Analysis of biodegradation in a 3-D heterogeneous porous medium using nonlinear stochastic finite element method

Bosma, 1995, SEATM, Dispersion of continuously injected, nonlinear adsorbing solute in chemically or physically heterogeneous porous formation, Journal of Contaminant Hydrology, 18, 181, 10.1016/0169-7722(95)00005-G Chaudhuri, 2005, Stochastic finite element method for probabilistic analysis of flow and transport in a 3-D heterogeneous porous formation, Water Resources Research, 41, W09404, 10.1029/2004WR003844 Chaudhuri, 2005, Analytical solutions for macrodispersion in a 3D heterogeneous porous medium with random hydraulic conductivity and dispersivity, Transport in Porous Media, 58, 217, 10.1007/s11242-004-6300-8 Chaudhuri A, Sekhar M. Stochastic modeling of solute transport in 3-D heterogeneous media with random source condition. Stochastic Environmental Research and Risk Assessment, in press. doi:10.1007/s00477-006-0053-6. Cirpka, 1999, Numerical simulation of biodegradation controlled by transverse mixing, Journal of Contaminant Hydrology, 40, 159, 10.1016/S0169-7722(99)00044-3 Cushman, 1997 Dagan, 1989 Gelhar, 1993 Ghanem, 1998, Probabilistic characterization of transport in heterogeneous media, Computer Methods in Applied Mechanics and Engineering, 158, 199, 10.1016/S0045-7825(97)00250-8 Ghanem, 1991 Ginn, 1995, Stochastic-convective transport with nonlinear reaction: biodegradation with microbial growth, Water Resources Research, 31, 2689, 10.1029/95WR02179 Ginn, 1999, On the distribution of multicomponent mixtures over generalized exposure time in subsurface flow and reactive transport: Foundation, formulations for groundwater age, chemical heterogeneity and biodegradation, Water Resources Research, 35, 1395, 10.1029/1999WR900013 Ginn, 2001, Stochastic-convective transport with nonlinear reactions and mixing: Finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion, Journal of Contaminant Hydrology, 294, 57 Hassan, 2001, Water flow and solute mass flux in heterogeneous porous formations with spatially random porosity, Journal of Hydrology, 242, 1, 10.1016/S0022-1694(00)00381-4 Hassan, 1998, A Monte Carlo assessment of Eulerian flow and transport perturbation models, Water Resources Research, 34, 1143, 10.1029/98WR00011 Hu, 1997, Nonlocal reactive transport with physical, chemical and biological heterogeneity, Advances in Water Resources, 20, 293, 10.1016/S0309-1708(96)00051-6 Huang, 2000, Nonlocal Nonreactive transport in heterogeneous porous media with interregional mass diffusion, Water Resources Research, 36, 1665, 10.1029/2000WR900118 Kaluarachchi, 2000, Stochastic analysis of oxygen- and nitrate-based biodegradation of hydrocarbons in aquifers, Journal of Contaminant Hydrology, 41, 335, 10.1016/S0169-7722(99)00072-8 Kapoor, 1994, Transport in three-dimensionally heterogeneous aquifers, 2. Prediction and observations of concentration fluctuations, Water Resources Research, 30, 1789, 10.1029/94WR00075 Keijzer H. Stochastic analysis of nonlinear biodegradation and transport in heterogeneous Aquifers. In: Transport of nonlinearly biodegradable contaminants in aquifers, PhD thesis. Wageningen University, The Netherlands, 2001. p. 102–24 [chapter 6]. Kleiber, 1992 Li, 1999, Stochastic analysis of solute transport in heterogeneous aquifers subject to spatiotemporal random recharge, Water Resources Research, 35, 953, 10.1029/1998WR900095 Lie, 2000, A stochastic variational formulation for nonlinear dynamic analysis of structure, Computer Methods in Applied Mechanics and Engineering, 190, 597, 10.1016/S0045-7825(99)00431-4 Lu, 2004, A comparative study on uncertainty quantification for flow in randomly heterogeneous media using Monte Carlo simulations and conventional and KL-based moment-equation approaches, SIAM Journal of Scientific Computation, 26, 558, 10.1137/S1064827503426826 Mohamed, 2006, Monte Carlo evaluation of microbial-mediated contaminant reactions in heterogeneous aquifers, Advances in Water Resources, 29, 1123, 10.1016/j.advwatres.2005.09.008 Manohar, 1999, Progress in structural dynamics with stochastic parameter variations 1987–1998, ASME Applied Mechanics Reviews, 52, 177, 10.1115/1.3098933 Miralles-Wilhelm, 1997, Stochastic analysis of oxygen-limited biodegradation in three dimensionally heterogeneous aquifers, Water Resources Research, 33, 1251, 10.1029/96WR03957 Miralles-Wilhelm, 2000, Stochastic analysis of oxygen-limited biodegradation in heterogeneous aquifers with transient microbial dynamics, Journal of Contaminant Hydrology, 4, 69, 10.1016/S0169-7722(99)00070-4 Osnes, 1998, An efficient probabilistic finite element method for stochastic groundwater flow, Advances in Water Resources, 22, 185, 10.1016/S0309-1708(97)00044-4 Oya S. Analysis of two dimensional random flow model. In: Solute transport and biodegradation characteristics for models of enhanced subsurface remediation, PhD thesis. University of Illinois at Urbana-Champaign, 1998. p. 118–49 [chapter 6]. Phanikumar, 2005, A three-dimensional model of microbial transport and biodegradation at the Schoolcraft, Michigan, site, Water Resources Research, 41, 10.1029/2004WR003376 Scholl, 2000, Effects of heterogeneity in aquifer permeability and biomass on biodegradation rate calculations-results from numerical simulations, Ground Water, 38, 702, 10.1111/j.1745-6584.2000.tb02706.x Severino, 2000, A note on transport of a pulse of nonlinearly reactive solute in a heterogeneous formation, Computational Geoscience, 4, 275, 10.1023/A:1011568118126 Spanos, 1989, Stochastic finite element expansion for random media, ASCE Engineering Mechanics, 115, 1035, 10.1061/(ASCE)0733-9399(1989)115:5(1035) Thampi SG. Studies on the transport of sorbing and biodegrading solutes in heterogeneous porous media, PhD thesis. Indian Institute of Science, Bangalore, India, 2002. p. 74–133. Vanmarcke, 1983 Wood, 1995, Effects of microbial metabolic lag in contaminant transport and biodegradation modeling, Water Resources Research, 31, 553, 10.1029/94WR02533 Wu, 2004, A numerical methods of moments for solute transport in a porous medium with multiscale physical and chemical heterogeneity, Water Resources Research, 40, 10.1029/2002WR001473 Xin, 1998, Stochastic analysis of biodegradation fronts in one-dimensional heterogeneous porous media, Advances in Water Resources, 22, 103, 10.1016/S0309-1708(98)00007-4 Xiu, 2002, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, Computer Methods in Applied Mechanics and Engineering, 191, 4927, 10.1016/S0045-7825(02)00421-8 Xiu D, Tartakovsky DM. Numerical methods for differential equation for random domain, SIAM Journal on Scientific Computing, in press.