In reactor design, it is often best to simplify a reactor by assuming ideal conditions. For a continuous stirred tank reactor $($CSTR$),$ the concentration inside the reactor is the same as the concentration of the cffluent stream. In a plug flow reactor $($PFR$),$ the concentrations of the inlet and outlet streams are different as the concentrations of the reactants change along the length of the tube. For a fluidized bed in which catalyst is removed from the top of the reactor, there exists both characteristics of a CSTR and PFR$.$ The difference between inside reactor concentration $(C_i)$ and effluent concentration $(C_e)$ gives the membership of either CSTR or PFR$,$ as seen in Fig. A$1\mathrm{.}1$

Find the difference in concentration that represents the optimum design, i$.$e$.,$ find the most representative value for the union of PFR and CSTR$.$ For each of the seven methods presented in this chapter assess $($a$)$ whether each is applicable and, if so$,(b)$ calculate the defuzzified value, $z^{**}.$

Figure $1$: A$1\mathrm{.}1$