Environ. Sci. Technol. 2005, 39, 6501-6507
Enhanced Coagulation for Satisfying the Arsenic Maximum Contaminant Level under Variable and Uncertain Conditions† D O M I N I C L . B O C C E L L I , * ,‡ MITCHELL J. SMALL, AND DAVID A. DZOMBAK Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
This study evaluated the effects of influent variability and model parameter uncertainty when utilizing enhanced coagulation modification to bring existing treatment plants into compliance with a stricter arsenic regulation. Enhanced coagulation modification options include: (1) increased ferric chloride dose, (2) addition of an acid dose, and (3) a combination of the individual options. Arsenic removal is described by adsorption to hydrous ferric oxide with a surface complexation model and subsequent removal through sedimentation and filtration. The leastcost modification for reliably satisfying the arsenic regulation is determined using an optimization algorithm that explicitly includes variability and uncertainty. The ferric chloride only modification is always the least-cost treatment modification. The ferric chloride and acid modification could be the least-cost option when considering waste handling processes due to a tradeoff between modification cost and sludge production. By inclusion of variability and uncertainty, the relative importance of individual parameter distributions for determining whether the arsenic regulation is reliably satisfied is assessed. Influent arsenic concentration variability is always critical, while variability in the influent pH and sulfate concentrations and uncertainty in the filter removal efficiency and equilibrium adsorption constant for the tFesOHCa2+ surface species are critical or important, depending on influent conditions.
1. Introduction In 2001, the U.S. Environmental Protection Agency (EPA) reduced the arsenic maximum contaminant level (MCL) from 50 to 10 µg/L with noncomplying utilities given until January 2006 to modify existing treatment. This regulatory update was the first to utilize a cost-benefit analysis to evaluate the tradeoff between national cost and health implications. National cost estimates (1, 2) have considered multiple treatment processes for satisfying a range of possible arsenic MCL levels. As part of these estimates, a number of utilities are assumed to comply with the new regulation through modification of their existing treatment process. However, these cost estimates use relatively simple arsenic removal models and do not provide treatment guidance at a local level. †
This paper is part of the Charles O’Melia tribute issue. * Corresponding author phone: (513)569-7654; fax: (513)487-2555; e-mail:
[email protected]. ‡ Current address: U.S. Environmental Protection Agency, ORD, NHSRC (MS 163), 26 West Martin Luther King Dr., Cincinnati, Ohio 45268. 10.1021/es050048i CCC: $30.25 Published on Web 07/26/2005
2005 American Chemical Society
While data indicate that less than 5-10% of the surface water sources in the U.S. have arsenic concentrations greater than 10 µg/L (3, 4), a significant number of community water suppliers must modify their treatment process to satisfy the new MCL. Data reported from the National Arsenic Occurrence Study (NAOS) indicate 58% of surface water utilities employ precipitative treatment (48% with aluminum sulfate, 10% with ferric sulfate) (2). Enhanced coagulation, initially intended to improve organic carbon removal (5), has been identified in many cases as the least-cost modification option to bring systems using precipitation-adsorption treatment into compliance with the reduced arsenic MCL (6). Early studies (7, 8) explored the use of ferric iron (FeCl3 and Fe2(SO4)2) and aluminum (Al2(SO4)3) coagulants for arsenic removal and indicated that ferric iron coagulants were more effective due to the high adsorption site density on precipitated hydrous ferric oxide (HFO) compared to aluminum hydroxide (9). The adsorption of arsenate, As(V), and arsenite, As(III), which occurs as the oxyanions AsO43- and AsO33and their protonated forms in water, depends on pH. Adsorption is maximum at lower and midrange pH values and decreases as pH is increased (10). Studies of arsenic removal from raw waters have shown that ferric iron coagulants efficiently remove As(V) over a range of conditions during coagulation treatment (11-17), while As(III) removal was not as efficient at the pH values typical of coagulation treatment (14, 15). In addition to increasing the coagulant dose, lowering system pH through acid addition can enhance arsenic removal. Arsenic removal through adsorptive processes can also be affected by competing species. From bench-scale studies using both adsorption and coagulation experiments, sulfate appears to have little competitive effect for adsorption sites with As(V) at drinking water pH values (14, 15, 18-20), while phosphate (18, 20, 21), silica (14, 2123), and natural organic matter (NOM) (15, 24) compete with As(V) for adsorption sites. However, the presence of calcium, a common aqueous inorganic species, during coagulation experiments has been shown to increase As(V) adsorption at above neutral pH and can negate the competitive effect of phosphate (15), silica (14), and NOM (20). When the appropriateness of enhanced coagulation as a treatment modification to precipitation-adsorption treatment for satisfying the new arsenic MCL is determined, influent water quality and current treatment practice must be considered. The use of process models to describe arsenic removal provides an efficient method for exploring various water quality and treatment conditions. Adsorption isotherm models, based on coagulant dose and influent arsenic concentration, describe arsenic removal from existing treatment plants relatively well (25, 26) without considering competing species. A two-layer (10) and triple-layer (27) surface complexation model performed reasonably well for describing As(V) removal under coagulation conditions. The two-layer surface complexation model tended to underestimate the observed As(V) removal and significantly overestimated sulfate competition but accounted for the increased adsorption due to calcium (15). The triple-layer model tended to overestimate the observed removal and significantly underestimated silica competition but did not consider a calcium species to investigate any model-predicted increase in As(V) adsorption (14). The two-layer surface complexation model, in conjunction with models for describing particle removal during sedimentation and filtration, adequately represented reported arsenic removals from existing treatment plants with little water quality information (Table S1, Supporting Information). These relatively simple models (26, VOL. 39, NO. 17, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Major Ion Concentrations (mg/L) and Hardness (as mg/L CaCO3), Estimated with the Calcium and Magnesium Concentrations, for Three Different Model Surface Waters (37) water type
Cl-
SO42-
HCO3-
Ca2+
Mg2+
K+
Na+
hardness
hard moderately hard soft
180 15 2.9
230 41 3.4
180 100 13
105 31 2.2
23 8.3 1
6.9 3.1 1.6
145 12 2.3
358 112 9.7
28) have been shown capable of representing pilot- and fullscale arsenic removals for waters with typical coagulation pH < 8.1 without considering competing species, which suggest there is little competition with arsenic adsorption during the coagulation of natural waters under these conditions. However, for waters with coagulation pH > 8.1 and high concentrations of competing species (e.g., silica), these simple models may not adequately represent arsenic adsorption. While the surface complexation model can incorporate local water quality conditions, uncertainty in the equilibrium constants can affect the predicted speciation (29). The effects of these uncertainties and influent water quality variability need to be considered when determining treatment options that are both robust and cost efficient. This study extends previous work (28) by explicitly incorporating influent water quality variability and model parameter uncertainty when determining least-cost treatment modifications for existing conventional sweep-floc treatment plants using a FeCl3 coagulant to satisfy reliably the reduced arsenic MCL. As(V) is the primary arsenic species of interest, as As(III) concentrations are typically negligible (6). The objectives of this study were (i) to explore the effects of influent variability and parameter uncertainty when determining values of the influent arsenate concentration, As(V)inf, and existing FeCl3 dose for which additional treatment will be required when As(V) removal controls the coagulant dose, (ii) when additional treatment is required, to determine the least-cost enhanced coagulation modification to bring the treatment plant into compliance, and (iii) to determine the relative importance of the individual variable and uncertain parameters in determining the modifications needed to satisfy the arsenic MCL. Additional considerations will be discussed related to practical considerations associated with enhanced coagulation, model uncertainty, and groundwater systems.
2. Solution Methodology Description of arsenic removal during sweep-floc conventional treatment (rapid mix, flocculation, sedimentation, filtration) with FeCl3 as the coagulation/adsorption agent requires the simulation of As(V) adsorption to the HFO and floc removal during sedimentation and filtration. This section provides an overview of the model used to represent the sweep-floc treatment process, influent water quality and model parameters, and the optimization routine. Details may be found elsewhere (28). 2.1. Process Model. Current models for describing changes in the particle size distribution (PSD) during rapid mix and flocculation are insufficient for representing sweepfloc conditions (30). As an alternative, the HFO PSD entering the sedimentation tank is represented by data from the effluent of a flocculation tank utilizing sweep-floc conditions (31). The sedimentation model describes the changes in the PSD using Smoluchowski’s equations (32) and particle removal using Stokes’ settling velocity. The filtration model assumes a bed of packed spheres with collection efficiencies based on a single collector approach (33, 34). The adsorption of As(V) to the HFO is described by the two-layer surface complexation model (10). In addition to As(V) and HFO, the adsorption model developed explicitly considers calcium, carbonate, chloride, magnesium, potassium, sodium, and sulfate. Magnesium has no reported 6502
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surface reactions and is included solely for the simulation of solution-phase reactions. Chloride, potassium, and sodium have no important solution-phase or surface reactions and are included solely for the simulation of ionic strength effects. The Supporting Information presents the reactions, equilibrium coefficients, and references for the species included in the equilibrium model (Table S2) and a brief description of the solution procedure. The adsorption of sulfate to HFO is not included in this study because experimental data indicate sulfate has little competitive effect on As(V) adsorption (15, 19, 20). Total As(V) removal is the product of the fraction of floc removed during sedimentation and filtration and the fraction of As(V) adsorbed to the HFO. When the cost of the system is determined, the treatment processes (coagulation, flocculation, sedimentation, and filtration) are assumed to be built with a FeCl3 dosing system capable of providing an initial FeCl3 dose. The associated costs for the enhanced coagulation modifications include: filtration operation and maintenance (OM) (modified from ref 35), the capital (CC) and OM costs for increasing the FeCl3 dosing capacity and/or adding a sulfuric acid dosing system (36), and the chemical costs (CHEM) of $394/ton for FeCl3 and $131/ton for sulfuric acid. Sludge-handling processes and the associated costs are not included in the framework. All costs are presented in 2003 dollars as the annualized capital cost (amortized over 20 years at 4%) plus the additional annual OM and chemical costs. 2.2. Study Conditions. Three different model surface waters, referred to as hard, moderately hard, and soft water, are used to explore the effect of influent water quality on As(V) adsorption to HFO. Table 1 contains the water quality characteristics of the three waters, based on actual river water data (37). The hardness values are provided for classification purposes only and are not used to specify alkalinity in the equilibrium model. There are nine variable influent parameters and nine uncertain model parameters considered in the decisionmaking framework. The variable parameters and the expected values considered in this study are flow rate (Q) as 10 million gallons per day (MGD), floc density (F) as 1.01 g/cm3, influent pH (pHinf) as 7.1, 7.8, and 8.5, influent arsenate (As(V)inf) as 15, 20, 40, 60, 80, and 100 µg/L, and influent concentrations of the inorganic constituents as given in Table 1 (Ca2+, CO32-, Mg2+, SO42-, and (Na+ + K+ + Cl-)). The nine uncertain model parameters and the expected values considered in this study are filter media removal efficiency (Rf) as 0.76, entrapped particle removal efficiency (Rf,p) as 0.08, and seven equilibrium adsorption parameters (Table S2, Supporting Information). Table S3, Supporting Information, provides the details of the variable and uncertain distributions. The parameters F, Rf, and Rf,p are empirical parameters that vary with operating conditions and water chemistry. The current process models do not explicitly relate these parameter values to operating conditions or water chemistry, rather these values are to be estimated experimentally. Therefore, to illustrate the approach, values from the literature were selected to represent F, Rf, and Rf,p (30, 31). 2.3. Optimization with Variability and Uncertainty. When existing treatment conditions are insufficient to satisfy the arsenic MCL reliably, the problem is to determine the least-cost addition of FeCl3 and/or acid to bring the plant
into compliance. The mathematical representation of the problem is
min x
∑CC + E [∑
OM +
∑CHEM]
subject to hf e 250 cm
(1) (2)
with robust constraints
0 e E[RR] e 0.15
(3)
6 e E[pHeff] e 9
(4)
and reliability constraints
Pr(Ceff e 0.6 mg/L) g γ
(5)
Pr(Aseff e 10 µg/L) g γ
(6)
Pr(tf g 12 h) g γ
and
Pr(tf e 168 h) g γ
(7)
where the objective function is to minimize the total expected cost of the system by altering the decision variables, x, the molar concentrations of FeCl3 coagulant and/or acid addition. The capital costs, CC, of the FeCl3 or acid systems are based on the maximum Q (i.e., the maximum possible feed rate) to ensure adequate dosing capacity. The minimum values of the decision variables are 10-6 mol/L. The expected operation and maintenance, OM, and chemical, CHEM, costs are dependent on realizations of the variable and uncertain parameters. The problem is constrained by both deterministic and stochastic constraints. The deterministic constraint considers the headloss across the filter, hf, before backwashing occurs. Robust stochastic constraints, based on expected value, consider the filter recycle ratio, RR, and effluent pH, pHeff. Reliable stochastic constraints, based on satisfying the constraint at some γ confidence level, consider effluent particulate and As(V) concentrations, Ceff and As(V)eff, respectively, and filter run time, tf. The optimization routine is solved using a nonlinear programming algorithm and Monte Carlo simulation to generate n realizations of the variable and uncertain parameters (28). All reliability constraints are satisfied in 95% of the n realizations (γ ) 0.95, n ) 300). This means that the effluent concentrations of particulate matter and As(V) must be reliably satisfied in 95% of the samples (the maximum number of violated samples is nviol ) (1 - γ)n ). The value of γ could be varied for this or other applications, with smaller values (e.g., γ ) 0.90) used for contaminants associated with less severe health or aesthetic effects or higher values (e.g., γ ) 0.995) used for contaminants with more severe, acute health effects. For the latter case, a larger value of n would be needed to ensure that the reliability constraint is satisfied. When enhanced coagulation is required to satisfy the arsenic MCL reliably, there are three modification options considered: ferric chloride only (increased FeCl3 coagulant), acid only (addition of an acid system), or ferric chloride and acid (a combination of both modifications). An optimization run is performed for each of the three modification options, with the least-cost option among the three selected as the appropriate modification.
3. Results and Discussion Figure 1 presents the regions of As(V)inf and existing FeCl3 coagulant dose that would require enhanced coagulation to satisfy the 10 µg/L arsenic MCL. Incorporating variability and uncertainty increases the operational regions of existing treatment that would require some type of enhanced coagulation. The increased operational region of enhanced coagulation is a result of ensuring that the simulated arsenic concentration reliably satisfies the arsenic MCL, rather than designing for conditions representing, for example, the expected
FIGURE 1. Minimum FeCl3 dose required to satisfy the 10 µg/L effluent As(V) concentration for the moderately hard water with (dashed line) and without (solid line) the inclusion of variability and uncertainty in the decision-making process. Regions to the right of the lines indicate “no modification” necessary; regions to the left of the lines indicate “enhanced” treatment is necessary to satisfy the As(V) effluent concentration constraint (expected pHinf of 7.8). The associated tabular data represents the increase in FeCl3 dose required by incorporating variability and uncertainty in the design process relative to the deterministic design for a range of influent As(V) concentrations. values of the model parameters. The tabular data within Figure 1 illustrate that there is an increase in the necessary FeCl3 dose ranging from 0.3 mg/L (when As(V)inf ) 15 µg/L) to 1.7 mg/L (when As(V)inf ) 100 µg/L) to satisfy the arsenic MCL when incorporating variability and uncertainty in the design. These increases in coagulant dosage rates correspond to percentage increases ranging from 24% to 63%, with greater relative increases required for the low influent arsenic and low initial dose cases. The resulting FeCl3 doses are in general agreement with FeCl3 doses reported for sweep-floc conventional treatment (32). Figures 2-4 and the associated discussions provide more detailed results using influent conditions based on the moderately hard water with As(V)inf ) 60 µg/L and pHinf ) 7.8 as an example. Results for other influent conditions remain qualitatively the same. Figure 2 provides the distribution of As(V)eff and range of pHeff and adsorption that occur in the presence of variability and uncertainty for the optimal solution. Figure 2a shows that 95% of the 300 simulated arsenic concentrations are below the 10 µg/L MCL, with an expected As(V)eff of 5 µg/L. Thus, decisions based on the consideration of variability and uncertainty will lead to a “safety factor” in the resulting design such that the expected As(V)eff remains below the MCL. Figure 2b illustrates the range of adsorption behavior that occurs through the incorporation of variability and uncertainty. The effluent pH ranges between 7.2 and 7.5, and the fraction of As(V) adsorbed to the HFO ranges between 80% and 99%. The lines represent the expected As(V) adsorption (solid) and the associated 95% confidence intervals (dashed). The simulated arsenic concentrations that exceed the MCL occur primarily in the regions where the predicted adsorption is lowest. This adsorption “cloud” represents the information that must be considered when developing a treatment design to adequately accommodate variability and uncertainty. The value of the stochastic solution is in reliably satisfying the arsenic MCL, though to accomplish this reliability, higher treatment costs are required. Using the optimal deterministic design results in an expected cost, E[costdet], of $41,744/yr. VOL. 39, NO. 17, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Tradeoff between reduction in sludge mass (dry wt solids) created by FeCl3 addition and increased annualized cost from acid addition over a range of molar acid dose concentrations. (Moderately hard water, optimal ferric-chloride-only dose of 5.41 mg/L (10-4.48 M Fe3+), initial FeCl3 dose of 3.24 mg/L (10-4.70 M Fe3+), expected pHinf of 7.8 and As(V)inf of 60 µg/L).
FIGURE 2. (a) Simulated distribution of effluent As(V) concentration, where the dashed line represents the 10 µg/L constraint at the 95th percentile. (b) Simulated values of As(V) adsorption percent and effluent pH (symbols) and the expected (solid line) and 95% confidence intervals (dashed lines) on predicted adsorption for the optimal solution of the moderately hard water (expected As(V)inf of 60 µg/L and pHinf of 7.8) with an optimal FeCl3 dose of 5.28 mg/L (n ) 300, nviol ) 15).
FIGURE 3. Expected modification cost for the three different enhanced treatment options of ferric-chloride-only, acid-only, and ferric chloride and acid additions to bring plants with a current FeCl3 dose, FeINITIAL, into compliance assuming the moderately hard water quality with an As(V)inf of 60 µg/L. The dashed line indicates acid only cost under deterministic conditions (modification cost ) capital cost annualized at 4% over 20 years + annual operation and maintenance cost + annual chemical cost). (The costs still vary due to the necessary variations in dosage rates needed to maintain the target FeCl3 concentration with varying influent flow rates.) The optimal stochastic solution 6504
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for the equivalent problem results in an expected cost, E[costunc], of $50,476/yr, a 20.9% increase in cost. However, by explicit incorporation of variability and uncertainty, the violation percentage of the As(V)eff constraint is reduced from 47.6% (for the deterministic solution) to the desired 5%. 3.1. Enhanced Coagulation Treatment Regions. To determine the least-cost treatment modification to satisfy the As(V)eff constraint reliably, various initial FeCl3 doses were evaluated (log(Fe3+) ) -5.6 to -4.4, log(M) in 0.2 increments) for each of the six As(V)inf. For each combination of initial FeCl3 dose and As(V)inf that required additional treatment to satisfy the arsenic MCL, the least-cost enhanced coagulation modification option was determined. The results for all three model waters are similar to the deterministic results (28): Ferric chloride only: This option is always the least-cost option (as with the deterministic study). Acid only: This option is generally the most expensive option and only feasible over a narrow range of existing FeCl3 dose conditions. Ferric chloride and acid: In general, the design of the acid addition system resulted in doses at the lower bound of 10-6 M, although suboptimal regions where acid addition was not at the minimum occurred for the moderately hard and hard waters with As(V)inf greater than 60 and 100 µg/L, respectively, with an expected pHinf of 8.5 The addition of FeCl3 remains more cost-effective than acid addition as the FeCl3 addition provides both additional adsorption sites and reduces pH, while the acid addition only decreases pH and enhances adsorption onto the existing sites (28). Figure 3 presents the expected modification costs for the three different modification options when considering variability and uncertainty and the cost curve for the acid-only option under deterministic conditions (dashed line). The inclusion of variability and uncertainty increases the cost of the ferric-chloride-only and ferric chloride and acid modifications, relative to the deterministic solution, between $10,000 and $12,000/yr, while the acid-only modification increases more than $45,000/yr. Unlike the acid-only modification, the ferric-chloride-only and ferric chloride and acid modifications are feasible over the entire range of initial FeCl3 doses explored. The feasible region of the acid-only option is limited by the available FeCl3 dose and decreases relative to the deterministic conditions due to the range of Aseff resulting from the variable and uncertain conditions. While the expected modification cost for all three options increases with decreasing initial FeCl3 dose, the acid-only design cost increases much more rapidly.
To this point, an important aspect of treatment plant decision-making has not been discussedssludge generation. The majority of the conditions requiring enhanced coagulation (Figure 1) would require utilities to increase the FeCl3 dosing capacities by amounts ranging from 50% to over 1500% (for high As(V)inf and low initial FeCl3 doses, Figure S1, Supporting Information). Assuming the sludge-handling capacity is based on the initial FeCl3 dose, such an increase in FeCl3 dose would require additional sludge-handling capacity. This can impact the least-cost modification option because sludge-management processes can account for between 18% and 95% of the total treatment cost (1). If the sludge-handling issues were explicitly considered, then the ferric chloride and acid configuration may become more economically attractive than the ferric-chloride-only option. While the inclusion of acid addition increases the modification cost, there would be an associated reduction in the total FeCl3 dose added to the system. This reduction in FeCl3 dose would reduce the additional cost incurred for sludge-handling. Figure 4 shows the tradeoff between FeCl3 reduction and the increase in modification cost for various molar concentrations of acid addition (optimal ferricchloride-only dose of 5.41 mg/L (10-4.48 M Fe3+), initial FeCl3 dose of 3.24 mg/L (10-4.70 M Fe3+)). A small addition of acid does not provide much sludge mass reduction. As the acid dose increases, the amount of sludge mass decreases although the overall modification cost increases. The maximum reduction in FeCl3 mass and increase in cost are 20.5% and $26,000/yr, respectively. Thus, if the savings in waste handling due to the decrease in solid generation is greater than the cost of the acid addition system, then the ferric chloride and acid modification option would become more cost-effective. 3.2. Important Variable and Uncertain Parameters. In addition to providing an improved basis for process decisions, the incorporation of variability and uncertainty provides information about the importance of the different variable and uncertain parameters. To test the importance of any one variable or uncertain parameter distribution, the generalized sensitivity method is used (38). With this method, the simulated variable or uncertain parameter values are separated into two categories: (1) “violation”, if the associated Aseff > 10 µg/L, and (2) “nonviolation”, if Aseff e 10 µg/L. The resulting violation and nonviolation distributions of the parameter are then compared using the Kolmogorov-Smirnov two-sample test to determine if the distributions are statistically different (39). If the violation and nonviolation distributions are different, then the associated variable or uncertain distribution may be considered important for reliably satisfying the As(V)eff constraint. Three classifications of the differences between the distributions are considered (38) with the confidence that the distributions are different given in parentheses: (1) critical (>99%), (2) important (90-99%), and (3) unimportant (
