Modeling and measuring biogeochemical reactions: system consistency, data needs, and rate formulations

This paper intends to lay-out a foundation of protocols for planning and an alyzing biogeochemical experiments, It presents critical theoretical issues that must be considered for proper application of reaction-based biogeoche mical models. The selection of chemical components is not unique and a deco mposition of the reaction matrix should be used for formal selection. The d ecomposition reduces the set of ordinary differential equations governing t he production-consumption of chemical species into three subsets of equatio ns: mass action; kinetic-variable; and mass conservation, The consistency o f mass conservation equations must be assessed with experimental data befor e kinetic modeling is initiated. Assumptions regarding equilibrium reaction s should also be assessed. For a system with M chemical species involved in N reactions with N-I linearly- independent reactions and N-E linearly-inde pendent equilibrium reactions, the minimum number of chemical species conce ntration vs. time curves that must be measured to evaluate the kinetic suit e of reactions using a reaction-based model will be (N-I - N-E). However, f or a partial assessment of system consistency, at least one more species mu st be measured [i.e. (N-I - N-E + 1)]. For a complete assessment of system consistency, (N-I - N-E + N-C) additional species would have to be measured , where N. is the number of chemical components. Reaction rates for kinetic reactions that are linearly independent of other kinetic reactions can be determined based on only one profile of a kinetic-variable concentration vs . time for each kinetic reaction. Reaction rates for parallel kinetic react ions that are linearly dependent on each other cannot be uniquely segregate d when they result in production of the same species, however, they must be included for simulation purposes. Kinetic reactions that are linearly depe ndent only on equilibrium reactions are redundant and do not have to be mod eled. The bioreduction of ferric oxide is used as an example to functionall y demonstrate these points, and shows that Henri-Michaelis-Benton-Monod kin etics should be applied with care to coupled abiotic and biotic systems. (C ) 2001 Elsevier Science Ltd. All rights reserved.