Optimal Times to Decrease Extraction Rates During Two-Stage Remediation Affected by Rate-Limited Transport
Jose A. Saez, Loyola Marymount University
Abstract
Saez and Harmon presented a two-stage pump and treat (PAT) groundwater remediation strategy in a recent Ground Water Journal publication (Saez and Harmon, 2006). The strategy entails aggressive pumping rates during early stages of remediation, followed by reduced pumping rates until remediation succeeds. The approach targets groundwater cleanup problems where solute transport is subject to rate-limited desorption, and to low-conductivity units that harbor organic contaminants and slow their release into the extracted water. The two-stage strategy can reduce the overall volume of extracted groundwater and corresponding pumping costs. The current work presents new remediation scenarios to expand the findings in the work cited. The two-stage strategy is applied to hypothetical scenarios with different levels of contaminant source removal and extraction wells locations. Incorporation of dimensionless groups, which address contaminant mass, pumping rates, extracted volumes, and advection and desorption rates, help generalize results and establish conditions in which the proposed PAT strategy is superior that steady pumping.
Background
Several rate-limited factors affect the efficiency of PAT. For example, investigators have shown that contaminant release from aquifer grains to the flowing groundwater result in mass-transfer limitations, which are often modeled through non-equilibrium and multi-rate models (Valocchi, 1985; Ball and Roberts, 1991; Kong and Harmon, 1996; Lawrence et all, 2002). Rate-limitations can also be applied to model the effect of clay units, which harbor contaminants and limit their release into the flowing groundwater (Zhang and Brusseau, 1999, Saez, 2004). The dissolution of non aqueous phase liquids (NAPL) into the fluid has also received considerable attention, because NAPL contaminants constitute persistent sources of contamination, which must be eliminated or significantly reduced prior to the onset of PAT remediation (Khachikian and Harmon. 2000; Saez and Harmon, 2006).
The factors above result in a slow and persistent slow release of contaminants from the soils to the groundwater that flows to the extraction wells. Consequently, the extraction of contaminants becomes inefficient and often turns the PAT effort into an endeavor that requires a longer remediation period than originally anticipated. PAT cleanup sites for hydrophobic organic chemicals exhibit these limitations in that efficient recovery of contaminants is achieved at the onset of remediation, but efficiencies later decrease due to the factors listed above (Saez, 2004). This occurs in typical cleanup efforts, where groundwater is extracted at steady rates from wells, but contaminants are not completely removed and/or concentrations rebound when water extraction ceases. The challenge then becomes of how to overcome, reduce, or at least manage such mass transfer limitations.
The mass transfer limitations and the hydraulic regime created by the extraction wells are closely linked. The operator of a PAT project has control on the extraction wells design and operation to improve the remediation effort. Improvement may be achieved through well placement (Haggerty and Gorelick, 1994) and/or through pumping rate-scheduling (Culver and Shoemaker, 1992). The current effort focuses on pump scheduling, but also shows benefits of well locations. Previous research efforts by Saez and Harmon (2006) focused on developing a dynamic two-stage PAT technique to reduce pumping volumes, which is treated here as a surrogate for pumping costs, while addressing rate-limited transport. The dynamic PAT strategy consists of aggressive pumping at the initial remediation times to take advantage of the abundance of contaminant and effectiveness of advection-dominated conditions that maximize solute extraction. The strategy reduces pumping rates at later remediation times, when solute transport begins to be controlled by rate-limited transport.
Results showed that the two-stage strategy results in less total water volume extracted than steady pumping under conditions of limited mass transfer. This was accomplished by using a groundwater management model that combines the nonlinear optimization package MINOS (Murtagh and Saunders, 1995) with a solute and transport groundwater model that incorporates finite element and the mass-transfer limitations described earlier (Kong and Harmon, 1996; Saez and Harmon, 2006). Results also showed that aggressive pumping should take place for a short initial period (often 10 % or less of the total remediation time), and that pumping aggressively for longer periods becomes costly and inefficient. The present effort provides additional results to develop and test practical criteria that identify the best time to reduce pumping rates under additional scenarios, which include pumping closer to the plume’s centroid and the presence of continuous contaminant source.
Methods
The two-dimensional flow and transport model and numerical solution techniques employed here are detailed by Kong and Harmon (1996). The model simulates flow and non-equilibrium sorption processes at the field-scale. The following flow equation allows the application of a spatial distribution of hydraulic conductivity.
K h
W t h Ss r
w
w
(1)Where: h = hydraulic head (L); Ss = specific storage (L-1); W = extracting/recharging
well(s) rate per volume of aquifer (T-1); and K = hydraulic conductivity (LT-1). The left side of equation (1) becomes zero under steady-state flow conditions, which are assumed to govern in each PAT stage in this work. Flow regimes generated for each pumping stage of the proposed PAT strategy were used to drive the contaminant transport model.
The primary transport processes are modeled using the following form of the advection-dispersion equation for non-equilibrium desorption (e.g., Goltz and Roberts, 1986; Kong and Harmon, 1996):
C
W
t
C
R
R
vC
R
C
D
R
t
C
w im m m im im m m m m m
r
w
w
T
T
w
w
1
1
(2) Where: Cm/Cim = mobile/immobile concentration of contaminant (Mx/L3); v = averagepore water velocity (LT-1); D = hydrodynamic dispersion coefficient (L2T-1); Tm/Tim = porosities (-); Rm = retardation factor for mobile (interparticle) zone (-); Rim = immobile
(intraparticle) zone retardation factor (-); and Cw = concentration in water from/to
extraction/recharge well (Mx/L3). The retardation factors are defined as:
m b d m
K
f
R
T
U
1
(3) im b d imK
f
R
T
U
1
1
(4)where Kd = equilibrium distribution coefficient (L3Mx-1); Ub = bulk density of porous medium
(ML-3); and f = fraction of sorption capacity occurring in the mobile zone ( - ).
Equation 2 is coupled to Equations 5 and 6, which further describe rate-limited transport of contaminant within immobile zones in the assumed spherical soil particles:
m im im i imC
C
R
t
C
mT
D
w
w
(5) 2 15 a Dp imT
D
(6)Where D (T-1) is a first-order mass transfer constant for a spherical particle of radius a (L).
Figure 1 shows a conceptual schematic of the remediation effort. The DNAPL source zone creates the contaminant plume, which develops and disperses as it travels downgradient, while the source is either maintained or eliminated after the initial contamination. Extraction PAT wells can be placed at different distances from the resulting aqueous plume to extract the contaminant, capture the plume, and prevent concentration violations at a downgradient compliance boundary.
pump-and-treat compliance hydraulic containment DNAPL aquifer clay confining unit
Figure 1. Problem schematic for PAT simulations in contaminated groundwater scenarios including active or inactive contaminant source and particle- and layer-scale mass transfer
The simulated aquifer used in this work is 400 m x 400 m x 10 m thick, and homogeneous. The natural groundwater flow gradient is from left to right at typical groundwater velocities for sand media of a few meters per year. A contaminant source of 5 mg/L of Trichloroethylene (TCE) is introduced at the upgradient boundary and allowed to pollute the site for 1000 days. The source is then eliminated or reduced to 0.05 mg/L, and the resulting plume is extracted through PAT. In these simulations, model aquifers were parameterized homogeneously. The nonequilibrium desorption parameter () was also varied to cover the range from moderate rate-limited desorption ( = 0.1 day -1) to very fast desorption ( = 1.0 day -1), which approaches the local equilibrium assumption (LEA).
A constant natural gradient of 0.005 (L/L) was imposed. PAT was tested using a strategy of installing a pump near the aqueous plume’s centroid (Gailey and Gorelick, 1993), which is referred to as “hotspot” location, and pumping continuously at a rate just sufficient to hydraulically capture the plume. Next, the same scenarios were simulated and coupled to the management model for a range of pre-set pumping rates (Q1) for stage 1 of the
remediation, and pumping rates for stage 2 (Q2), which result from the optimization model.
As mentioned earlier, the resulting management problems were solved using the nonlinear optimization package MINOS (Murtagh and Saunders, 1995). For both the continuous and two-phase strategies, the total remediation horizon was fixed at 2000, 6000 and 15000 days, and maximum mobile-zone contaminant level of 0.005 mg/L (5 ppb) was the required the cleanup constraint. Maximum allowable drawdown constrains were also included to limit the pumping rates.
The objective function and constraints are summarized as follows:
Objective Function Explanation (units)
Minimize [Q1t1 + Q2(tF – t1)] Uses pumping rates (Q) and durations (t) in each
PAT stage to represent total volume extracted (L3)
Subject to the following constraints:
hi Hmin Heads in domain must exceed a minimum head (L)
Cm, Cim CCBmax Mobile and immobile concentrations in
groundwater must not exceed a maximum level at compliance boundary (M/L3)
MR Mmax Contaminant mass remaining at end of remediation
period (tF) must not exceed a preset level (M)
0 Q1, Q2 Qmax Cumulative pumping rates during stages 1 and 2
must fall within a preset range (L3/T)
Results
Multiple runs of the groundwater management model were conducted to evaluate the efficiency of the two-stage PAT strategy under a wide range of conditions. The scenarios included changes in initial pumping rates, degree of mass transfer limitation in terms of sorption and heterogeneity, strength of continuous contaminant source, and length of total remediation period. The results were analyzed by developing plots that relate pertinent parameters and non-dimensional groups, as is further described in this section.
Extraction Well Location
Saez and Harmon (2006) focused on modeling two-stage PAT cleanup with extraction wells located downgradient of the plume. This approach is conservative in that it helps ensure plume capture as is referred to as “downgradient.” The present effort focuses on pumping the contaminated groundwater more upgradient and closer to the plume’s centroid in what is referred as the “hotspot” location. The hotspot approach has been shown to be more efficient that the “downgradient” approach in terms of extracting more mass at the same flow rates, although this difference decreases when the total remediation horizon increases (Haggerty and Gorelick, 1994). The hotspot arrangement presents the risk of not capturing the plume at higher natural hydraulic gradients, but this can be overcome through proper spacing among wells and adequate pumping rates.
Figure 2 compares the required pumping rates under steady and two-stage PAT with wells at downgradient and at hotspot locations. Steady pumping downgradient is treated as the baseline case. The figure shows that pumping at the hotspot requires lower pumping rates while achieving the same mass removal that downgradient PAT. Figure 2 also shows that the two-stage strategy resulted in higher volume savings relative to continuous pumping for downgradient that for hotspot. These advantages are more apparent at the higher remediation times.
Figure 2: Average pumping at hotspot and downgradient well locations, several PAT periods, and initial pumping rates in homogeneous aquifer ( = 0.1 day-1)
Magnitude of Initial and Steady Pumping
Figure 3 shows the savings in volume extracted at two levels of stage 1 pumping under non-equilibrium conditions and presence of continuous contaminant source. The figure suggests that the two-stage strategy is more effective with more aggressive stage 1 pumping and longer total remediation periods.
Figure 3: Volume savings vs. initial pumping for two-stage PAT in homogeneous aquifer and continuous contaminant source ( = 0.1 day-1)
It is relevant to study how the two-stage strategy compares with steady pumping when the latter is changed. Figure 4 provides insight to this question by showing the benefits of two-stage PAT compared with several baseline steady rates. The two-stage strategy is less
advantageous at low or high steady baseline rates. It is also relevant to note that that the period of aggressive pumping during stage 1 tends to be short (< 10% of remediation period).
Figure 4: Effectiveness of two-stage PAT in homogeneous aquifer and continuous contaminant source under various steady baseline extraction rates ( = 0.1 day-1)
Monitoring Well as Heuristic Indicator of Switching Times
It is challenging to translate the results of numerical optimization into practical criteria for use in real cleanup applications. Saez and Harmon (2006) proposed the use of a monitoring well strategically located to monitor the concentration history of the contaminant as a heuristic indicator of when to switch from stage 1 to stage 2 of PAT. Saez and Harmon proposed that the switch should occur after mobile concentrations reach a peak and decrease at a monitoring well 40 meters upgradient of the extraction wells. Saez and Harmon (2006) proposed, “The optimal switching times for the 6000 and 15000-day scenarios, in which the two-stage strategy proved to be advantageous, occur after the passing of the peak mobile concentration and when tailing is evident. Hence, tailing behavior is a promising criterion for switching pumping rates.” The current works applies this heuristic approach to the case where there is a continuous contaminant source and PAT is at the hotspot location. The current effort also tests this heuristic approach using two locations: one 40 meters upgradient of the extraction well and another one at the extraction well. Figure 5 (a, b, c) shows the first 2000 days of mobile and immobile concentration histories at monitoring wells 0 meters and 40 meters upgradient of the extraction wells and PAT periods of 2000, 6000 and 15000 days. As shown earlier, the optimal switching times tend to be short when compared with the total remediation period. The figure also shows that immobile concentrations remain relatively constant, because they are subject to significant slow desorption, which limits the release of contaminant to the mobile water. Conversely, the mobile concentrations vary considerably due to the advective flow regime.
a) 2000-Day PAT
b) 6000-day PAT
c) 15000-day PAT
Figure 5: Mobile and immobile concentrations for two-stage PAT in homogeneous aquifer with continuous contaminant source and several remediation periods ( = 0.1 day-1)
The magnitudes of the concentrations in the two monitoring wells are different. For example, higher concentrations are found in the upgradient monitoring well, because the well is closer to the plume’s centroid. The heuristic approach proposed by Saez and Harmon (2006) proved satisfactory for either monitoring well location, as the optimal switching time occurs after peak and subsequent decrease of the mobile concentration, and tailing are evident. This is shown in both the 6000-day and 15000-day cases, where enough time is provided to allow a reduction of mobile concentrations to establish favorable desorption.
The heuristic approach does not hold for the 2000-day scenario, but it is important to remember that the two-stage strategy did not prove successful for this case. The optimization model showed that the optimal switching time was quite low, which results in no volume savings. This switching time occurs earlier than the peak, decrease, and tailing of the mobile concentration, which occurs after several hundred days. As noted by Saez and Harmon (2006) “The management model identified an optimal switching time approaching zero in an effort to allow time to recoup the volumes accumulated by early aggressive pumping, but this failed to produce any volume savings when compared to single-stage pumping”.
Non-Equilibrium Transport
Saez and Harmon (2006) incorporated the mass transfer and advective transport parameters to provide further insight on the two-stage PAT approach. These investigators applied work from Goltz and Oxley (1991), who proposed the following characteristic diffusion (Rd) and advection (Ra) rates to analyze nonequilibrium sorption conditions:
im im d
R
R
T
D
(7)*
*
r
R
r
v
R
m m a (8)Where: r* = radius of contamination of mobile concentration (L) and vm(r*) =
velocity in mobile zone at radius of contamination (L/T).
The application of these rates in the current work is described by Saez and Harmon (2006). It is sufficient to state here that the dimensionless ratio Rd/Ra ratio accounts for the
relative contributions of diffusion and advection processes to PAT. Values of Rd/Ra
approximate or greater than 100 indicate LEA conditions, while values from 100 to 0.001 indicate mass transfer limitations. Values under 0.001 are not relevant here (Saez and Harmon, 2006).
Saez and Harmon (2006) applied the approach to the NAPL-free case and PAT downgradient, while the current work expands the approach to an aquifer with continuous contaminant source and extraction wells at the hotspot, as shown in Figure 6 (a, b and c).
a) 2000-day PAT
b) 6000-day PAT
c) 15000-day PAT
Figure 6: Rd/Ra for steady and two-stage PAT in homogeneous aquifer with continuous
The results are similar to those of Saez and Harmon (2006) as rd/ra quickly decreases
below 100 at the onset of PAT, which indicates advective conditions due to the high pumping, and results in switching to lower extraction rates. This is followed by higher rd/ra
values during stage 2, when pumping is reduced and slow desorption dominates cleanup.
Conclusions
This work helps improve the understanding of rate-limited solute transport processes that limit the success of PAT. The work confirmed results from Saez and Harmon (2006) under different conditions. These findings may result in improved strategies and cost savings during PAT. For example, practical guidelines may be developed to determine the best time to reduce pumping rates when applying the two-stage strategy, as well as conditions when the strategy is of little or no benefit.
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Author Information Jose a. Saez, Ph.D., P.E.
Department of Civil Engineering and Environmental Science
Loyola Marymount University 1 LMU Drive
Los Angeles, CA 90045 Office: 310-338-5880 Fax: 310-338-2780 email: [email protected]
Jose A. Saez is an Assistant Professor at Loyola Marymount University’s Department of Civil Engineering and Environmental Science, where he teaches courses in groundwater hydrology, open channel hydraulics, fluid mechanics, wastewater treatment and industrial waste pretreatment. His research focuses on understanding contaminant transport in groundwater and improving pump-and-treat remediation strategies. Dr. Saez is also a Registered Professional Engineer in the State of California with more than 18 years of professional and research experience, while he worked as a supervising engineer for the Los Angeles County Sanitation Districts and as a consultant in projects that involve groundwater quality, wastewater treatment and industrial waste pretreatment.