Material balances recycle loop reactor

From a computational viewpoint, the presence of recycle streams is one of the impediments in the sequential solution of a flowsheeting problem. Without recycle streams, the flow of information would proceed in a forward direction, and the cal-culational sequence for the modules could easily be determined from the precedence order analysis outlined earlier. With recycle streams present, large groups of modules have to be solved simultaneously, defeating the concept of a sequential solution module by module. For example, in Figure 15.8, you cannot make a material balance on the reactor without knowing the information in stream S6, but you have to carry out the computations for the cooler module first to evaluate S6, which in turn depends on the separator module, which in turn depends on the reactor module. Partitioning identifies those collections of modules that have to be solved simultaneously (termed maximal cyclical subsystems, loops, or irreducible nets). 

The material balance around the mixing point of a loop reactor is given by Equation (4.21) for the case of constant fluid density. How would you work a recycle problem with variable density Specifically, write the variable-density counterpart of Equation (4.21) and explain how you would use it. 

A.6. Perform structural analysis based on a steady-state model and evaluate the possibilities for decomposition of the control problem. To simply this step, we assume that the pressure and temperature control loops are essentially decoupled from the plant holdups (integrating modes), the compositions, and the liquid flows. If this assumption is approximately valid, we can analyze a core plant model ( core model ) that comprises the reactor, flash unit, and recycle tank—all assumed to operate isothermally and isobarically (see Fig. H.5). Thus, the approximate plant model consists only of material balances but includes the key flows, levels, and compositions. This type of approach, in which temperatures and pressures are assumed to remain constant at their nominal values, was employed by Robinson et al. (2001) in their analysis of a similar plant. 

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