A transition in the spatially integrated reaction rate of bimolecular reaction-diffusion systems

作者：Arshadi Masoud^*; Rajaram Harihar

来源：Water Resources Research, 2015, 51(9): 7798-7810.

DOI：10.1002/2015WR017674

• bimolecular
• reaction
• diffusion
• transition

Numerical simulations of diffusion with bimolecular reaction demonstrate a transition in the spatially integrated reaction rate-increasing with time initially, and transitioning to a decrease with time. In previous work, this reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), leading to predictions that front motion scales as root t pt, and correspondingly the spatially integrated reaction rate decreases as the square root of time 1/root t. We present a general nondimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the spatially integrated reaction rate scales as root t rather than 1/root t. The duration of this early time regime (where the spatially integrated reaction rate is kinetically rather than diffusion controlled) is shown to depend on the kinetic rate parameters, diffusion coefficients, and initial concentrations of the two species. Numerical simulation results confirm the theoretical estimates of the transition time. We present illustrative calculations in the context of in situ chemical oxidation for remediation of fractured rock systems where contaminants are largely dissolved in the rock matrix. We consider different contaminants of concern (COCs), including TCE, PCE, MTBE, and RDX. While the early time regime is very short lived for TCE, it can persist over months to years for MTBE and RDX, due to slow oxidation kinetics.

• 出版日期2015-9