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Simulating use of foam in aquifer remediation
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Simulating use of foam in aquifer remediation C. K. Mamun a, J. G. Rong b, S. I. Kam a, H. M. Liljestrand b, and W. R. Rossen a aDepartment of Petroleum and Geosystems Engineering University of Texas at Austin, Austin, TX 78712-1061, U.S.A. bDepartment of Civil Engineering University of Texas at Austin, Austin, TX 78712-1076, U.S.A.
Foams, long studied in the petroleum industry, can enhance the efficiency of groundwater-remediation processes by diverting the flow of gases and remediation liquids to contaminant plumes. This report summarizes laboratory study of foam under conditions relevant to groundwater remediation and simulation of field applications based on parameters fit to laboratory data. 1. INTRODUCTION Foam, long studied for application in the petroleum industry. 1'2 can divert the flow of injected gas or liquid used in remediating contaminated aquifers, s In porous media foam is a dispersion of gas in a continuous liquid phase, with the bubbles thought to be at least as large as the pores. Foam does not directly alter the flow of liquid; that is, it does not change the water relative-permeability function krw(Sw). Foam does dramatically restrict the flow of gas, however, and by restricting the flow of gas drives down the water saturation Sw. In petroleum applications, foam appears to exist in one of two flow regimes, 4 depending on the flowing gas volume fraction fg, or "quality," of the injected fluids. Figure 1 shows an example from petroleum research. 4 At high foam quality (upper left portion of Figure 1), pressure gradient is independent of gas flow rate; at low foam quality (lower right), pressure gradient is independent of liquid flow rate. The existence of two regimes is important because they depend on different mechanisms and respond differently to changes in conditions. It appears that behavior at high foam .~uality is controlled by foam stability and foam collapse at a "limiting capillary pressure, .2 ' while at low quality bubble size is fixed and mobility is controlled by trapping and mobilization of bubbles. The transition foam quality fg* between regimes depends on surfactant formulation, the porous Figure 1. Pressure gradient in psi/ft as a function of gas (Ug) and liquid (Uw) volumetric fluxes for one foam formulation in Berea sandstone. 4 Upper-left portion represents highquality regime (Vp independent of Ug). Lower-right portion represents low-quality regime (Vp independent of Uw).
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868 medium, and other factors. 4 Alvarez et al. predict the effects of various factors on the two flow regimes and on fg*. Segregation of liquid and gas under gravity is a crucial problem for foam application in both petroleum and groundwater applications. A simple correlation for the distance foam travels before complete gravity segregation has worked remarkably well for continuous-foam-injection process in petroleum applications: 5 L
= VGR -
~ Aog ~ L - % ~ z
(1)
where Lg is the distance to the point of complete gravity segregation, L the length and H the height of the rectilinear porous medium, Vpf the pressure gradient in the foam bank at the injection well, Ap the density difference between liquid and gas, g gravitational acceleration, and kx and kz the permeabilities in the horizontal and vertical directions, respectively. The validity of Eq. 1 has been confirmed by computer simulation over a wide range of foam qualities, foam strengths, flow rates, reservoir geometries, and foam models, s Eq. 1 indicates that driving foam across long distances depends primarily on the pressure gradient, and, by implication, the rise in injection pressure, that can be tolerated. This conclusion is especially important for foam applications in the shallow subsurface, where pressure rise is severely limited. It may be possible to avoid this constraint by forming foam by alternate injection of liquid and gas instead of steady foam injection. 3'~ Eq. 1 has been tested only for geometries sealed above and below the injection interval, as in petroleum applications; its applicability to groundwater applications, with a large unconfined vadose zone above the aquifer, has not yet been tested. A separate, but related, finding from petroleum research is that even creating foam may require exceeding a minimum pressure gradient] Hydrocarbons are detrimental to foam stability in petroleum applications. 1'2 Halogenated hydrocarbons present in DNAPL's have much less effect on foam) Since hydrocarbons affect foam stability, which governs the high-quality regime, it seems likely that they would affect primarily the high-quality foam-flow regime, but this has not previously been confirmed. This study seeks to extend the technology of foam from petroleum to groundwater applications. First, we map the behavior of foam at high and low foam qualities (cf. Figure 1) with a variety of surfactant formulations and concentrations at the high permeabilities and low pressures typical of groundwater applications, in the presence and absence of hydrocarbon. Second, we examine the feasibility of foam generation at the low pressure gradients practical for groundwater applications. Third, using parameters derived from the steady-state data, we simulate foam application in generic field geometries. 2. STEADY-STATE FOAM BEHAVIOR 2.1 Experimental Apparatus, Materials and Method Five synthetic surfactants were used: anionics sodium dihexyl sulfosuccinate (Aerosol MA-80I), from CYTEC industries (Wayne, N3); disodium hexadecyldiphenyloxide disulfonate (Dowfax 8390), Dow Chemical Co. (Midland, MI); sodium ~-olefin sulfonate (Bio-Terge AS-40), from Stepan Co. (Northfield, IL); and a mixture of Poly(oxyethylene) lauryl ether and sodium laurel ether sulfate (STEOL CS-330), also from Stepan; and nonionic decyldimethyl phosphine oxide (Triton X-100), from Dow. Each was mixed with 1 wt% NaC1. Sand for sandpacks was obtained from U.S. Silica Company (Ottawa, IL). Figure 2 is a schematic of the apparatus. A sand-packed plastic column with diameter 3/8 in and two ft long is held vertically, with gas and liquid injected from the top. A bank of Validyne differential pressure transducers (model DP15, Validyne Engr. Corp., Northridge, CA) measure pressure drop across four sections of length 4, 8, 8, and 4 in., respectively. A Brooks Instruments (Hatfield, PA) model 5850E mass-flow-controller sets the nitrogen flow rate into the column. A Mity-Mite back pressure regulator (model s-
869 Mass flow controller
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.,,~ .r-, ff
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Oil p u m p
W a s t e liquid Figure 2. Schematic of experimental apparatus.
Table 1. Experimental conditions and results Surf. Permeaconc. bility Expt. Surf. (wt%) Sand (Darcy) MA-1 MA-2 MA-3 MA-4 MA-5*
Computer
MA-80I MA-80I MA-80I MA-80I MA-80I Bio-1 Bio-Terge Bio-2 AS-40 Tri-1 Triton xTri-2 100 Dow-1 Dowfax Dow-2 8390 * - In Experiment MA-5,
1 20/40 65 0.7 20/40 65 2 20/30 210 0.5 20/30 210 2 20/30 210 0.15 20/30 210 0.15 F-95 39 1 20/30 210 0.02 20/30 210 0.05 20/30 210 0.05 F95 39 22 vol.% decane is injected
fg* 0.76 0.65 0.89 0.71 0.77 0.90 0.62 0.80 0.57 0.83 0.48 along
Power-law exponents LowHighquality quality regime regime 0.39 0.59 0.24 0.20 0.24 1.32 0.78 1.29 0.24 0.59 O.28 0.53 0.74 0.32 0.24 0.81 1.86 0.68 0.44 0.71 2.57 with the liquid and gas.
91XW, Grove Valve and Regulation Co., Oakland, CA) placed at the outlet of the apparatus maintains a back-pressure of 100 psi on the entire system. A PC with a National Instruments Co. (Austin, TX) PNP-M16 data-acquisition card records the pressure data. Labview | software from National Instruments Co. coordinates the data-acquisition process. All experiments were conducted at room temperature. At the start, a vacuum pump evacuates the dry column for at least 2 hours. Then 1 wt% NaC1 brine is drawn into the column and porosity determined. Permeability is measured with the column horizontal, by measuring brine flow rate through the column between two reservoirs of known difference in height. The column is then filled with surfactant solution before introducing foam. Then gas and surfactant solution are injected at the pack back-pressure of 100 psi. In tests of the effect of oil, decane is injected with the surfactant and gas. Steady state is reached when the pressure drop holds constant for at least 8 pore volumes, and after at least 24 hours injection. Then liquid or gas flow rate is changed to obtain a new steady-state datum. This process is repeated many times to obtain each of the plots shown below. Foam qualities and gas flow rates depend on pressure. As foam raises the pressure drop across the column, the actual volumetric gas flow rate in the upstream sections of the pack is reduced by gas compression. The data here are corrected for this effect using the ideal-gas equation.
870
The contour plots shown below are created using Deltagraph 4 | software (Deltapoint Inc., Monterey, CA). Every dark point shown on the plot displays a steady-state datum. The software constructs linear contours between nearest-neighbor triplets of data: we do not attempt to smooth the data, to avoid possibly biasing the interpretation of data. 4 2.2 Results and Discussion of Steady-State Foam Experiments Table 1 and Figures 3 to 5 show the results of the experiments. The approximate value of fg* in each case is estimated from the slope of a line from the origin to the transition zone between regimes. The apparent power-law exponent in each regime is calculated by the method of Alvarez et al. 4 An exponent less than one indicates shear-thinning behavior; greater than one, shear-thickening behavior. The values of fg* and power-law exponents in Table 1 should be taken as approximate, not as individually quantitative. Figures 3 to 5, which illustrato some of the results, show both striking resemblance to Figure 1 and the ambiguity in determining these parameters from limited data. The contours are not perfectly vertical or horizontal, so there is some ambiguity in the value of Ug or Uw for a given Vp. The uncertainty in power-law exponents is greatest when the range in flow rates tested in the given regime is narrow. Figures 3a and 3b illustrate the effect of surfactant concentration. Alvarez e t al. 4 ,I,
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Figure 3a. Pressure gradient Vp (psi/ft) as function of flow rate (experiment MA-1).
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871
predict that reducing surfactant concentration should affect Vp in the high-quality regime but not in the low-quality regime. In this case Vp is reduced in both regimes, but more drastically in the high-quality regime. As a result, fg* decreases from about 0.76 to 0.65 when surfactant concentration increases. The effect of permeability on foam differs in the two regimes. 4 In the high-quality regime, Vp may decrease moderately or even increase as permeability increases. In the low-quality regime, Vp decreases as permeability increases. As a result, as illustrated in Figure 4 and Table 1, fg* decreases as permeability decreases. In Figure, 4 Vp in the highquality regime is nearly unaffected by the change in permeability. Oil can destabilize foam in porous media. Alvarez e t al. 4 predict that foam in highquality regime could be dramatically affected by oil, but less so the low-quality regime. Comparing the results from experiment MA-5 (Figure 5b) with MA-3 (Figure 5a), Vp decreases drastically in the high-quality regime and moderately in the low-quality regime. As a result, fg* decreases from 0.89 to 0.76 with 22 vol.% decane injected with the liquid and gas. These results show that the two foam-flow regimes found in petroleum applications are present also at the low pressures and high permeabilities of groundwater applications. The predictions of Alvarez e t al. 4 on the effect of permeability, surfactant concentration and oil are supported in large part if not exactly. These results agree with their finding that foam rheology is shear-thinning in low-quality regime. 3. FOAM GENERATION AT LOW PRESSURE GRADIENT It has been observed that foam generation requires exceeding a minimum pressure gradient, 7'8 and, if flow rates are fixed, Vp thereafter may jump to values too high for groundwater applications. Further experiments probed foam behavior at moderate, fixed Vp. The apparatus and procedure were similar to those above, except that liquid was injected at fixed flow rate and gas at fixed pressure drop, through a pressure regulator. A Brooks mass flow controller measured gas flow rate but did not control it. There was no back-pressure imposed across the core, because pressure drop across the core was relatively small. The packing of glass beads of diameter 100 ~tm has permeability of 30.4 Darcy and porosity 0.31. The pack holder is 0.89 in. in diameter and 1 ft in length. The liquid phase contained 3 wt% NaC1 and 0.01 wt% CaC12 plus surfactant. There was no foam generator upstream of the pack. Figures 6 and 7 show experiments using Aerosol MA80I and STEOL CS-330 surfactants, respectively at different concentrations. There exist three different foam-
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872
generation regimes, which are distinct from the steady-state regimes discussed above. When pressure gradient is small gas flow rate increases with Vp, indicating coarse foam at insufficient Vp for foam generation. 7 When pressure gradient is large, gas flow rate again increases with Vp, suggesting strong foam; at the highest Vp, Vp becomes independent of gas flow rate as in the steady-state high-quality regime discussed above. In between these two regimes, there exists an unstable regime where gas flow rate decreases with increasing Vp. In this regime flow rates alternate in time between higher and lower values; the flow rates reported below are averages over these fluctuations. These findings are consistent with a wider body of work on foam generation for petroleum applications. 8 It is not clear yet how this process would play out in three dimensions in groundwater applications at low imposed Vp. 4. SIMULATION OF FOAM APPLICATIONS This simulation study demonstrates how one can fit the steady-state foam data from Section 2 into a foam simulator, and tests how Eq. 1 applies to unconfined aquifers overlain by a vadose zone. The simulator is not yet predictive, nor is this a test of optimal injection strategies for foam in groundwater remediation. Foam-generation mechanisms illustrated in Section 3 are not yet incorporated into the simulator, which assumes that steady-state strong foam (cf. Figure 1) is created wherever surfactant solution and gas are present, regardless of Vp. The optimal injection strategy for foam may involve injection of alternating slugs of gas and liquid at low pressures, and take advantage of foam generation mechanisms unique to heterogeneous deposits) This study assumes steady co-injection of gas and liquid and that steady-state foam rheology applies, and asks whether foam propagation at low Vp is feasible over distances corresponding to groundwater remediation. For simplicity, contaminant is excluded from this preliminary study. The foam simulator is described by Cheng et al. 9 Behavior in the high-quality regime is controlled by the water saturation at which foam collapses, Sw*. Behavior in the lowquality regime is controlled by R, a factor by which gas mobility is reduced, and c;, a power-law exponent that scales the value of R with gas velocity. The procedure for fitting these parameters is given by Cheng e t al. 9 Figure 8 illustrates the fit of this model to the data in Figure 3a. The model fits the shear-thinning behavior of the low-quality regime but imposes Newtonian rheology on the high-quality regime. The model behind Eq. 1 for gravity segregation assumes that foam is incompressible and Newtonian in whatever regime foam is present. Therefore we require a Newtonian version of the model foam for comparison with that equation. We take the value of R corresponding to 15 psi/ft and assume (y = 1 to extrapolate this behavior to other gas velocities; this gives Newtonian foam throughout the right-hand plot in Figure 8. We also assume that gas compressibility is zero. The reservoir is assumed to be rectangular; permeability is uniform throughout but the ratio of vertical to horizontal permeability (kx/kz) is 1:3. Porosity is 0.25. Foam is injected at constant flow rate and fg = 0.8 (80% quality) into a reservoir initially filled with brine (except for the vadose zone, if present). The length of the reservoir L (Eq. 1) is 70 ft.,
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Figure 8. Model fit to data in Figure 3a. Left: fit to data allowing for shear-thinning in the low-quality regime; Right: fit forcing foam to be Newtonian in the low-quality regime.
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Lateral Distance (ft)
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9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
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Figure 9. Sweep efficiency with q = 30 ft3/day; kx = 60 Darcy; VGR = 0.75. Top row of plots shows surfactant concentration, and bottom row gas saturation; first column, confined case at 2 pore volumes (PV) injection; middle column, confined case at 5 PV injection, or steady state; third column, unconfined case at 1.5 PV injection (steady state). Since pore volume for unconfined case is larger, the actual amount of foam injected is larger in third column than the middle column, but both are at steady state. Large white or black region in right-hand column is vadose zone. In all three cases, foam sweeps about 75% of the way across the aquifer before complete segregation, in excellent agreement with Eq. 1. Microemulsion Surfactant Concentration at 0.2 PVI
Microemulsion Surfactant Concentration at 0.5 PVI
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0.000
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Gas Saturation at 3.0 PVI
0
5
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
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Figure 10. Unconfined case with q = 50 ft3/day; kx = 60 Darcy; VGR = 1.26. Top row of plots shows surfactant concentration, bottom row gas saturation. First column is at 0.2 PV; middle column 0.5 PV, and third column 3 PV injection. Surfactant solution encroaches a little on the vadose zone as injection continues. Foam sweeps the entire aquifer, in agreement with Eq. 1. Confined case would give similar sweep efficiency (Eq. 1).
874 with well-to-well distance of 66.5 ft.; the height of the reservoir H is 30 ft. if the top of the reservoir is sealed. The reservoir thickness in the third dimension is 5 ft. Both injection and production wells are completed over the entire 30 ft. interval. In cases with a vadose zone, the aquifer is 50 ft thick, overlain by a vadose zone 100 ft. thick. As a result, the total pore volume of the unconfined case is five times that of the confined case. The injection and production wells are completed in the bottom 30 ft of the aquifer. In both cases the reservoir is sealed on right and left edges. In all cases the producer is maintained at 23 psi at the top of the producing interval, which is just above the hydrostatic pressure of the 20 ft. of aquifer above this point in the unconfined case. Communication between the vadose zone and the atmosphere is simulated by placing a 70-ft long horizontal well, maintained at 14.7 psia, at the top of the vadose zone. Figure 9 compares behavior in a confined and unconfined geometry with the same value of VGR and other parameters. Injected foam quality is 80%. In both cases foam sweeps 75% of the distance across the aquifer before complete gravity segregation, in excellent agreement with Eq. 1. In Figure 10, with VGR = 1.26, foam sweeps the entire aquifer, in agreement with Eq. 1, and even encroaches slightly on the vadose zone. The total well-to-well average pressure gradient in this case is 0.183 psi/ft, which is well below 1 psi/ft and therefore seems feasible for groundwater applications - if steady-state strong foam generation occurs at this low Vp, as discussed above. These very preliminary results suggest that Eq. 1 works well for aquifers overlain by vadose zones as well as oil reservoirs sealed at the top. 5. CONCLUSIONS 1. Stead~,-state data confirm that the two steady-state flow regimes identified by Alvarez et al. exist under conditions relevant to groundwater remediation. The low-quality regime is strongly shear-thinning, in agreement with Alvarez et al. Their predictions on the effects of surfactant concentration, permeability and effect of oil are followed roughly but not perfectly. 2. Foam generation at fixed, moderate Vp is complex. Foam exhibits a coarse or weak foam at low Vp, a strong foam at high Vp, and an unstable regime in between. It is not clear how this unstable regime would appear in 3D flow in the field. 3. Foam data in the two steady-state strong-foam flow regimes can be fitted to a foam simulator. Preliminary results suggest that Eq. 1, which describes gravity segregation in reservoirs sealed above and below, works well for aquifers overlain by a vadose zone. Foam propagation over distances of 70 ft is at an overall average Vp of well under 1 psi/ft. REFERENCES 1. L.L. Schramm, (ed.): Foams: Fundamentals and Applications in the Petroleum Industry, ACS Advances in Chemistry Series No. 242, Am. Chem. Soc., Washington, DC (1994). 2. W.R. Rossen, Foams in Enhanced Oil Recovery, in R. K. Prudhomme and S. Khan, eds., Foams: Theory, Measurements and Applications, Marcel Dekker, New York, 1996. 3. G.J. Hirasaki, et al., Proc. 1997 SPE Annual Technical Conference, San Antonio, TX. 4. J.M. Alvarez, et al., SPE J 3, 325 (Sept. 2001). 5. J.-X. Shi and W.R. Rossen, SPE Reserv. Eval. and Eng. 1, 148 (April 1998). 6. J.-X. Shi and W.R. Rossen, Proc. SPE IOR Symposium, Tulsa, OK, 1998. 7. W.R. Rossen and P.A. Gauglitz, AIChE J. 36, 1176 (1990). 8. P.A. Gauglitz, et al., Proc. SPE IOR Symp., Tulsa, OK, 2002. 9. L. Cheng, et al., Proc. SPE IOR Symp. Tulsa, OK, 2000.
Simulating use of foam in aquifer remediation C. K. Mamun a, J. G. Rong b, S. I. Kam a, H. M. Liljestrand b, and W. R. Rossen a aDepartment of Petroleum and Geosystems Engineering University of Texas at Austin, Austin, TX 78712-1061, U.S.A. bDepartment of Civil Engineering University of Texas at Austin, Austin, TX 78712-1076, U.S.A.
Foams, long studied in the petroleum industry, can enhance the efficiency of groundwater-remediation processes by diverting the flow of gases and remediation liquids to contaminant plumes. This report summarizes laboratory study of foam under conditions relevant to groundwater remediation and simulation of field applications based on parameters fit to laboratory data. 1. INTRODUCTION Foam, long studied for application in the petroleum industry. 1'2 can divert the flow of injected gas or liquid used in remediating contaminated aquifers, s In porous media foam is a dispersion of gas in a continuous liquid phase, with the bubbles thought to be at least as large as the pores. Foam does not directly alter the flow of liquid; that is, it does not change the water relative-permeability function krw(Sw). Foam does dramatically restrict the flow of gas, however, and by restricting the flow of gas drives down the water saturation Sw. In petroleum applications, foam appears to exist in one of two flow regimes, 4 depending on the flowing gas volume fraction fg, or "quality," of the injected fluids. Figure 1 shows an example from petroleum research. 4 At high foam quality (upper left portion of Figure 1), pressure gradient is independent of gas flow rate; at low foam quality (lower right), pressure gradient is independent of liquid flow rate. The existence of two regimes is important because they depend on different mechanisms and respond differently to changes in conditions. It appears that behavior at high foam .~uality is controlled by foam stability and foam collapse at a "limiting capillary pressure, .2 ' while at low quality bubble size is fixed and mobility is controlled by trapping and mobilization of bubbles. The transition foam quality fg* between regimes depends on surfactant formulation, the porous Figure 1. Pressure gradient in psi/ft as a function of gas (Ug) and liquid (Uw) volumetric fluxes for one foam formulation in Berea sandstone. 4 Upper-left portion represents highquality regime (Vp independent of Ug). Lower-right portion represents low-quality regime (Vp independent of Uw).
Ug [Wday] 5 4.5 4
i
,11~,
3.5 3
3r4-o0H \
2.6 2 1.5 1 0.5
J I LU : , - ,.,',....~ ~ ' x " " , ~ m ~. . ,I~3~4oo
~
_______--~---= s0o ~
,6oo-------
im'~dc2dO~'"~--"3oo"au--m
0
ols
4
~i+
~ uwtm.~
2s
868 medium, and other factors. 4 Alvarez et al. predict the effects of various factors on the two flow regimes and on fg*. Segregation of liquid and gas under gravity is a crucial problem for foam application in both petroleum and groundwater applications. A simple correlation for the distance foam travels before complete gravity segregation has worked remarkably well for continuous-foam-injection process in petroleum applications: 5 L
= VGR -
~ Aog ~ L - % ~ z
(1)
where Lg is the distance to the point of complete gravity segregation, L the length and H the height of the rectilinear porous medium, Vpf the pressure gradient in the foam bank at the injection well, Ap the density difference between liquid and gas, g gravitational acceleration, and kx and kz the permeabilities in the horizontal and vertical directions, respectively. The validity of Eq. 1 has been confirmed by computer simulation over a wide range of foam qualities, foam strengths, flow rates, reservoir geometries, and foam models, s Eq. 1 indicates that driving foam across long distances depends primarily on the pressure gradient, and, by implication, the rise in injection pressure, that can be tolerated. This conclusion is especially important for foam applications in the shallow subsurface, where pressure rise is severely limited. It may be possible to avoid this constraint by forming foam by alternate injection of liquid and gas instead of steady foam injection. 3'~ Eq. 1 has been tested only for geometries sealed above and below the injection interval, as in petroleum applications; its applicability to groundwater applications, with a large unconfined vadose zone above the aquifer, has not yet been tested. A separate, but related, finding from petroleum research is that even creating foam may require exceeding a minimum pressure gradient] Hydrocarbons are detrimental to foam stability in petroleum applications. 1'2 Halogenated hydrocarbons present in DNAPL's have much less effect on foam) Since hydrocarbons affect foam stability, which governs the high-quality regime, it seems likely that they would affect primarily the high-quality foam-flow regime, but this has not previously been confirmed. This study seeks to extend the technology of foam from petroleum to groundwater applications. First, we map the behavior of foam at high and low foam qualities (cf. Figure 1) with a variety of surfactant formulations and concentrations at the high permeabilities and low pressures typical of groundwater applications, in the presence and absence of hydrocarbon. Second, we examine the feasibility of foam generation at the low pressure gradients practical for groundwater applications. Third, using parameters derived from the steady-state data, we simulate foam application in generic field geometries. 2. STEADY-STATE FOAM BEHAVIOR 2.1 Experimental Apparatus, Materials and Method Five synthetic surfactants were used: anionics sodium dihexyl sulfosuccinate (Aerosol MA-80I), from CYTEC industries (Wayne, N3); disodium hexadecyldiphenyloxide disulfonate (Dowfax 8390), Dow Chemical Co. (Midland, MI); sodium ~-olefin sulfonate (Bio-Terge AS-40), from Stepan Co. (Northfield, IL); and a mixture of Poly(oxyethylene) lauryl ether and sodium laurel ether sulfate (STEOL CS-330), also from Stepan; and nonionic decyldimethyl phosphine oxide (Triton X-100), from Dow. Each was mixed with 1 wt% NaC1. Sand for sandpacks was obtained from U.S. Silica Company (Ottawa, IL). Figure 2 is a schematic of the apparatus. A sand-packed plastic column with diameter 3/8 in and two ft long is held vertically, with gas and liquid injected from the top. A bank of Validyne differential pressure transducers (model DP15, Validyne Engr. Corp., Northridge, CA) measure pressure drop across four sections of length 4, 8, 8, and 4 in., respectively. A Brooks Instruments (Hatfield, PA) model 5850E mass-flow-controller sets the nitrogen flow rate into the column. A Mity-Mite back pressure regulator (model s-
869 Mass flow controller
S1
Liq~fid p r o p
.,,~ .r-, ff
..~ Back pressure
Oil p u m p
W a s t e liquid Figure 2. Schematic of experimental apparatus.
Table 1. Experimental conditions and results Surf. Permeaconc. bility Expt. Surf. (wt%) Sand (Darcy) MA-1 MA-2 MA-3 MA-4 MA-5*
Computer
MA-80I MA-80I MA-80I MA-80I MA-80I Bio-1 Bio-Terge Bio-2 AS-40 Tri-1 Triton xTri-2 100 Dow-1 Dowfax Dow-2 8390 * - In Experiment MA-5,
1 20/40 65 0.7 20/40 65 2 20/30 210 0.5 20/30 210 2 20/30 210 0.15 20/30 210 0.15 F-95 39 1 20/30 210 0.02 20/30 210 0.05 20/30 210 0.05 F95 39 22 vol.% decane is injected
fg* 0.76 0.65 0.89 0.71 0.77 0.90 0.62 0.80 0.57 0.83 0.48 along
Power-law exponents LowHighquality quality regime regime 0.39 0.59 0.24 0.20 0.24 1.32 0.78 1.29 0.24 0.59 O.28 0.53 0.74 0.32 0.24 0.81 1.86 0.68 0.44 0.71 2.57 with the liquid and gas.
91XW, Grove Valve and Regulation Co., Oakland, CA) placed at the outlet of the apparatus maintains a back-pressure of 100 psi on the entire system. A PC with a National Instruments Co. (Austin, TX) PNP-M16 data-acquisition card records the pressure data. Labview | software from National Instruments Co. coordinates the data-acquisition process. All experiments were conducted at room temperature. At the start, a vacuum pump evacuates the dry column for at least 2 hours. Then 1 wt% NaC1 brine is drawn into the column and porosity determined. Permeability is measured with the column horizontal, by measuring brine flow rate through the column between two reservoirs of known difference in height. The column is then filled with surfactant solution before introducing foam. Then gas and surfactant solution are injected at the pack back-pressure of 100 psi. In tests of the effect of oil, decane is injected with the surfactant and gas. Steady state is reached when the pressure drop holds constant for at least 8 pore volumes, and after at least 24 hours injection. Then liquid or gas flow rate is changed to obtain a new steady-state datum. This process is repeated many times to obtain each of the plots shown below. Foam qualities and gas flow rates depend on pressure. As foam raises the pressure drop across the column, the actual volumetric gas flow rate in the upstream sections of the pack is reduced by gas compression. The data here are corrected for this effect using the ideal-gas equation.
870
The contour plots shown below are created using Deltagraph 4 | software (Deltapoint Inc., Monterey, CA). Every dark point shown on the plot displays a steady-state datum. The software constructs linear contours between nearest-neighbor triplets of data: we do not attempt to smooth the data, to avoid possibly biasing the interpretation of data. 4 2.2 Results and Discussion of Steady-State Foam Experiments Table 1 and Figures 3 to 5 show the results of the experiments. The approximate value of fg* in each case is estimated from the slope of a line from the origin to the transition zone between regimes. The apparent power-law exponent in each regime is calculated by the method of Alvarez et al. 4 An exponent less than one indicates shear-thinning behavior; greater than one, shear-thickening behavior. The values of fg* and power-law exponents in Table 1 should be taken as approximate, not as individually quantitative. Figures 3 to 5, which illustrato some of the results, show both striking resemblance to Figure 1 and the ambiguity in determining these parameters from limited data. The contours are not perfectly vertical or horizontal, so there is some ambiguity in the value of Ug or Uw for a given Vp. The uncertainty in power-law exponents is greatest when the range in flow rates tested in the given regime is narrow. Figures 3a and 3b illustrate the effect of surfactant concentration. Alvarez e t al. 4 ,I,
fg=~ :
70.00
0.TG
20--
!
~
~
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,ooo_
,.,22~'~/ ..~20.~il
" z,~hi 1 8
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~176176 oo 20'00 40~00 eo~oo 80'.00 10d.00120.00 5
10
15
20
25
30
Uw(l"o'd)
35
Figure 3b. Pressure gradient Vp as function of flow rate (experiment MA-2).
Uw(fi/d)
Figure 3a. Pressure gradient Vp (psi/ft) as function of flow rate (experiment MA-1).
35.0 30.0 -
24.0
2 2 . 0 -2 0 . 0 -18.0-16.0-"~---" 1 4 . 0 - ::~ 1 2 . 0 - 10.0-8.0-6.0-- I 4"%.0
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210
310 410 U w ('l'tt d)
510
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~176
o'5
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1'.5 270
Figure 4a. Result for experiment Bio-1 in 210-Darcy sand; f~* = 0.9.
2'5
a'o
35
Uw(ttld)
7.0
Figure 4b. Result for experiment Bio-2 in 39-Darcy sand; f~* = 0.62.
13'0.0-
120 01
t
100-01
~o.o /lllllLIIIitl~--Z~ = 45678
10
=
A
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~
tl
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~oo ,/,.
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o
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0 0
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10.0 15.0 2 0 . 0 2 5 . 0 3>6.0 3g.O 4 6 . 0 4 5 0 U w (~cl)
~176
51o
I
d.o
1 ~.0
2d.o
24.0
u w (l'Ud)
Figure 5a. Results for experiment MA-3, with no oil present.
30.0
Figure 5b Result in experiment MA-5, with 22 vol.% decane injected along with liquid and gas. Note change of scale.
871
predict that reducing surfactant concentration should affect Vp in the high-quality regime but not in the low-quality regime. In this case Vp is reduced in both regimes, but more drastically in the high-quality regime. As a result, fg* decreases from about 0.76 to 0.65 when surfactant concentration increases. The effect of permeability on foam differs in the two regimes. 4 In the high-quality regime, Vp may decrease moderately or even increase as permeability increases. In the low-quality regime, Vp decreases as permeability increases. As a result, as illustrated in Figure 4 and Table 1, fg* decreases as permeability decreases. In Figure, 4 Vp in the highquality regime is nearly unaffected by the change in permeability. Oil can destabilize foam in porous media. Alvarez e t al. 4 predict that foam in highquality regime could be dramatically affected by oil, but less so the low-quality regime. Comparing the results from experiment MA-5 (Figure 5b) with MA-3 (Figure 5a), Vp decreases drastically in the high-quality regime and moderately in the low-quality regime. As a result, fg* decreases from 0.89 to 0.76 with 22 vol.% decane injected with the liquid and gas. These results show that the two foam-flow regimes found in petroleum applications are present also at the low pressures and high permeabilities of groundwater applications. The predictions of Alvarez e t al. 4 on the effect of permeability, surfactant concentration and oil are supported in large part if not exactly. These results agree with their finding that foam rheology is shear-thinning in low-quality regime. 3. FOAM GENERATION AT LOW PRESSURE GRADIENT It has been observed that foam generation requires exceeding a minimum pressure gradient, 7'8 and, if flow rates are fixed, Vp thereafter may jump to values too high for groundwater applications. Further experiments probed foam behavior at moderate, fixed Vp. The apparatus and procedure were similar to those above, except that liquid was injected at fixed flow rate and gas at fixed pressure drop, through a pressure regulator. A Brooks mass flow controller measured gas flow rate but did not control it. There was no back-pressure imposed across the core, because pressure drop across the core was relatively small. The packing of glass beads of diameter 100 ~tm has permeability of 30.4 Darcy and porosity 0.31. The pack holder is 0.89 in. in diameter and 1 ft in length. The liquid phase contained 3 wt% NaC1 and 0.01 wt% CaC12 plus surfactant. There was no foam generator upstream of the pack. Figures 6 and 7 show experiments using Aerosol MA80I and STEOL CS-330 surfactants, respectively at different concentrations. There exist three different foam-
" ~
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•
I
1
-- 1.6 w t % o f MA 8011
~Uw=0.088
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I-
m/day
- A-
Uw=0.264
m/day
[
~,.---
~ .....
C o n c e n t r a t i o n of S T E O L = 0 . 7 w t % in both e x p e r i m e n t s
~.~r .L uw is kept 0.088 m/day " ~ L t h r o u g 2 throughout experiments Q.
"-'--''-~~ "
0
0
5
10
-'15
0
20
Ug, m/day
Figure 6. Foam generation experiments using two different concentrations of surfactant Aerosol MA 801 at fixed gas pressure and fixed liquid flow rate.
|
0
. . . . .
|
5
-
10 Ug,
"
. . . . . . .
15
20
m/day
Figure 7. Foam generation experiments using STEOL CS-330 at fixed gas pressure and two different fixed liquid flow rates.
872
generation regimes, which are distinct from the steady-state regimes discussed above. When pressure gradient is small gas flow rate increases with Vp, indicating coarse foam at insufficient Vp for foam generation. 7 When pressure gradient is large, gas flow rate again increases with Vp, suggesting strong foam; at the highest Vp, Vp becomes independent of gas flow rate as in the steady-state high-quality regime discussed above. In between these two regimes, there exists an unstable regime where gas flow rate decreases with increasing Vp. In this regime flow rates alternate in time between higher and lower values; the flow rates reported below are averages over these fluctuations. These findings are consistent with a wider body of work on foam generation for petroleum applications. 8 It is not clear yet how this process would play out in three dimensions in groundwater applications at low imposed Vp. 4. SIMULATION OF FOAM APPLICATIONS This simulation study demonstrates how one can fit the steady-state foam data from Section 2 into a foam simulator, and tests how Eq. 1 applies to unconfined aquifers overlain by a vadose zone. The simulator is not yet predictive, nor is this a test of optimal injection strategies for foam in groundwater remediation. Foam-generation mechanisms illustrated in Section 3 are not yet incorporated into the simulator, which assumes that steady-state strong foam (cf. Figure 1) is created wherever surfactant solution and gas are present, regardless of Vp. The optimal injection strategy for foam may involve injection of alternating slugs of gas and liquid at low pressures, and take advantage of foam generation mechanisms unique to heterogeneous deposits) This study assumes steady co-injection of gas and liquid and that steady-state foam rheology applies, and asks whether foam propagation at low Vp is feasible over distances corresponding to groundwater remediation. For simplicity, contaminant is excluded from this preliminary study. The foam simulator is described by Cheng et al. 9 Behavior in the high-quality regime is controlled by the water saturation at which foam collapses, Sw*. Behavior in the lowquality regime is controlled by R, a factor by which gas mobility is reduced, and c;, a power-law exponent that scales the value of R with gas velocity. The procedure for fitting these parameters is given by Cheng e t al. 9 Figure 8 illustrates the fit of this model to the data in Figure 3a. The model fits the shear-thinning behavior of the low-quality regime but imposes Newtonian rheology on the high-quality regime. The model behind Eq. 1 for gravity segregation assumes that foam is incompressible and Newtonian in whatever regime foam is present. Therefore we require a Newtonian version of the model foam for comparison with that equation. We take the value of R corresponding to 15 psi/ft and assume (y = 1 to extrapolate this behavior to other gas velocities; this gives Newtonian foam throughout the right-hand plot in Figure 8. We also assume that gas compressibility is zero. The reservoir is assumed to be rectangular; permeability is uniform throughout but the ratio of vertical to horizontal permeability (kx/kz) is 1:3. Porosity is 0.25. Foam is injected at constant flow rate and fg = 0.8 (80% quality) into a reservoir initially filled with brine (except for the vadose zone, if present). The length of the reservoir L (Eq. 1) is 70 ft.,
30 27 24 ._,21 ~12 9 6 3 0
-••
3~
Permeability:60Darcy [ I I / / •: 0"5333(shearthinning)
27 ,-, 24t 21 [ I ,~ 15
I I / ~
ff 120369
15 ~ . ~
I
/
Permeability:60D 1kO:l(Newt~ s ~
10psi/It
0 1 2 3 4 UwS"ft/d fi-'~ay) 7 8 9 10
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Uw(ft/day)
Figure 8. Model fit to data in Figure 3a. Left: fit to data allowing for shear-thinning in the low-quality regime; Right: fit forcing foam to be Newtonian in the low-quality regime.
873
0
0.000
0.005 0.010 0.015 Concentration Scale
5
Lateral Distance (ft)
Lateral Distance (ft)
0.000
0.020
Gas Saturation at 2.0 PVI
0.005 0.010 0.015 Concentration Scale
0.020
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.000
0 . 0 0 5 0.010 0.015 Concentration Scale
0.020
Gas Saturation at 5.0 PVI
,,, 0
5
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.2
0
5
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (It)
0.2
0.4 0.6 0.8 SaUn'ation Scale
0
5
0.4 0.6 0.8 Saturation Scale
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.000 0.200 0.400 0.600 0,800 Saturation Scale
Figure 9. Sweep efficiency with q = 30 ft3/day; kx = 60 Darcy; VGR = 0.75. Top row of plots shows surfactant concentration, and bottom row gas saturation; first column, confined case at 2 pore volumes (PV) injection; middle column, confined case at 5 PV injection, or steady state; third column, unconfined case at 1.5 PV injection (steady state). Since pore volume for unconfined case is larger, the actual amount of foam injected is larger in third column than the middle column, but both are at steady state. Large white or black region in right-hand column is vadose zone. In all three cases, foam sweeps about 75% of the way across the aquifer before complete segregation, in excellent agreement with Eq. 1. Microemulsion Surfactant Concentration at 0.2 PVI
Microemulsion Surfactant Concentration at 0.5 PVI
I I 1 0
5 0 ~ 5 9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance fit)
0.000
0 . 0 0 5 0.010 0.015 Concentration Scale
0
0.020
5
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.2
0.4 0.6 0.8 Saturation Scale
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance fit)
0.000
Gas Saturation at 0.2 PVI
0
5
0
5
0 . 0 0 5 0.010 0 .015 0.020 Concentration Scale
0,000
Gas Saturation at 0.5 PVI
0
5 9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.2
0.4 0.6 0.8 Saturation Scale
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance fit)
0.005 0.010 0.015 Concentration Scale
0.020
Gas Saturation at 3.0 PVI
0
5
9 14 19 23 28 33 37 42 47 51 56 61 65 70 Lateral Distance (ft)
0.20
0.40 0.60 0.80 Saturation Scale
Figure 10. Unconfined case with q = 50 ft3/day; kx = 60 Darcy; VGR = 1.26. Top row of plots shows surfactant concentration, bottom row gas saturation. First column is at 0.2 PV; middle column 0.5 PV, and third column 3 PV injection. Surfactant solution encroaches a little on the vadose zone as injection continues. Foam sweeps the entire aquifer, in agreement with Eq. 1. Confined case would give similar sweep efficiency (Eq. 1).
874 with well-to-well distance of 66.5 ft.; the height of the reservoir H is 30 ft. if the top of the reservoir is sealed. The reservoir thickness in the third dimension is 5 ft. Both injection and production wells are completed over the entire 30 ft. interval. In cases with a vadose zone, the aquifer is 50 ft thick, overlain by a vadose zone 100 ft. thick. As a result, the total pore volume of the unconfined case is five times that of the confined case. The injection and production wells are completed in the bottom 30 ft of the aquifer. In both cases the reservoir is sealed on right and left edges. In all cases the producer is maintained at 23 psi at the top of the producing interval, which is just above the hydrostatic pressure of the 20 ft. of aquifer above this point in the unconfined case. Communication between the vadose zone and the atmosphere is simulated by placing a 70-ft long horizontal well, maintained at 14.7 psia, at the top of the vadose zone. Figure 9 compares behavior in a confined and unconfined geometry with the same value of VGR and other parameters. Injected foam quality is 80%. In both cases foam sweeps 75% of the distance across the aquifer before complete gravity segregation, in excellent agreement with Eq. 1. In Figure 10, with VGR = 1.26, foam sweeps the entire aquifer, in agreement with Eq. 1, and even encroaches slightly on the vadose zone. The total well-to-well average pressure gradient in this case is 0.183 psi/ft, which is well below 1 psi/ft and therefore seems feasible for groundwater applications - if steady-state strong foam generation occurs at this low Vp, as discussed above. These very preliminary results suggest that Eq. 1 works well for aquifers overlain by vadose zones as well as oil reservoirs sealed at the top. 5. CONCLUSIONS 1. Stead~,-state data confirm that the two steady-state flow regimes identified by Alvarez et al. exist under conditions relevant to groundwater remediation. The low-quality regime is strongly shear-thinning, in agreement with Alvarez et al. Their predictions on the effects of surfactant concentration, permeability and effect of oil are followed roughly but not perfectly. 2. Foam generation at fixed, moderate Vp is complex. Foam exhibits a coarse or weak foam at low Vp, a strong foam at high Vp, and an unstable regime in between. It is not clear how this unstable regime would appear in 3D flow in the field. 3. Foam data in the two steady-state strong-foam flow regimes can be fitted to a foam simulator. Preliminary results suggest that Eq. 1, which describes gravity segregation in reservoirs sealed above and below, works well for aquifers overlain by a vadose zone. Foam propagation over distances of 70 ft is at an overall average Vp of well under 1 psi/ft. REFERENCES 1. L.L. Schramm, (ed.): Foams: Fundamentals and Applications in the Petroleum Industry, ACS Advances in Chemistry Series No. 242, Am. Chem. Soc., Washington, DC (1994). 2. W.R. Rossen, Foams in Enhanced Oil Recovery, in R. K. Prudhomme and S. Khan, eds., Foams: Theory, Measurements and Applications, Marcel Dekker, New York, 1996. 3. G.J. Hirasaki, et al., Proc. 1997 SPE Annual Technical Conference, San Antonio, TX. 4. J.M. Alvarez, et al., SPE J 3, 325 (Sept. 2001). 5. J.-X. Shi and W.R. Rossen, SPE Reserv. Eval. and Eng. 1, 148 (April 1998). 6. J.-X. Shi and W.R. Rossen, Proc. SPE IOR Symposium, Tulsa, OK, 1998. 7. W.R. Rossen and P.A. Gauglitz, AIChE J. 36, 1176 (1990). 8. P.A. Gauglitz, et al., Proc. SPE IOR Symp., Tulsa, OK, 2002. 9. L. Cheng, et al., Proc. SPE IOR Symp. Tulsa, OK, 2000.