 6-9-min lag between initiation of flow at the inlet fracture face and observation of PCE at the exit face, and the PCE flow rate throughout emplacement was approximately 6 mL/min. At 1957 Pa (runs F1-H1 through F1-H4), PCE was observed at the exit face almost immediately upon initiating flow, and the PCE flow rate was approximately 400 mL/min. PCE also exited the fracture face at more sites as emplacement pressure increased. Examination of the last column of data in Table 3 shows a general trend of increasing residual retention with decreased emplacement capillary pressure. At 1957 Pa, an average (runs F1-H1 through F1-H4) of 11.7% of the fracture pore volume contained residual PCE after emplacement, compared with an average (runs F1-H11 and F1-H12) of 22.7% at 147 Pa. This appears to be in sharp contrast with observations in porous media that a higher capillary pressure achieved during main drainage results in a larger non-wetting-phase residual saturation following imbibition of the wetting phase (3, 28). However, the currently observed behavior is likely a result of the existence of viscous forces during emplacement and can be explained using porous media observations. Experiments in porous media suggest that the average length of a trapped NAPL blob depends on the ratio of viscous to capillary forces during entrapment (29). Thus, for a given rate of non-wetting fluid flow, there will be a maximum residual blob size that can form. The length of the residual blob in the direction of flow cannot be greater than the length over which the pressure drop due to viscous force equals the capillary pressure, or trapping will not occur. This suggests that larger blobs will be trapped at smaller emplacement flow rates, resulting in larger residual volumes at lower emplacement capillary pressures. The observed relationship between retention capacity and emplacement capillary pressure may also be a result of NAPL pathway connectivity following emplacement. Since lower emplacement capillary pressures result in fewer connected NAPL pathways through the fracture, longer blobs may remain trapped following initial water imbibition. Overall, fracture retention capacity ranged between 11% and 26% of the estimated fracture volume for the 12 experiments. In comparison, residual DNAPL values reported for porous media have ranged from 1% to 40% of pore space in laboratory columns and within individual laminations in the field (1, 3). Thus, the DNAPL retention capacity for this rough-walled fracture falls within the range expected for a porous medium. Water Flood Mobilization Behavior. Evidence of flow channeling within the fracture plane was observed during water flooding, with mobilized PCE blobs repeatedly exiting
TABLE 4. Precision of Measurements parameter
precision
water flow volume (100-mL graduated cylinder) water flow volume (1000-mL graduated cylinder) time, t hydraulic head, h fracture sample length, L fracture sample width, w interfacial tension, σ PCE volume (gravimetric), V PCE volume (GC method), V
(0.5 mL (5 mL (0.5 s (0.5 mm (0.5 mm (0.5 mm (0.0005 N/m (0.01 mL (5%
from the same sites on the exit face. While the sites at which PCE exited the fracture varied for different applied gradients, they remained relatively consistent between runs at a given hydraulic gradient. In every run, some residual was mobilized from the fracture at the lowest applied hydraulic gradient (∇h ) 0.025). This generally corresponded to a capillary number of about 7 × 10-5. Residual mobilization continued as hydraulic gradient was increased; however, even at a hydraulic gradient of 1.0 some fraction of the initial residual remained in the fracture. Increasing the capillary number almost 2 orders of magnitude was insufficient to completely remove PCE residual from this fracture sample. Figure 4 presents the relationship between NC (defined using eq 11) and SNWr/S*NWr for each of the 12 experimental runs (referred to as capillary number curves). For all 12 runs, error in the reduced residual values was less than 8%, and error in the capillary number values was less than 9%. Table 4 presents measurement precision values for the parameters used to calculate reduced residual and capillary number values. Inspection of the capillary number curves indicates that they are beginning to flatten out as capillary number increases. This suggests that progressively less PCE mass may be mobilized at hydraulic gradients beyond 1.0, a finding consistent with a shift toward smaller blob sizes as capillary number increases. This behavior contrasts with some results that have been obtained for porous media where capillary number curves are shown to both decrease linearly with increased NC, and in other cases decrease with an inflection point as observed in the current study (4, 25). Comparison of the curves in Figure 4a indicates a shift to the right with increased emplacement pressure. At a given NC, a greater fraction of the initial residual is retained in the fracture when the PCE was emplaced under a higher capillary pressure. Comparing the replicate curves in Figure 4a with the curves at lower emplacement pressures suggests that the differences are more significant than inherent variability between experiments. This trend is consistent with the suggestion that larger blobs are formed under lower emplacement pressures. Large blobs are more easily mobilized by a given hydraulic gradient and should result in a lower SNWr/S*NWr. At higher PC, residual is also able to access smaller aperture areas in which higher capillary number conditions are required for mobilization. Figure 4b,c, however, suggests that this effect diminishes with higher emplacement volumes. The data for all of the water floods can be represented by the correlation band in Figure 5, which describes the range of retention and mobilization behavior of this natural roughwalled fracture. Comparison of this correlation with those presented previously for porous media (25) indicates retention characteristics for this fracture which fall between those for consolidated sandstone and packed glass beads. The apparent tailing of the fracture correlation at high capillary number suggests that some fraction of the fracture apertures are small enough to retain NAPL in the fracture until a capillary number of 10-2 or greater is reached. This behavior suggests a high variability in fracture aperture within VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Correlation of PCE mobilization behavior with emplacement volume: (a) 1000 mL of PCE emplaced.
FIGURE 5. Comparison of rough-walled fracture behavior with porous media correlations (*24). the fracture plane. This conclusion is supported by the overall shape of the fracture correlation in Figure 5 and by the fact that NC spans approximately 2 orders of magnitude. Polymer Flood Mobilization Behavior. An alcohol flood was required at the end of each run to completely remove PCE residual from the fracture. The persistence of trapped PCE blobs even after water flooding at a hydraulic gradient of 1.0 suggests that these trapped blobs were extremely small in size or that some areas of the fracture plane (at the microscopic scale) were not exposed to the higher gradients. In experiments with sandstone cores, Chatzis et al. (30) observed that, even at high capillary numbers, there were still a significant number of branched blobs trapped in the 2452
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porous medium: blobs that were obviously not exposed to the high water flood gradients. To investigate which of these mechanisms was responsible for the fraction of residual remaining in the fracture at high water gradients, xanthan gum (XG) polymer was added to the aqueous fluid. Polymers have been historically used to increase aqueous-phase viscosity in enhanced oil recovery applications (e.g., refs 31-33). Traditionally, they have been added to stabilize chemical and water floods that can exhibit viscous instabilities. The addition of polymer to an aqueous flooding phase increases the displacing fluid viscosity and can lead to more piston-like displacement of a viscous nonwetting phase (34, 35). In the current study, however, the residual displacement process was hydrodynamically stable. More recently, injection of increased viscosity flood solutions into heterogeneous media has been shown to result in cross-flow from high-permeability to low-permeability regions of the medium (36). The presence of polymer solution in a region of high relative aqueous-phase permeability decreases the conductivity of that zone, forcing fluid flow through regions of the medium previously poorly contacted by the displacing phase. Thus, polymers may have the potential to increase local flow in low-aperture areas of the fracture plane, resulting in improved residual removal. Previous investigations using XG suggest that the interaction of XG with the porous medium is low (32, 37). Estimates of adsorption for XG in water-wet sandstones and sand packs are typically below 30 µg/g of rock (38, 39). Molecules that do sorb have been described as doing so along their full length (40), resulting in an adsorbed layer of insignificant thickness. Literature values suggest a molecular length between 0.3 and 1.0 µm (40-42) and a diameter of about 4 nm (41). Thus, it is unlikely that the permeability of a relatively large aperture fracture (eh ) 374 µm) would be reduced significantly by any adsorption of XG molecules that does occur. Aqueous flow rates in the current study were nearly identical before and after polymer flooding, supporting the conclusion that adsorption of XG monomer to the fracture surface is minimal. Polymer solutions exhibit shear-thinning (non-Newtonian) behavior and retain strong pseudoplastic flow characteristics even at high shear rates (32, 43). The effects of salinity, temperature, shear rate, and mixing on the properties of polymer solutions are discussed by Unsal et al. (41). Since solution viscosity increases with polymer concentration, three aqueous concentrations were used for the current set of experiments (Table 5). The apparent viscosity of each solution was estimated using Darcy’s law and a measure of the polymer flow rate through the medium at each hydraulic gradient (Table 6). This method has been described in the literature by previous researchers (44-46). Displacing fluid viscosity does not affect the magnitude of the capillary forces trapping non-wetting-phase blobs in the medium (see eq 2), and inspection of eq 10 indicates that variation of displacing fluid viscosity should theoretically not affect capillary number. Therefore, any increase in residual removal at a given hydraulic gradient should be due to improved sweep by the displacing fluid and not to a difference in capillary number. Note that eq 10 was derived with the assumption that there is no momentum transfer between phases in a flowing two-fluid system. Inspection of Figure 6 shows SNWr/S*NWr increasing for a given capillary number as polymer concentration increases. At NC ) 3 × 10-4 (∇h ) 0.1), the water flood removed 44% of the initial residual, whereas the 600 mg/L polymer solution achieved less than 10% removal. As gradient increases, SNWr/S*NWr values become closer for a given capillary number. Overall, water flooding removed 92% of the initial PCE residual, and 600 mg/L polymer solution removed 77%. However, over 1000 pore volumes (PV) of water were used
TABLE 5. Polymer Run Conditions
run
polymer concentration (mg/L)
emplacement capillary pressure (Pa)
emplacement volume (ml)
PCE retained in fracture, S*NWr (% of PV)
volume of flood fluid (PV)
F1-P1 F1-P2 F1-P3
200 300 600
979 979 979
750 750 750
27.8 15.9 21.7
676 626 381
TABLE 6. Apparent Viscosity (cP) of Polymer Solutions (23-25 °C) polymer concentration in solution (mg/L) 200 300 600
hydraulic gradient
0
0.025 0.05 0.1 0.5 1.0
0.96 0.96 0.96 0.96 0.96
5.12 3.36 2.67 1.80 1.52
4.71 4.34 4.44 2.39 1.84
17.65 14.98 5.26 3.24
TABLE 7. Flow Time (s) for 1 PV of Solution (23-25 °C) hydraulic gradient 0.025 0.05 0.1 0.5 1.0
polymer concentration in solution (mg/L) 0 200 300 600 110 57 26 5 3
585 201 73 10 5
539 259 122 14 6
1056 410 30 10
FIGURE 6. PCE mobilization using a polymer solution flood. for the water flood, compared to only 381 PV of polymer solution for the chemical flood. Thus, the polymer flood was able to achieve 84% of the total water flood removal using only 38% of the fluid volume. Due to the increased viscosity of the polymer flood, however, 1 PV of polymer solution took significantly longer to flow through the fracture than did 1 PV of water, especially under low applied gradients (see Table 7). Thus, polymer flooding increased overall displacement efficiency, but it also significantly increased the flood duration necessary for mobilization of a given fraction of initial residual and the magnitude of hydraulic gradient required to do so. To ensure that removal at a given gradient was complete prior to moving to the next flood gradient, flow of polymer solution at each gradient used in the current study was continued for a significant time after PCE had stopped exiting the fracture face. At ∇h ) 0.1, for example, flow was maintained for at least 45 min after the last PCE droplets were observed. This time allowed flow through the fracture of an additional 6.5 PV of the 600 mg/L solution and more than 20 PV of the more dilute polymer solutions. Thus, it is unlikely that increased flow times would have led to increased removal of PCE for a given capillary number. The lack of increased PCE removal by polymer solutions over that by water flooding at a given NC indicates that there
FIGURE 7. Correlation of reduced residual saturation from polymer solution floods with a modified capillary number. was no increase in sweep efficiency as a result of polymer addition; the fracture plane was obviously equally well-swept by the water flood. The fact that PCE removal by the polymer solutions was actually less than that by the water flood under equivalent capillary numbers indicates that the addition of polymers affected some variable other than viscosity in eq 10 or that NC is not an appropriate indicator of mobilization behavior for displacing fluids containing polymer additives. The effect of viscosity on non-wetting-phase trapping and mobilization has been investigated in the porous media literature (e.g., refs 47-49). Morrow (49) observed that the product of displacing phase velocity and viscosity required for a given level of residual mobilization was a constant. Ng et al. (48) observed that the critical flood gradient necessary to mobilize a trapped residual blob varied inversely with the viscosity of the displacing fluid. Both concluded that capillary number was effectively able to represent mobilization under their viscosity conditions. Since polymer solutions behave as non-Newtonian fluids, inverse variation of viscosity with flow rate is an inherent characteristic of their flow. An increase in µW will be counteracted by a proportional decrease in q in eq 11, resulting in no net increase in NC. Abrams (47) investigated mobilization behavior in a number of core materials under varying viscosity ratios and observed residual trapping (S*NWr) to be more significant at lower µW/µNW ratios for a given value of the dimensionless group νµW/σ, where ν is the linear flood velocity. He suggested multiplying NC by (µW/µNW)n to obtain a more correct dimensionless group with which to correlate initial residual saturation, with n ) 0.4 giving the best fit to his data. Whether or not this value of n was appropriate for correlation with reduced residual saturation was not investigated. The inclusion of µNW in the capillary number correlation is physically based on the fact that the breakup and subsequent trapping of mobilized blobs are the result of necking and snap-off mechanisms, which are hydrodynamic processes dependent on the ratio of wetting-phase to non-wetting-phase viscosity. Figure 7 plots the data from the current study using Abrams’ modified capillary number with n ) -0.5 (arrived at by trial-and-error). The modified dimensionless group NC(µW/µNW)-0.5 provides excellent correlation between reduced residual values for the four runs. The results establish that mobilization of PCE residual from the medium is a function of the viscosity ratio between the displacing and displaced fluids and that a modified capillary number must be used in the case where µW/µNW differs from unity. In VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Abrams’ experiments, an exponent of n ) 0.4 described trapping behavior when a viscous, continuous oil phase (µNW ) 30 cP) was displaced by water (µW ≈ 1 cP), both Newtonian fluids. In that case, displacement was inherently unstable. Thus, as the ratio of µW/µNW approached unity, the viscosity difference between the two fluids decreased, displacement became more stable, and residual trapping (S*NWr) was reduced. In the current study, a hydrodynamically stable displacement is occurring. Thus, the best-fit exponent n ) -0.5 reflects a velocity effect on the mobilization of residual using polymer solutions, the influence of which increases as solution viscosity (µW) increases. Although four different viscosity ratios were examined in this study, it cannot be concluded on the basis of this study alone that n ) -0.5 is the most appropriate exponent for differing values of nonwetting-phase viscosity. The fact that a smaller fraction of trapped residual PCE is displaced from the fracture at a given capillary number as solution viscosity increases indicates that the effect of decreased solution velocity (or flow rate) outweighs any benefit from increased solution viscosity for this system. Thus, in addition to the traditional components of capillary number, the results suggest that flooding fluid viscosity will affect the magnitude of residual mobilization achievable through flooding a rough-walled fracture. Inclusion of a factor of (µW/µNW)-0.5 most appropriately accounts for viscosity effects in this fluid system. It should be cautioned, however, that best-fit n values may be fluid-dependent, especially for fluids which exhibit shear-thinning behavior, and experimental data will be required to determine n for a given system.
Acknowledgments Financial assistance for this work was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) through Strategic Grant No. 0181515, a postgraduate student scholarship, and a research grant. Financial assistance was also provided by the University Solvents-InGroundwater Consortium through contributions from Boeing, Ciba Specialty Chemicals, General Electric, ICI, Eastman Kodak, Motorola, PPG Industries, and United Technologies Corp. The financial assistance of Queen’s University is also acknowledged.
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Received for review July 22, 1998. Revised manuscript received April 15, 1999. Accepted April 19, 1999.
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