Chapter 8, Problem 8.76P

A mixture containing 35.0 mole% n-butane and the balance isobutane at 10°C enters a heat exchanger at a rate of 24.5 kmol/h and a pressure high enough for the mixture to be a liquid. The exchanger has been designed to heat and vaporize the liquid and heat the vapor mixture to 180°C. The heating fluid is a high molecular weight liquid with a constant heat capacity C_p= 2.62 kJ/(kg·°C). It enters the exchanger at 215°C and flows countercurrently to the hydrocarbon mixture.

1. Estimate the minimum pressure (bar) required for the hydrocarbon feed to be a liquid.

Assuming that the heat capacities and heats of vaporization of n-butane and isobutane are independent of pressure (so that the values in Tables B.l and B.2 may be used), calculate the enthalpy change $\Delta \stackrel{\dot{}}{H}\left(kJ/h\right)$undergone by the hydrocarbon mixture in the heat exchanger. Show the process paths you use for n-butane and /-butane in your calculation. (Hint: Since you don’t have heat capacities for liquid n-butane and /-butane in this text, use process paths that don't require them.)According to the heat exchanger design calculations, the heating fluid exit temperature should be 45°C. Assuming that all the heat lost by the heating fluid is transferred to the hydrocarbon mixture, what is the required mass flow rate of die heating fluid, ${\stackrel{\dot{}}{m}}_{hf}\left(kg/h\right)$

?

When the heat exchanger is run with ${\stackrel{\dot{}}{m}}_{hf}$

equal to the value calculated in Part (b), the exit temperature of the hydrocarbon mixture is measured and found to be only 155°C instead of the design value of 180°C. The process operator observes that the outside of the exchanger is hot to the touch, indicating that some of the heat lost by the heating fluid is escaping into the plant instead of being transferred to the hydrocarbon mixture. After discussing the situation with a production engineer, the operator gradually increases the flow rate of the heating fluid while continuing to monitor the outlet temperature of the hydrocarbon. When the flow rate reaches 2540 kg/h, the outlet fluid temperatures level out at their design values (180°C for the hydrocarbon and 45°C for the heating fluid). At what rate (kJ/h) is heat being transferred from the exchanger to the plant air?

When the heating fluid leaves the exchanger, it passes through a heater, which raises its temperature back to 215°C, and is recycled back to the exchanger. How is the profitability of the process being decreased by the heat loss from the exchanger to the surroundings? (Try to think of two costs that result from the heat loss.)

The engineer proposes adding more insulation to the heat exchanger, which would cut down on die heat loss and reduce the required heating fluid flow rate. What are advantages and disadvantages of the two responses to the heat loss problem (adding insulation versus increasing the heating fluid flow rate)? Which would you guess would be the preferable response in the long run, and why?