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

The argument of what is the rate of an equilibrium reaction in a transport system is very controversial. It has been argued that the rate of an equilibrium reaction "can be mathematically abstracted as infinity" for the convenience of decoupling equilibrium reactions from kinetic reactions. It has also been argued that the rate of an equilibrium reaction is indefinite. This controversy should not have been aroused at all since, by definition, an equilibrium reaction should not have been associated with a rate per se. We can associate a rate to an equilibrium reaction only if we treat it 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 asymptotically tending 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. Transport processes and kinetic reactions try to alter the concentrations at each time and at each point of the computational domain. The rates of equilibrium reactions are those rates which are "necessary" to assure that the thermodynamic equations remain fulfilled, i.e., the solution of the concentration field remains on the manifold defined by thermodynamic equations. With this definition of the rates of equilibrium reactions, we can calculate the posteriori equilibrium rates using a subset of decomposed transport equations after all species concentrations are solved. Thus the rate of a fast equilibrium reaction is finite and definite. On the other hand, rates of kinetic reactions require either proposition of reaction pathways or empirical rate equations. Two example problems are used to demonstrate how consistent sets of governing equations are employed to simulate rates of asymptotic kinetic reactions or fast/equilibrium reactions.