In this question you will determine the size of a storage vessel of a highly cor

Question

In this question you will determine the size of a storage vessel of a highly corrosive material (oversizing is highly penalized by increased capital cost). Feed liquid is delivered to the plant side periodically, and the plant downstream the storage vessel is operated continuously. A tank is provided to store the feed liquid, according to the sketch below. Assume that the storage tank is initially empty and the feed delivery is given bellow. The capital cost of the tank depends on its size: 4. C(s) 500 V(m2) (a) Determine the volume that will prevent overflow between the times 0 to 100 hours and calculate the capital cost. in Raw material flow Downstream process Fig. 3. Process Schematics of a storage vessel

Explanation / Answer

a) volume required after 1st 20 hrs= 20*30 - 12*20 = 600 - 240 = 360 m3.

volume required after 1st 50 hrs=360 - 15*12 + 15*25 - 15*12 = 375 m3

volume required after 1st 75 hrs= 375 - 10*12 + 15* 15 - 12*15 = 300 m3

After that phase rate of flow is less than 12 m3/h. So, we are not considering the volume after 75 hrs for maximum volume required. So, maximum volume required is 375 m3.

Delivery cost= 12*100*500= Rs. 6,00,000 = 6 lakhs

b) considering output flow rate to be 13 m3/h,

volume required after 1st 20 hrs= 20*30 - 13*20 = 600 - 240 = 340 m3.

volume required after 1st 50 hrs=340 - 15*13 + 15*25 - 15*13 = 325 m3

volume required after 1st 75 hrs= 325 - 10*13 + 15* 15 - 13*15 = 225 m3

After that phase rate of flow is less than 13 m3/h. So, we are not considering the volume after 75 hrs for maximum volume reached. So, maximum volume required is 340 m3.

c)

considering output flow rate to be 6 m3/h,

volume required after 1st 20 hrs= 20*30 - 6*20 = 600 - 120 = 480 m3.

volume required after 1st 50 hrs=480 - 15*6 + 15*25 - 15*6 = 675 m3

volume required after 1st 75 hrs= 675 - 10*6 + 15* 15 - 6*15 = 750 m3

So, if the vessel is of 700 m3, the time at which it overflows is= 60+((700-(675-10*6))/15)=65.66 hrs

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