Equilibrium Reaction Theory
The feature Equilibrium Reaction is described in this section. A chemical equilibrium reaction system is defined by the stoichiometry of the reaction and the relation between the chemical activities of the chemical species participating in the reaction (the equilibrium condition).
The kinetics of the reaction is so fast that the equilibrium condition is fulfilled at all times in all space coordinates.
The equilibrium condition is commonly based on the stoichiometric coefficients, νi (dimensionless), of the reaction, the species activities of the reacting species ai (dimensionless), and an equilibrium constant, Keq (1) according to:
where the species activities are defined as
where ca0 (SI unit: mol/m3) is the standard molarity, and γc,i (dimensionless) an activity coefficient.
Defining the stoichiometric coefficients positive for products and negative for reactants, the above equilibrium condition can also be written:
The Equilibrium Reaction node solves for a reaction rate so that the equilibrium condition is always fulfilled in the domain.
γc,i is set to unity when the Equilibrium constant is selected on the Settings window. For non-unity activity coefficients, a user defined equilibrium condition can be used.
Equilibrium Reactions and Inflow Boundary Conditions
Contradictory constraints arise if the boundary conditions for concentrations or activities are set so that the domain equilibrium condition is not fulfilled. Special treatment is therefore needed at Inflow boundaries, where the concentrations are set for all species in the mass transport interfaces.
One way of avoiding competing constraints on an inflow boundary is to add an additional reaction coordinate degree of freedom, solved for to create a set of modified inflow concentrations that fulfill the domain equilibrium condition. The reaction coordinate gives rise to a concentration shift, which is the offset to the inflow concentrations provided by the user. The shift for each species obeys the stoichiometry of the reaction and the equilibrium expression. The modified inflow concentrations are then used in the boundary conditions for the domain mass transport equations. The resulting modified inflow concentrations can be seen as the stationary solution for a batch reactor with the user inflow concentrations as initial concentrations. In addition, the domain reaction rate degree of freedom of the equilibrium reaction is constrained to zero on all Inflow boundaries.
Equilibrium Reactions and Concentration Boundary Conditions
No special treatment is made with regards to input concentration values of the Concentration boundary node. Using this feature, you can explicitly set one or a set of concentrations, and the equilibrium condition acts on the rest of the concentrations. However, there is no solution to the problem if more concentrations than the number of species minus the number of equilibrium reactions are set using this feature.
Equilibrium Reactions and Time-Dependent Simulations
Spurious oscillations may occur in a time-dependent problem if the initial conditions do not fulfill the equilibrium condition. Since equilibrium reactions are assumed to be infinitely fast, the solution is to initialize the problem using an additional study step, solving for a stationary problem with all non-equilibrium reaction rates set to zero. Manual scaling of the reaction rate dependent variables is needed in this study step.