Journal of Scientific & Industrial Research Vol. 64, October 2005, pp. 717-721 Mathematical model for phytoremediation of pulp and paper industry wastewater S Kumar 1, K K Dube 1 and J P N Rai 2, * 1 Department of Mathematics, Statistics & Computer Science, 2 Department of Environmental Science, G B Pant University of Agriculture & Technology, Pantnagar 263 145 Received 17 November 2004; revised 21 June 2005; accepted 21 July 2005 A mathematical model for studying the phytoremediation potential of water hyacinth (Eichhornia crassipes) against pulp and paper industry effluent is developed and analyzed. Initially, phytoremediation potential increased for short time and then leveled off, resulting into consequent pollutant removal, which enabled to calculate logistic differential equation for developing uninhibited growth model. The model developed is applied to some important physico-chemical parameters (ph, EC, BOD, COD, TSS, TDS, Na and K) of the effluent treated using cost effective phytoremediation technology. Keywords: Mathematical model, Phytoremediation, Water hyacinth, Pulp and paper industry, Wastewater IPC Code: C0F3/32 Introduction The physico-chemical processes employed in industrial waste treatment for the removal of dissolved materials are screening, coagulation, flocculation, activated carbon treatment, reverse osmosis, electrodialysis, ion exchange, chemical oxidation, trickling filteration and activated sludge digestion. All these processes involve high energy and large capital investments. Phytoremediation, the use of plants to remediate environmental media, is being pursued as a new approach for the cleanup of contaminated soils and waters, including groundwater. It involves the interaction of plant roots and microorganisms associated with these root systems to remediate soils containing elevated concentrations of organic compounds. This technique could provide cost-effective methods of remediating soils and groundwater contaminated with metals, radionuclides, and various types of organics, with fewer secondary wastes and less environmental impact than would be generated using traditional remediation methods. All plants extract nutrients, including metals, from their soil and water environments. Some plants (hyperaccumulators) have the ability to store large amounts of metals, even some metals that do not appear to be required for plant functioning. In addition, plants can take up various organic chemicals *Author for correspondence E-mail: raijpn@yahoo.com from environmental media and degrade or otherwise process them for use in their physiological processes. Additional research, including genetic engineering, is being conducted to improve the natural capabilities of plants to perform remediation functions and to investigate other plants with potential phytoremediation applications 1-4. Efforts have been made to develop mathematical models for physical and chemical means of wastewater treatment 5,6. In present paper, attempt has been made to develop a mathematical model for the prediction of pollution load removal from one of the deadliest wastewater of pulp and paper industry employing phytoremediation by water hyacinth (Eichhornia crassipes Solms). Mathematical Model Assumptions Variation in the parameters is assumed due to phytoremediation by E. crassipes of the effluent of pulp and paper industry containing heavy load of organic and inorganic compounds. In this study, it is assumed that with increasing time, the concentration and/or efficacy of the pollutants decreases by the aquatic weeds that can scavenge inorganic and some organic compounds from wastewater. However, beyond attainment of equilibrium (equal to plant carrying capacity for pollutant sequestration) plants seize to contribute towards pollution removal. The variation in parameters 7-9 caused by phytoremediation of industrial effluent cannot exceed beyond finite limit and is maximum at the first day of experiment.
718 J SCI IND RES VOL 64 OCTOBER 2005 Phytoremediation Model Let P be the phytoremediation potential of the water hyacinth at time t from initial day of the experiment. Then the rate of change in P with respect to t from initial day of the experiment upto the time when plants attain equilibrium is directly proportional to P, at that time. dp P P dt α = µ (1) where µ is a constant. Integrating Eq. (1), ln P = µ t + C, (2) where C is the constant of integration. To get the value of C, put the initial condition in Eq. (2) as at the starting day of the experiment, i.e. t = 0; P will be maximum, let it be P 0. Then, ln P 0 =µ. 0 + C or C = ln P 0. Putting the value of C in Eq. (2), ln P = µt + ln P 0 or ln P ln P 0 = µt or ln(p/ P 0 ) = µt or P/ P 0 = exp (µt) or P = P 0 exp (µt) (3) Now when plant attains equilibrium after 45 days, change in P with respect to t tends to zero, dp 0 dt = Which implies that, P = b (4) where b is a constant. Now combining Eqs 3 and 4, P=P 0 exp (µt) (before attaining equilibrium) = b (after attaining equilibrium) (5) Properties of the Model The model derived is valid only for t > 0 days. The value of µ depends upon the curve of difference according to the time lapse, i.e. µ will be positive if the curve is increasing, otherwise negative. From Eq. (3) µ = {ln (P/ P 0 )}/t Now take t at equal interval, let these be t 1, t 2, t 3,, t N. Then µ i = {ln(p i / P 0 )}/t i, where i= 1, 2, 3, N. µ = N µ 1 i N Then by putting the value of µ in the Eq. (3), one can predict the activity. Materials and Methods Young aquatic plants of E. crassipes collected from the natural pond at Baheri (near Pantnagar) were washed thoroughly with running tap water to avoid any surface contamination and kept in cemented tank containing tap water. The experiment was performed with five replicates in plastic tubs (15 cm deep; 40 cm diam; capacity, 8 l). Based on earlier study 10, industrial wastewater (25% conc.) collected from Century Pulp and Paper Industry, Lalkuan was used. In each tub, one plant was allowed to grow for 60 days. The corresponding control treatment devoid of plants was also maintained to find out the declination in effluent characteristics caused by factors other than phytoremediator plants. In order to provide dissolved oxygen to the plant roots, mechanical aeration was given by air pump (10 min/tub) at three days interval through out the experimental period. Analysis of ph, electrical conductivity (EC), biochemical oxygen demand (BOD), chemical oxygen demand (COD), total suspended solids (TSS), total dissolved solids (TDS), Na and K of the effluent drawn from experimental treatments was done at 0, 15, 30, 45 and 60 days of start of the experiment using standard methods outlined in APHA 11 (Table 1). The plant growth parameters such as leaf area, chlorophyll content and biomass yield were also recorded on each observation date. For application of the model to the observed data, method discussed in the above section and in an earlier publication 12 was used. For three-equidistant time intervals, observations corresponded to 0, 15, 30 and 45 days. Phytoremediator plant attained fatigue for sequestering nutrients from industrial waste after 45 days of phytoremediation, hence data collected beyond 45 days has been omitted from calculating µ. From these observations, value of µ was calculated (Tables 2-3) and the predicted value of P of E. crassipes was compared with the observed value (Figs 1-2).
KUMAR et al: PHYTOREMEDIATION OF PULP AND PAPER INDUSTRY WASTEWATER 719 Table 1 Effect of E. crassipes on physiochemical characteristics (±SE) of pulp and paper industry effluent phytoremediated for different duration Phytoremediation period Effluent parameter d 0 15 30 45 60 ph 7.85±0.01 7.61±0.01 7.48±0.01 7.32±0.01 7.30±0.01 EC, µs/cm 963.3±3.33 693.3±3.33 483.3±3.33 260±3.33 258±3.33 BOD, ppm 310.3±5.77 170±5.77 124.3±5.77 85.3±5.77 85.3±5.70 COD, ppm 800±17.77 448±17.77 309.3±17.77 192±17.77 190±16.00 TSS, ppm 406.7±17.54 213.3±17.54 213.3±17.54 100±17.54 98±15.54 TDS, ppm 633.3±32.54 346.7±32.54 253.3±32.54 140±32.54 140±32.54 Na, ppm 19.3±0.12 15.4±0.12 13.5±0.12 11.9±0.12 11.5±0.12 K, ppm 39.4±0.17 30.5±0.17 26.6±0.17 22.3±0.17 23.0±0.16 Table 2 Calculation of µ for ph, EC, COD and BOD t i P i P i /Po Ln(P/P 0 ) µi =ln(p/p 0 )/s Mean µ ph 0 7.85 1 0 15 7.61 0.969427-0.03105-0.00207-0.00174 30 7.48 0.952866-0.04828-0. 00161 45 7.32 0.932484-0.0699-0.00155 EC 0 963.3 1 0 15 683.3 0.709333-0.34343-0.0229-0.0229 30 483.3 0.501713-0.68973-0.02299 45 345 0.358144-1.02682-0.02282 COD 0 800 1 0 15 497.4 0.62175-0.47522-0.03168-0.03169 30 309.3 0.386625-0.9503-0.03168 45 192 0.24-1.42712-0.03171 BOD 0 310.3 1 0 15 197 0.634869-0.45434-0.03029-0.03027 30 124.3 0.40058-0.91484-0.03049 45 80.3 0.258782-1.35177-0.03004 Table 3 Calculation of µ for TSS, TDS, Na and K t I P I P I /Po Ln(P/P 0 ) µ I =ln(p/p 0 )/s Mean µ TSS 0 406.7 1 0 15 279.3 0.686747-0.37579-0.02505-0.02507 30 191.3 0.470371-0.75423-0.02514 45 132 0.324564-1.12527-0.02501 TDS 0 633.3 1 0 15 398.8 0.629717-0.46248-0.03083-0.03068 30 253.3 0.399968-0.91637-0.03055 45 159.3 0.25154-1.38016-0.03067 Na 0 19.3 1 0 15 16.4 0.849741-0.16282-0.01085-0.01085 30 13.9 0.720207-0.32822-0.01094 45 11.9 0.61658-0.48357-0.01075 K 0 39.4 1 0 15 32.6 0.827411-0.18945-0.01263-0.01271 30 26.8 0.680203-0.38536-0.01285 45 22.3 0.56599-0.56918-0.01265
720 J SCI IND RES VOL 64 OCTOBER 2005 Fig.1 Comparison between estimated value and observed values of ph, EC, COD and BOD with respect to phytoremediation period (days) Fig.2 Comparison between estimated value and observed values of TSS, TDS, Na and K with respect to phytoremediation period (days) Results and Discussion All parameters exhibited exponential decrease in P of water hyacinth from the date of start of the experiment upto 45 days, and thereafter showed negligible decrease till termination of the experiment. Such plant behavior (upto 45 days) for sorption of nutrient from industrial waste could be attributed to attainment of equilibrium up to carrying capacity of phytoremediator plants, owing to engagement of all the binding sites in root zone, as has been reported earlier 13. Besides, this might be also due to negative impact exerted by high elemental concentration in plant bodies, which resulted into relatively poor plant growth measured in terms of leaf area, chlorophyll content and biomass yield (Table 4), beyond 45 days of experiment. Such feeble growth of plants might have stopped absorption of organic and inorganic contents from the wastewater. A comparison between the estimated values and observed values of a given parameter of the effluent (Figs 1-2) shows minimum variation. However, some inconsistency in observed value and estimated value could be accounted for the subjectivity that lies with the experiment. Again, with increase in phytoremediation duration, observed value of ph exceeds estimated value, especially beyond 40 days.
KUMAR et al: PHYTOREMEDIATION OF PULP AND PAPER INDUSTRY WASTEWATER 721 Growth parameter Table 4 Effect of 25% pulp and paper mill effluent on growth of E. crassipes (±SE) Phytoremediation period d 0 15 30 45 60 Leaf area, cm 2 /plant 145.3±7.2 181.6±6.3 202.5±5.8 234.3±6.8 225.8±5.9 Chlorophyll, mg/g fw 1.25±.01 1.46±.03 1.52±.02 1.62±.04 1.53±.03 Biomass, g dw/plant 1.04±.002 1.24±.012 1.38±.005 1.32±.004 1.29±.005 This supports that with increase in phytoremediation duration the phytoremediator has attained equilibrium level of absorption and/or degradation of the pollutants present in the effluent and thus beyond that stage the reduction in parameters studied was stopped. Conclusions Based on present investigation, the proposed model is useful in predicting the trend of phytoremediation potential of E. crassipes for pulp and paper industry effluent and other similar industries at any time interval. This is quite helpful in rapid monitoring of industrial pollution treatment. Mathematical model presented here demonstrates a fairly accurate remedial measure for industrial wastewater pollution employing plant like E. crassipes, which could be profitably used to remediate ill effects of pulp and paper mill effluent, at least on experimental basis. Acknowledgement Financial assistance received from CSIR, New Delhi in the form of a research project is gratefully acknowledged. References 1 Salt D E, Smith R D & Ruskin I, Phytoremediation. Annu Rev Plant Physiol Mol Biol 49 (1998) 643-668. 2 Rai U N, Sinha S, Tripathi R D & Chandra P, Wastewater treatability potential of some aquatic macrophytes: Removal of heavy metals, Ecol Engg, 5 (1995) 5-12. 3 Kumar P B A & Nanda E L, Phytoextraction: The use of plants to remove heavy metals from soils, Environ Sci Technol, 29, (1995) 1232-1236. 4 Schnoor J L, Phytoremediation of organic and nutrient contaminants, Environ Sci Technol, 29 (1995) 318-323. 5 Innes G, Dynamics analysis in soft sciences studies, in Math problems in Biology, edited by P V D Drissche (Springer Verlag, New York) 1974, 43-52. 6 Kapur J N, Mathematical Models in Biology and Medicine (Affiliated East-West Press Private Limited, New Delhi) 1985, 21-32. 7 Reddy K R & Debusk W F, Nutrient removal potential of selected aquatic macrophytes. J Enviorn Qual, 14 (1985) 459-462. 8 Singhal V, Kumar A & Rai J P N, Phytoremediation of pulp and paper mill and distillery effluents by channel grass (Vallisneria spiralis), J Sci Ind Res, 62 (2003) 319-328. 9 Singh Y P, Phytoremediation of heavy metals containing industrial effluent by Eichhornia crassipes and Trapa bispinosa, Ph D Thesis, G B Pant Univ of Agric and Technol, Pantnagar, India, 2004. 10 Singhal V, Assessment of phytoremediation potential of Eichhornia crassipes and Vallisnenria spiralis against pulp and paper mill and distillery wastewater, Ph D Thesis, G B Pant Univ of Agric and Technol, Pantnagar, India, 2002. 11 American Public Health Association, Standard methods for examination of water and wastewater, 19 th edn (APHA publishers, Washington DC) 1995. 12 Kumar S, Dube K K, Saxena M & Rai J P N. A mathematical model for prediction of soil microbial functional attributes affected by pulp and paper industry effluent, J Sci Ind Res, 63 (2004) 908-912. 13 Mehta S K & Gaur J P, Characterization & optimization of Ni & Cu sorption from aqueous solution by Chlevella vulgaris, Ecol Engg, 18 (2001) 1-13.