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Mathematical modeling of cadmium removal in free water surface constructed wetlands
Journal of Hazardous Materials 163 (2009) 1322–1331
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Mathematical modeling of cadmium removal in free water surface constructed wetlands P. Pimpan a , R. Jindal b,∗ a Chemistry Program, Department of Science, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, 398, Sawanwithee Road, Muang, Nakhon Sawan 60000, Thailand b Environmental Engineering Program, Department of Civil Engineering, Faculty of Engineering, Mahidol University, 25/25, Putthamonthon 4 Road, Salaya, Nakhorn Pathom 73170, Thailand
a r t i c l e
i n f o
Article history: Received 29 January 2008 Received in revised form 27 June 2008 Accepted 24 July 2008 Available online 5 August 2008 Keywords: Cadmium Constructed wetlands Free water surface Mathematical modeling STELLA program
a b s t r a c t A mathematical model was developed for the cadmium removal process in the free water surface (FWS) constructed wetlands using a dynamic software program STELLA. Earlier, laboratory-scale experiments were conducted at the Suranaree University of Technology Campus in Northeastern Thailand to investigate the effect of high cadmium loading on the performance of FWS constructed wetlands under different environmental conditions. The predicted values of cadmium concentrations in effluents as well as in various components of the FWS constructed wetlands system, as simulated by the developed and calibrated model, had a good agreement with the experimental results. Thus, the mathematical model developed in this study could be used to explain the cadmium removal process in the FWS constructed wetlands. Hence, it could also be used to predict the fate of cadmium in the industrial effluents treated in FWS constructed wetlands system. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Mathematical modeling techniques can be used to aid in predicting the nature and sequence of relationships between interdependent components and processes in a system. A mathematical model is an idealization of a real situation, in which the most important components are identified and their interactions are described and used as a tool to solve problems [1,2]. A model can be regarded as an assembly of concepts in the form of one or more mathematical equations that approximate the behavior of a natural system or phenomena. Simulation models address the formulation of a mathematical model that simulates a specific situation, with the development of mathematical relationships and solution through a structured and validated process [3]. Many experimental studies have been conducted on the use of constructed wetlands for heavy metals removal from the wastewater effluents [4–19]. However, only little work has been reported on the mathematical modeling of the constructed wetland processes for wastewater treatment [20–24].
The present work was aimed at developing a dynamic mathematical model for describing the fate of cadmium in wastewater treated in a free water surface (FWS) constructed wetlands system. The developed model was validated with the results of the laboratory-scale experiments conducted earlier. 2. Methodology A mathematical model was developed for the cadmium removal process in the FWS constructed wetlands using STELLA program. STELLA is a graphical programming language developed by HPS [25] specifically for system dynamics study. As a graphical programming language, it allows a modeler using the program’s graphical tools and functions to build dynamic models. Models can be configured to run independently with set inputs (either numerically or graphically specified) or in an interactive “flight simulator” mode. Model output can be observed via numerical readouts, tables, and graphs [25,26]. 2.1. Experimental study
∗ Corresponding author. Tel.: +66 81 329 2091; fax: +66 2 889 2138x6388. E-mail addresses: [email protected] (P. Pimpan), [email protected] (R. Jindal). 0304-3894/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhazmat.2008.07.128
Laboratory-scale experiments were conducted earlier at the Suranaree University of Technology Campus in Thailand to investigate the effect of high cadmium loading on the performance of FWS constructed wetlands under different environmental
P. Pimpan, R. Jindal / Journal of Hazardous Materials 163 (2009) 1322–1331
conditions. The experimental setup consisted of five laboratoryscale FWS constructed wetland units designated as R1, R2, R3, R4, and R5 made of zinc plate, with the dimensions (length × width × depth = 2.5 × 0.25 × 0.85 m) and length-to-width ratio of 10:1. Each unit had a 20 cm thick layer of sand with about 0.1 cm particle diameter at the bottom and a 40 cm layer of clay loam soil and sand mixture in 3:1 ratio at the top. Bulrush (Cyperus corymbosus Rottb.) plants were cultivated in the wetland units at approximately 0.15 m intervals, corresponding to 23 rhizomes/m2 , with a planting depth of 0.10 m. A water level of 0.15 m above the substratum surface was maintained in the FWS constructed wetlands. Influent was prepared by mixing a synthetic wastewater with CdCl2 ·H2 O at concentrations of 5, 10, 25, and 50 mg/L for each of the four simultaneous experiments during three runs designated as Runs I–III, respectively. The four simultaneous experiments in the wetland units during the three runs (Runs I–III) were designated as R11, R12, R13, R14, R15; R21, R22, R23, R24, R25; and R31, R32, R33, R34, R35, respectively. The three runs were conducted consecutively by changing the HRT to 5, 7, and 10 d, respectively [19]. 2.2. Sampling and analyses Wastewater samples were collected daily from the influent and effluent points and analyzed for soluble chemical oxygen demand (S-COD) concentration until quasi-steady-state conditions were reached. Subsequently, four parameters were analyzed in the influent and effluent streams including: pH, dissolved oxygen (DO), S-COD, and cadmium. Samples from soils and plants were also analyzed for cadmium accumulations at 2-week intervals and at the end of each run. The wetland was divided into four compartments along the reactor length; 1, 2, 3 and 4. Each compartment representing 1/4 of the reactor volume had Cd removal in three components of wetlands: plants, wastewater, and soil. Samples of wastewater and top soil at five sampling points (including inlet and outlet)
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along the reactor length of the wetland, and four samples of stems, one each from four compartments were taken. At the end of each run, soil samples were taken at the five locations along the lengths and at the depths of 0, 15, 30 and 45 cm from the top of the soil bed. The plants’ samples, both roots and stems, one each from the four compartments were also collected. All samples were analyzed for Cd concentration by flame atomic adsorption spectrometry (FAAS). The concentrations of cadmium initially present in the soil bed were measured in the four compartments. These initial values were multiplied by the volume of soil in the compartment (one-fourth of the wetland) to obtain the amount of Cd accumulation in milligrams (mg). Similar approach was applied to obtain the mass concentrations of cadmium in plants and wastewater. 3. Model development 3.1. Conceptual model The conceptual model for cadmium removal in FWS constructed wetland is shown in Fig. 1. The Cd present in the three components of wetland was expressed by three parameters; cadmium in plants (Cdp), cadmium in wastewater (Cdww), and cadmium in soil (Cds). 3.2. General parameters for cadmium removal model Flow diagram of cadmium removal in FWS constructed wetland using STELLA simulation program is presented in Fig. 2. For Cdp, Cdww and Cds parameters, the suffices 1, 2, 3, and 4 were used for the first, second, third, and fourth compartment, respectively. The other system parameters used in cadmium removal model in this study are shown in Table 1.
Fig. 1. General conceptual model of cadmium removal in FWS constructed wetland.
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Fig. 2. Flow diagram of cadmium removal in FWS constructed wetland using STELLA simulation program.
Eq. (2) may be multiplied by the dry weight of soil, Ms (kg dw), (bulk density of soil, kg dw/m3 × soil volume, m3 ), as shown below:
3.3. Model equations 3.3.1. Adsorption equations of cadmium removal in soil A simplified Freundlich equation, shown in Eq. (1), was chosen to describe the adsorption process in the FWS constructed wetland.
Cds (mg) = 3.678 (L/kg dw)
Cdww (mg) Vwater (L)
+17.621 (mg/kg dw) Ms (kg dw) Cds = K Cdww + b
(3)
(1)
where K is adsorption coefficient (slope) and b is a constant (intercept). Using Eq. (1), the results of regression analysis between Cd accumulation in soil (Cds) and Cd concentration in wastewater (Cdww) helped to obtain the following equation to express the correlation between Cds (mg/kg dw) and Cdww (mg/L):
The resulting equation for each compartment is shown as below:
Cds (mg) =
3.678 (L/kg dw) Ms (kg dw)/4 Vwater (L)/4 +17.621 (mg/kg dw)
Cdww (mg)
Ms (kg dw) 4
(4)
Cds (mg/kg dw) = 3.678 (L/kg dw) Cdww (mg/L) +17.621 (mg/kg dw),
R2 = 0.5324
(2)
Table 1 System parameters used in cadmium removal model in free water surface (FWS) constructed wetlands Parameter Bulk density of soil Total volume of soil in each reactor Dry weight of soil per one-fourth of reactor (Ms) Volume of wastewater per one-fourth of reactor (Vwater )
Value 1210 kg dw/m 0.375 m3 113.44 kg dw 64.69 L
Source 3
Measured Measured Calculated Calculated
3.3.2. Model equations for adsorption used in STELLA simulation program After setting up the model in a flow diagram form (Fig. 2), STELLA program automatically converted the graphical representation to the basic equations. Subsequently, the input data were put in the basic equations to obtain model equations. Finally, the simulation could be started. The basic model equation for cadmium accumulation in soil was transformed from flow diagram as follows: Cds (t) INIT Cds
= Cds (t − dt) + (adsorption − desorption) dt 0.32 mg/kg dw × dry weight of soil(1210 kg dw/m3 × 0.375 m3 ) = 4
where t is the current simulation time and dt is the time interval between calculations (iteration step).
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The adsorption is described by the following expression: INFLOWS:
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Eq. (6) may be multiplied by mp (kg dw) to obtain the equation for each compartment as shown below:
Adsorption = IF(Cds < slope × Cdww + intercept)
Cdp1−4 (mg) =
THEN (slope × Cdww + intercept − Cds) ELSE(0)
140.801 (L/kg dw2 ) [mp1−4 (kg dw)]2 Cdww (mg) Vwater (L) +346.813 (mg/kg dw) mp1−4 (kg dw)
(7)
The subtracted term Cds represents the Cd already present in soil upto that time and a difference is being added to the soil. The expression states that if the concentration in soil is less than the equilibrium concentration, adsorption will occur. The adsorption is in equilibrium with the desorption; thus, the above expressions can be used to describe both processes. Desorption is described as: OUTFLOWS:
where p1–4 , f1–4 , and mp1–4 represent the values for the four compartments (1–4).
Desorption = IF (Cds > slope × Cdww + intercept) THEN((Cds
Cdp (t) INIT Cdp
−intercept)/slope − Cdww) ELSE(0)
3.3.4. Model equations for plant uptake used in STELLA simulation program The basic equation of the model for cadmium removal by plants uptake was transformed from flow diagram as follows: = Cdp (t − dt) + (Uptake1) dt = 16.988 (mg/kg dw) × mp (kg dw)
INFLOWS:
The subtracted term Cdww represents the Cd already present in wastewater upto that time and a difference is being added to the wastewater. The concentration in soil has to be larger than the equilibrium concentration for desorption to occur. 3.3.3. Equations of cadmium removal by plant uptake Initial plant biomass was measured at the beginning of each run. The average value of initial plant biomass was found to be 0.563 kg dw/m2 . Thus, each compartment of the reactor (1/4 of wetland) had an initial plant biomass of 0.1408 kg dw. The mean growth rate (average of three runs) of the bulrush (C. corymbosus Rottb.) in the wetlands were observed to be 0.00294 kg dw/d in the first compartment, 0.00586 kg dw/d in the second compartment, 0.00710 kg dw/d in the third compartment and 0.00588 kg dw/d in the last compartment. Assuming a linear growth, these growth rate values were added to the mass of plants each day, with the resulting values inserted into the model.
Uptake = ((f × mp × Cdww) + Intercept − Cdp) The subtracted term Cdp represents the Cd already present in plants upto that time and a difference is being added to the plants. 3.3.5. Equations for outflow The initial values for Cd in wastewater in four compartments (Cdww1–4 ) and inlet were measured at five sampling points in the wetlands. The average Cd concentration in any compartment was obtained from the concentrations at the starting and end part of it and was multiplied by the volume of water in the compartment (one-fourth of the wetland volume). 3.3.6. Model equations of outflow used in STELLA simulation program The basic equation of the model for instantaneous cadmium concentration in wastewater at time “t” for each compartment was transformed from flow diagram as follows (mass balance):
Cdww (t) = Cdww (t − dt) + (inflow + desorption − uptake − adsorption − outflow)dt INIT Cdww = 0.2 × Vwater INFLOWS: Inflow, mg/d Desorption
= (inflow, L/d) × (input Cd, mg/L) = IF (Cds > slope × Cdww + intercept) THEN((Cds − intercept)/slope − Cdww) ELSE (0) OUTFLOWS:
Uptake Adsorption Outflow, mg/d
= ((f × mp × Cdww) + intercept − Cdp) = IF (Cds < slope × Cdww + intercept) THEN (slope × Cdww + intercept − Cds) ELSE (0) = Cdww
The plants uptake is described by the following equation [22]: Cdp = f × Cdww × mp + c
(5)
where f is a multiplication factor (slope); mp is the dry weight of plants, kg dw and c is a constant (intercept). The relationship between Cd uptake by plants (Cdp) and Cd concentration in wastewater (Cdww) were obtained by regression analysis after multiplying Eq. (5) with dry weight of plants (mp) in four reactors during three runs. Value of “f” was determined from the correlation between Cdp (mg/kg dw) and Cdww × mp (mg × kg dw/L) as follows: Cdp (mg/kg dw) = 140.801 (L/kg dw2 ) Cdww × mp (mg ×kg dw/L) + 346.813 (mg/kg dw), R2 = 0.6218
(6)
4. Result and discussion 4.1. Model calibration The four simultaneous experiments in the wetland units during the three runs (Runs I–III) were designated as R11 (control), R12, R13, R14, R15; R21 (control), R22, R23, R24, R25; and R31 (control), R32, R33, R34, R35, respectively. The model was calibrated by using the equations for Cd accumulation in soil, and for plant uptake for three experiments (R14, R24, and R34). For the calibration of the developed mathematical model, the simulation program was run repeatedly, adjusting the model parameters by trial and error (within reasonable range) until its predictions under similar conditions had good agreement with the selected experimental data. A calibration sequence was followed, starting with the cadmium removal in soil and then uptake by plants.
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Fig. 3. Model calibration for adsorption of Cd in the soil in four compartments during the experiment R14 (mg/d).
4.1.1. Model calibration for adsorption in soil The model calibration by using the experimental data for four compartments of the reactor 4 in the first run, R14 (Cd = 25 mg/L), is illustrated in Fig. 3. For adsorption process, a multiplication factor of 0.05 was used in model calibration as shown below: INFLOWS: Cds < 3.678 × Cdww + 17.621 Adsorption = (3.678 × Cdww + 17.621 − Cds) × 0.05
4.1.3. Comparison of predicted and experimental values of outflow (effluent) in model calibration The comparison of predicted and experimental values of outflow in model calibration for R14 is shown in Fig. 7.
4.2. Model validation The model was validated using the data from the remaining nine experiments (R12, R13, R15, R22, R23, R25, R32, R33, and R35) of the first, second, and third run, respectively.
The correlation between the measured and simulated values of cadmium accumulation in soil for R14 is shown in Fig. 4. The slope of the regression line for R14 was close to 0.5 and correlation (R2 ) was close to 0.9, indicating a good agreement between predicted and observed values.
4.1.2. Model calibration for plant uptake The model calibration by using the experimental data for four compartments of the reactor 4 in run 1 (experiment R14), is illustrated in Fig. 5. For plants uptake, a multiplication factor of 0.09 was used in calibration as shown below: INFLOWS: Uptake =
((140.801 mp2 × Cdww) + 346.813 − Cdp) × 0.09 (64.6875 L)
The correlation between the measured and simulated values of cadmium removal by plants uptake for R14 is shown in Fig. 6. For R14, the slope of the regression line was close to 1, and the correlation (R2 ) was close 0.9, which supports a good model calibration. There was good agreement between the simulated and the experimental values of cadmium accumulation in soil and of plants uptake for the three selected experiments (HRTs of 5, 7 and 10 d at cadmium concentration of 25 mg/L) used for model calibration.
Fig. 4. Correlation between simulated and measured cadmium accumulation in soil for R14.
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Fig. 5. Model calibration for plants uptake of Cd in four compartments during the experiment R14 (mg/d).
4.2.1. Model validation for adsorption in soil The model validation by using the experimental data for four compartments in reactor 3 of the first run, experiment R13 (Cd = 10 mg/L), is illustrated in Fig. 8. The correlation between the measured and simulated values of cadmium accumulation in soil for R13 is shown in Fig. 9. The slope of the regression line for R13 was close to 0.7, and correlations (R2 ) was close to 0.9, which supported a good model validation. 4.2.2. Model validation for plant uptake The model validation for cadmium accumulation by plants uptake for experiment R13 is shown in Fig. 10.
The correlation between the measured and simulated values of cadmium removal by plants uptake for R13 is shown in Fig. 11. The slope of the regression line and R2 for R13 were both close to 0.9, which also supported a good model validation. 4.2.3. Comparison of predicted and experimental values of outflow (effluent) in model validation The comparison of predicted and experimental values of outflow in model validation for R13 is shown in Fig. 12. 4.3. Mass balance The cadmium flows (Cd loading) through all the compartments (state variables), expressed in mg/d, were simulated by the model. The Cd in wastewater was transported to the soil by adsorption process and returned back to wastewater by desorption process. Cadmium in the roots and stems accumulated by plants uptake could be used for their growth, although there is some possibility that decomposed plants mass returned to wastewater. The Cd in plants can be removed from the constructed wetlands system per-
Fig. 6. Correlation between simulated and measured cadmium removal by plants uptake for R14.
Fig. 7. Comparison of predicted and experimental value of outflow in model calibration for R14 (mg/d).
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Fig. 8. Model validation for adsorption of Cd in the soil in four compartments during the experiment R13 (mg/d).
manently by harvesting the plants. Comparison of the simulated and calculated mass balance for the nine experiments is presented in Table 2. The simulated values of cadmium mass fraction present in the effluents relative to the total intake were in the range of 16.7–38.3% in Run I, 5.8–36.8% in Run II, and 0.43–34.6.7% in Run III. The maximum cadmium removal predicted by the model occurred through the accumulation in the soil with mass fraction values of 33.6–56.3% for HRT = 5 d, 35.0–66.9% for HRT = 7 d, and 37.0–76.6% for HRT = 10 d. The mass fraction of the Cd lost via other sinks ranged between 3.5–6.6%, 2.4–6.5%, and 0.3–6.3% of total cadmium intake in Runs I, II, and III, respectively. Predicted mass fractions of cadmium, accumulated in plants, ranged between 21.6–23.7% during Run I, 21.8–24.9% during Run II, and 22.1–23.5%, during Run III. The simulated and measured average Cd removal efficiencies in FWS constructed wetland as shown in Fig. 13 were in the range of 61.7–83.3% and 74.6–82.0% for HRT = 5 d, 63.2–94.2% and 87.2–91.0% HRT = 7 d, and 65.4–99.6% and 95.2–96.5% for HRT = 10 d. The simulated and measured average cadmium removal efficiencies were statistically compared for nine experiments selected for model validation. t-test was used to compare two indepen-
Fig. 9. Correlation between simulated and measured cadmium accumulation in soil for R13.
Table 2 Simulated and measured mass balance of cadmium during nine experiments Experiments
R12 R13 R15 R22 R23 R25 R32 R33 R35
Simulated Cd mass fraction (%)
Measured Cd mass fraction (%)
Eff
Plants
Soil
Other
R.E.
Eff
Plants
Soil
Other
R.E.
16.71 23.63 38.28 5.79 16.49 36.78 0.43 16.71 34.57
23.46 23.73 21.56 24.91 24.82 21.79 22.71 23.46 22.10
56.29 47.24 33.58 66.90 53.87 34.98 76.58 56.29 37.04
3.54 5.40 6.58 2.40 4.82 6.45 0.28 3.54 6.29
83.29 76.37 61.72 94.21 83.51 63.22 99.57 83.29 65.43
18.03 19.21 25.45 9.04 10.94 12.81 3.53 4.29 4.82
22.50 22.91 15.44 14.43 16.90 21.42 18.90 19.91 22.94
57.93 56.31 57.50 74.84 70.37 63.89 75.45 73.61 69.91
1.54 1.56 1.61 1.69 1.79 1.88 2.12 2.19 2.33
81.97 80.79 74.55 90.96 89.06 87.19 96.47 95.71 95.18
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Fig. 10. Model validation for plants uptake of Cd in four compartments during the experiment R13 (mg/d).
Table 3 The independent samples t-test of measured and simulated average Cd removal efficiencies Independent samples test
Cd removal
Equal variances assumed Equal variances not assumed
Levene’s test for equality of variances
t-test for equality of means
F
Sig.
t
d.f.
Sig. (2-tailed)
Mean difference
Standard error difference
Lower
Upper
3.283
0.089
1.752
16
0.099
9.0300
5.15428
−1.89658
19.95658
1.752
12.632
0.104
9.0300
5.15428
−2.13824
20.19824
95% Confidence interval of the difference
dent groups (independent samples t-test). Table 3 shows results of statistical analysis. It can be seen that the level of significance in the Levene’s test for equality of variances was 0.089. Thus, the predicted and measured values of the Cd removal in FWS constructed wetlands were in good agreement. Therefore, the developed mathematical model in this study could be used to describe the cadmium removal process in the FWS constructed wetlands.
Fig. 11. Correlation between simulated and measured cadmium removal by plants uptake for R13.
Fig. 12. Comparison of predicted and experimental value of outflow in model validation for R13 (mg/d).
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Fig. 13. Comparison of simulated and measured average Cd removal efficiencies during three experimental runs.
5. Conclusions A mathematical model for describing the cadmium removal process in the FWS constructed wetlands was developed using STELLA program. The simulated values of cadmium concentrations in effluents as well as in various components of the FWS constructed wetlands system had a good agreement with the experimental results. The Cd in wastewater was transported to the soil by adsorption process and returned back to wastewater by desorption process. Cadmium in the roots and stems accumulated by plants uptake could be used for their growth, although there is some possibility that decomposed plants mass returned to wastewater. The Cd can be removed from the constructed wetlands system permanently by harvesting the plants. The simulated and measured average Cd removal efficiencies for nine experiments, used for model validation (ranging between 61.7–99.6% and 74.6–96.5%, respectively). t-test was used to compare two independent groups (independent samples ttest). The predicted and measured values of the Cd removal in FWS constructed wetlands were in good agreement. Therefore, the developed mathematical model in this study could be used to describe the cadmium removal process in the FWS constructed wetlands. Acknowledgements This study was supported by the funding from the Royal Golden Jubilee Ph.D. Scholarship Grant (RGJ-Ph.D.) of Thailand Research Fund (TRF), Thailand. The authors also acknowledge the assistance provided by the Suranaree University of Technology (SUT). References [1] S.E. Jorgensen, Fundamentals of Ecological Modeling, 9, Elsevier, Amsterdam, 1986. [2] G.T. Daigger, C.P.L. Grady, The dynamics of microbial growth on soluble substrate: a unifying theory, Water Res. 16 (1982) 365–382. [3] K. Tantrakarnapa, Performance evaluation and modeling of upflow anaerobic sludge blanket process treating dairy wastewater, Doctoral Dissertation, Suranaree University of Technology, Nakhon Ratchasima, Thailand, 2003. [4] R.L.P. Kleinmann, M.A. Girts, Acid mine water treatment in wetlands: an overview of a emergent technology, in: K.R. Reddy, W.H. Smith (Eds.), Aquatic Plants for Wastewater Treatment and Resources Recovery, Magnolia Public, Orlando, Florida, 1987, pp. 255–259.
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Mathematical modeling of cadmium removal in free water surface constructed wetlands P. Pimpan a , R. Jindal b,∗ a Chemistry Program, Department of Science, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, 398, Sawanwithee Road, Muang, Nakhon Sawan 60000, Thailand b Environmental Engineering Program, Department of Civil Engineering, Faculty of Engineering, Mahidol University, 25/25, Putthamonthon 4 Road, Salaya, Nakhorn Pathom 73170, Thailand
a r t i c l e
i n f o
Article history: Received 29 January 2008 Received in revised form 27 June 2008 Accepted 24 July 2008 Available online 5 August 2008 Keywords: Cadmium Constructed wetlands Free water surface Mathematical modeling STELLA program
a b s t r a c t A mathematical model was developed for the cadmium removal process in the free water surface (FWS) constructed wetlands using a dynamic software program STELLA. Earlier, laboratory-scale experiments were conducted at the Suranaree University of Technology Campus in Northeastern Thailand to investigate the effect of high cadmium loading on the performance of FWS constructed wetlands under different environmental conditions. The predicted values of cadmium concentrations in effluents as well as in various components of the FWS constructed wetlands system, as simulated by the developed and calibrated model, had a good agreement with the experimental results. Thus, the mathematical model developed in this study could be used to explain the cadmium removal process in the FWS constructed wetlands. Hence, it could also be used to predict the fate of cadmium in the industrial effluents treated in FWS constructed wetlands system. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Mathematical modeling techniques can be used to aid in predicting the nature and sequence of relationships between interdependent components and processes in a system. A mathematical model is an idealization of a real situation, in which the most important components are identified and their interactions are described and used as a tool to solve problems [1,2]. A model can be regarded as an assembly of concepts in the form of one or more mathematical equations that approximate the behavior of a natural system or phenomena. Simulation models address the formulation of a mathematical model that simulates a specific situation, with the development of mathematical relationships and solution through a structured and validated process [3]. Many experimental studies have been conducted on the use of constructed wetlands for heavy metals removal from the wastewater effluents [4–19]. However, only little work has been reported on the mathematical modeling of the constructed wetland processes for wastewater treatment [20–24].
The present work was aimed at developing a dynamic mathematical model for describing the fate of cadmium in wastewater treated in a free water surface (FWS) constructed wetlands system. The developed model was validated with the results of the laboratory-scale experiments conducted earlier. 2. Methodology A mathematical model was developed for the cadmium removal process in the FWS constructed wetlands using STELLA program. STELLA is a graphical programming language developed by HPS [25] specifically for system dynamics study. As a graphical programming language, it allows a modeler using the program’s graphical tools and functions to build dynamic models. Models can be configured to run independently with set inputs (either numerically or graphically specified) or in an interactive “flight simulator” mode. Model output can be observed via numerical readouts, tables, and graphs [25,26]. 2.1. Experimental study
∗ Corresponding author. Tel.: +66 81 329 2091; fax: +66 2 889 2138x6388. E-mail addresses: [email protected] (P. Pimpan), [email protected] (R. Jindal). 0304-3894/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhazmat.2008.07.128
Laboratory-scale experiments were conducted earlier at the Suranaree University of Technology Campus in Thailand to investigate the effect of high cadmium loading on the performance of FWS constructed wetlands under different environmental
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conditions. The experimental setup consisted of five laboratoryscale FWS constructed wetland units designated as R1, R2, R3, R4, and R5 made of zinc plate, with the dimensions (length × width × depth = 2.5 × 0.25 × 0.85 m) and length-to-width ratio of 10:1. Each unit had a 20 cm thick layer of sand with about 0.1 cm particle diameter at the bottom and a 40 cm layer of clay loam soil and sand mixture in 3:1 ratio at the top. Bulrush (Cyperus corymbosus Rottb.) plants were cultivated in the wetland units at approximately 0.15 m intervals, corresponding to 23 rhizomes/m2 , with a planting depth of 0.10 m. A water level of 0.15 m above the substratum surface was maintained in the FWS constructed wetlands. Influent was prepared by mixing a synthetic wastewater with CdCl2 ·H2 O at concentrations of 5, 10, 25, and 50 mg/L for each of the four simultaneous experiments during three runs designated as Runs I–III, respectively. The four simultaneous experiments in the wetland units during the three runs (Runs I–III) were designated as R11, R12, R13, R14, R15; R21, R22, R23, R24, R25; and R31, R32, R33, R34, R35, respectively. The three runs were conducted consecutively by changing the HRT to 5, 7, and 10 d, respectively [19]. 2.2. Sampling and analyses Wastewater samples were collected daily from the influent and effluent points and analyzed for soluble chemical oxygen demand (S-COD) concentration until quasi-steady-state conditions were reached. Subsequently, four parameters were analyzed in the influent and effluent streams including: pH, dissolved oxygen (DO), S-COD, and cadmium. Samples from soils and plants were also analyzed for cadmium accumulations at 2-week intervals and at the end of each run. The wetland was divided into four compartments along the reactor length; 1, 2, 3 and 4. Each compartment representing 1/4 of the reactor volume had Cd removal in three components of wetlands: plants, wastewater, and soil. Samples of wastewater and top soil at five sampling points (including inlet and outlet)
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along the reactor length of the wetland, and four samples of stems, one each from four compartments were taken. At the end of each run, soil samples were taken at the five locations along the lengths and at the depths of 0, 15, 30 and 45 cm from the top of the soil bed. The plants’ samples, both roots and stems, one each from the four compartments were also collected. All samples were analyzed for Cd concentration by flame atomic adsorption spectrometry (FAAS). The concentrations of cadmium initially present in the soil bed were measured in the four compartments. These initial values were multiplied by the volume of soil in the compartment (one-fourth of the wetland) to obtain the amount of Cd accumulation in milligrams (mg). Similar approach was applied to obtain the mass concentrations of cadmium in plants and wastewater. 3. Model development 3.1. Conceptual model The conceptual model for cadmium removal in FWS constructed wetland is shown in Fig. 1. The Cd present in the three components of wetland was expressed by three parameters; cadmium in plants (Cdp), cadmium in wastewater (Cdww), and cadmium in soil (Cds). 3.2. General parameters for cadmium removal model Flow diagram of cadmium removal in FWS constructed wetland using STELLA simulation program is presented in Fig. 2. For Cdp, Cdww and Cds parameters, the suffices 1, 2, 3, and 4 were used for the first, second, third, and fourth compartment, respectively. The other system parameters used in cadmium removal model in this study are shown in Table 1.
Fig. 1. General conceptual model of cadmium removal in FWS constructed wetland.
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Fig. 2. Flow diagram of cadmium removal in FWS constructed wetland using STELLA simulation program.
Eq. (2) may be multiplied by the dry weight of soil, Ms (kg dw), (bulk density of soil, kg dw/m3 × soil volume, m3 ), as shown below:
3.3. Model equations 3.3.1. Adsorption equations of cadmium removal in soil A simplified Freundlich equation, shown in Eq. (1), was chosen to describe the adsorption process in the FWS constructed wetland.
Cds (mg) = 3.678 (L/kg dw)
Cdww (mg) Vwater (L)
+17.621 (mg/kg dw) Ms (kg dw) Cds = K Cdww + b
(3)
(1)
where K is adsorption coefficient (slope) and b is a constant (intercept). Using Eq. (1), the results of regression analysis between Cd accumulation in soil (Cds) and Cd concentration in wastewater (Cdww) helped to obtain the following equation to express the correlation between Cds (mg/kg dw) and Cdww (mg/L):
The resulting equation for each compartment is shown as below:
Cds (mg) =
3.678 (L/kg dw) Ms (kg dw)/4 Vwater (L)/4 +17.621 (mg/kg dw)
Cdww (mg)
Ms (kg dw) 4
(4)
Cds (mg/kg dw) = 3.678 (L/kg dw) Cdww (mg/L) +17.621 (mg/kg dw),
R2 = 0.5324
(2)
Table 1 System parameters used in cadmium removal model in free water surface (FWS) constructed wetlands Parameter Bulk density of soil Total volume of soil in each reactor Dry weight of soil per one-fourth of reactor (Ms) Volume of wastewater per one-fourth of reactor (Vwater )
Value 1210 kg dw/m 0.375 m3 113.44 kg dw 64.69 L
Source 3
Measured Measured Calculated Calculated
3.3.2. Model equations for adsorption used in STELLA simulation program After setting up the model in a flow diagram form (Fig. 2), STELLA program automatically converted the graphical representation to the basic equations. Subsequently, the input data were put in the basic equations to obtain model equations. Finally, the simulation could be started. The basic model equation for cadmium accumulation in soil was transformed from flow diagram as follows: Cds (t) INIT Cds
= Cds (t − dt) + (adsorption − desorption) dt 0.32 mg/kg dw × dry weight of soil(1210 kg dw/m3 × 0.375 m3 ) = 4
where t is the current simulation time and dt is the time interval between calculations (iteration step).
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The adsorption is described by the following expression: INFLOWS:
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Eq. (6) may be multiplied by mp (kg dw) to obtain the equation for each compartment as shown below:
Adsorption = IF(Cds < slope × Cdww + intercept)
Cdp1−4 (mg) =
THEN (slope × Cdww + intercept − Cds) ELSE(0)
140.801 (L/kg dw2 ) [mp1−4 (kg dw)]2 Cdww (mg) Vwater (L) +346.813 (mg/kg dw) mp1−4 (kg dw)
(7)
The subtracted term Cds represents the Cd already present in soil upto that time and a difference is being added to the soil. The expression states that if the concentration in soil is less than the equilibrium concentration, adsorption will occur. The adsorption is in equilibrium with the desorption; thus, the above expressions can be used to describe both processes. Desorption is described as: OUTFLOWS:
where p1–4 , f1–4 , and mp1–4 represent the values for the four compartments (1–4).
Desorption = IF (Cds > slope × Cdww + intercept) THEN((Cds
Cdp (t) INIT Cdp
−intercept)/slope − Cdww) ELSE(0)
3.3.4. Model equations for plant uptake used in STELLA simulation program The basic equation of the model for cadmium removal by plants uptake was transformed from flow diagram as follows: = Cdp (t − dt) + (Uptake1) dt = 16.988 (mg/kg dw) × mp (kg dw)
INFLOWS:
The subtracted term Cdww represents the Cd already present in wastewater upto that time and a difference is being added to the wastewater. The concentration in soil has to be larger than the equilibrium concentration for desorption to occur. 3.3.3. Equations of cadmium removal by plant uptake Initial plant biomass was measured at the beginning of each run. The average value of initial plant biomass was found to be 0.563 kg dw/m2 . Thus, each compartment of the reactor (1/4 of wetland) had an initial plant biomass of 0.1408 kg dw. The mean growth rate (average of three runs) of the bulrush (C. corymbosus Rottb.) in the wetlands were observed to be 0.00294 kg dw/d in the first compartment, 0.00586 kg dw/d in the second compartment, 0.00710 kg dw/d in the third compartment and 0.00588 kg dw/d in the last compartment. Assuming a linear growth, these growth rate values were added to the mass of plants each day, with the resulting values inserted into the model.
Uptake = ((f × mp × Cdww) + Intercept − Cdp) The subtracted term Cdp represents the Cd already present in plants upto that time and a difference is being added to the plants. 3.3.5. Equations for outflow The initial values for Cd in wastewater in four compartments (Cdww1–4 ) and inlet were measured at five sampling points in the wetlands. The average Cd concentration in any compartment was obtained from the concentrations at the starting and end part of it and was multiplied by the volume of water in the compartment (one-fourth of the wetland volume). 3.3.6. Model equations of outflow used in STELLA simulation program The basic equation of the model for instantaneous cadmium concentration in wastewater at time “t” for each compartment was transformed from flow diagram as follows (mass balance):
Cdww (t) = Cdww (t − dt) + (inflow + desorption − uptake − adsorption − outflow)dt INIT Cdww = 0.2 × Vwater INFLOWS: Inflow, mg/d Desorption
= (inflow, L/d) × (input Cd, mg/L) = IF (Cds > slope × Cdww + intercept) THEN((Cds − intercept)/slope − Cdww) ELSE (0) OUTFLOWS:
Uptake Adsorption Outflow, mg/d
= ((f × mp × Cdww) + intercept − Cdp) = IF (Cds < slope × Cdww + intercept) THEN (slope × Cdww + intercept − Cds) ELSE (0) = Cdww
The plants uptake is described by the following equation [22]: Cdp = f × Cdww × mp + c
(5)
where f is a multiplication factor (slope); mp is the dry weight of plants, kg dw and c is a constant (intercept). The relationship between Cd uptake by plants (Cdp) and Cd concentration in wastewater (Cdww) were obtained by regression analysis after multiplying Eq. (5) with dry weight of plants (mp) in four reactors during three runs. Value of “f” was determined from the correlation between Cdp (mg/kg dw) and Cdww × mp (mg × kg dw/L) as follows: Cdp (mg/kg dw) = 140.801 (L/kg dw2 ) Cdww × mp (mg ×kg dw/L) + 346.813 (mg/kg dw), R2 = 0.6218
(6)
4. Result and discussion 4.1. Model calibration The four simultaneous experiments in the wetland units during the three runs (Runs I–III) were designated as R11 (control), R12, R13, R14, R15; R21 (control), R22, R23, R24, R25; and R31 (control), R32, R33, R34, R35, respectively. The model was calibrated by using the equations for Cd accumulation in soil, and for plant uptake for three experiments (R14, R24, and R34). For the calibration of the developed mathematical model, the simulation program was run repeatedly, adjusting the model parameters by trial and error (within reasonable range) until its predictions under similar conditions had good agreement with the selected experimental data. A calibration sequence was followed, starting with the cadmium removal in soil and then uptake by plants.
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Fig. 3. Model calibration for adsorption of Cd in the soil in four compartments during the experiment R14 (mg/d).
4.1.1. Model calibration for adsorption in soil The model calibration by using the experimental data for four compartments of the reactor 4 in the first run, R14 (Cd = 25 mg/L), is illustrated in Fig. 3. For adsorption process, a multiplication factor of 0.05 was used in model calibration as shown below: INFLOWS: Cds < 3.678 × Cdww + 17.621 Adsorption = (3.678 × Cdww + 17.621 − Cds) × 0.05
4.1.3. Comparison of predicted and experimental values of outflow (effluent) in model calibration The comparison of predicted and experimental values of outflow in model calibration for R14 is shown in Fig. 7.
4.2. Model validation The model was validated using the data from the remaining nine experiments (R12, R13, R15, R22, R23, R25, R32, R33, and R35) of the first, second, and third run, respectively.
The correlation between the measured and simulated values of cadmium accumulation in soil for R14 is shown in Fig. 4. The slope of the regression line for R14 was close to 0.5 and correlation (R2 ) was close to 0.9, indicating a good agreement between predicted and observed values.
4.1.2. Model calibration for plant uptake The model calibration by using the experimental data for four compartments of the reactor 4 in run 1 (experiment R14), is illustrated in Fig. 5. For plants uptake, a multiplication factor of 0.09 was used in calibration as shown below: INFLOWS: Uptake =
((140.801 mp2 × Cdww) + 346.813 − Cdp) × 0.09 (64.6875 L)
The correlation between the measured and simulated values of cadmium removal by plants uptake for R14 is shown in Fig. 6. For R14, the slope of the regression line was close to 1, and the correlation (R2 ) was close 0.9, which supports a good model calibration. There was good agreement between the simulated and the experimental values of cadmium accumulation in soil and of plants uptake for the three selected experiments (HRTs of 5, 7 and 10 d at cadmium concentration of 25 mg/L) used for model calibration.
Fig. 4. Correlation between simulated and measured cadmium accumulation in soil for R14.
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Fig. 5. Model calibration for plants uptake of Cd in four compartments during the experiment R14 (mg/d).
4.2.1. Model validation for adsorption in soil The model validation by using the experimental data for four compartments in reactor 3 of the first run, experiment R13 (Cd = 10 mg/L), is illustrated in Fig. 8. The correlation between the measured and simulated values of cadmium accumulation in soil for R13 is shown in Fig. 9. The slope of the regression line for R13 was close to 0.7, and correlations (R2 ) was close to 0.9, which supported a good model validation. 4.2.2. Model validation for plant uptake The model validation for cadmium accumulation by plants uptake for experiment R13 is shown in Fig. 10.
The correlation between the measured and simulated values of cadmium removal by plants uptake for R13 is shown in Fig. 11. The slope of the regression line and R2 for R13 were both close to 0.9, which also supported a good model validation. 4.2.3. Comparison of predicted and experimental values of outflow (effluent) in model validation The comparison of predicted and experimental values of outflow in model validation for R13 is shown in Fig. 12. 4.3. Mass balance The cadmium flows (Cd loading) through all the compartments (state variables), expressed in mg/d, were simulated by the model. The Cd in wastewater was transported to the soil by adsorption process and returned back to wastewater by desorption process. Cadmium in the roots and stems accumulated by plants uptake could be used for their growth, although there is some possibility that decomposed plants mass returned to wastewater. The Cd in plants can be removed from the constructed wetlands system per-
Fig. 6. Correlation between simulated and measured cadmium removal by plants uptake for R14.
Fig. 7. Comparison of predicted and experimental value of outflow in model calibration for R14 (mg/d).
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Fig. 8. Model validation for adsorption of Cd in the soil in four compartments during the experiment R13 (mg/d).
manently by harvesting the plants. Comparison of the simulated and calculated mass balance for the nine experiments is presented in Table 2. The simulated values of cadmium mass fraction present in the effluents relative to the total intake were in the range of 16.7–38.3% in Run I, 5.8–36.8% in Run II, and 0.43–34.6.7% in Run III. The maximum cadmium removal predicted by the model occurred through the accumulation in the soil with mass fraction values of 33.6–56.3% for HRT = 5 d, 35.0–66.9% for HRT = 7 d, and 37.0–76.6% for HRT = 10 d. The mass fraction of the Cd lost via other sinks ranged between 3.5–6.6%, 2.4–6.5%, and 0.3–6.3% of total cadmium intake in Runs I, II, and III, respectively. Predicted mass fractions of cadmium, accumulated in plants, ranged between 21.6–23.7% during Run I, 21.8–24.9% during Run II, and 22.1–23.5%, during Run III. The simulated and measured average Cd removal efficiencies in FWS constructed wetland as shown in Fig. 13 were in the range of 61.7–83.3% and 74.6–82.0% for HRT = 5 d, 63.2–94.2% and 87.2–91.0% HRT = 7 d, and 65.4–99.6% and 95.2–96.5% for HRT = 10 d. The simulated and measured average cadmium removal efficiencies were statistically compared for nine experiments selected for model validation. t-test was used to compare two indepen-
Fig. 9. Correlation between simulated and measured cadmium accumulation in soil for R13.
Table 2 Simulated and measured mass balance of cadmium during nine experiments Experiments
R12 R13 R15 R22 R23 R25 R32 R33 R35
Simulated Cd mass fraction (%)
Measured Cd mass fraction (%)
Eff
Plants
Soil
Other
R.E.
Eff
Plants
Soil
Other
R.E.
16.71 23.63 38.28 5.79 16.49 36.78 0.43 16.71 34.57
23.46 23.73 21.56 24.91 24.82 21.79 22.71 23.46 22.10
56.29 47.24 33.58 66.90 53.87 34.98 76.58 56.29 37.04
3.54 5.40 6.58 2.40 4.82 6.45 0.28 3.54 6.29
83.29 76.37 61.72 94.21 83.51 63.22 99.57 83.29 65.43
18.03 19.21 25.45 9.04 10.94 12.81 3.53 4.29 4.82
22.50 22.91 15.44 14.43 16.90 21.42 18.90 19.91 22.94
57.93 56.31 57.50 74.84 70.37 63.89 75.45 73.61 69.91
1.54 1.56 1.61 1.69 1.79 1.88 2.12 2.19 2.33
81.97 80.79 74.55 90.96 89.06 87.19 96.47 95.71 95.18
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Fig. 10. Model validation for plants uptake of Cd in four compartments during the experiment R13 (mg/d).
Table 3 The independent samples t-test of measured and simulated average Cd removal efficiencies Independent samples test
Cd removal
Equal variances assumed Equal variances not assumed
Levene’s test for equality of variances
t-test for equality of means
F
Sig.
t
d.f.
Sig. (2-tailed)
Mean difference
Standard error difference
Lower
Upper
3.283
0.089
1.752
16
0.099
9.0300
5.15428
−1.89658
19.95658
1.752
12.632
0.104
9.0300
5.15428
−2.13824
20.19824
95% Confidence interval of the difference
dent groups (independent samples t-test). Table 3 shows results of statistical analysis. It can be seen that the level of significance in the Levene’s test for equality of variances was 0.089. Thus, the predicted and measured values of the Cd removal in FWS constructed wetlands were in good agreement. Therefore, the developed mathematical model in this study could be used to describe the cadmium removal process in the FWS constructed wetlands.
Fig. 11. Correlation between simulated and measured cadmium removal by plants uptake for R13.
Fig. 12. Comparison of predicted and experimental value of outflow in model validation for R13 (mg/d).
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Fig. 13. Comparison of simulated and measured average Cd removal efficiencies during three experimental runs.
5. Conclusions A mathematical model for describing the cadmium removal process in the FWS constructed wetlands was developed using STELLA program. The simulated values of cadmium concentrations in effluents as well as in various components of the FWS constructed wetlands system had a good agreement with the experimental results. The Cd in wastewater was transported to the soil by adsorption process and returned back to wastewater by desorption process. Cadmium in the roots and stems accumulated by plants uptake could be used for their growth, although there is some possibility that decomposed plants mass returned to wastewater. The Cd can be removed from the constructed wetlands system permanently by harvesting the plants. The simulated and measured average Cd removal efficiencies for nine experiments, used for model validation (ranging between 61.7–99.6% and 74.6–96.5%, respectively). t-test was used to compare two independent groups (independent samples ttest). The predicted and measured values of the Cd removal in FWS constructed wetlands were in good agreement. Therefore, the developed mathematical model in this study could be used to describe the cadmium removal process in the FWS constructed wetlands. Acknowledgements This study was supported by the funding from the Royal Golden Jubilee Ph.D. Scholarship Grant (RGJ-Ph.D.) of Thailand Research Fund (TRF), Thailand. The authors also acknowledge the assistance provided by the Suranaree University of Technology (SUT). References [1] S.E. Jorgensen, Fundamentals of Ecological Modeling, 9, Elsevier, Amsterdam, 1986. [2] G.T. Daigger, C.P.L. Grady, The dynamics of microbial growth on soluble substrate: a unifying theory, Water Res. 16 (1982) 365–382. [3] K. Tantrakarnapa, Performance evaluation and modeling of upflow anaerobic sludge blanket process treating dairy wastewater, Doctoral Dissertation, Suranaree University of Technology, Nakhon Ratchasima, Thailand, 2003. [4] R.L.P. Kleinmann, M.A. Girts, Acid mine water treatment in wetlands: an overview of a emergent technology, in: K.R. Reddy, W.H. Smith (Eds.), Aquatic Plants for Wastewater Treatment and Resources Recovery, Magnolia Public, Orlando, Florida, 1987, pp. 255–259.
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