You are designing a biogas plant where you are heating the digester feedstock wi

Question

You are designing a biogas plant where you are heating the digester feedstock with waste heat from your cogeneration process. You have selected a thin-walled double-pipe counter-flow heat exchanger. If your feedstock (which approximately has the properties of water) is entering the heat exchanger at 2 °C and at a flow rate of 40 t/day, and the 50% ethylene glycol solution you are using to remove heat from your co-gen process has a specific heat of 3.42 kJ/kg °C, is entering the heat exchanger at 85 °C at a rate of 3000 kg/hr and leaving at 50 °C, (a) what is the rate of heat exchange in the exchanger and (b) what is the outlet temperature of the digester feedstock.

Explanation / Answer

>> Now,

Let, T1i = Inlet temperature of our feedstock = 2°C

T1o = Outlet temperature of our feedstock = ?

T2i = Inlet temperature of ethylene glycol solution = 85 °C

T2o = Outet temperature of ethylene glycol solution = 50 °C

>> C1 = Specific Heat of Feedstock = 4.18 KJ/Kg-°C

>> C2 = Specific Heat of Ethylene Glycol Solution = 3.42 KJ/Kg-°C

>>m1 = Flow Rate of Feedstock = 40 t/day = 40*41.667 kg/hr = 1666.67 Kg/hr   [because 1 t/day = 41.667 kg/hr]

>> m2 = Flow Rate of ethylene glycol solution = 3000 kg/hr

>> Now, as

        m1 C1 (T1o - T1i) = m2 C2 (T2i - T2o)

=> 1666.67*4.18*(T1o - 2) = 3000*3.42*(85 - 50)

=> T1o = Outlet Temperature of the digester feedstock = 53.55 °C    .....ANSWER.....

>> Now, in Counter Flow Heat Exchanger,

>> So, Heat Flow rate, Q = m1 C1 (T1o - T1i) = m2 C2 (T2i - T2o)

=> So, Heat Flow = 3000*3.42*(85 - 50) = 99.75 KJ/s = 99.75 kW ......ANSWER....

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