Nitrate removal in woodchip denitrification bioreactor – an approach combining mathematical modelling and PI control
Abstract
A mathematical model of nitrate removal in woodchip denitrification bioreactor based on field experiment measurements was developed in this study. The approach of solving inverse problem for nonlinear system of differential convection-reaction equations was applied to optimize the efficiency of nitrate removal depending on bioreactor’s length and flow rate. The approach was realized through the developed algorithm containing a nonlocal condition with an incorporated PI controller. This allowed to adjust flow rate for varying inflow nitrate concentrations by using PI controller. The proposed model can serve as a useful tool for bioreactor design. The main outcome of the model is a mathematical relationship intended for bioreactor length selection when nitrate concentration at the inlet and the flow rate are known. Custom software was developed to solve the system of differential equations aiming to ensure the required nitrate removal efficiency.
Keyword : environmental processes modeling, mathematical modeling, nitrate removal, denitrification bioreactor, PI control
How to Cite
Nečiporenko, A., Ivanauskas, F., Dabulytė-Bagdonavičienė, J., Povilaitis, A., & Laurinavičius, V. (2022). Nitrate removal in woodchip denitrification bioreactor – an approach combining mathematical modelling and PI control. Journal of Environmental Engineering and Landscape Management, 30(1), 13-21. https://doi.org/10.3846/jeelm.2022.15295
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Addy, K., Gold, A. J., Christianson, L. E., David, M. B., Schipper, L. A., & Ratigan, N. A. (2016). Denitrifying bioreactors for nitrate removal: A meta-analysis. Journal of Environmental Quality, 45(3), 873–881. https://doi.org/10.2134/jeq2015.07.0399
Åström, K. J., & Hägglund, T. (1995). PID controllers: Theory, design, and tuning (2nd ed.). Instrument society of America. https://aiecp.files.wordpress.com/2012/07/1-0-1-k-j-astrom-pid-controllers-theory-design-and-tuning-2ed.pdf
Baronas, R., Ivanauskas, F., & Kulys, J. (2009). Biosensor Action. In Springer series on chemical sensors and biosensors: Vol. 9. Mathematical modeling of biosensors: An introduction for chemists and mathematicians (pp. 3–8). Springer Science & Business Media. https://doi.org/10.1007/978-90-481-3243-0_1
Blowes, D., Robertson, W., Ptacek, C., & Merkley, C. (1994). Removal of agricultural nitrate from tile-drainage effluent water using in-line bioreactors. Journal of Contaminant Hydrology, 15(3), 207–221. https://doi.org/10.1016/0169-7722(94)90025-6
Blum, J.-M., Su, Q., Ma, Y., Valverde-Pérez, B., DomingoFélez, C., Jensen, M. M., & Smets, B. F. (2018). The pH dependency of N-converting enzymatic processes, pathways and microbes: Effect on net N2O production. Environmental Microbiology, 20(5), 1623–1640. https://doi.org/10.1111/1462-2920.14063
Bürger, R., Careaga, J., Diehl, S., Mejías, C., Nopens, I., Torfs, E., & Vanrolleghem, P. A. (2016). Simulations of reactive settling of activated sludge with a reduced biokinetic model. Computers & Chemical Engineering, 92, 216–229. https://doi.org/10.1016/j.compchemeng.2016.04.037
Cameron, S. G., & Schipper, L. A. (2010). Nitrate removal and hydraulic performance of organic carbon for use in denitrification beds. Ecological Engineering, 36(11), 1588–1595. https://doi.org/10.1016/j.ecoleng.2010.03.010
Christianson, L. E., Bhandari, A., & Helmers, M. J. (2011b). Pilot-scale evaluation of denitrification drainage bioreactors: Reactor geometry and performance. Journal of Environmental Engineering, 137(4), 213–220. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000316
Christianson, L. E., Bhandari, A., & Helmers, M. J. (2012). A practice-oriented review of woodchip bioreactors for subsurface agricultural drainage. Applied Engineering in Agriculture, 28(6), 861–874. https://doi.org/10.13031/2013.42479
Christianson, L., Bhandari, A., & Helmers, M. (2009). Emerging technology: Denitrification bioreactors for nitrate reduction in agricultural waters. Journal of Soil and Water Conservation, 64(5), 139A–141A. https://doi.org/10.2489/jswc.64.5.139A
Christianson, L., Bhandari, A., & Helmers, M. (2011a). Potential design methodology for agricultural drainage denitrification bioreactors. In World Environmental and Water Resources Congress 2011: Bearing Knowledge for Sustainability – Proceedings of the 2011 World Environmental and Water Resources Congress (pp. 2740–2748). American Society of Civil Engineers. https://doi.org/10.1061/41173(414)285
Chun, J., Cooke, R., Eheart, J., & Cho, J. (2010). Estimation of flow and transport parameters for woodchip-based bioreactors: II. field-scale bioreactor. Biosystems Engineering, 105(1), 95–102. https://doi.org/10.1016/j.biosystemseng.2009.09.018
Cooke, R., Doheny, A., & Hirschi, M. (1998). Bio-reactors for edge-of-field treatment of tile outflow. In 2001 ASAE Annual Meeting. American Society of Agricultural and Biological Engineers.
Feyereisen, G. W., Christianson, L. E., Moorman, T. B., Venterea, R. T., & Coulter, J. A. (2017). Plastic biofilm carrier after corn cobs reduces nitrate loading in laboratory denitrifying bioreactors. Journal of Environmental Quality, 46(4), 915–920. https://doi.org/10.2134/jeq2017.02.0060
Feyereisen, G. W., Moorman, T. B., Christianson, L. E., Venterea, R. T., Coulter, J. A., & Tschirner, U. W. (2016). Performance of agricultural residue media in laboratory denitrifying bioreactors at low temperatures. Journal of Environmental Quality, 45(3), 779–787. https://doi.org/10.2134/jeq2015.07.0407
Greenan, C. M., Moorman, T. B., Parkin, T. B., Kaspar, T. C., & Jaynes, D. B. (2009). Denitrification in wood chip bioreactors at different water flows. Journal of Environmental Quality, 38(4), 1664–1671. https://doi.org/10.2134/jeq2008.0413
Halaburka, B. J., LeFevre, G. H., & Luthy, R. G. (2017). Evaluation of mech anistic models for nitrate removal in woodchip bioreactors. Environmental Science & Technology, 51(9), 5156–5164. https://doi.org/10.1021/acs.est.7b01025
Hassanpour, B., Giri, S., Pluer, W. T., Steenhuis, T. S., & Geohring, L. D. (2017). Seasonal performance of denitrifying bioreactors in the Northeastern United States: Field trials. Journal of Environmental Management, 202(Part 1), 242–253. https://doi.org/10.1016/j.jenvman.2017.06.054
Hoover, N. L., Bhandari, A., Soupir, M. L., & Moorman, T. B. (2016). Woodchip denitrification bioreactors: Impact of temperature and hydraulic retention time on nitrate removal. Journal of Environmental Quality, 45(3), 803–812. https://doi.org/10.2134/jeq2015.03.0161
Ivanauskas, F., Laurinavičius, V., Sapagovas, M., & Nečiporenko, A. (2017). Reaction-diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor. Nonlinear Analysis: Modelling and Control, 22(2), 261–272. https://doi.org/10.15388/NA.2017.2.8
Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for optimization. MIT Press. https://mitpress.mit.edu/books/algorithms-optimization
Lee, K., Choi, Y., Lee, B. S., & Nam, K. (2017). Differential mode of denitrification by pseudomonas sp. KY1 using molasses as a carbon source. KSCE Journal of Civil Engineering, 21, 2097–2105. https://doi.org/10.1007/s12205-016-0780-2
Lepine, C., Christianson, L., Sharrer, K., & Summerfelt, S. (2016). Optimizing hydraulic retention times in denitrifying woodchip bioreactors treating recirculating aquaculture system wastewater. Journal of Environmental Quality, 45(3), 813–821. https://doi.org/10.2134/jeq2015.05.0242
Leschine, S. B. (1995). Cellulose degradation in anaerobic environments. Annual Review of Microbiology, 49, 399–426. https://doi.org/10.1146/annurev.mi.49.100195.002151
Povilaitis, A., Rudzianskaite, A., Miseviciene, S., Gasiunas, V., Mi seckaite, O., & Živatkauskiene, I. (2018). Efficiency of drainage practices for improving water quality in Lithuania. Transactions of the ASABE, 61(1), 179–196. https://doi.org/10.13031/trans.12271
Samarskii, A. A. (2001). The theory of difference schemes (Vol. 240). Marcel Dekker. https://doi.org/10.1201/9780203908518
Schipper, L. A., Robertson, W. D., Gold, A. J., Jaynes, D. B., & Cameron, S. C. (2010). Denitrifying bioreactors – an approach for reducing nitrate loads to receiving waters. Ecological Engineering, 36(11), 1532–1543. https://doi.org/10.1016/j.ecoleng.2010.04.008
Štikonas, A. (2014). A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions. Nonlinear Analysis: Modelling and Control, 19(3), 301–334. https://doi.org/10.15388/NA.2014.3.1
Tinoco, I., Sauer, K., Wang, J. C., Puglisi, J. D., Harbison, G., & Rovnyak, D. (1995). Physical chemistry: Principles and applications in biological sciences (Vol. 545). Prentice Hall.
Torà, J. A., Lafuente, J., Garcia-Belinchón, C., Bouchy, L., Carrera, J., & Baeza, J. A. (2014). High-throughput nitritation of reject water with a novel ammonium control loop: Stable effluent generation for anammox or heterotrophic denitritation. Chemical Engineering Journal, 243, 265–271. https://doi.org/10.1016/j.cej.2013.11.056
Van Driel, P., Robertson, W., & Merkley, L. (2006). Denitrification of agricultural drainage using wood-based reactors. Transactions of the ASABE, 49(2), 565–573. https://doi.org/10.13031/2013.20391
Verma, S., Bhattarai, R., Cooke, R., Chun, J. A., & Goodwin, G. E. (2010, June). Evaluation of conservation drainage systems in Illinois – bioreactors. American Society of Agricultural and Biological Engineers. https://doi.org/10.13031/2013.30015
Åström, K. J., & Hägglund, T. (1995). PID controllers: Theory, design, and tuning (2nd ed.). Instrument society of America. https://aiecp.files.wordpress.com/2012/07/1-0-1-k-j-astrom-pid-controllers-theory-design-and-tuning-2ed.pdf
Baronas, R., Ivanauskas, F., & Kulys, J. (2009). Biosensor Action. In Springer series on chemical sensors and biosensors: Vol. 9. Mathematical modeling of biosensors: An introduction for chemists and mathematicians (pp. 3–8). Springer Science & Business Media. https://doi.org/10.1007/978-90-481-3243-0_1
Blowes, D., Robertson, W., Ptacek, C., & Merkley, C. (1994). Removal of agricultural nitrate from tile-drainage effluent water using in-line bioreactors. Journal of Contaminant Hydrology, 15(3), 207–221. https://doi.org/10.1016/0169-7722(94)90025-6
Blum, J.-M., Su, Q., Ma, Y., Valverde-Pérez, B., DomingoFélez, C., Jensen, M. M., & Smets, B. F. (2018). The pH dependency of N-converting enzymatic processes, pathways and microbes: Effect on net N2O production. Environmental Microbiology, 20(5), 1623–1640. https://doi.org/10.1111/1462-2920.14063
Bürger, R., Careaga, J., Diehl, S., Mejías, C., Nopens, I., Torfs, E., & Vanrolleghem, P. A. (2016). Simulations of reactive settling of activated sludge with a reduced biokinetic model. Computers & Chemical Engineering, 92, 216–229. https://doi.org/10.1016/j.compchemeng.2016.04.037
Cameron, S. G., & Schipper, L. A. (2010). Nitrate removal and hydraulic performance of organic carbon for use in denitrification beds. Ecological Engineering, 36(11), 1588–1595. https://doi.org/10.1016/j.ecoleng.2010.03.010
Christianson, L. E., Bhandari, A., & Helmers, M. J. (2011b). Pilot-scale evaluation of denitrification drainage bioreactors: Reactor geometry and performance. Journal of Environmental Engineering, 137(4), 213–220. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000316
Christianson, L. E., Bhandari, A., & Helmers, M. J. (2012). A practice-oriented review of woodchip bioreactors for subsurface agricultural drainage. Applied Engineering in Agriculture, 28(6), 861–874. https://doi.org/10.13031/2013.42479
Christianson, L., Bhandari, A., & Helmers, M. (2009). Emerging technology: Denitrification bioreactors for nitrate reduction in agricultural waters. Journal of Soil and Water Conservation, 64(5), 139A–141A. https://doi.org/10.2489/jswc.64.5.139A
Christianson, L., Bhandari, A., & Helmers, M. (2011a). Potential design methodology for agricultural drainage denitrification bioreactors. In World Environmental and Water Resources Congress 2011: Bearing Knowledge for Sustainability – Proceedings of the 2011 World Environmental and Water Resources Congress (pp. 2740–2748). American Society of Civil Engineers. https://doi.org/10.1061/41173(414)285
Chun, J., Cooke, R., Eheart, J., & Cho, J. (2010). Estimation of flow and transport parameters for woodchip-based bioreactors: II. field-scale bioreactor. Biosystems Engineering, 105(1), 95–102. https://doi.org/10.1016/j.biosystemseng.2009.09.018
Cooke, R., Doheny, A., & Hirschi, M. (1998). Bio-reactors for edge-of-field treatment of tile outflow. In 2001 ASAE Annual Meeting. American Society of Agricultural and Biological Engineers.
Feyereisen, G. W., Christianson, L. E., Moorman, T. B., Venterea, R. T., & Coulter, J. A. (2017). Plastic biofilm carrier after corn cobs reduces nitrate loading in laboratory denitrifying bioreactors. Journal of Environmental Quality, 46(4), 915–920. https://doi.org/10.2134/jeq2017.02.0060
Feyereisen, G. W., Moorman, T. B., Christianson, L. E., Venterea, R. T., Coulter, J. A., & Tschirner, U. W. (2016). Performance of agricultural residue media in laboratory denitrifying bioreactors at low temperatures. Journal of Environmental Quality, 45(3), 779–787. https://doi.org/10.2134/jeq2015.07.0407
Greenan, C. M., Moorman, T. B., Parkin, T. B., Kaspar, T. C., & Jaynes, D. B. (2009). Denitrification in wood chip bioreactors at different water flows. Journal of Environmental Quality, 38(4), 1664–1671. https://doi.org/10.2134/jeq2008.0413
Halaburka, B. J., LeFevre, G. H., & Luthy, R. G. (2017). Evaluation of mech anistic models for nitrate removal in woodchip bioreactors. Environmental Science & Technology, 51(9), 5156–5164. https://doi.org/10.1021/acs.est.7b01025
Hassanpour, B., Giri, S., Pluer, W. T., Steenhuis, T. S., & Geohring, L. D. (2017). Seasonal performance of denitrifying bioreactors in the Northeastern United States: Field trials. Journal of Environmental Management, 202(Part 1), 242–253. https://doi.org/10.1016/j.jenvman.2017.06.054
Hoover, N. L., Bhandari, A., Soupir, M. L., & Moorman, T. B. (2016). Woodchip denitrification bioreactors: Impact of temperature and hydraulic retention time on nitrate removal. Journal of Environmental Quality, 45(3), 803–812. https://doi.org/10.2134/jeq2015.03.0161
Ivanauskas, F., Laurinavičius, V., Sapagovas, M., & Nečiporenko, A. (2017). Reaction-diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor. Nonlinear Analysis: Modelling and Control, 22(2), 261–272. https://doi.org/10.15388/NA.2017.2.8
Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for optimization. MIT Press. https://mitpress.mit.edu/books/algorithms-optimization
Lee, K., Choi, Y., Lee, B. S., & Nam, K. (2017). Differential mode of denitrification by pseudomonas sp. KY1 using molasses as a carbon source. KSCE Journal of Civil Engineering, 21, 2097–2105. https://doi.org/10.1007/s12205-016-0780-2
Lepine, C., Christianson, L., Sharrer, K., & Summerfelt, S. (2016). Optimizing hydraulic retention times in denitrifying woodchip bioreactors treating recirculating aquaculture system wastewater. Journal of Environmental Quality, 45(3), 813–821. https://doi.org/10.2134/jeq2015.05.0242
Leschine, S. B. (1995). Cellulose degradation in anaerobic environments. Annual Review of Microbiology, 49, 399–426. https://doi.org/10.1146/annurev.mi.49.100195.002151
Povilaitis, A., Rudzianskaite, A., Miseviciene, S., Gasiunas, V., Mi seckaite, O., & Živatkauskiene, I. (2018). Efficiency of drainage practices for improving water quality in Lithuania. Transactions of the ASABE, 61(1), 179–196. https://doi.org/10.13031/trans.12271
Samarskii, A. A. (2001). The theory of difference schemes (Vol. 240). Marcel Dekker. https://doi.org/10.1201/9780203908518
Schipper, L. A., Robertson, W. D., Gold, A. J., Jaynes, D. B., & Cameron, S. C. (2010). Denitrifying bioreactors – an approach for reducing nitrate loads to receiving waters. Ecological Engineering, 36(11), 1532–1543. https://doi.org/10.1016/j.ecoleng.2010.04.008
Štikonas, A. (2014). A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions. Nonlinear Analysis: Modelling and Control, 19(3), 301–334. https://doi.org/10.15388/NA.2014.3.1
Tinoco, I., Sauer, K., Wang, J. C., Puglisi, J. D., Harbison, G., & Rovnyak, D. (1995). Physical chemistry: Principles and applications in biological sciences (Vol. 545). Prentice Hall.
Torà, J. A., Lafuente, J., Garcia-Belinchón, C., Bouchy, L., Carrera, J., & Baeza, J. A. (2014). High-throughput nitritation of reject water with a novel ammonium control loop: Stable effluent generation for anammox or heterotrophic denitritation. Chemical Engineering Journal, 243, 265–271. https://doi.org/10.1016/j.cej.2013.11.056
Van Driel, P., Robertson, W., & Merkley, L. (2006). Denitrification of agricultural drainage using wood-based reactors. Transactions of the ASABE, 49(2), 565–573. https://doi.org/10.13031/2013.20391
Verma, S., Bhattarai, R., Cooke, R., Chun, J. A., & Goodwin, G. E. (2010, June). Evaluation of conservation drainage systems in Illinois – bioreactors. American Society of Agricultural and Biological Engineers. https://doi.org/10.13031/2013.30015