6. Overall Mass Balance for Unsteady-State Process. A storage vessel is well sti

Question

6. Overall Mass Balance for Unsteady-State Process. A storage vessel is well stirred and contains 500 kg of total solution with a concentration of 5.0% salt. A constant flow rate of 900 kg/h of salt solution containing 16.67% salt is suddenly introduced into the tank and a constant withdrawal rate of 600 kg/h is also started. These two flows remain constant thereafter. Derive an equation relating the outlet withdrawal concentration as a function of time. Also, calculate the concentration after 2.0 h.

Explanation / Answer

Unsteady state Mass balance:

Inlet + Accumulation = outlet

Initial balance,For unit hour: 900*0.1667 +500*0.05 = 600*x

Which gives x= 0.2917

Now for unsteady state, cconcentration inside vessel varies once constant flows of inlet and outlet are maintained.

Thus outlet concentration is 29.17% salt solution.

Now Here assuming the outlet stream also has similar concentration C as the vessel,mass balance gives:

900*0.1667 + dC/dt = 600*C

dC/dt = 600C + 150.3

Integration results from time '0' to time 't' gets following answer:

(1/600)*ln(600C +150.3) = t, C goes from C to Cf

(1/600)*ln((600Cf +150.3)/(600C + 150.3))= t

To calculate concentration after 2 hours put C = 0.05 and t= 2 hours and get Cf.

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