# American Institute of Mathematical Sciences

2006, 3(4): 615-634. doi: 10.3934/mbe.2006.3.615

## Mathematical modeling of biowall reactors for in-situ groundwater treatment

 1 Department of Mathematics, William Paterson University, Wayne, NJ 07470, United States 2 Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, United States

Received  March 2005 Revised  March 2006 Published  August 2006

In this paper we develop a comprehensive model for the remediation of contaminated groundwater in a passive, in-ground reactor, generally known as a biowall. The model is based on our understanding of the component transport and biokinetic processes that occur as water passes through a bed of inert particles on which a biofilm containing active microbial degraders, typically aerobic bacteria, is developing. We give a detailed derivation of the model based on accepted engineering formulations that account for the mass transport of the contaminant (substrate) to the surface of the biofilm, its diffusion into the biofilm to the proximity of a microbe, and its subsequent destruction within that degrader. The model has been solved numerically and incorporated in a robust computer code. Based on representative input values, the results of varying key parameters in the model are presented. The relation between biofilm growth and biowall performance is explored, revealing that the amount of biomass and its distribution within the biowall are key parameters affecting contaminant removal.
Citation: Donna J. Cedio-Fengya, John G. Stevens. Mathematical modeling of biowall reactors for in-situ groundwater treatment. Mathematical Biosciences & Engineering, 2006, 3 (4) : 615-634. doi: 10.3934/mbe.2006.3.615
 [1] Emma Smith, Volker Rehbock, Norm Adams. Deterministic modeling of whole-body sheep metabolism. Journal of Industrial and Management Optimization, 2009, 5 (1) : 61-80. doi: 10.3934/jimo.2009.5.61 [2] Angelo Antoci, Marcello Galeotti, Mauro Sodini. Environmental degradation and indeterminacy of equilibrium selection. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5755-5767. doi: 10.3934/dcdsb.2021179 [3] Yongzhi Xu. A free boundary problem model of ductal carcinoma in situ. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 337-348. doi: 10.3934/dcdsb.2004.4.337 [4] Messoud A. Efendiev, Sergey Zelik, Hermann J. Eberl. Existence and longtime behavior of a biofilm model. Communications on Pure and Applied Analysis, 2009, 8 (2) : 509-531. doi: 10.3934/cpaa.2009.8.509 [5] Brandon Lindley, Qi Wang, Tianyu Zhang. A multicomponent model for biofilm-drug interaction. Discrete and Continuous Dynamical Systems - B, 2011, 15 (2) : 417-456. doi: 10.3934/dcdsb.2011.15.417 [6] Hermann J. Eberl, Messoud A. Efendiev, Dariusz Wrzosek, Anna Zhigun. Analysis of a degenerate biofilm model with a nutrient taxis term. Discrete and Continuous Dynamical Systems, 2014, 34 (1) : 99-119. doi: 10.3934/dcds.2014.34.99 [7] Mudassar Imran, Hal L. Smith. A model of optimal dosing of antibiotic treatment in biofilm. Mathematical Biosciences & Engineering, 2014, 11 (3) : 547-571. doi: 10.3934/mbe.2014.11.547 [8] Fadoua El Moustaid, Amina Eladdadi, Lafras Uys. Modeling bacterial attachment to surfaces as an early stage of biofilm development. Mathematical Biosciences & Engineering, 2013, 10 (3) : 821-842. doi: 10.3934/mbe.2013.10.821 [9] Etsushi Nakaguchi, Koichi Osaki. Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2627-2646. doi: 10.3934/dcdsb.2013.18.2627 [10] Hanwu Liu, Lin Wang, Fengqin Zhang, Qiuying Li, Huakun Zhou. Analyzing the causes of alpine meadow degradation and the efficiency of restoration strategies through a mathematical modelling exercise. Mathematical Biosciences & Engineering, 2018, 15 (3) : 765-773. doi: 10.3934/mbe.2018034 [11] Jianing Xie. Blow-up prevention by quadratic degradation in a higher-dimensional chemotaxis-growth model with indirect attractant production. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 4007-4022. doi: 10.3934/dcdsb.2021216 [12] Hassan Khassehkhan, Messoud A. Efendiev, Hermann J. Eberl. A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 371-388. doi: 10.3934/dcdsb.2009.12.371 [13] Blessing O. Emerenini, Stefanie Sonner, Hermann J. Eberl. Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects. Mathematical Biosciences & Engineering, 2017, 14 (3) : 625-653. doi: 10.3934/mbe.2017036 [14] Fazal Abbas, Rangarajan Sudarsan, Hermann J. Eberl. Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates. Mathematical Biosciences & Engineering, 2012, 9 (2) : 215-239. doi: 10.3934/mbe.2012.9.215 [15] Nikodem J. Poplawski, Abbas Shirinifard, Maciej Swat, James A. Glazier. Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment. Mathematical Biosciences & Engineering, 2008, 5 (2) : 355-388. doi: 10.3934/mbe.2008.5.355

2018 Impact Factor: 1.313

## Metrics

• PDF downloads (31)
• HTML views (0)
• Cited by (2)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]