Ž . Journal of Contaminant Hydrology 42 2000 69–97 www.elsevier.comrlocaterjconhyd Stochastic analysis of oxygen-limited biodegradation in heterogeneous aquifers with transient microbial dynamics Fernando Miralles-Wilhelm a, ) , Lynn W. Gelhar b a Department of CiÕil and EnÕironmental Engineering, Northeastern UniÕersity, Boston, MA 02115, USA b Department of CiÕil and EnÕironmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Received 5 November 1998; received in revised form 2 August 1999; accepted 19 August 1999 Abstract A stochastic theory of multiple species transport and transformation is developed for the problem of oxygen-limited biodegradation of contaminants in aquifers, considering the presence of transient microbial growth dynamics. The theory incorporates the effects of physical, chemical and microbiological heterogeneities into a stochastic analysis of the coupled transportrtransformation equations for a system consisting of a contaminant, an oxidizer, i.e., dissolved oxygen, and active biomass in heterogeneous and anisotropic aquifers. The developed theory is used to quantify the effects of mean concentrations on the field scale coefficients of decay, retardation and macrodis- persion, and to evaluate the assumption of a steady-state biomass, previously reported in the w literature. A comparison between the steady state assumption Miralles-Wilhelm, F., Gelhar, L.W., Kapoor, V., 1997. Stochastic analysis of oxygen-limited biodegration in three dimensionally in Ž.x heterogeneous aquifers. Water Resour. Res., 33 6 and this work for hypothesized field conditions shows that the effects of transient microbial growth on the effective retardation factor and macrodispersivities are minor, while the effects are modest for the effective decay rate. Transient microbial growth dynamics are found to occur over most contaminant and dissolved oxygen mean concentration ranges, and therefore a transient mean balance equation for biomass should be included in modeling efforts directed at quantifying oxygen-limited biodegradation at field scales. As in previous research, the effective decay rate is found to be less than the mean, ) Corresponding author. Fax: q1-617-373-4419; e-mail: fmiralle@coe.neu.edu 0169-7722r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved. Ž . PII: S0169-7722 99 00070-4