Reactor models, applications perfect mixing

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

The application of the equations to chemical reactions requires the proper definition of the above quantities as well as correctly defining the transition probabilities pjj and pjk this is established in the following. It should also be noted that the models derived below for numerous chemical reactions, are applicable to chemical reaction occurring in a perfectly-mixed batch reactor or in a single continuous plug-flow reactor. Other flow systems accompanied with a chemical reaction will be considered in next chapters. 

Flush The flush reaction path model is analogous to the perfectly mixed-flow reactor or the continuously stirred tank reactor in chemical engineering (Figure 2.5). Conceptually, the model tracks the chemical evolution of a solid mass through which fresh, unreacted fluid passes through incrementally. In a flush model, the initial conditions include a set of minerals and a fluid that is at equilibrium with the minerals. At each step of reaction progress, an increment of unreacted fluid is added into the system. An equal amount of water mass and the solutes it contains is displaced out of the system. Environmental applications of the flush model can be found in simulations of sequential batch tests. In the experiments, a volume of rock reacts each time with a packet of fresh, unreacted fluids. Additionally, this type of model can also be used to simulate mineral carbonation experiments. 

Where n is the single parameter of the cellular model, equal to the number of cells (devices) in a cascade of perfect mixing reactors. Plug flow mode is achieved at —> o<= [1]. It is assumed [124] that if the number of cells in a reactor n > 8, calculation methods for plug flow reactors can be applied to such a device with accuracy sufficient for industrial application. 

There is another practical method for estimating conversions in reactors with residence time distribution, for perfect micro-mixing, that is also applicable to other reaction orders. To this end the reactor is simulated by a model that consists of a cascade on N perfectly mixed equal reactors (section 3.3.3). The RTD-function of the cascade with total residence time x can be calculated ... 

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