The final, overall objective of any process control application should always be to maximise the profitability of the process under control. This is normally achieved via a rationalisation of the value added by the process with the energy that is consumed by the process. For example, in a conventional distillation column, increasing the internal vapour and liquid flows nearly always increases the separation of key components and, therefore, increases either the product yield or its value. However, the increase in internal flow rates is only achieved at the expense of additional energy consumption in both the condenser and reboiler. With most reactors and many other unit operations, this principle often manifests itself with respect to the heating or cooling requirement, or the recycle rate. An effective control application adjusts the process operation towards an optimum where the incremental value added is just less than the incremental cost of the energy and raw materials.
Reactive distillation combines the functionality of both the reaction and purification stages of a process and the main operating objective for a reactive distillation column should reflect both roles. The conversion of lower value reactants to higher value products is the facet of reactor operation that contributes value to a process and this is usually best measured via the molar conversion of the limiting reactant. The effectiveness of a distillation process can be measured via a separation factor, which relates the purity of the top and bottoms products (e.g. equation 9.1).
The overall benefit of a reactive distillation process arises from both the conversion of reactants and the separation of products. Therefore, an appropriate metric for reactive distillation should combine both measurements (e.g. equation 9.2).
The conversion of the limiting reactant, X, and the separation factor, S, are both bounded between 0 and 1. Therefore, the reactive distillation metric, V, will also be bounded between 0 and 1. Presumably, the value of V will increase with the energy consumed by the process so that a minimisation problem can be constructed to determine the optimal operating conditions, However, it will usually not be possible to show that the minimisation problem is convex, and several results from Chapters 4 to 6 suggest that V might not always increase monotonically with energy consumption. Therefore, an alternative formulation of the process objective(s) is warranted.
This can be achieved by considering the process and operating constraints. The product value from any chemical process is rarely a smooth function of its properties. Instead, the product will often have a constant value provided that its properties are between certain limits or specifications. Under these conditions, the maximum value from the process is often obtained at the coincidence of two or more constraints. For example, the profitability of a reactive ETBE column might be maximised when isobutene conversion is maximised and ETBE losses (in the distillate) are minimised whilst maintaining the ETBE product purity between specification limits. The process objectives arising from this statement are:
a) maximum isobutene conversion;
b) minimum ETBE in the distillate;
c) ETBE purity in the bottoms maintained at a designated value.
With different economic circumstances, the value added by the process coupled with high demand for the product will be more significant than the incremental energy cost and there is an incentive to operate the system to maximise throughput up to the equipment constraints while maintaining product quality at the minimum acceptable value. For example, the value of ETBE (compared with the raw materials and energy) might be such that throughput is a more important consideration than both the isobutene conversion and any loss of product in the distillate. The requirements for maximum profitability in this
situation are maximum throughput whilst maintaining the ETBE product purity between specification limits. The specific process objectives would then be expressed as:
a) maximum bottoms draw rate;
b) ETBE purity in the bottoms maintained at a designated value.
Whatever the operating objectives are determined to be (and they will vary depending on the economic circumstances and other external factors), the controller design should focus on these criteria. It should be noted, however, that it might not be possible to satisfy all of the process objectives simultaneously.
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