Reaction Rates in a Transport System with Both Kinetic and Equilibrium Reactions

摘要

The argument of what is the rate of an equilibrium reaction in a transport systemis very controversial. It has been argued that the rate of an equilibrium reaction “canbe mathematically abstracted as infinity” for the convenience of decouplingequilibrium reactions from kinetic reactions. It has also been argued that the rate ofan equilibrium reaction is indefinite. This controversy should not have been arousedat all since, by definition, an equilibrium reaction should not have been associatedwith a rate per se. We can associate a rate to an equilibrium reaction only if we treatit as an extremely fast kinetic reaction. Then it is legitimate to ask what its rate is.For an extremely fast reaction, its forward and backward rates are asymptoticallytending to infinity. The question is then what is its net rate? To answer this question,it is necessary to understand the interplay between transport and reactions. Transportprocesses and kinetic reactions try to alter the concentrations at each time and at eachpoint of the computational domain. The rates of equilibrium reactions are those rateswhich are "necessary" to assure that the thermodynamic equations remain fulfilled,i.e., the solution of the concentration field remains on the manifold defined bythermodynamic equations. With this definition of the rates of equilibrium reactions,we can calculate the posteriori equilibrium rates using a subset of decomposedtransport equations after all species concentrations are solved. Thus the rate of a fastequilibrium reaction is finite and definite. On the other hand, rates of kineticreactions require either proposition of reaction pathways or empirical rate equations.Two example problems are used to demonstrate how consistent sets of governingequations are employed to simulate rates of asymptotic kinetic reactions orfast/equilibrium reactions.