KINETICS QUASIINVARIANTS OF CHEMICAL REACTIONS IN OPEN SYSTEMS

The methods of nonequilibrium multi-experiments are one of the new approaches to solving inverse problems of chemical kinetics and optimization of chemical reactors. Currently, these methods are developed only for closed isothermal systems. In this paper, a generalization of the dual-experiment method and its extended version of the multi-experiment method for open systems is obtained, which allows to determine the approximate kinetic invariants (quasiinvariants) of chemical reactions in open continuous stirred tank reactor. The multi-experiment method for open systems is based on conducting two or more special nonequilibrium (unsteady) experiments under certain conditions. For nonlinear reactions of arbitrary complexity (multi-step, multi-equilibria), simple relations are obtained that allow to calculate the conditions for nonequilibrium experiments necessary for the identification of the reaction mechanism under study. The method allows to use any permissible values, except equilibrium ones, as initial values of reagent concentrations. The technique of carrying out multi-experiments and performing the necessary numerical calculations based on the multiple integration of systems of ordinary differential equations under different initial conditions is developed. The examples of using the developed method for one-stage linear and two-stage nonlinear reactions with two and three reagents are given. Found with the help of this method, the kinetic curves of the nonequilibrium quasiinvariants compared with the nonequilibrium curves of change of concentrations during the whole reaction. It is shown that quasiinvariant curves change within narrower limits than concentrations in different experiments, i.e. remain practically constant in time. The obtained results are also applicable for open nonisothermal systems.

Reactive transport with wellbore storages in a single-well push–pull test

Using the single-well push–pull (SWPP) test to determine the in situ biogeochemical reaction kinetics, a chase phase and a rest phase were recommended to increase the duration of reaction, besides the injection and extraction phases. In this study, we presented multi-species reactive models of the four-phase SWPP test considering the wellbore storages for both groundwater flow and solute transport and a finite aquifer hydraulic diffusivity, which were ignored in previous studies. The models of the wellbore storage for solute transport were proposed based on the mass balance, and the sensitivity analysis and uniqueness analysis were employed to investigate the assumptions used in previous studies on the parameter estimation. The results showed that ignoring it might produce great errors in the SWPP test. In the injection and chase phases, the influence of the wellbore storage increased with the decreasing aquifer hydraulic diffusivity. The peak values of the breakthrough curves (BTCs) increased with the increasing aquifer hydraulic diffusivity in the extraction phase, and the arrival time of the peak value became shorter with a greater aquifer hydraulic diffusivity. Meanwhile, the Robin condition performed well at the rest phase only when the chase concentration was zero and the solute in the injection phase was completely flushed out of the borehole into the aquifer. The Danckwerts condition was better than the Robin condition even when the chase concentration was not zero. The reaction parameters could be determined by directly best fitting the observed data when the nonlinear reactions were described by piece-wise linear functions, while such an approach might not work if one attempted to use nonlinear functions to describe such nonlinear reactions. The field application demonstrated that the new model of this study performed well in interpreting BTCs of a SWPP test.

How imperfect mixing and differential diffusion accelerate the rate of nonlinear reactions in microfluidic channels

Enhanced mixing in a microfluidic channel slows down the progress of a nonlinear chemical reaction.