Modeling of process systems with recycle and purge

Modeling of process systems with recycle and purge 

Let Fq denote the feed flow rate to the first unit, Fio the rate at which the impurity is input to the system,1 Fj, j = 1. N, the outlet flow rate from the jth unit, Fr the recycle flow rate, and Fp the purge flow rate. Also, let W, i = 1. C — 1 and N denote the net rates at which the th component and, respectively, the impurity, are separated from the recycle loop. 

1 The impurity feed stream Fjo has no physical equivalent but is a convenient means to increase the generality of the model, since it can capture multiple practical scenarios concerning the origin of the impurities, e.g., as part of the feed stream Fq, leaks from the environment into the process or as the product of undesired secondary reactions. 

Assuming that the individual process units can be modeled as lumped-parameter systems, the mathematical model that describes the overall and component material balances of the process takes the form 

In order to capture the impact of the purge stream on the dynamics of this generic process, let us define the purge number. 

---