Modeling biogeochemical dynamics in porous media: Practical considerations of pore scale variability, reaction networks, and microbial population dynamics in a sandy aquifer

Simulating degradation of organic compounds accounting for the growth of microorganisms (Monod kinetics) in a fully Lagrangian framework

Biologically mediated degradation of organic compounds in porous media is a complex mathematical problem, described by a non-linear differential equation. The organic compound gets in contact with the biomass, and an enzyme-catalysed reaction takes place. The net result is that part of the parent compound degrades into some daughter product, while some of the organic carbon is used for microbial growth. The rate of biomass growth in the presence of a limiting nutrient supply is usually modelled with the experimentally derived Monod equation, i.e., it is proportional to the actual existing biomass multiplied by a factor that is non-linear in terms of available organic matter. This non-linearity in the degradation equation implies a strong difficulty in directly implementing a numerical solution within a fully Lagrangian framework, and thus, numerical solutions have traditionally been sought in either an Eulerian, or else an Eulerian-Lagrangian framework. Here we pursue a fully Lagrangian solution to the problem. First, the Monod empirical equation is formulated as the outcome of a two-step reaction; while the approach is less general than other derivations existing in the literature based on a full understanding of the thermodynamics of the process, it allows two things: 1) providing some physical meaning to the actual parameters in the Monod equation, and more interestingly, 2) formulating a methodology for the solution of the degradation equation incorporating Monod kinetics by means of a particle tracking formulation. For the latter purpose, both reactants and biomass are represented by particles, and their location at any given time is represented by a kernel that accounts for the uncertainty in the actual physical location. By solving the reaction equation in a kernel framework, we can reproduce the Monod kinetics and, as a particular result in the case no biomass growth is allowed, the Michaelis-Menten kinetics. The methodology proposed is then successfully applied to reproduce two studies of microbially induced degradation of organic compounds in porous media, first, the observed kinetics of Pseudomonas putida F1 in batch reactors while growing on benzene, toluene and phenol, and second, the column study of carbon tetrachloride biodegradation by the denitrifying bacterium Pseudomonas Stutzeri KC.

Upscaling of microbially driven first-order reactions in heterogeneous porous media

Reactions mediated by microorganisms determine the fate of many chemicals in natural porous media. At the pore scale, the distribution of chemicals and microorganisms is not homogeneous, leading to heterogeneous distribution of microbial activities at the pore scale. We conducted pore scale reactive transport simulations to investigate the scaling of microbially mediated consumption reaction rates under a range of flow and reaction conditions. The results reveal that the scaling effects largely depended on Péclet and Damköhler numbers. Consumption rate estimates based on volume-averaged concentrations and reaction kinetics overestimated the true volumetric reaction rates, and large-sized biomass aggregates intensified these scaling errors. In contrast, the macroscopic rates estimated via flux-weighted concentrations underestimated the true volumetric reaction rates, with large microbial aggregates reducing scaling errors. This study also demonstrated that macroscopic rate estimates can be improved by combining information on the reaction kinetics with the flux-weighted concentrations.

Functional Resistance to Recurrent Spatially Heterogeneous Disturbances Is Facilitated by Increased Activity of Surviving Bacteria in a Virtual Ecosystem

Bacterial degradation of organic compounds is an important ecosystem function with relevance to, e.g., the cycling of elements or the degradation of organic contaminants. It remains an open question, however, to which extent ecosystems are able to maintain such biodegradation function under recurrent disturbances (functional resistance) and how this is related to the bacterial biomass abundance. In this paper, we use a numerical simulation approach to systematically analyze the dynamic response of a microbial population to recurrent disturbances of different spatial distribution. The spatially explicit model considers microbial degradation, growth, dispersal, and spatial networks that facilitate bacterial dispersal mimicking effects of mycelial networks in nature. We find: (i) There is a certain capacity for high resistance of biodegradation performance to recurrent disturbances. (ii) If this resistance capacity is exceeded, spatial zones of different biodegradation performance develop, ranging from no or reduced to even increased performance. (iii) Bacterial biomass and biodegradation dynamics respond inversely to the spatial fragmentation of disturbances: overall biodegradation performance improves with increasing fragmentation, but bacterial biomass declines. (iv) Bacterial dispersal networks can enhance functional resistance against recurrent disturbances, mainly by reactivating zones in the core of disturbed areas, even though this leads to an overall reduction of bacterial biomass.