CSTRs in Series RTD

For CSTRs in parallel with the feed split as for optimal performance, the fact that two (or more) reactors behave the same as one CSTR of the same total volume means that the RTD is also the same in each case. Here, we consider the RTD for CSTRs in series, as in a multistage CSTR (Section 14.4). In the following example, the RTD is obtained for two tanks in series. The general case of N tanks in series is considered in Chapter 

19 as a model for nonideal flow through a single vessel. For the purpose of obtaining the RTD, we treat the CSTRs simply as two stirred tanks in series, with the flow in each being BME 

To develop E(B) for two CSTRs in series, we use a slightly different, but equivalent, method from that used for a single CSTR in Section 13.4.1.1. Thus, consider a small amount (moles) of tracer M, nMo = F,dt, where Ft is the total steady-state molar flow rate, added to the first vessel at time 0. The initial concentration of M is cMo = nMo/(V/2). We develop a material balance for M around each tank to determine the time-dependent outlet concentration of M from the second vessel, cM2(l). 

For vessel 1, there is no subsequent input of tracer, the outlet flow rate is cM1, and the accumulation rate is (V/2)dcm/dt. Thus, at any subsequent time t, 

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