The steady state model from Section 3.2.2 must be modified to allow material accumulation and to show the relationship between the state parameters with time. This was done by considering the derivative of the molar hold-up on each equilibrium stage. Although this fundamental change is sufficient to create a time-variant model of the reactive distillation process, the resulting model would be impractical as the set of DAEs would not be solvable with available techniques. Additional equations are required to close the problem. Many formulations of these equations are possible, but a combination was selected which promotes integration with other stage models so that the global set of DAEs was also solvable.
The complete set of dynamic equations is given as equations (7.1)-(7.14), below. As with the steady state model, the heat of reaction is calculated implicitly and does not need to be separately specified. The additional equations required for model closure are equations (7.13) and (7.14). The parameters of these equations were selected empirically to restrict the extent of accumulation on each stage. Fully rigorous equations are available but the parameters do not alter the steady state problem solution and only have a minor affect on the system dynamics and, therefore, contribute unnecessarily to the complexity of the model. Equation (7.13) relates directly to the physical dimensions of the equipment being simulated. The relevant parameters were based on a pilot scale laboratory system to allow the model to be tested against experimental data.
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