This problem requires you to analyze the startup of a CSTR under two conditions.

Question

This problem requires you to analyze the startup of a CSTR under two conditions. In each case, the reactor initially contains pure water. At time greaterthanorequalto 0, an aqueous stream containing reactant A is fed into the reactor. The reactor volume V is constant. First, consider startup of the reactor at a temperature T_1. At this temperature, the reaction of A is so slow that it can be considered negligible. The conditions corresponding to the feed are shown below. Write the design equation (ODE) for C_A(t) during the transient operation of the CSTR. Then solve this ODE for C_A(t). Thereby, calculate C_A at a time = 20 min. Compare this value to that of C_A as t rightarrow infinity.

Explanation / Answer

The moles balance equation for a CSTR can be written as

FAO= FA+ dNA/dt +(-rA)*V

since there is no chemical reaction, -rA= 0

FAO= FA+ dNA/dt, FAO = inital flow rate and FA = Flow rate at time t

T= V/VO and     T= VCAO/FA

CAO- CA= T dCA/dt

dCA/dt +1/T CA= CAO

this is in the form dy/dx+ Py =Q

P= 1/T

when integrated and noting that at t=0 CA=0

CA= CAO*{1-exp -[1+1/T)}

at T= 20 min

CA= 2*(1- exp-(1+1/20)

CA= 1.3 mol/L

as t--->infirnity, 1/T =0

CA= 2*{1-exp-(1) =1.26

CAO- CA=

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