A general paradigm to model reaction‐based biogeochemical processes in batch systems

Abstract

[1] This paper presents the development and illustration of a numerical model of reactionbased geochemical and biochemical processes with mixed equilibrium and kinetic reactions. The objective is to provide a general paradigm for modeling reactive chemicals in batch systems, with expectations that it is applicable to reactive chemical transport problems. The unique aspects of the paradigm are to simultaneously (1) facilitate the segregation (isolation) of linearly independent kinetic reactions and thus enable the formulation and parameterization of individual rates one reaction by one reaction when linearly dependent kinetic reactions are absent, (2) enable the inclusion of virtually any type of equilibrium expressions and kinetic rates users want to specify, (3) reduce problem stiffness by eliminating all fast reactions from the set of ordinary differential equations governing the evolution of kinetic variables, (4) perform systematic operations to remove redundant fast reactions and irrelevant kinetic reactions, (5) systematically define chemical components and explicitly enforce mass conservation, (6) accomplish automation in decoupling fast reactions from slow reactions, and (7) increase the robustness of numerical integration of the governing equations with species switching schemes. None of the existing models to our knowledge has included these scopes simultaneously. This model (BIOGEOCHEM) is a general computer code to simulate biogeochemical processes in batch systems from a reaction-based mechanistic standpoint, and is designed to be easily coupled with transport models. To make the model applicable to a wide range of problems, programmed reaction types include aqueous complexation, adsorption-desorption, ionexchange, oxidation-reduction, precipitation-dissolution, acid-base reactions, and microbial mediated reactions. In addition, user-specified reaction types can be programmed into the model. Any reaction can be treated as fast/equilibrium or slow/ kinetic reaction. An equilibrium reaction is modeled with an infinite rate governed by a mass action equilibrium equation or by a user-specified algebraic equation. Programmed kinetic reaction rates include multiple Monod kinetics, nth order empirical, and elementary formulations. In addition, user-specified rate formulations can be programmed into the model. No existing models to our knowledge offer these simultaneous features. Furthermore, most available reaction-based models assume chemical components a priori so that reactions can be written in basic (canonical) forms and implicitly assume that fast equilibrium reactions occur only for homogeneous reactions. The decoupling of fast reactions from slow reactions lessens the stiffness typical of these systems. The explicit enforcement of mass conservation overcomes the mass conservation error due to numerical integration errors. The removal of redundant fast reactions alleviates the problem of singularity. The exclusion of irrelevant slow reactions eliminates the issue of exporting their problematic rate ...

Using a Reaction-Based Differential-Algebraic Equation Approach for Reactive Transport Modeling in Hydrologic Systems

“…Fang et al [7] have described detailed step-by-step decomposition procedures, and we do not repeat the lengthy description here. Although they did not include instantaneous reactions, the essential details concerning decomposition were clearly explained in their paper.…”

“…To achieve this, we first pick basis species, followed by implementing Gauss-Jordan elimination with full pivoting to decompose the reaction network. The selection of basis species can be arbitrary [7]. Different selections will produce different decomposition results, but all the decomposition results are mathematically equivalent.…”

“…The DAE approach [5,6] models equilibrium-controlled reactions with mass action equations to overcome the time step drawback associated with the primitive approach. Fang et al [7,8] proposed a general paradigm to generate and solve reaction equations automatically and systematically, where an RB-DAE approach was presented. In their RB-DAE approach, the governing equations consist of reaction-based rate equations and mass conservation equations, which are mathematically equivalent to the species-based rate equations used in the primitive approach.…”

Nuclear Energy Advanced Modeling and Simulation (NEAMS) Waste Integrated Performance and Safety Codes (IPSC) : FY10 development and integration.

“…This code is a descendant of the KEMOD code and includes additional features for simulation of microbial processes. It incorporates a new paradigm of reaction-based approaches to biogeochemical processes (Fang et al 2003) which allows description of the reaction system on an ad hoc empirical basis or in terms of more fundamental basic reactions. The modular nature of the HYDROGEOCHEM code family is an attractive feature for Waste IPSC.…”

A Reaction-Based River/Stream Water Quality Model: Reaction Network Decomposition and Model Application

“…A few reaction-based watershed models can handle contaminant transport with kinetic reactions (Yeh et al 1998;Cheng et al 2000) using a "primitive" approach, in which the partial differential equations (PDEs) governing reactive transport are integrated directly to yield distributions of water quality constituents in a region of interest over time. However, when some reactions exhibit very fast kinetics (near equilibrium behavior), the PDEs become infinitely stiff making their solution using the primitive approach intractable (Fang et al 2003). This difficulty has been overcome by the introduction of mixed differential and algebraic equations (DAEs) for combinations of water quality constituents according to equilibrium reaction expressions and eliminating equilibrium reactions from the simultaneous solution of PDEs (Zhang et al 2008).…”