Consider a tank that works with constant volume and the input volumetric flow q1

Question

Consider a tank that works with constant volume and the input volumetric flow q1(t) that changes with the time and q2 constant. Inside the tank there's a reaction, which the velocity is r = k[Ca(t)]2. Assume the concentration inside the tank is the same as the concentration in the output flow.

1. Do the mass balance for substance A in stable and transcient state, in order to relate the changes in its concentration at the output of the reactor in function to its initial concentration.

2. Consider the data: : V = 25ft3, k = 0.2ft3/(min lb), qi' = q2= 6 ft3/min y q'=12 ft3/min. Get the transfer functions.

a) If the concentration in the input A suddenly changes from 0.5 to 0.8 lb/ft^3, calculate the A concentration at the output of A and the stabilizing time using the tranfer function obtained from the last question.

b) If q1(t) suddenly rises in 50%, calculate the final concentration of A at the exit and the time of stabilizing using the pertinent transfer function.

q, q1, q2              flujos en ft3/min

cA (t) , cB (t), cC (t)     concentraciones en lb /ft3

V             volume in the reacted mix stored inside the tank
k             constant in ft3/lb-min
t time in minuntes

Explanation / Answer

The q1(t) is an input flow that depends on time, while cAi(t) being a concentration that also depends on time; (ft3/min) on a solute, q2, is a constant flow, and cBi(t) is the concentration of another solute. The output concentration of cBo(t) and cCo(t) are irrelevant, since the mass balance is only on to substance A. There is an assumption that the reactor is a perfcet mix, and A+B->C

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