Theoretical and Experimental Considerations Related to Reaction-Based Modeling: A Case Study Using Iron(III) Oxide Bioreduction

Abstract

The kinetics of reductive dissolution of hematite ( f -Fe 2 O 3 ) by the dissimilatory iron-reducing bacterium Shewanella putrefaciens strain CN32 under nongrowth conditions with H 2 as the electron donor was measured and then modeled using a reaction-based biogeochemical model. Minimum data needs and a reaction matrix decomposition procedure are presented from a reaction-based modeling perspective and used to design subsequent experiments. Detailed step-by-step modeling methodology is presented. Independent experiments were performed to determine if Fe 2+ sorption to S. putrefaciens CN32 or hematite could be described as either kinetic or equilibrium reactions (i.e., slow or fast, respectively, relative to the time-scale of the bioreduction experiments). Fe 2+ sorption to S. putrefaciens CN32 was an equilibrium reaction and a linear adsorption isotherm was used to determine the associated equilibrium constant. Fe 2+ sorption to hematite was a kinetic reaction and an elementary rate formulation was independently determined from abiotic experiments. The ratio of the forward rate divided by the backward rate [log(k f /k b )] for the sorption of Fe 2+ to hematite was 6.33 - 0.14 (n = 2) and the corresponding log(k f ) was 6.66 - 0.28 (n = 2, M -1 h -1 ). Three different kinetic reaction rate formulations were used to model hematite bioreduction, an elementary rate law for the overall reaction, an empirical rate law physically based on hematite "free" surface sites, and an empirical rate law physically based on hematite free surface sites and bacterial inhibition caused by Fe(II) biosorption. All rate formulations modeled the measured results reasonably well (R 2 values ranged from 0.83 to 0.99). For the elementary rate formulation, log(k f /k b ) was 24.37 - 0.15 (n = 4) and the corresponding forward rate [log(k f )] was 26.46 - 0.27 (n = 4, M -4 h -1 ). These results demonstrate that independently determined reaction-based rate formulations were applicable in another experimental system, as theoretically expected. Therefore, the simulation and prediction of complex biogeochemical systems may eventually be able to be performed using reaction-based models.