20 research outputs found

    Mathematical modeling of circulation in two-dimensional plane flow

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    June 1980.CER79-80VMP-SBY59.Includes bibliographical references.Final report to the National Science Foundation, Grant no. CME-7805458

    A General Simulator For Reaction-Based Biogeochemical Processes

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    As more complex biogeochemical situations are being investigated (e.g., evolving reactivity, passivation of reactive surfaces, dissolution of sorbates), there is a growing need for biogeochemical simulators to flexibly and facilely address new reaction forms and rate laws. This paper presents an approach that accommodates this need to efficiently simulate general biogeochemical processes, while insulating the user from additional code development. The approach allows for the automatic extraction of fundamental reaction stoichiometry and thermodynamics from a standard chemistry database, and the symbolic entry of arbitrarily complex user-specified reaction forms, rate laws, and equilibria. The user-specified equilibria and kinetic rates (i.e., they are not defined in the format of the standardized database) are interpreted by the Maple V (Waterloo Maple) symbolic mathematical software package. FORTRAN 90 code is then generated by Maple for (1) the analytical Jacobian matrix (if preferred over the numerical Jacobian matrix) used in the Newton-Raphson solution procedure, and (2) the residual functions for governing equations, user-specified equilibrium expressions and rate laws. Matrix diagonalization eliminates the need to conceptualize the system of reactions as a tableau, which comprises a list of components, species, the stoichiometric matrix, and the formation equilibrium constant vector that forms the species from components (Morel and Hering, 1993), while identifying a minimum rank set of basis species with enhanced numerical convergence properties. The newly generated code, which is designed to operate in the BIOGEOCHEM biogeochemical simulator, is then compiled and linked into the BIOGEOCHEM executable. With these features, users can avoid recoding the simulator to accept new equilibrium expressions or kinetic rate laws, while still taking full advantage of the stoichiometry and thermodynamics provided by an existing chemical database. Thus, the approach introduces efficiencies in the specification of biogeochemical reaction networks and eliminates opportunities for mistakes in preparing input files and coding errors. Test problems are used to demonstrate the features of the procedure. Ā© 2005 Elsevier Ltd. All rights reserved

    A uranium bioremediation reactive transport benchmark

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    A reactive transport benchmark problem set has been developed based on in situ uranium bio-immobilization experiments that have been performed at a former uranium mill tailing site in Rifle, CO, USA. Acetate-amended groundwater stimulates indigenous microorganisms to catalyze the reduction of U(VI) to a sparingly soluble U(IV) mineral. The interplay between the flow, acetate loading periods and rates, and microbially mediated and geochemical reactions leads to dynamic behavior in metal- and sulfate-reducing bacteria, pH, alkalinity, and reactive mineral surfaces. The benchmark is based on an 8.5 m long one-dimensional model domain with constant saturated flow and uniform porosity. The 159-day simulation introduces acetate and bromide through the upgradient boundary in 14- and 85-day pulses separated by a 10 day interruption. Acetate loading is tripled during the second pulse, which is followed by a 50 day recovery period. Terminal electron-accepting processes for goethite, phyllosilicate Fe(III), U(VI), and sulfate are modeled using Monod-type rate laws. Major ion geochemistry modeled includes mineral reactions as well as aqueous and surface complexation reactions for UO, Fe2+, and H+. In addition to the dynamics imparted by the transport of the acetate pulses, U(VI) behavior involves the interplay between bioreduction, which is dependent on acetate availability, and speciation-controlled surface complexation, which is dependent on pH, alkalinity, and available surface complexation sites. The general difficulty of this benchmark is the large number of reactions (74), multiple rate law formulations, a multisite uranium surface complexation model, and the strong interdependency and sensitivity of the reaction processes. Results are presented for three simulators: HYDROGEOCHEM, PHT3D, and PHREEQC

    Oxidation of H 2

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