A mixture containing 35.0 mole% n-butane and the balance isobutene at 10°C enters a he3t exchanger at a rate of 24.5k mol/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 180oC. The heating fluid is a high molecular weight liquid with a constant heat capacity Cp = 2.62kJ (kg ∙ ˚C). It enters the exchanger at 215°C and flows counter currently to the hydrocarbon mixture.

(a) Estimate the minimum pressure (bar) required for the hydrocarbon feed to be a liquid.. Use Raoult’s law and the Cox chart (Figure 6.1-4) in your calculation.

(b) Assuming that the heat capacities and heats of vaporization of n-butane and isobutene are independent of pressure (so that the values in Tables B. 1 and B.2 may be used).calculate the enthalpy change H (kJ/h) undergone by the hydrocarbon mixture in the heat exchanger. Show the process paths you use for n-butane and i-butane in your calculation.

(c) 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 the heating fluid mhf (kg/h)?

(d) When the heat exchanger is run with mhf 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 IKO°C. The process operator observes that the outside of the exchanger 25 hot to the touch indicating that some of the heat lost h 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 2540kg/h, the outlet fluid temperatures level out at their design values (180°C for the hydro. carbon and 45°C for the heating fluid). At what rate (kJ/h) is heat being transferred from the exchanger to the plant air?

(e) 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 surroundings7 (Try to think of two costs that result from the heat loss.)

(f) The engineer proposes adding more insulation to the heat exchanger, which would cut down on the 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?