Environ. Sci. Technol. 1996, 30, 1328-1335
Influence of Viscous and Buoyancy Forces on the Mobilization of Residual Tetrachloroethylene during Surfactant Flushing K U R T D . P E N N E L L , * ,† GARY A. POPE,‡ AND LINDA M. ABRIOLA§ School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, Department of Petroleum Engineering, University of Texas at Austin, Austin, Texas 78712, and Department of Civil and Environmental Engineering, The University of Michigan, Ann Arbor, Michigan 48109
The potential for nonaqueous phase liquid (NAPL) mobilization is one of the most important considerations in the development and implementation of surfactantbased remediation technologies. Column experiments were performed to investigate the onset and extent of tetrachloroethylene (PCE) mobilization during surfactant flushing. To induce mobilization, the interfacial tension between residual PCE and the aqueous phase was reduced from 47.8 to 0.09 dyn/ cm by flushing with different surfactant solutions. The resulting PCE desaturation curves are expressed in terms of a total trapping number (NT), which relates viscous and buoyancy forces to the capillary forces acting to retain organic liquids within a porous medium. The critical value of NT required to initiate PCE mobilization fell within the range of 2 × 10-5 to 5 × 10-5, while complete displacement of PCE was observed as NT approached 1 × 10-3. The interplay of viscous and buoyancy forces during PCE mobilization is illustrated in horizontal column experiments, in which angled banks of PCE were displaced through the columns. These results demonstrate the potential contribution of buoyancy forces to PCE mobilization and provide a novel approach for predicting NAPL displacement during surfactant flushing.
Introduction Organic solvents and other petroleum-based products frequently enter the subsurface as a separate organic phase or nonaqueous phase liquid (NAPL). As the NAPL migrates * Corresponding author telephone: 404-894-9365; Fax: 404-8948266; e-mail address:
[email protected]. † Georgia Institute of Technology. ‡ University of Texas at Austin. § The University of Michigan.
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through the subsurface, a portion of the organic liquid will be retained within soil pores as discrete globules or ganglia due to capillary forces. Under normal flow regimes, this residual NAPL phase is immobile and often represents a long-term source of aquifer contamination. It is now widely acknowledged that pump-and-treat remediation technologies are an ineffective and costly means of aquifer restoration when NAPLs are present (1). To overcome such limitations, surfactants have been proposed as a means for improving the performance of conventional pump-andtreat remediation technologies. This approach is based on the ability of surfactants to (a) increase the aqueous solubility of NAPLs via micellar solubilization and (b) mobilize or displace entrapped NAPL ganglia by lowering the interfacial tension between the organic and aqueous phases. Over the past several years, a number of research groups have demonstrated the capacity of surfactants to enhance the recovery of NAPLs from unconsolidated porous media (2-4). Although mobilization has been shown to be a far more efficient method than micellar solubilization for removing entrapped NAPLs from soil columns (5), utilization of this approach in the field could lead to uncontrolled migration of the mobilized NAPL phase. This is of particular concern in the case of dense nonaqueous phase liquids (DNAPLs), which would tend to migrate downward through an aquifer formation due to gravitational forces. Although non-wetting phase entrapment and viscous displacement have received considerable attention in the enhanced oil recovery literature (e.g., refs 6-10), few studies have considered the potential impact of buoyancy forces on NAPL mobilization (11-13). In most treatments of this subject, buoyancy forces were either neglected or, more commonly the nonwetting and wetting phases were selected so that their respective densities were identical (13). The purpose of this study was to investigate the influence of viscous and buoyancy forces on the mobilization of residual tetrachloroethylene (PCE), a representative DNAPL, during surfactant flushing. Soil column experiments were performed to quantify the onset and extent of PCE mobilization in four size fractions of Ottawa sand. To achieve PCE mobilization, the interfacial tension (IFT) between the entrapped PCE and aqueous phase was reduced from 47.8 to 0.09 dyn/cm by injecting different surfactant solutions. By considering the forces acting on a single NAPL globule, a total trapping number (NT) was derived that relates viscous and buoyancy forces to the capillary forces acting to retain NAPLs within a porous medium. Experimentally determined desaturation curves are used to evaluate the utility of this approach for characterizing the mobilization of PCE during surfactant flushing. Soil column experiments were also conducted in a horizontal orientation to illustrate the interplay of viscous and buoyancy forces on the displacement of PCE in twodimensional domains.
Theoretical Development of the Total Trapping Number For water-wetting porous media, the conditions governing the mobilization of an entrapped NAPL can be evaluated by considering the forces acting on a single NAPL “globule”.
0013-936X/96/0930-1328$12.00/0
1996 American Chemical Society
PR - PA - Fog∆l sin R )
2βσow cos θ rn
(4a)
In vector notation, equation 4a can be expressed as:
-∇P‚lˆ∆l - Fogkˆ ‚lˆ∆l )
FIGURE 1. Schematic diagram of the pore entrapment model and corresponding coordinate system.
Figure 1 depicts a single pore within which a NAPL globule is entrapped as idealized by the pore snap-off model (14). The pore is oriented in a direction l, which makes an arbitrary angle, R, with the horizontal axis. Within this pore, pressure and gravity forces, which act to mobilize the globule, are balanced by capillary forces acting to retain the NAPL globule. Shear forces relevant to this system would be a function of the viscosity contrast between the aqueous and NAPL phases. It is customarily assumed, however, that shear forces do not play a substantial role in such systems (e.g., ref 13), and these will be neglected herein. A balance of forces in the direction of the pore permits a quantitative assessment of the conditions under which globule mobilization can occur within that pore. The conditions under which mobilization forces balance retention forces are termed the critical conditions for mobilization. Summation of the pressure and gravity forces acting on the globule along the l direction yields
PR(πrb2) - PA(πrb2) - Fog(πrb2)∆l sin R
(
2σow
)
cos θA cos θR πrb2 rn rp
(2)
where σow is the interfacial tension between the organic liquid and water; θA and θR are the advancing and receding contact angles, respectively; rp is the radius of the pore body; and rn is the radius of the pore neck. This expression assumes that the globule has a uniform internal pressure. Assuming that the contact angles of the advancing and receding ends of the NAPL globule are similar, expression 2 may be rewritten as:
(4b)
Here ˆl and kˆ are the unit vectors in the l and z directions, respectively. The left-hand side of eq 4b can be reformulated directly in terms of the viscous and buoyancy forces. An alternative representation for the pressure gradient can be obtained from Darcy’s law:
qw ) -
kkrw (∇P + Fwgkˆ ) µw
(5)
where qw is the Darcy velocity of the aqueous phase, k is the intrinsic permeability of the porous medium, krw is the relative permeability to the aqueous phase, and µw is the dynamic viscosity of the aqueous phase. In eq 5, it has been assumed, for simplicity, that the medium is isotropic. Using eq 5 to express ∇P and substituting into eq 4b yields
µw∆l 2βσow cos θ qw‚lˆ + ∆Fgkˆ ‚lˆ∆l ) kkrw rn
(6)
Here ∆F ) Fw - Fo. Equation 6 may be rearranged as
qwl µw σow cos θ
+
∆Fgkkrw 2βkkrw sin R ) σow cos θ ∆lrn
(7a)
or
(1)
Here, PR is the pressure force on the receding side (foot) of the globule, PA is the pressure force on the advancing foot, ∆l is the average length of the globule, Fo is the density of the organic liquid, g is the gravity acceleration constant, πrb2 is the globule area normal to the vector l, and the globule volume, Vo, has been approximated as πrb2∆l. Under the critical conditions for mobilization, pressure and gravity forces will be balanced by the maximum net capillary pressure force the globule can sustain within the pore. This capillary pressure force can be approximated using Laplace’s equation (15):
2βσow cos θ rn
NCa + NB sin R )
2βkkrw ∆lrn
(7b)
where
NCa )
qwl µw σow cos θ
NB )
∆Fgkkrw σow cos θ
(7c)
Here, the capillary number (NCa) is defined in terms of the aqueous flow component in the direction of the pore. This dimensionless quantity relates viscous to capillary forces. The bond number (NB) represents the ratio of the buoyancy to capillary forces. Note that an alternative representation of eq 7b may be written as
N′Ca + N′B sin R )
2βk ∆lrn
(7b′)
where N′Ca and N′B are alternative capillary and bond numbers defined as
| |
∂Φ k ∂l 1 N′Ca ) N ) krw Ca σow cos θ
(3)
1 N ) krw B ∆Fgk (7c′) σow cos θ
The critical condition for mobilization can be found by equating expressions 1 and 3 and dividing through by πrb2:
Here Φ ) P + Fwgz, where z is the elevation. The alternative capillary number expression has been employed by Delshad et al. (16).
2βσow cos θ (πrb2) rn
where β ) 1 -
rn rb
N′B )
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The right-hand side of eq 7b or 7b′ is a function of porespace topography and globule size. Thus, this development suggests that a weighted sum of the bond and capillary numbers may be used to assess the potential for organic liquid mobilization in a pore. These equations also suggest that, for a vertically oriented pore, the dimensionless capillary and bond numbers are additive. Traditionally, the bond number has been derived in terms of the particle radius squared, a microscopic length scale (11, 17). When using this form of the bond number to describe vertical NAPL displacement, however, Morrow et al. (12) found it necessary to multiply the bond number by 0.001412 in order to directly sum the two dimensionless numbers. In contrast, the derivation presented herein yields a macroscopic representation of the bond number which incorporates effective permeability (L2) as the length scale. Thus, the bond and capillary numbers, eq 7c, are derived using the same length scale, which allows the dimensionless terms to be directly summed together without the need for an arbitrary correction factor. A further advantage of this approach is that the effective permeability can be readily measured or estimated, while alternative microscopic length scales such as globule radius (rb) are extremely difficult to determine even in laboratory experiments. The development given above is limited in that it considered only one pore, consisting of two pore throats oriented along a single line. In natural porous media, however, pores will generally be oriented in all directions and will have many throats. Thus, a more general formulation must be sought to assess the critical conditions for mobilization in a porous medium. The net force acting to displace an arbitrary NAPL globule will be the sum of the pressure and gravity forces. This net force per unit area may be represented in terms of its horizontal and vertical components as:
F ∂P ∂P ) - dbıˆ + - db - Fogdb kˆ A ∂x ∂z
(
)
(8)
where the globule diameter, db, is used as the characteristic globule “length” and ıˆ represents a unit vector in the horizontal (x) direction. In terms of the Darcy velocity components and assuming an isotropic medium, the net force expression 8 may be rewritten as
(
)
µw µw F qwxdbıˆ + q d + ∆Fgdb kˆ ) A kkrw kkrw wz b
(9)
Under the critical condition for mobilization, the magnitude of this force will be equal to the average capillary force acting to retain the organic liquid:
||
F ) A
db
x( )
2µw µw 2 [(qwx)2 + (qwx)2] + (∆Fg)2 + q ∆Fg ) kkrw kkrw wz 2σow cos θβ (10) rn
where β and rn are now representative of average pore characteristics of the medium. Eq 10 can be rewritten in terms of the capillary and bond number to yield an expression for a total trapping number (NT):
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NT ) xNCa2 + 2NCaNB sin R + NB2 )
2kkrwβ (11) rndb
Here, R is the angle the flow makes with the positive x axis (counter-clockwise), and NCa is the capillary number defined in terms of the magnitude of qw:
|qw| )
xq
2 wx
+ qwz2
(12)
Equation 11 may be compared to the single pore formulation presented in eq 7b. The right-hand side of this equation is a function of pore topography and globule size. Note that for the case of horizontal flow (R ) 0°), the expression for NT reduces to:
NT ) xNCa2 + NB2
(13)
and for vertical flow (R ) 90°), in the direction of the buoyancy force, the expression for NT becomes:
NT ) |NCa + NB|
(14)
Thus, examination of eq 11 reveals that buoyancy forces must be considered when evaluating the potential for NAPL mobilization, regardless of the flow direction. Also note that an alternative expression to eq 11 may be written in terms of the capillary and bond numbers defined in eq 7c′. In the remainder of this paper, results obtained from a series of column experiments are presented to assess the utility of the trapping number for describing the onset and extent of NAPL mobilization.
Experimental Methods Materials. Four size fractions of Ottawa sand (20-30, 6080, 100-120, and 40-270 mesh) were used as the solid phase in the column experiments. The 20-30 mesh and 40-270 mesh (F-95) size fractions of Ottawa sand were obtained from Fisher Scientific and U.S. Silica, respectively. The F-95 sand was then sieved to obtain 60-80 and 100120 mesh size fractions. Tetrachloroethylene (PCE) was used as the nonaqueous phase liquid and is representative of chlorinated solvents commonly found at NAPL-contaminated sites. Tetrachloroethylene is sparingly soluble in water (200 mg/L) and has a density of 1.63 g/cm3 at 20 °C (18). In several of the column experiments, PCE was colored with an organic soluble dye, Oil-red-o (Fisher Scientific), for visualization purposes. The presence of the dye at a concentration of 1 × 10-4 M had no discernible effect on the amount or rate of PCE mobilization during surfactant flushing. Three surfactant formulations were used in the column studies to obtain a range of interfacial tensions between PCE and the aqueous surfactant phase. The surfactant formulations consisted of polyoxyethylene (POE) (20) sorbitan monooleate (Witconol 2722, Witco Corp.), a 4:1 mixture of sodium dihexyl sulfosuccinate and sodium dioctyl sulfosuccinate (Aerosol MA/OT, American Cyanamid), and a 1:1 mixture of sodium diamyl sulfosuccinate and sodium dioctyl sulfosuccinate (Aerosol AY/OT, American Cyanamid). Relevant properties of the surfactant solutions are given in Table 1. All of the surfactants were used as received from the manufacturer, except for sodium dihexyl sulfosuccinate (Aerosol MA-80), which was distilled to remove water and ethanol prior to use. Aqueous surfactant solutions (4% wt) were prepared with deionized,
TABLE 1
Relevant Properties of Displacing Fluids Used in the PCE Mobilization Experiments IFTa (dyn/cm)
displacing fluid MilliQ water 4% Witconol 2722 4% 4:1 Aerosol MA/OT 4% 1:1 Aerosol AY/OT a Pennell et al. (5) at 22 °C. at 22 °C.
b
PCE solubility (mg/L)
47.8 5.0 (0.05)b 0.58 (0.004) 0.09 (0.003)
200c 34 100a 16 300d 71 720d
G (g/cm3) 1.005 (0.005) 1.009 (0.006) 1.027 (0.005)
Standard error of mean, measurements at 22 °C. c Gillham and Rao (18) at 20 °C.
distilled water that had passed through a Barnstead purification system. A background electrolyte, 500 mg/L CaCl2, was added to the sodium sulfosuccinate mixtures. Soil Column Procedures. Soil column experiments were conducted following the procedures described by Pennell et al. (5). The column apparatus consisted of a Kontes chromatography column made of borosilicate glass (4.8 cm i.d.) and a column adapter that allowed the bed length to be adjusted from 1 to 13 cm. The columns were packed under vibration with either 20-30, 60-80, 100-120, or 40270 mesh Ottawa sand. Prior to water saturation, the soil columns were purged with carbon dioxide to enhance dissolution of entrapped gas phase. Approximately 15 pore volumes of de-aired water were then pumped through the column using a Rainin HPLC pump equipped with a pulse damper and back-pressure regulator. The weight of the column was measured before and after water saturation to determine the bulk density, porosity, and pore volume of the soil column. Residual saturations of PCE were established in the initially water-saturated soil columns by injecting PCE liquid at a flow rate of 0.4 mL/min using a high-pressure syringe pump (Harvard Apparatus). Since PCE has a greater density than water, the neat liquid was introduced in an upflow mode to achieve stable displacement of water from the column. When approximately 70% of the pore volume was occupied by PCE, the flow was reversed, and 3 pore volumes of water was pumped through the column in a downflow mode to displace free product from the column. The resulting PCE saturation (So) was determined gravimetrically, based on the difference in the density of water and PCE (17). The intrinsic permeability (k) of the porous medium and effective permeability (ke ) kkrw) following PCE emplacement were determined using pressure transducers located at the column inlet and outlet. Following the establishment of residual PCE by water displacement, either Witconol 2722, Aerosol MA/OT, or Aerosol AY/OT was pumped through the soil columns as a single pulse injection. If no PCE mobilization was observed after flushing with the first surfactant solution, a second surfactant was injected into the soil column (e.g., Witconol 2722 followed by Aerosol AY/OT). To minimize the removal of the entrapped PCE by micellar solubilization, less than 2 pore volumes of each surfactant solution was injected into the soil columns. Column effluent was collected in glass vials, and the amount of PCE displaced as free product was determined volumetrically using test tubes graduated to 0.1 mL. When the Aerosol surfactant mixtures were injected into the finer-textured sands, macroemulsions were often observed in the column effluent. The macroemulsion appeared as a milky layer between the PCE liquid and the aqueous phase. These macroemulsions were broken by gravity settling or cen-
µ (cpi)
0.988e
d
0.955e 1.25 (0.05) 1.30 (0.06) 1.19 (0.04)
Jin (22) at 22 °C. e Weast (23)
trifugation prior to measuring the volume of PCE. The PCE saturation in the column was determined from the cumulative volume of PCE recovered in the column effluent and the change in column weight after flushing with each solution. The discrepancy between these two mass balance measures was typically less than 5%. This difference can be attributed to experimental error and micellar solubilization of PCE that occurred during the column experiment. In general, solubilization accounted for less than 2.5% of the mass removed from each soil column. All experiments were conducted at 22 ( 1 °C. Initially, the soil columns were oriented vertically, and the surfactant solutions were injected in a downflow mode. Desaturation curves were developed for each size fraction of Ottawa sand by plotting the measured PCE saturations against the total trapping number (NT). The different flow rates and IFTs employed in these experiments resulted in 6-12 unique data points along each PCE desaturation curve. In later experiments, soil columns were oriented horizontally to further study the interplay of viscous and buoyancy forces in a two-dimensional system. For these experiments, soil columns were rotated 90° after the entrapment of residual PCE using a vertical orientation. A 4% solution of Aerosol AY/OT was then pumped through the column at flow rates ranging from 1 to 5 mL/min. The amount of PCE displaced from the horizontal columns was determined volumetrically, and qualitative assessments of PCE profiles during surfactant flushing were obtained through the use of Oil-red-o dye.
Results and Discussion Vertical Displacement. The initial surfactant flushing experiments focused on the mobilization of PCE in vertically oriented columns packed with 20-30 mesh Ottawa sand. Prior to surfactant flushing, the residual saturation of PCE ranged from 11 to 14%. The entrapped PCE was observed as small droplets or globules uniformly distributed along the wall of the soil column (Figure 2a). Following the introduction of either water (IFT ) 47.8 dyn/cm) or a 4% solution of Witconol 2722 (IFT ) 5.0 dyn/cm), the distribution and saturation of PCE in the soil columns were essentially unchanged. Flushing with a 4% solution of Aerosol MA/OT (IFT ) 0.58 dyn/cm), however, resulted in the displacement of significant amounts of PCE (e.g., 4 and 6 mL) as a separate liquid phase. The corresponding PCE saturations for these experiments were approximately 5 and 3%, respectively. These data indicate that the critical condition required for the onset of PCE mobilization in 20-30 mesh Ottawa was exceeded at an IFT of 0.58 dyn/ cm and a Darcy velocity of 1.66 cm/h. When a 4% solution of Aerosol AY/OT (IFT ) 0.09 dyn/ cm) was injected into the soil column, a distinct bank of PCE liquid formed in front of the surfactant pulse (Figure
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FIGURE 2. Vertical mobilization of PCE in 20-30 mesh Ottawa sand after flushing with: (a) 1.5 pore volumes of water (b) 0.23 pore volumes, (c) 0.39 pore volumes, and (d) 0.59 pore volumes of 4% Aerosol AY/OT. Experimental conditions: L ) 11.5 cm; pore volume ) 71.4 mL; initial So ) 14.2%; k ) 1.6 × 10-7 cm2.
FIGURE 3. Cumulative volume of PCE displaced from 20-30 mesh Ottawa sand after flushing with a 4% solution of Aerosol AY/OT.
2b). As the experiment progressed, the bank of PCE continued to move downward through the soil column. Many of the mobilized PCE droplets migrated downward at a rate greater than the average velocity of the surfactant solution (Figure 2, panels c and d). As the droplets moved away from the surfactant front, the IFT between the organic liquid and aqueous phase increased, and the droplets were again entrapped within the soil pores. The bank of PCE also appeared to migrate past entrapped PCE droplets that had not yet been in contact with the surfactant solution. This redistribution process resulted in the displacement of PCE liquid from the column after only 0.63 pore volumes of Aerosol AY/OT had been injected. The volume of PCE recovered from the column is plotted in Figure 3 as a function of the pore volumes of surfactant solution injected.
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Here it can be seen that PCE appeared in the column effluent well before surfactant breakthrough, which is consistent with the displacement of free product in front of the surfactant pulse. The fact that mobilized PCE droplets moved downward through the soil column at a rate greater than the advective flow clearly demonstrates the need to account for gravitational forces in addition to viscous forces when assessing the extent of DNAPL mobilization during surfactant flushing. After injecting less than 1.5 pore volumes of the Aerosol AY/OT solution, approximately 95% of the residual PCE (6.5 mL) was displaced as a separate organic phase from the soil column as shown in Figure 3. These results indicate that middle-phase microemulsions and the corresponding ultra-low IFTs (
