A reactor model for pulsed pumping groundwater remediation

ARTICLE IN PRESS Water Research 38 (2004) 3869–3880 www.elsevier.com/locate/watres A reactor model for pulsed pumping groundwater remediation C.M. Tenneya, C.M. Lastoskiea,, M.J. Dybasb a Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI 48824-1226, USA b Received 8 July 2003; received in revised form 28 May 2004; accepted 11 June 2004 Abstract A hybrid in situ bioremediation/pulsed pumping strategy has been developed to cost effectively remediate a carbon tetrachloride plume in Schoolcraft, Michigan. The pulsed pumping system uses a line of alternating injection and extraction wells perpendicular to the direction of natural groundwater flow. The wells pump periodically to clean the recirculation zone between adjacent wells. During the pump-off phase, natural groundwater flow brings new contaminant into the recirculation zone. The wells are pumped again prior to breakthrough of contaminant from the recirculation zone. A computationally efficient reactor model has been developed, which conceptually divides the aquifer into injection, extraction, and recirculation zones, which are represented by a network of chemical reactors. Solute concentration histories from three-dimensional finite difference simulations and from field data confirm the reactor model predictions. The reactor model is used to investigate the optimal well configuration, pumping rate, and pumping schedule for achieving maximum pollutant degradation. r 2004 Elsevier Ltd. All rights reserved. Keywords: In situ bioremediation; Reactor model; Pulsed pumping; Process optimization 1. Introduction Pulsed pumping remediation refers to the use of periodic rather than continuous pumping for the capture and degradation of groundwater contaminants. During the pump-off phase of the pulsed pumping approach, contaminants are transported by natural gradient groundwater flow into an adsorption zone proximate to a transect of alternating injection and extraction wells. Contaminant adsorbs onto aquifer solids in this region until near saturation is attained, where upon the well pumps are activated to establish recirculation between adjacent injection and extraction wells. The Corresponding author. Tel.: +1-734-647-7940; fax: +1734-763-2275. E-mail address: cmlasto@umich.edu (C.M. Lastoskie). recirculation zone is then flushed with augmented water to stimulate chemical or biological degradation of the adsorbed contaminant. Once the zone has been cleansed of contaminant, the pumps are shut off, allowing fresh contaminant to adsorb onto the aquifer solids from the next parcel of groundwater that enters the treatment zone by natural gradient flow. The alternating sequence of pump-off (contaminant adsorption) and pump-on (contaminant degradation) events is continued for the duration of the treatment project. A hybrid scheme involving bioaugmentation and pulsed pumping operation has been developed for the in situ bioremediation of Schoolcraft Plume A, a carbon tetrachloride plume in an unconfined aquifer in southwest Michigan (Hyndman et al., 2000). Bioaugmentation of Plume A with Pseudomonas stutzeri strain KC, a non-native microorganism, enables transformation of 0043-1354/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2004.06.029 ARTICLE IN PRESS 3870 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 Nomenclature a C D E F H k K L N P Q R S t v V w x spatial coordinate of point source/sink (m) concentration (mol/m3) well borehole or injection/extraction zone diameter (m) exit-age residence time distribution (h
1) feed-normalized residence time distribution (
) aquifer layer thickness (m) degradation rate constant (h
1) aquifer layer conductivity (m/h) well-line length (m) number of wells (
) porosity (
) volumetric flowrate (m3/h) retardation factor (
) well line stagger (offset) (m) time (h) fluid velocity (m/h) natural gradient specific discharge (m/h) complex potential function (m2/h) spatial coordinate perpendicular to natural gradient (m) carbon tetrachloride into carbon dioxide and other nonvolatile organic compounds without production of chloroform. By contrast, biostimulation of indigenous Plume A microflora results in substantial chloroform production (Dybas et al., 1998). Pulsed pumping operation was implemented for a 15-well plume transect at the Schoolcraft site, with weekly pumping events interrupting passive adsorption of carbon tetrachloride from the groundwater onto the aquifer solids in the treatment zone. Over a 600-day field test (Dybas et al., 2002), more than 96% of the adsorbed carbon tetrachloride was transformed, with minimal production of chloroform and a substantial reduction of operating cost relative to continuous pump-and-treat remediation, which would require pumping and disposal of large volumes of water. To achieve maximum effectiveness from pulsed pumping remediation, the placement of injection/extraction wells and the pumping schedule must be judiciously chosen. In this paper, we present a reactor model that has been developed for use as a computationally efficient pulsed pumping design optimization tool. This model is primarily intended for use in the early stages of system design, when detailed aquifer properties are not likely known, to rapidly evaluate a large range of potential system configurations. For comparison with pulsed pumping systems, the model can also predict the transient and steady-state behavior of continuously y z spatial coordinate in the direction of natural gradient (m) complex spatial coordinate (m) Greek letters C t F stream function (m2/h) residence time (h) velocity potential (m2/h) Subscripts b c d e i j k m r bypass stream captured stream discharge stream extracted stream injected stream layer index well index midpoint of timestep recirculated stream pumped remediation systems, which are fundamentally equivalent to pulsed systems with infinite pump-on times. The reactor model is largely analytic and is thus resource efficient in comparison to numerical model packages such as MODFLOW (US Geological Survey) and MT3D (Waterloo Hydrogeologic). 2. Methodology The aquifer is divided into laterally homogeneous layers with specific hydraulic conductivities. The reactor model partitions each aquifer layer into injection, extraction, and recirculation zones, as depicted in Fig. 1(a) for a two-well system. The injection and extraction well casings are enclosed by circular regions of diameter D equal to the well borehole diameter. Ideal radial plug flow is assumed in the injection and extraction zones. The recirculation zone is defined as the region between adjacent wells through which pumped water flows from the injection zone to the extraction zone. Plug flow does not occur in this region, but rather a distribution of fluid velocities and residence times is presumed. Each of the three zones within an aquifer layer is modeled as a separate chemical reactor, as indicated in Fig. 1(b) for a single-layer aquifer. For multiple-layer aquifers, with physical properties that vary across layers, vertical dispersion is neglected, such that the ARTICLE IN PRESS C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 3871 recirculation zones are modeled according to residence time distributions rather than spatial location. Assuming that the diameter of the well casing is negligible relative to the borehole diameter, the solute residence time t for radial plug flow in the injection zone and the extraction zone is t ¼ pD2 PRH=ð8Qe Þ; Fig. 1. (a) Injection, extraction, and recirculation zones for a two-well system. (b) Conceptual reactor network model for an arbitrary number of wells. The dashed box encloses subsurface flow within a single aquifer layer. Additional layers operate in parallel with the layer shown. recirculation zones of the layers operate in parallel and flow and reaction in each layer occur independently of the other layers. The outflows from the recirculation zones combine and mix completely within a singleextraction zone that vertically spans all layers. Similarly, the injection zone is completely mixed, so that the injected fluid composition is the same in all layers. For systems of more than two wells, there are multiple injection, extraction, and recirculation zones within each aquifer layer. For computational efficiency these zones are mathematically combined into single injection, extraction, and recirculation reactor units that collectively represent the total flow and reaction occurring within a given layer. This simplification is possible without loss of generality in the final results because reaction and flow in the injection, extraction, and (1) where Qe =H is the volumetric extraction rate per unit layer thickness for a given well; P is the porosity; and R is the retardation factor for the solute in question assuming equilibrium linear adsorption. The boundaries of the recirculation zone within a given layer and the fluid residence time distribution (RTD) within this zone depend upon the well configuration and spacing and the pumping extraction rate Qe : For very low values of Qe ; the extraction rate is insufficient to establish recirculation between adjacent wells, and the bypass flowrate Qb of incoming fluid not captured by the extraction well is non-zero. For larger extraction rates that represent typical pumping conditions, all incoming groundwater is captured (Qb ¼ 0), and the recirculation zone volume and its associated RTD are calculated using an analytic two-dimensional potential flow model (Bird et al., 1960; Columbini, 1999). The potential flow model assumes steady-state, continuous, incompressible, inviscid, irrotational, twodimensional flow which occurs within homogeneous, isotropic layers of a confined aquifer. The natural gradient groundwater flow or specific discharge V is in the positive direction along the y-coordinate. A set of N injection/extraction wells are evenly spaced along a line of length L in the x-coordinate, with perpendicular stagger S between consecutive wells. Sample configurations for two- and three-well systems are shown in Fig. 2. All wells are assumed to be fully screened ideal sources or sinks. Continuity and irrotational flow require that dvx dvy þ ¼ 0; dx dy (2) dvx dvy ¼ 0;
dx dy (3) where vx and vy are the rectangular components of the fluid velocity. A solution may be obtained in terms of the stream function C and velocity potential F, which are combined into the complex potential w(z), where z = x+i y: wðzÞ ¼ Fðx; yÞ þ iCðx; yÞ; vx ¼
vy ¼ qC qF ¼
; qy qx qC qF ¼
: qx qx (4) (5) (6) ARTICLE IN PRESS 3872 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 Fig. 2. Streamlines and groundwater velocity contours for a single confined layer with Qe ¼ 4:8: The natural groundwater flow gradient is in the positive y-direction. (a) Two-well system with extraction well on the left and injection well on the right. (b) Staggered three-well system with two extraction wells and one injection well. For a single layer, two-well system with an injection rate þQe =H at z ¼ þL=2 and extraction rate
Qe =H at z ¼
L=2 superimposed on the specific discharge, the complex potential reported in terms of the dimensionless pumping rate Qe ¼ Qe =ðHLV Þ is
  Q z
1=2 w ðz Þ ¼ e ln  þ iz ; (7) z þ 1=2 2p For an N-well system in an M-layer heterogeneous aquifer, the dimensionless complex potential wj ¼ w=ðLV j Þ in layer j is the same as that given by Eqs. (8)–(10), except that the dimensionless pumping rate in Eq. (9) is where z ¼ z=L and w ¼ w=ðLV Þ: For a single-layer, Nwell system with even-numbered extraction wells staggered a distance S in the +y direction behind oddnumbered injection wells along a line of length L, the complex potential is where Hj and Vj are the respective thickness and specific discharge of the jth layer. The velocity field vj(z) of layer j is obtained from the derivative of the complex potential: w ðz Þ ¼ N X Q ek k¼1 Qek ¼ ak ¼ 2p lnðz
ak Þ þ iz; 8 Qe ; < int½ðNþ1 Þ=2 Qe :
; int½N=2 vj ðzÞ ¼ (8) k odd; (9) k even;   k
1
12 þ N
1 þ i S2 ; k odd;  1 k
1  
2 þ N
1
i S2 ; k even; ( Q Qne ¼ PM e ; L j¼1 H j V j (10) where int[x] is the truncated integer value of x and S ¼ S=L: Eq. (9) stipulates that the total volumetric flowrate Qe is distributed equally across the extraction wells and injection wells; e.g., for a five-well system with S ¼ 1; groundwater is extracted at a rate –Qe =2 from wells 2 and 4 at coordinates a2  ¼ ð21=4; 2i=2Þ and a4  ¼ ðþ1=4; 2i=2Þ; and injected at a rate þQe =3 from wells 1, 3 and 5 at coordinates a1*=(–1/2, +i/2), a3 ¼ ð0; þi=2Þ; and a5 ¼ ðþ1=2; þi=2Þ: N X dwj Qek 1   þ iV j ; ¼ Vj 
a 2p dz z k k¼1 (11) (12) where the x- and y-components of the velocity are given as the real and imaginary portions of Eq. (12), respectively. Fig. 2(a) shows the flow streamlines and groundwater velocity contours calculated for a two-well system with Qe ¼ 4:8: Fig. 2(b) shows the results for a staggered three-well system with the same pumping rate. Each well has a corresponding stagnation point, indicated by the dark contours of Figs. 2(a) and (b). The difference in stream function values calculated at the stagnation points of consecutive wells is used to determine the groundwater capture rate Qc and the recirculation flowrate Qr ¼ Qe 2Qc for each well (or well pair) in the pulsed pumping system. A similar approach has been used to delineate well capture zones in two-dimensional groundwater flow models (Bakker and Strack, 1996). The recirculation zone is modeled as a segregated flow reactor (Levenspiel, 1999; Fogler, 1999) in which a set of ARTICLE IN PRESS 3873 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 plug flow reactors (PFRs) with a distribution of residence times operate in parallel. The RTD of the segregated flow reactor is determined from the fluid streamlines in the recirculation zone obtained for a given well geometry and pumping rate. The PFR reactor network shown in Fig. 1(b) permits analytic solution of the contaminant concentration versus time at any point within the network once the initial conditions (i.e. C e ; C i ; and C r in Fig. 1(b) at t ¼ 0), aquifer physical properties, kinetic parameters, and well geometry and pumping rates are specified. The solute concentration C c of incoming captured groundwater is assumed constant within a given layer. Equilibrium linear adsorption and first-order reaction are also assumed, with a degradation rate constant k specific to each reactor unit. For first-order reaction, the contaminant concentration C i ðtÞ exiting the radial PFR that represents the injection zones is obtained from the concentration C e ðtÞ entering this zone as: C i ðtÞ ¼ C e ðt
tÞ expð
ktÞ; (13) Eq. (15) is then discretized to obtain the exit concentration from the recirculation zone. Once initial conditions are specified, the time-dependent concentrations C e ; C i ; and C i are solved using EðtÞ for the specified well geometry and pumping rate by combining Eqs. (13)–(15) into one equation with t as the only unknown. The extraction well concentration C e is typically of interest to compare against groundwater field measurements, whereas the discharge concentration C d ¼ ðQc =Qd ÞC i þ ðQb =Qd ÞC c ; (18) 1 2 wells S* = 0 0.5 where t is given by Eq. (1). Similarly, for the extraction zone: C e ðtÞ ¼ ½ðQc =Qe ÞC c þ ðQr =Qe ÞC r ðt
tÞ expð
ktÞ: (14) The outlet concentration from the recirculation zone is given by the convolution integral Z 1 EðtÞC i ðt
tÞ expð
ktÞdt; (15) C r ðtÞ ¼ 0 0 0 where the RTD EðtÞ is calculated using a second-order numerical particle-tracking algorithm. This is the only non-analytic calculation performed in solving the reactor model. A selected number of particles are uniformly distributed around the circumference of the injection well. The trajectory of each particle is tracked forward in time until it either reaches an extraction well or it moves beyond a specified distance (i.e. along a streamline outside of the recirculation zone; these particles are discarded in the RTD analysis). The particle location at the end of the next timestep is calculated from its current position and the analytic velocity field as zðt þ DtÞ ¼ zðtÞ þ ½vm =jvm jDt; (16) vm ¼ vðz þ 12½vðzÞ=jvðzÞjDtÞ; (17) where Dt is the time increment and the velocity v ðzÞ ¼
vx þ ivy at the spatial coordinate z: Fig. 3 shows the particle travel time distributions for two- and three-well systems with Qe ¼ 9:6 in which the effects of porosity and retardation are neglected. The travel time distribution is multiplied by the porosity and retardation factor to yield EðtÞ for the recirculation zone. The integral of 0.5 1 1.5 2 Travel Time (multiples of L/V) (a) 1 3 wells S* = 0 0.5 0 (b) 0 0.5 1 1.5 2 Travel Time (multiples of L/V) Fig. 3. Dimensionless RTD E  ¼ EL=V reported in terms of dimensionless time t ¼ tV =L for (a) two-well and (b) threewell systems with Qe ¼ 9:6: ARTICLE IN PRESS 3874 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 where Qd ¼ Qc þ Qb ; is relevant in regard to regulatory compliance. 3. Results Transport tests with conservative tracers and reactive solutes were simulated using the reactor model and the results were compared with calculations from a threedimensional finite difference (FD) MODFLOW/MT3D model using a 10 m 10 m 6 m grid with a grid spacing of 0.1 m in the lateral (x- and y-) coordinates. Advection within the FD model is simulated using a fourth-order Runge–Kutta hybrid method of characteristics solution algorithm. The simulated pulsed pumping system consists of 1 m diameter reactive (injection/extraction) zones around two wells spaced 2 m apart within a 6 m thick confined aquifer that is assumed to be initially free of solute. Transient solute concentrations are calculated for a hypothetical 10 h pumping interval with constant injection concentration C i ¼ 100 ppm: Results for single-and three-layer aquifers are compared for the model systems listed in Table 1. The following invariant parameter values were used in the finite difference simulations: porosity=0.3, dispersivity=0.1 m, head gradient=0.01, and leakance between layers=0.01 h
1. Fig. 4(a) shows the extraction-well concentration C e predicted for a conservative tracer in a homogeneous, single-layer confined aquifer. Tracer extraction begins after approximately 2 h in the FD model, and after 3.5 h in the reactor model. The difference is due to longitudinal dispersion, which is accounted for in the FD model but neglected in the reactor model. After approximately 4 h, the extracted tracer concentrations predicted by the reactor model are very close to those of the FD model. The inability of the reactor model to simulate early, low-concentration, dispersion-induced breakthrough of solute is not expected to limit the model’s utility because pulse-pumped systems are not generally expected to use such relatively short pump-on times. Simulations with three-layer, homogeneous FD and reactor models yielded similar results as those shown in Fig. 4(a) and are not presented here. Fig. 4(b) shows FD and reactor model simulation results for a conservative tracer in a three-layer, heterogeneous confined aquifer in which the top and bottom aquifer layers have a lower conductivity than the middle layer. The combined pumping rate Qe for the three layers matches the pumping rate for the case shown in Fig. 4(a). The tracer breakthrough times for the FD and reactor models agree more closely for the heterogeneous aquifer of Fig. 4(b) than for the homogeneous aquifer of Fig. 4(a). It appears that neglect of longitudinal dispersion in the reactor model becomes less significant as heterogeneity is added to the system and dispersion effects are spread across several layers. The extraction-well concentration curves are again in good agreement at later times. Fig. 4(c) shows FD and reactor model simulation results for a reactive solute in a single-layer confined aquifer with fully screened wells. This case is identical to that of Fig. 4(a), except that solute degradation with first-order kinetics occurs within the aquifer. It is again observed that the reactor model predicts a longer breakthrough time than the FD model, due to the neglect of dispersion, whereas agreement between the models at later times is quite good. Fig. 4(d) shows a comparison of the FD and reactor models for a conservative tracer in a confined aquifer with partially screened wells. The FD model is comprised of three layers, with a well screen present only in the middle layer, so that groundwater can be injected and extracted only from this layer and not the others. The reactor model results of Fig. 4(d), meanwhile, are reported only for the layer in which the well screen is present. The solute concentration curves predicted by the FD and reactor models in Fig. 4(d) differ significantly. As in the previous cases, the two models predict different tracer breakthrough times due to the effect of dispersion. More significant is that the reactor model overestimates the extraction-well concentration at longer pumping times. There are two reasons Table 1 Varied finite difference model parameters Model Figure Homogeneous Heterogeneous 4a 4b Reactive k ¼ 0:2 h
1 Partial screen 4c 4d Layer 1 1 2 3 1 1 2 3 H (m) 6 2 2 2 6 2 2 2 K (m/h) 0.1 0.075 0.15 0.075 0.1 0.1 0.1 0.1 Qe (m3/h) 2 0.5 1 0.5 2 — 0.67 — Computational time (s) FD model Reactor model 450 2670 9 10 420 1580 9 9 ARTICLE IN PRESS 3875 50 50 40 40 30 30 Ce (ppm) Ce (ppm) C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 20 10 10 0 0 0 2 4 (a) 6 8 10 0 4 6 8 10 6 8 10 t (hr) 50 40 Ce (ppm) 15 Ce (ppm) 2 (b) t (hr) 20 10 5 30 20 10 0 0 0 (c) 20 2 4 6 8 10 t (hr) 0 (d) 2 4 t (hr) Fig. 4. Extraction zone concentration histories from FD simulation (solid squares) and from the reactor model (open squares) in a confined aquifer with two wells. (a) Conservative solute in a homogeneous aquifer with fully screened wells. (b) Conservative solute in a heterogeneous aquifer with fully screened wells. (c) Degradable solute in a homogeneous aquifer with fully screened wells. (d) Conservative solute in a homogeneous aquifer with partially screened wells. In part (d), the open squares and open diamonds show the reactor model results for 100% and 75% efficiency, respectively. for this. First, solute arrival is delayed because some fluid streamlines in the three-dimensional FD flow model are able to travel through the unscreened layers, which results in residence times longer than predicted by the two-dimensional analytic solution used in the reactor model. Second, the addition of unscreened layers above and below the recirculation zone FD model allows for greater solute loss due to dispersion from the recirculation zone. The reactor model curve in Fig. 4(d) labeled 100% efficiency assumes, as in Figs. 4(a–c), that no solute is lost from the recirculation zone. The reactor model curve labeled 75% efficiency in Fig. 4(d) is obtained if one assumes that 25% of the solute entering the recirculation zone is permanently lost to dispersion before it reaches the extraction well. With this empirical adjustment, the reactor model predictions can be brought into close agreement with the FD model results for times out to 10 h. Although not shown, a 90% efficiency factor provides a better fit when steady state is achieved near 100 h, suggesting that only 10% of the solute is actually lost to dispersion and providing an estimate of the degree to which the remaining solute took a longer-than-predicted average path. Further study is needed to determine the extent to which model predictions vary as actual system properties depart from those assumed in the model. Recalling that this model is primarily intended to rapidly and efficiently evaluate a large number of potential operational configurations during the early stages of system design when detailed aquifer properties may not be known, application of an ARTICLE IN PRESS C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 empirical adjustment based upon prior experience to account for non-idealities should still provide conceptually useful results. The FD and reactor model calculation times on a 400 MHz Intel Celeron processor are shown for 10 h of simulated pumping for each case in Table 1. The reactor model possesses a significant computational advantage relative to the FD model, which enables more rapid investigation of well geometries or changes in aquifer physical properties. The aquifer at the Schoolcraft Plume A site is composed primarily of sand and gravel glaciofluvial sediments with significant vertical heterogeneity. A regional layer of clay exists approximately 27 m below ground surface (bgs), and the water table is approximately 4.5 m bgs (Hyndman et al., 2000). A pulsed pumping system of 15 wells arranged in a line 14 m long with no stagger was installed and screened from 9.1–24.4 m bgs. Table 2 lists the average hydraulic conductivities for 3 m thick layers from 9 to 27 m bgs as measured from well cores collected during installation of the system. A hydraulic head gradient of 0.0011, based on regional measurements, was used to calculate specific discharge for each layer. During an initial tracer study, groundwater was extracted from odd-numbered wells at a total rate of 9.1 m3/h and injected into even-numbered wells for a period of 5 h. Sodium bromide was added continuously to the injected groundwater to bring the average injected bromide concentration to 16 ppm. Bromide concentration was measured at each extraction well at 30 min intervals. Fig. 5 shows the average extracted bromide concentration during the 5 h tracer test. The error bars denote one standard deviation of the concentrations measured across the eight extraction wells. Variations in extracted concentration among the individual wells at any given time are primarily due to a combination of heterogeneity between the wells and variations in well spacing. A five-layer aquifer reactor model was developed using the physical property data of Table 2 and assuming an aquifer porosity of 0.3. The predictions of the reactor model are compared to the experimental tracer data in Fig. 5. As in Fig. 4(d), for 100% recirculation efficiency the reactor model overstates the extracted bromide concentration, but at 75% recircula- tion efficiency a good fit to the experimental data is obtained. The difference between the model predictions and field tracer measurements is primarily attributed to the assumption of fully screened wells in the reactor model. Comparison of the reactor model and FD predictions indicates that the reactor model yields quantitative predictions of the extracted solute concentration over intermediate to long timescales, provided that the assumption of full-well screening in a confined aquifer is met. When the reactor model is applied to partially screened well systems in confined or unconfined aquifers, the solute breakthrough curves are qualitatively similar to FD model results and experimental data, but a scaling factor that accounts for the effect of partial screening is required to achieve quantitative agreement. 6 5 4 Ce (ppm) 3876 3 2 1 0 0 1 2 3 4 5 t (hr) Fig. 5. Measured and predicted tracer concentration histories for a 15-well field system. The experimental tracer measurements are shown as the solid squares; the reactor model results for 100% and 75% efficiency are given by the open squares and open diamonds, respectively. Table 2 Average measured hydraulic conductivity at 15-well site (Hyndman et al., 2000) Depth (m) Number of measurements Average (cm/s) Standard deviation Coefficient of variation (%) 9–12 41 0.012 0.006 53 12–15 35 0.012 0.003 25 15–18 44 0.027 0.011 40 18–21 33 0.023 0.013 54 21–24 41 0.046 0.024 53 24–27 26 0.057 0.022 38 ARTICLE IN PRESS 3877 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 4. Discussion Ce (ppm) 80 60 40 20 0 0 4 (a) 8 12 t (hr) 16 20 100 Ce (ppm) 80 60 40 20 0 0 4 8 12 t (hr) 16 20 0 4 8 12 t (hr) 16 20 (b) 100 80 Ce (ppm) The effect of the reaction rate constant, well density, and pumping rate on the extraction well contaminant concentration is shown in Figs. 6(a), (b) and (c) respectively. The results reported in Figs. 6(a), (b), and (c) are for a 2 m line of unstaggered wells in a single confined layer with C c ¼ 100 ppm; V ¼ 0:001 m=h; P ¼ 0:3; H ¼ 6 m; and D ¼ 0:30 m: Degradation is assumed to occur only in the injection and extraction zones, and retardation due to adsorption is neglected. For systems with an odd number of wells, the end wells are operated as extraction wells. The initial contaminant concentration in all zones is 100 ppm. Fig. 6(a) shows the sensitivity of the extracted solute concentration to changes in the first-order degradation rate constant for a three-well system with Qe ¼ 2:0 m3 =h: For k ¼ 2:0 h
1 ; approximately 50% of the solute is degraded with each pass through the reactor network. This value of the rate constant is comparable to that measured for CT degradation by strain KC (Dybas et al., 1995). As might be expected, changing the rate constant by an order of magnitude in Fig. 6(a) significantly alters both the steady-state extraction well solute concentration and the rate of approach to the steady-state condition. Fig. 6(b) shows how the extracted groundwater solute concentration changes as the number of wells is varied while the well-line length is held constant. Increasing the well density increases the groundwater retention time within the injection and extraction zones, because the total volumetric flow is divided among a greater number of wells. The higher well density also increases the fraction Qr =Qe of injected groundwater that is recirculated. The higher recirculation ratio leads to longer overall retention times and lower steady-state concentrations. The increased degradation efficiency afforded by a high well density is achieved, however, at the expense of a higher well installation cost per unit well-line length. Fig. 6(c) shows the effect of varying the pumping rate on the extracted solute concentration for a three-well system with a degradation rate constant of 2.0 h
1. Increasing the groundwater extraction rate has two competing effects. The recirculation ratio Qr =Qe increases as the pumping rate increases, resulting in longer overall retention times within the system. As the extraction rate increases, however, the fluid residence time in the injection and extraction zones decreases, so that the amount of degradation per fluid pass decreases at high pumping rates. For the three-well system of Fig. 6(c), the effect of the shorter reactive zone residence time negates the benefit of increased recirculation, so that high pumping rates result in low-degradation efficiency (i.e. C e values). Furthermore, since operating costs increase as the total pumping burden increases, there is an economic disincentive to operating at very high extraction rates. 100 60 40 20 0 (c) Fig. 6. Extraction zone solute concentration histories obtained for variation of key parameters. (a) Three-well system with Qe ¼ 2:0 m3 =h and k ¼ 0:20 (diamonds), 2.0 (squares), and 20. h
1 (triangles); (b) Two-well (diamonds), three-well (squares) and five-well (triangles) systems with Qe ¼ 2:0 m3 =h and k ¼ 2:0 h
1 ; (c) Three-well system with k ¼ 2:0 h
1 and Qe ¼ 8:0 (diamonds), 2.0 (squares) and 0.50 m3/h (triangles). ARTICLE IN PRESS 3878 C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 0 This is equivalent to calculating the volume traversed by streamlines in the recirculation zone that arrive at the extraction well within the interval t. Dividing the swept volume by the well spacing and aquifer layer thickness yields an estimate of the swept recirculation zone width. The allowable pump-off time for a given layer is the time required for a parcel of groundwater traveling at the natural gradient velocity to cross this width. Fig. 7 shows the recirculation zone width and maximum pump-off time for a heterogeneous, twolayer, two-well aquifer, assuming negligible dispersion, chemical reaction, and adsorption. For continuous pumping, all aquifer layers have the same recirculation zone width, irrespective of their conductivities; but for intermittent pumping, the recirculation zone width increases more rapidly with pump-on time for the higher conductivity layer, as shown in Fig. 7(a). The maximum time interval between pumping events that avoids solute breakthrough in each layer is shown in Fig. 7(b). For short pump-on time, breakthrough during the pump-off phase occurs first in the lower conductivity layer, because the swept width of the recirculation zone in this layer is narrower than in the higher conductivity layer. In fact, for pumping durations of less than 7.5 h, the width of the swept region is zero in the lower conductivity layer, because there is insufficient Recirculation Zone Width (m) 4 High K 3 Low K 2 1 0 0 5 10 15 20 Pump -On Time (hours) (a) 30 Low K Pump-Off Time (days) For very low pumping rates, much lower than those shown in Fig. 6(c), the bypass flowrate Qb becomes nonzero, and the overall degradation efficiency decreases due to the uncaptured groundwater fraction. Thus, there is an optimum intermediate pumping rate, dependent on the number and configuration of wells, that maximizes overall degradation of the contaminant. In order to minimize total pumping costs, the pumping schedule for pulsed pumping operation should provide the largest possible ratio of pump-off time to total pumped groundwater volume. The principal pulsed pumping operating constraint is that the breakthrough of contaminant in the recirculation zone during the pump-off phase is prohibited. Specific pulsed pumping remediation systems may have additional constraints; for example, the microorganisms in an in situ bioremediation system may require scheduled delivery of nutrients by pumping. An estimate of the allowable pump-off time, as a function of the pump-on treatment time, can be obtained from the recirculation zone RTD in each aquifer layer. Assuming that uncontaminated and/or nutrient enriched water is continuously injected during the pump-on phase, the fraction of the recirculation zone volume in each layer that is fully swept by injected water is equal to the value of the feed-normalized RTD, F ðtÞ; for pumping time t Z t F ðtÞ ¼ E ðtÞdt: (19) 20 10 High K 0 0 (b) 5 10 15 20 Pump -On Time (hours) Fig. 7. (a) Effective recirculation zone width and (b) maximum allowable pump-off time as a function of pump-on time for pulsed pumping operation in a confined two-layer heterogeneous aquifer. The conductivities of the low- and highconductivity layers are 0.075 and 0.15 m/h, respectively. time for injected groundwater to reach the extraction well. For long pump-on times (e.g. t ¼ 15 h), the allowable pump-off time becomes greater for the lower conductivity layer. Although the swept width of the recirculation zone is always larger in the higher-conductivity layer, natural gradient flow is sufficiently slower in the lower conductivity layer so that it takes longer for a parcel of ARTICLE IN PRESS C.M. Tenney et al. / Water Research 38 (2004) 3869–3880 groundwater to cross the swept width of this layer. The crossover point, at which both layers have the same breakthrough time, occurs at a pump-on interval of 11 h for the particular two-layer aquifer investigated in Fig. 7. If no contaminant is to be allowed to exit the swept portion of the recirculation zone during the pump-off phase, then the pulsed pumping system must be operated such that the interval between pumping events does not exceed the shortest of the allowable pump-off times for each aquifer layer; e.g. in Fig. 7(b), a pump-off or ‘‘trapping’’ interval of 18 days for each pump-on or ‘‘treatment’’ period of 20 h. Under this constraint, maximum pulsed pumping efficiency is achieved by operating at the point of crossover in the pump-off curves; i.e. in Fig. 7(b), by adopting a schedule of 11 h of pumping once every 12 days. The pump-on times shorter than this duration are disadvantageous because rapid breakthrough in the swept zone of the lower conductivity layer compels more frequent pumping. The pump-on times longer than the optimum 11 h duration, meanwhile, are also disadvantageous because the benefit of the longer pump-off time interval is negated by a disproportionately larger increase in the total pumping burden incurred due to the longer pump-on time. For well configurations and for aquifers with physical properties that are different from the two-well, twolayer case considered in Fig. 7, the preceeding analysis will of course yield a different preferred pumping scheme. However, the same process optimization considerations will apply. If solute adsorption is significant during both phases of operation, the swept recirculation zone width increases more slowly over time, and the allowable pump-off time increases. The curves of Fig. 7(a) will then shift rightward, and those of Fig. 7(b) rightward and upward, by an amount proportional to the retardation factor. In Fig. 7(b), it was assumed that no reaction occurs between pumping events, but if solute degradation does occur during the pump-off phase, the maximum pump-off time again increases and the curves of Fig. 7(b) shift upward. Also, the results shown in Fig. 6 indicate that for certain conditions, the pumps must remain activated for a period of time before the injected water becomes sufficiently ‘‘clean’’, i.e., the discharge concentration attains its desired or steady-state concentration. In such cases, a longer pumping time is required to effectively sweep the recirculation zone, and the curves of Figs. 7(a) and (b) shift rightward by an amount equal to the period of time needed to achieve the desired discharge concentration. 5. Conclusion The two-dimensional flow, recycle reactor model presented in this work is intended as a tool for rapid 3879 initial design and analysis of pulsed pumping remediation systems. The model predicts transient and steadystate solute concentrations for different configurations of intermittently pumped field treatment systems. Comparisons with three-dimensional FD model calculations demonstrate that the reactor model accurately predicts solute transport in systems with first-order reaction, fully screened wells, and heterogeneous layers when dispersion is not significant. The reactor model predictions also compare reasonably well with tracer breakthrough measurements from field experiments conducted at the Schoolcraft Plume A site. Extension of the reactor model to include multiple solutes and phases, and to incorporate more complicated kinetics and adsorption equilibria, is possible at the expense of computational speed. The semianalytic reactor model is computationally efficient for optimization of well spacing and geometry, pump extraction rate, and pumping schedule for pulsed pumping operations. For process modeling of aquifers with significant lateral dispersion or vertical flow, a fully three-dimensional approach using FD or other numerical methods is recommended. Additionally, the reactor model provides a simple framework for thinking about relationships between remediation system behavior and general changes in aquifer properties, well configuration, and pumping rate and schedule. Future research will illustrate some of these relationships, which might not be readily apparent when working with conventional finite difference groundwater flow models, and provide dimensionless correlations for use in initial design studies. Acknowledgements Support for this project was provided by the Michigan Department of Environmental Quality under contract Y40386 and the National Science Foundation under award CTS-9733086. References Bakker, M., Strack, O., 1996. Capture zone delineation in twodimensional groundwater flow models. Water Resour. Res. 32, 1309–1315. 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