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Efficient Algorithms for Modeling the Transport and Biodegradation of Chlorinated Ethenes in Groundwater

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Abstract

Predicting the fate of chlorinated ethenes in groundwater requires the solution of equations that describe both the transport and the biodegradation of the contaminants. Here, we present a model that accounts for (1) transport of chlorinated ethenes in flowing groundwater, (2) mass transfer of contaminants between mobile groundwater and stationary biofilms, and (3) diffusion and biodegradation within the biofilms. Equations for biodegradation kinetics account for biomass growth within the biofilms, the effect of hydrogen on dechlorination, and competitive inhibition between vinyl chloride and cis–dichloroethene. The overall model consists of coupled, non-linear, partial differential equations; solution of such a model is challenging and requires innovative numerical algorithms. We developed and tested two new numerical algorithms to solve the equations in the model; these are called system splitting with operator splitting (SSOS) and system splitting with Picard iteration (SSPI). We discuss the conditions under which one of these algorithms is superior to the other. The contributions of this paper are as follows: first, we believe that the mathematical model presented here is the first transport model that also accounts for diffusion and non-linear biodegradation of chlorinated ethenes in biofilms; second, the SSOS and SSPI are new computational algorithms developed specifically for problems of transport, mass transfer, and non-linear reaction; third, we have identified which of the two new algorithms is computationally more efficient for the case of chlorinated ethenes; and finally, we applied the model to compare the biodegradation behavior under diffusion-limited, metabolism-limited, and hydrogen-limited (donor-limited) conditions.

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References

  • An Y.-J., Kampbell D.H., Weaver J.W., Wilson J.T., Jeong S.-W.: Natural attenuation of trichloroethene and its degradation products at a lake-shore site. Environ. Pollut. 130, 325–335 (2004)

    Article  Google Scholar 

  • Atkinson L.V., Harley P.J., Hudson J.D.: Numerical Methods with Fortran 77: A Practical Introduction. Addison-Wesley, Wokingham (1989)

    Google Scholar 

  • Bae W., Odencrantz J.E., Rittmann B.E., Valocchi A.J.: Transformation kinetics of trace-level halogenated organic contaminants in a biologically active zone (BAZ) induced by nitrate injection. J. Contam. Hydrol. 6, 53–68 (1990)

    Article  Google Scholar 

  • Bagley D.M.: Systematic approach for modeling tetrachloroethene biodegradation. J. Environ. Eng. (ASCE) 124, 1076–1086 (1998)

    Article  Google Scholar 

  • Baveye P., Valocchi A.: An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers. Water Resour. Res. 25, 1413–1421 (1989)

    Article  Google Scholar 

  • Ballapragada B.S., Stensel H.D., Puhakka J.A., Ferguson J.F.: Effect of hydrogen on reductive dechlorination of chlorinated ethenes. Environ. Sci. Technol. 31, 1728–1734 (1997)

    Article  Google Scholar 

  • Beranger S.C., Sleep B.E., Sherwood-Lollar B., Perez-Monteagudo F.: Transport, biodegradation and isotopic fractionation of chlorinated ethenes: Modeling and Parameter estimation methods. Adv. Water Resour. 28, 87–98 (2005)

    Article  Google Scholar 

  • Carrayrou J., Moisé R., Behra P.: Operator-splitting procedures for reactive transport and comparison of mass balance errors. J. Contam. Hydrol. 68, 239–268 (2004)

    Article  Google Scholar 

  • Celia M.A., Bouloutas E.T., Zarba R.L.: A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res. 26, 1483–1496 (1990)

    Article  Google Scholar 

  • Chambon J.C., Broholm M.M., Binning P.J., Bjerg P.L.: Modeling multi-component transport and enhanced anaerobic dechlorination processes in a single fracture-clay matrix system. J. Contam. Hydrol. 112, 77–90 (2010)

    Article  Google Scholar 

  • Chiang C.Y., Dawson C.N., Wheeler M.F.: Modeling of in situ biorestoration of organic compounds in groundwater. Transp. Porous Med. 6, 667–702 (1991)

    Article  Google Scholar 

  • Clement T.P., Sun Y., Hooker B.S., Petersen J.N.: Modeling multispecies reactive transport in ground water. Ground Water Monit. Remediat. 18(2), 79–92 (1998)

    Article  Google Scholar 

  • Clement T.P., Johnson C.D., Sun Y.W., Klecka G.M., Bartlett C.: Natural attenuation of chlorinated ethene compounds: Model development and field-scale application at the Dover site. J. Contam. Hydrol. 42, 113–140 (2000)

    Article  Google Scholar 

  • Crittenden J.C., Hutzler N.J., Geyer D.G., Oravitz J.L., Friedman G.: Transport of organic compounds with saturated groundwater flow: Model development and parameter sensitivity. Water Resour. Res. 22(3), 271–284 (1986)

    Article  Google Scholar 

  • Cunningham J.A., Mendoza-Sanchez I.: Equivalence of two models for biodegradation during contaminant transport in groundwater. Water Resour. Res. 42, W02416 (2006)

    Article  Google Scholar 

  • Cupples A.M., Spormann A.M., McCarty P.L.: Vinyl chloride and cis-dichloroethene dechlorination kinetics and microorganism growth under substrate limiting conditions. Environ. Sci. Technol. 38, 1102–1107 (2004)

    Article  Google Scholar 

  • Dillon R., Fauci L.: A microscale model of bacterial and biofilm dynamics in porous media. Biotechnol. Bioeng. 68(5), 536–547 (2000)

    Article  Google Scholar 

  • Eberl H.J., Picioreanu C., Heijnen J.J., van Loosdrecht M.C.M.: A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem. Eng. Sci. 55, 6209–6222 (2000)

    Article  Google Scholar 

  • El-Farhan Y.H., Scow K.M., de Jonge L.W., Rolston D.E., Moldrup P.: Coupling transport and biodegradation of toluene and trichloroethylene in unsaturated soils. Water Resour. Res. 34, 437–445 (1998)

    Article  Google Scholar 

  • Fennell D.E., Gossett J.M.: Modeling the production of and competition for hydrogen in a dechlorinating culture. Environ. Sci. Technol. 32, 2450–2460 (1998)

    Article  Google Scholar 

  • Haest P.J., Springael D., Smolders E.: Modelling reactive CAH transport using batch experiment degradation kinetics. Water Res. 44, 2981–2989 (2010)

    Article  Google Scholar 

  • Hammond G.E., Valocchi A.J., Lichtner P.C.: Application of Jacobian-free Newton-Krylov with physics-based preconditioning to biogeochemical transport. Adv. Water Resour. 28, 359–376 (2005)

    Article  Google Scholar 

  • Hoelen T.P., Cunningham J.A., Hopkins G.D., Lebron C.A., Reinhard M.: Bioremediation of cis-DCE at a sulfidogenic site by amendment with propionate. Ground Water Monit. Remediat. 26(3), 82–91 (2006)

    Article  Google Scholar 

  • Hossain A., Corapcioglu M.Y.: Modeling primary substrate controlled biotransformation and transport of halogenated aliphatics in porous media. Transp. Porous Med. 24(2), 203–220 (1996)

    Article  Google Scholar 

  • Kaluarachchi J.J., Morshed J.: Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 1. First-order reaction. Adv. Water Resour. 18, 89–100 (1995)

    Article  Google Scholar 

  • Kasten P.R., Lapidus L., Amundson N.R.: Mathematics of adsorption in beds: V. Effect of intraparticle diffusion in flow systems in fixed beds. J. Phys. Chem. 56(6), 683–688 (1952)

    Article  Google Scholar 

  • Lanser D., Verwer J.G.: Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modeling. J. Comput. Appl. Math. 111, 201–216 (1999)

    Article  Google Scholar 

  • Lensing H.J., Vogt M., Herrling B.: Modeling of biologically mediated redox processes in the subsurface. J. Hydrol. 159, 125–143 (1994)

    Article  Google Scholar 

  • Lu X.J., Sun Y.W., Petersen J.N.: Analytical solutions of TCE transport with convergent reactions. Transp. Porous Med. 51, 211–225 (2003)

    Article  Google Scholar 

  • MacQuarrie K.T.B., Sudicky E.A.: Multicomponent simulation of wastewater derived nitrogen and carbon in shallow unconfined aquifers: I. Model formulation and performance. J. Contam. Hydrol. 47, 53–84 (2001)

    Article  Google Scholar 

  • Mendoza-Sanchez, I.: Effects of pore-scale velocity and pore-scale physical processes on contaminant biodegradation during transport in groundwater: Modeling and experiments. Ph.D. Dissertation, Texas A&M University, College Station, Texas (2007)

  • Mendoza-Sanchez I., Cunningham J.: Efficient algorithm for modeling transport in porous media with mass exchange between mobile fluid and reactive stationary media. Transp. Porous Med. 68, 285–300 (2007)

    Article  Google Scholar 

  • Mendoza-Sanchez I., Autenrieth R.L., McDonald T.J., Cunningham J.A.: Effect of pore velocity on biodegradation of cis-dichloroethene (DCE) in column experiments. Biodegradation 21, 365–377 (2010)

    Article  Google Scholar 

  • Nash J.E., Sutcliffe J.V.: River flow forecasting through conceptual models part I—a discussion of principles. J. Hydrol. 10(3), 282–290 (1970)

    Article  Google Scholar 

  • Rasmuson A., Neretnieks I.: Exact solution of a model for diffusion in particles and longitudinal dispersion in packed beds. AIChE J. 26(4), 686–690 (1980)

    Article  Google Scholar 

  • Rittmann B.E.: The significance of biofilms in porous media. Water Resour. Res. 29, 2195–2202 (1993)

    Article  Google Scholar 

  • Rittmann B.E., VanBriesen J.M.: Microbiological processes in reactive modeling. In: Lichtner, P.C., Steefel, C.I., Oelkers, E.H. (eds) Reactive Transport in Porous Media, vol. 34. Reviews in Mineralogy, pp. 311–334. Mineralogical Society of America, Chantilly, VA (1996)

    Google Scholar 

  • Rosen J.B.: Kinetics of a fixed bed system for solid diffusion into spherical particles. J. Chem. Phys. 20(3), 387–394 (1952)

    Article  Google Scholar 

  • Schaefer C.E., Callaghan A.V., King J.D., McCray J.E.: Dense nonaqueous phase liquid architecture and dissolution in discretely fractured sandstone blocks. Environ. Sci. Technol. 43(6), 1877–1883 (2009)

    Article  Google Scholar 

  • Schaefer C.E., Towne R.M., Vainberg S., McCray J.E., Steffan R.J.: Bioaugmentation for treatment of dense non-aqueous phase liquid in fractured sandstone blocks. Environ. Sci. Technol. 44(13), 4958–4964 (2010)

    Article  Google Scholar 

  • Sun Y., Lu X., Petersen J.N., Buscheck T.A.: An analytical solution of tetrachloroethylene transport and biodegradation. Transp. Porous Med. 55, 301–308 (2004)

    Article  Google Scholar 

  • Tompson A.F.B., Knapp R.B., Hanna M.L., Taylor R.T.: Simulation of TCE migration and biodegradation in a porous medium under conditions of finite degradation capacity. Adv. Water Resour. 17, 241–249 (1994)

    Article  Google Scholar 

  • Valocchi A.J., Malmstead M.: Accuracy of operator splitting for advection-dispersion-reaction problems. Water Resour. Res. 28, 1471–1476 (1992)

    Article  Google Scholar 

  • Williamson K., McCarty P.L.: A model of substrate utilization by bacterial films. J. Water Pollut. Control Fed. 48, 9–24 (1976)

    Google Scholar 

  • Yu S.H., Dolan M.E., Semprini L.: Kinetics and inhibition of reductive dechlorination of chlorinated ethylenes by two different mixed cultures. Environ. Sci. Technol. 39, 195–205 (2005)

    Article  Google Scholar 

  • Zysset A., Stauffer F., Dracos T.: Modeling of reactive groundwater transport governed by biodegradation. Water Resour. Res. 30(8), 2423–2434 (1994)

    Article  Google Scholar 

Download references

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Author notes

  1. Itza Mendoza-Sanchez

    Present address: Department of Civil and Environmental Engineering, Tufts University, Medford, MA, USA

Authors and Affiliations

  1. Escuela Superior de Ingeniería y Arquitectura, Instituto Politécnico Nacional, Mexico City, Mexico

    Itza Mendoza-Sanchez

  2. Department of Civil and Environmental Engineering, University of South Florida, 4202 East Fowler Avenue, Tampa, 33620, FL, USA

    Jeffrey Cunningham

Authors
  1. Itza Mendoza-Sanchez
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  2. Jeffrey Cunningham
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Correspondence to Jeffrey Cunningham.

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Mendoza-Sanchez, I., Cunningham, J. Efficient Algorithms for Modeling the Transport and Biodegradation of Chlorinated Ethenes in Groundwater. Transp Porous Med 92, 165–185 (2012). https://doi.org/10.1007/s11242-011-9896-5

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