Environ. Sci. Technol. 2000, 34, 4835-4841
Predictive and Diagnostic Simulation of In Situ Electrical Heating in Contaminated, Low-Permeability Soils C. R. CARRIGAN* AND J. J. NITAO Earth Sciences Division (L-204), Lawrence Livermore National Laboratory, Livermore, California 94550
By in situ heating, contaminants can be mobilized by vaporization, modified into a harmless chemical state, or entrapped by soil vitrification. However, effective heating may be difficult or impossible by depending solely upon conduction of heat externally applied to a contaminated target layer. Heating a layer internally by passing an electric current through it has been employed in several different in situ remediation field experiments. We present a threedimensional computer model of groundwater flow and transport in an electrically heated, partially saturated, porous regime. Simulations are used to show that the uniformity of heating can be enhanced by increasing the number of electrical phases employed in supplying current to the electrodes. However, a more serious concern for the fieldscale application of this internal heating method is the nonuniform heating of the target layer because of large heating-rate differences between the near-electrode region and the center of the array. Finally, for a dissolved solvent like TCE, we show that ohmic heating is exceptionally effective at clearing the layer by vapor-phase partitioning. Once expelled from the low-permeability layer, the solvent that is not already thermally destroyed by a pyrolytic reaction is available for extraction.
Introduction The injection of steam into the vadose zone followed by the extraction of steam plus condensate from the heated formation that results is one means of mobilizing and removing soil and groundwater contaminants such as volatile nonaqueous phase liquids (NAPLs) (1). This approach assumes that the targeted zone for remediation is highly permeable between the injection and extraction wells and that the contamination is accessible through high permeability pathways. If low permeability, clay layers, or lenses are also present and represent a source of trapped contamination, then the steam injection and extraction process may only partially clean a site by sweeping contamination just from the highest-permeability pathways. Steam injection can be expected to treat the smaller or thinner low permeability zones by the conduction of heat into them. However, larger or thicker zones will tend to remain contaminated. Steam injection may still adequately extract contaminants to meet water quality standards in the short term, but eventually leaching from the larger, unremediatiated, zones of low permeability will occur causing a gradual increase in levels * Corresponding author phone: (925)422-3941; fax: (925)423-1997; e-mail:
[email protected]. 10.1021/es001506k CCC: $19.00 Published on Web 10/07/2000
2000 American Chemical Society
of groundwater contamination. Electrical resistance heating of the soil and groundwater is one practical means of applying heat to zones of low permeability that are not accessible to steam and that are too large to be heated adequately by thermal conduction alone. Resistance heating of low permeability layers and lenses is intended to produce vaporization causing the enhanced mobility of the contaminant phase or, at the least, an increased partitioning of a liquid state contaminant into an already existent mobile air or gas phase. Further, the resulting higher pressure of the resistively heated low permeability zone will drive the vapor state contaminants into adjacent higher permeability regions that are accessible to extraction methods. In conjunction with the steam injection and vacuum extraction (2) or vacuum extraction alone (3), electrical resistance or ohmic heating has been successfully employed to heat regions of low permeability that are adjacent to steamswept regions of higher permeability. We have found that the application of multiphase, alternating current, resistive heating technology to complex hydrogeologic regimes along with the need to optimize the timing of ohmic heating, steam injection, and vapor-extraction operations requires the development and use of numerical models for both predictive and diagnostic analysis of an in situ treatment facility. To this end, we have developed a generalized numerical 3-D model of the in situ ohmic heating process that has been coupled to an existing 3-D simulator for nonisothermal porous flow and transport (NUFT (4)). The resulting program permits a full simulation of ohmic heat production and transport in a hydrologic medium of arbitrary complexity. In this paper we describe the mathematical basis for the ohmic heating module (OHM). We then employ the module both separately and coupled to the NUFT program to simulate several aspects of a multiphase a.c., ohmic heating, electrode array, and its interdependence with the hydrologic system. The modeling illustrates how electrical phasing of the electrode array can affect heating uniformity. With the coupled OHM-NUFT model, local heating on the scale of several electrode diameters is predicted to significantly affect the functionality of the technique unless the evolution of the thermohydrologic system is adequately considered in the design of the electrode array. Finally, we simulate the elimination of a solvent in a tight layer with the ohmic-heating approach. The Basic Ohmic Heating Model. Figure 1 illustrates the planview of a hypothetical electrode array involving six electrodes emplaced in a volume of electrically conducting material. An alternating current power supply energizes the electrodes. The currents supplied to each electrode are phaseshifted by a designated amount. Thus, a three-phase, sixelectrode system might consist of electrode pairs with each pair supplied by current that was 120° out of phase with an adjacent electrode pair. Electrodes in a six-phase, sixelectrode system might be phase shifted sequentially so that the electric potential at each electrode is shifted 60° relative to adjacent electrodes. This latter arrangement can be shown to yield the most uniform heating of the zone targeted for ohmic heating. The conservation of electric charge requires that
∇‚Jc ) Q
(1)
where Jc is the current density vector (A/m2), Q is the electric charge injected or extracted at a location per unit volume and per unit time, and ∇ is the gradient operator. In this application, the time derivative of the volumetric charge VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Three- and six-phase cabling schematic with planview illustrating relative locations of electrode wells in low permeability target layer. density has been set to zero in eq 1 since it is assumed that the time dependent variation of the driving electric field (typically 50-60 Hz) is slow enough for capacitive effects to be neglected (see ref 5 for a discussion of this and other assumptions). Ohm’s law relates the electric potential Φ needed to produce a current density J in a conducting medium to the electrical conductivity σ(x,y,z,T,S) of the medium
Jc ) -σ∇Φ
(2)
where the electrical conductivity is explicitly dependent on the spatial coordinates, temperature T, and soil saturation S for a prescribed set of groundwater and soil chemical properties influencing electrical conductivity. Combining eqs 1 and 2 yields
-∇‚σ∇Φ ) Q
(3)
energization (1/50-1/60 of a second) are exceedingly different. In our numerical model it would be highly impractical to track this long term implicit time dependence using timestep sizes limited by the explicit a.c. potential variation. To avoid this, we will eliminate the explicit time dependence by separating it out and analytically integrating over time to obtain power-cycle averages of the relevant quantities such as current density and ohmic heating rate. Thus, the separability of Φ and Q into spatial and temporal parts, i.e., Φ ) λ(x,y,z)f (t) and Q ) q(x,y,z)f (t), is an important assumption of our method for obtaining a practical timedependent solution. The obvious time dependence of the form sin(ωt + χ), where χ is a phase angle, is not separable because χ is dependent on the spatial coordinates in the porous medium for multiphase heating. (This becomes apparent in a multiphase arrangement like Figure 1 by recognizing that the effective phase angle in the porous medium at a point will be most strongly influenced by the nearest electrode. As a particular electrode is approached, the phase angle in the porous medium will approach the value for that electrode.) However, single-phase solutions are separable since χ is not dependent on the spatial coordinates if polarity reversals are modeled by absorbing the sign changes between electrodes into the spatial part of Φ. The superposition of two singlephase solutions of the ohmic heating problem is then used to obtain a multiphase solution for the ohmic heating, that is, Φ ) λ1 f (t) + λ2 f ′(t). The two, separate, single-phase solutions must satisfy two, separate, single-phase, electrodearray boundary conditions that, themselves, produce the specified multiphase, electrode array boundary condition when they are linearly superposed. Thus, we assume the existence of two single-phase solutions of eq 4 having the form
λ1 f (t) ) λ1(x,y,z) sinωt
(6)
λ2 f ′(t) ) λ2(x,y,z) sin(ωt + χ)
where the subscript p indicates quantities evaluated in the porous domain. In the electrode domain, Q is nonzero, and the electrical conductivity can be taken to be a constant in eq 3. Because the electrical conductivity σe is so much greater in the electrodes than in the surrounding porous domain, the gradient of potential in the electrode required to produce a given flux of charge, that is, electrical current, into the porous domain will be very small which implies that Φ does not significantly vary over the volume of the electrode. Thus, in the electrode domain
where χ is constant and the λ’s remain to be determined numerically. As stated, the single-phase boundary conditions for each of these solutions must superpose to yield the desired multiphase array boundary condition. Examples of two single-phase electrode arrays that sum to a desired boundary condition for a multiphase array are given in Table 1. These single-phase electrode arrays have been constructed by using vector addition with renormalization and by representing any phases 180° from a given value of χ in a single-phase solution as reverse polarizations. For example, consider the construction for electrode #3 of the three-phase/threeelectrode case of Table 1. In a three-phase electrical system, the potential of this electrode is represented by Vsin(ωt + ζ) where ζ ) 240°. To get this result, we must superpose two boundary conditions out of phase by χ ) 120°. We vectorially add λ1f (t) and λ2 f ′(t) to obtain an expression for the potential at ζ ) 60° (for χ ) 120° renormalization is unnecessary):
σe ) constant . σp
Vsin(ωt + 60°) ) Vsinωt + Vsin(ωt + 120°)
In the porous domain itself, no source or sink of electrical charge exists so that Q ) 0 and
-∇‚σp∇Φ ) 0
porous domain
(4)
(5)
(7)
Φe ) Φ(t) (spatially constant)
Changing the sign of a potential with a 60° phase angle is equivalent to an additional phase shift of 180°, that is
The electrodes specified by eq 5 and the electrically insulating boundary of the porous volume (σbndy ) 0) provide boundary conditions for the solution of eq 4 in the porous domain. Numerical Solution Technique. The solution for Φ is an explicit function of time since a.c. power is used to energize the electrodes. It is also an implicit function of time because the electrical conductivity will change with the temperature and saturation as the formation is heated. The time scales for heating the formation (hours to days) and for a.c.
Vsin(ωt + 240°) ) -Vsin(ωt + 60°)
(8)
Vsin(ωt + 240°) ) -Vsinωt - Vsin(ωt + 120°)
(9)
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so that
The conditions λ1f (t) and λ2f ′(t), as given by the terms on the right-hand side in eq 9, are readily orthogonalized as indicated in the footnote of Table 1.
TABLE 1. Electrode Boundary Conditions for Solution of Φ(x,y,z,t) in Porous Mediuma
phases - electr
1 phase - 2 electr
2 phase - 4 electr
3 phase - 3 electr
3 phase - 6 electr
6 phase - 6 electr
angle between f(t) and f ′(t)
χ ) 0°
χ ) 90°
χ ) 120°
χ ) 120°
χ ) 120°
constant phase electr bndy con (V ) const)
λ 1f ( t )
λ2f ′(t)
+Vsinωt -Vsinωt
0 0
λ 1f ( t )
λ2f ′(t)
λ 1f ( t )
λ2f ′(t)b
λ1f(t)
λ2f ′(t)b
λ 1f ( t )
λ2f ′(t)b
+Vsinωt +Vsinωt 0 0 -Vsinωt -Vsinωt
0 0 +Vsin(ωt+ χ) +Vsin(ωt+ χ) -Vsin(ωt+ χ) -Vsin(ωt+ χ)
+Vsinωt +Vsinωt 0 -Vsinωt -Vsinωt 0
0 +Vsin(ωt+ χ) +Vsin(ωt+ χ) 0 -Vsin(ωt+ χ) -Vsin(ωt+ χ)
electrodes 1 2 3 4 5 6
+Vsinωt 0 0 +Vcosωt -Vsinω 0 0 -Vcosωt
+Vsinωt 0 0 +Vsin(ωt+ χ) -Vsinωt -Vsin(ωt+ χ)
a [Φ(x,y,z,t) ) λ (x,y,z) f(t) + λ (x,y,z) f ′(t)]. b Rewriting λ f ′(t) with sin(ωt + χ) ) sinωt cosχ + cosωt sinχ and combining sines and cosines of 1 2 2 λ1f(t) and λ2f ′(t) orthogonalizes boundary conditions, e.g., orthogonalized values for electrode #3 in a three-phase/three-electrode configuration are λ1f(t) ) -V/2 sinωt and λ2f ′(t) ) -x3/2 cosωt.
FIGURE 2. OHM generated planviews of initial electrical heating distribution for 1, 3, and 6 electrical phases. The numbers are indicative of the power dissipation levels at the different locations in the planviews. Note how the area of uniform heating increases with the increasing number of electrical phases used to power the electrodes. An integrated finite difference or finite volume approach (6) is used to obtain the two spatial solutions of eq 4, λ1 and λ2, that satisfy the two distinct sets of single-phase-electrode boundary conditions given in Table 1. The matrices generated by the finite differencing are solved by a direct method or by an iterative method using either a Gauss-Seidel approach or a conjugate gradient scheme with preconditioning. Once the spatial component of the potential field solution has been obtained for each of the two sets of electrode boundary conditions, i.e., λ1 and λ2, the instantaneous power density may be calculated locally from the relationship
P ) σp E 2
(10)
where E ) -∇Φ where Φ ) λ1 f(t) + λ2 f ′(t). Averaging eq 10 over one power cycle yields the average dissipative heating power density at a location. It is this value that is substituted into the source term of the energy equation. The value of the electrical conductivity in the formation σp is treated as a function of temperature, saturation, electrolyte ionic conductivity, porosity, and the cation exchange capacity of the soil formation. The Waxman-Smits model (7), which incorporates these parameters, is used to calculate the electrical conductivity distribution at every time step. In our modeling, we find that it is the decreasing
saturation near electrodes that most influences the formation conductivity and that places the greatest limitations on the success of the ohmic heating method. We discuss this problem in a later section of the paper. The Ohmic Heating Module and Initial Heating Effects. Used independently, the module gives information on the initial distribution of heating rate produced by a given electrode arrangement in a porous medium with a given electrical conductivity distribution. Such calculations give an indication of the uniformity of heating in the target formation prior to any significant changes in the electrical conductivity caused by heating induced saturation or temperature changes. For the purposes of designing an electrode array, such modeling should only be considered as a lowestorder approximation to the distribution of dissipative heating. It is at this level of approximation that arguments for the increased heating uniformity by maximization of the number of electrical phases have their greatest significance. Indeed, single-, three-, and six-phase models of sixelectrode arrays in uniform media illustrate the advantages of increasing the number of phases that drive an electrode array. Figure 2 clearly demonstrates that the spatial uniformity of initial dissipation rates improves by increasing the number of electrical phases powering the electrodes sequentially. However, the dissipation rate “hot spots” that are evident VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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around all the electrodes, irrespective of the number of electrical phases employed, represent a very significant departure from heating uniformity that requires reduction or elimination as part of any effort to optimize the ohmicdissipation technique. Ultimately, such hot spots lead to dryout of the formation and become zones of high resistivity around electrodes that can electrically isolate one or more of them from the rest of the array. However, before dryout has progressed to a level that isolation occurs, local resistance increases around the electrodes may temporarily enhance dissipation rates contributing to heating-induced failure. Simply cooling the inside wall of the electrode casing with water poured downhole does not appear adequate either to cool or resaturate the heated and dried out soil in the nearelectrode region of the target formation owing to its assumed low permeability. Coupling of Ohmic Heating and Hydrologic Models. The OHM module was integrated into the NUFT program to permit simulation of the coupling between the electric, hydrologic, and thermal regimes. NUFT is an integrated finite difference simulator for numerically modeling the flow and transport of heat and chemical species in a porous medium where liquid water, vapor, and air may be simultaneously present. In NUFT, the requirement for mass balance of each component γ is satisfied by the equation
∂ ∂t
(∑
)
∑∇‚φ S (F ω V
φFRSRωγR + Fγs ) -
R
R
R
γ R R
+ J γR) -
R
∑λ φF S ω γ R
R R
γ R
- λγs Fγs +
R
∑q
γ R
(11)
R
in which FR is the mass density of the R-phase, SR is the saturation of the phase, λγR are optional decay coefficients, ωγR is the mass fraction of component γ existing in the phase, and φ is the porosity of the medium. Mass is transported by the pore velocity VR of each phase as well as by the diffusive fluxes, JγR, for each component in each phase. In addition nonzero source terms, qγR, for each component in each phase can be included. Equilibrium partitioning of each component between phases is assumed. Energy must also be conserved in a manner that takes into account the partitioning of a multiphase, multicomponent system. Local thermal equilibrium between fluid and solid phases is assumed. In our simulations, the energy distribution is governed by
∂ ∂t
[∑ R
]
φFRuRSR + (1 - φ)FscpT )
∑∑
-
γ
R
[∇‚φhγR SR(FRωγRVR + J γR)] + ∇‚KH∇T +
∑ ∑h γ
γ R
q γR + qH (12)
R
The change in total energy of the fluid at a point as expressed in terms of the thermal energy as given by the specific heat term, Fscp, multiplying the absolute temperature, T, and the internal energy, uR, of each phase, R, that is present equals the volumetric divergence of terms involving the partial mass specific enthalpy, hγR, multiplying the advective and diffusive mass fluxes for each component of each phase. Finally, there may be additional contributions from heat, hRγqR, carried by the mass source terms and the heat source term qΗ. The volumetric heat production calculated in the OHM module at each time step on an element-by-element basis gives the value of qΗ at each nodal point used in the energy eq 12 of the hydrologic model. The resulting temperature T and saturation SR of the flow is supplied to the ohmic heating 4838
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model on a per-time-step basis to permit updating of the conductivity and, hence, ohmic dissipation distribution. Advective fluxes are modeled by Darcy’s law
SRφVR ) -
KkrR(SR) ‚(∇pR + FRg∇z ) µR
(13)
where the volumetric flux, SRφVR, of each component is linearly related to the sum of the imposed phase pressure, pR, for each phase R and the hydrostatic pressure for each phase through the constant of proportionality consisting of the permeability, K, the relative permeability for each phase, krR, and the dynamic viscosity of each phase, µR. In addition the diffusive flux, J γR, for each component γ in each phase is accounted for through Fick’s law expressed in the form
J γR ) -FRτRD γR∇ωγR
(14)
in which the tortuosity factor for each phase is given by τR and the binary diffusion coefficient by D γR. For additional information on the implementation of eqs 11-14 into the NUFT hydrologic model, the reader is referred to the discussion by Nitao (4). Electrical Heating and Vapor-Phase Partitioning. Extensive 3-D simulations were carried out with a hexagonal planform of electrodes traversing a 6-m-thick low permeability (2.5 × 10-15 m2) zone that simulates the hydrologic response of a clay layer of the type targeted for remediation at a Lawrence Livermore National Laboratory site where volatile components of gasoline are known to reside (2). This low-permeability target layer is bounded on the top by a high-permeability, sandy layer (USZ) and on the bottom by another sandy layer (LSZ). The water table is taken to be at the interface between the target layer and the upper sandy layer. The radius of the hexagonal array is just over 3 m (20 ft. diameter) and is centered in a cylindrical numerical domain. Six-phase/400 V a.c. power is supplied to the hexagonal array which is similar to the voltage values employed in the Livermore experiments. The electrode wells are assumed to be cooled by circulating water in the well bore allowing a 60 °C temperature to be maintained. The water level in the porous-electrode wells is assumed to be maintained about 5 m above the water table so that a positive pressure exists on the coolant (1.5 bar or 1.5 × 105 Nt./m2). Figure 3a,b illustrates both a planview in the clay layer at mid-level and a cross section along a diameter of the array showing the temperature distribution at an intermediate time (2.5 days) after turning on the power. The regions of maximum heating in the clay layer are around the electrodes and also at the center of the array in the clay layer. From Figure 3b, it is apparent that most of the heating occurs in the clay layer since the electrodes are positioned at that level and the saturated clay tends to channel electric current owing to its higher electrical conductivity. Hot spots surrounding the electrodes have temperatures exceeding 200 °C and potentially can cause a premature shut down of heating owing to local desaturation interrupting the flow of current to the rest of the formation. Figure 3c,d illustrates the saturation field at 2.5 days into the heating period. Partially desaturated zones are apparent around the electrodes and at the center. At this time, the saturation level near the electrodes and at the center has fallen to about 0.65. However, much of the region within the electrodes remains nearly saturated. Initially as the formation heats, the accompanying increase in ionic conductivity more than offsets any decrease owing to desaturation. Eventually, though, the electrode current does reach a maximum and then begins a slow decrease as illustrated in Figure 4. This decrease results from the continuing desaturation within the clay layer which finally
FIGURE 3. (a) Planview of the temperature distribution in middle of the target clay layer occurring at 2.5 days following the start of heating assuming the application of 6 phase/400 V a.c. power. The diameter of the electrode array is approximately 6 m (20 feet). At just 2.5 days the highest temperatures already approach 200 °C (yellow to orange). (b) Cross section of the heated layer temperature field including two electrodes at opposite sides of the array. The electrodes are maintained at 60 °C by recirculation in the wells and therefore appear cooler (green). (c) Planview of the saturation field at 2.5 days. Near electrodes, the saturation is strongly decreased. If the vapor pressure cannot be maintained near the electrodes, boiling may ultimately lead to dryout and a loss of electrical conductivity. (d) Cross section of the saturation field. Electrodes are filled with slightly pressurized water so that they appear fully saturated. The vadose zone above is indicated by the green - orange fringe.
FIGURE 4. Electric current versus time for one of the electrode elements showing rapid increase as a result of the temperature dependence of ionic conductivity of the groundwater. Beyond 3 days of heating, the current starts to decrease slowly as the gradual saturation decrease increases the soil resistivity. increases layer resistivity faster than the rising temperature, through ionic conductivity, can decrease it. Figure 5a,b illustrates the temperature field in the layer 2 days following the snapshot given by Figure 3. The times (2.5 and 4.5 days)
selected for illustrating the temperature and saturation distributions are just before and after the maximum in electrical current is reached. By 4.5 days (Figure 5), most of the clay layer interior to the electrode array is now heated to a temperature exceeding 200 °C, and as Figure 5c,d shows, the saturation level in the layer has fallen below 0.5. It might be expected that the desaturation in the soil around the electrodes would continue to occur at a higher rate than in the rest of the target layer. However, Figure 5c,d shows that the saturation differences between the hotspots and interior actually appear to decrease with time. This slightly surprising result is explained by the progressive development of a large pressure gradient in the heated layer. Near the center, pressures grow progressively with heating while within the porous electrode wells maintained at temperature of 60 °C, the pressure is maintained at 1.5 bar. Vapor is driven outward from the center of the array toward the electrode wells. As the vapor flows toward the electrodes both the pressure and temperature fall off, but the decreasing temperature ultimately dominates and condensation of the vapor phase occurs. It is the condensation of the vapor being driven toward the porous electrodes that allows the nearby saturation levels to be maintained.
Discussion Vapor-phase partitioning of dissolved volatiles has been recognized as a potentially important part of the remediation process (8, 9). From our modeling, we find that electrical VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 5. (a) At 4.5 days, the temperature of the target zone is somewhat more uniform at around 200 °C. (b) Cross sectional view also indicates a reasonably uniform thermal environment between electrodes. (c) The saturation is now at about 50% in the interior of the array. (d) Cross section showing the decreased saturation within the target layer. The target zone is not dry with the high pressures in the clay preventing complete dryout. However, complete dry out is not required for expelling volatile solvents. heating is particularly effective for volatilizing contaminants such as TCE. The high pressure of the vapor phase, resulting from electrical heating of a low-permeability layer, drives the contaminant into adjacent, high-permeability layers. Figure 6 illustrates the distribution of liquid-phase contaminant, having an initial concentration of 1 × 10-6 in the clay layer, following only 72 h of heating. The region between the electrodes is virtually swept clean owing to vaporization caused by ohmic heating. There is significant evidence that the thermomechanical effect of high internal pressures promotes fractures or spalls in low-permeability materials, causing enhanced bulk permeability (10). Thus, less time and heating may be required to exhaust the contaminants from the layer than is indicated by our model. It is also apparent from Figure 6 that the contamination has been driven into the liquid-phase of the high-permeability zones both above and below the heated clay layer. This implies that ohmic heating should be considered in conjunction with a steam-injection and vacuum-extraction program that is aimed at removing contaminants from adjoining, highpermeability layers. Another mechanism for the elimination of TCE in a tight layer involves destroying it by a highly accelerated hydrous pyrolysis reaction. Knauss et al. (11) found large enhancements of the oxidation rate with heating leading to the rapid breakdown of TCE and the formation of CO2 and Cl- in systems with stoichiometrically sufficient amounts of O2. In the absence of dissolved oxygen, the oxidation reaction can still occur in conjunction with the reductive dissolution of minerals such as MnO2. Even if hydrous pyrolysis is prevented in a low-permeability, clay or silt layer, destruction is still possible as solvent vapor is expelled from the layer into the 4840
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FIGURE 6. For a solvent with the partitioning characteristics of TCE, ohmic heating is very effective at expelling contamination from the layer (initial concentration ) 1 × 10-6 mol/mol) after only 72 h of operation. It is probably not necessary for the layer to be heated to this extent to ensure pressure-driven expulsion of solvent since thermomechanical alteration resulting from steam production is expected to enhance permeability. In this respect, the heating times, temperatures, and pressures required to achieve vapor expulsion are upper limits. adjacent, heated, higher-permeability, more oxygen rich environments. Future simulations will investigate the roles
of peripheral heating and hydrous pyrolysis for destroying TCE that has been expelled from an ohmically heated layer into a surrounding higher permeability regime.
Acknowledgments We thank R. Aines, K. Knauss, R. Newmark, A. Tompson, J. Yow at LLNL, J. Holland of the USACE Waterways Experiment Station, M. Gilbertson of DOE-EM, and R. Hirsch of DOEER. Funding was provided by the Department of Energy, Office of Technology Development, Enviromental Management Science Program and a DOD-SERDP contract. Research performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-ENG-48.
(4) (5) (6) (7) (8)
(9) (10)
Literature Cited (1) Udell, K. S. In Subsurface Restoration; Ward, C. H., Cherry, J. A., Scalf, M. R., Eds.; Ann Arbor Press: Chelsea, MI, 1997; pp 251271. (2) Dynamic Underground Stripping Project: LLNL Gasoline Spill Demonstration Report; UCRL-ID-116964; Lawrence Livermore National Laboratory: Livermore, CA, 1994; Vol. 4, pp 6-50. (3) Peurrung, L. M.; Bergsman T. M.; Powell, T. D.; Roberts, J. S.; Schalla, R. In Physical, Chemical, and Thermal Technologies;
(11)
Wickramanayake, G. B., Hinchee, R. B., Eds.; Battelle Press: Columbus, OH, 1998; pp 63-68. Nitao, J. J. User’s Manual for the USNT Module of the NUFT Code, Version 2.0; UCRL-MA-130653; Lawrence Livermore National Laboratory: Livermore, CA, 1998. Lessor, D. L.; Eyler, L. L.; Lowery, P. S. Glastech. Ber. 1991, 64, 95. Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Taylor and Francis: London, U.K., 1980; 197 pages. Waxman, M. H.; Smits, L. J. M. Soc. Pet. Eng. J. (Trans. AIME) 1968, 243, 107-122. Heron, G.; Christensen, T. H.; Van Zutphen, M.; Enfield, C. G. In Physical, Chemical, and Thermal Technologies; Wickramanayake, G. B., Hinchee, R. B., Eds.; Battelle Press: Columbus, OH, 1998; pp 37-42. Udell, K. S.; Itamura, M. T. In Physical, Chemical, and Thermal Technologies; Wickramanayake, G. B., Hinchee, R. B., Eds.; Battelle Press: Columbus, OH, 1998; pp 57-62. Roberts, J.; Bonner, B. P.; Duba, A. Geothermal Resources Council Trans. 1999, 23, 35-39. Knauss, K. G.; Dibley, M. J.; Leif, R. N.; Mew, D. A.; Aines, R. D.; Appl. Geochem. 1999, 14, 531.
Received for review July 20, 2000. Revised manuscript received August 8, 2000. Accepted August 9, 2000. ES001506K
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