Dimethyl ether (DME) synthesis provides a simple prototype of many petrochemical processes. Ten tonnes (10,000 kg) per hour of methanol are fed at 25°C. The entire process operates at roughly 10 bar. It is 50% converted to DME and water at 250°C. The reactor effluent is cooled to 75°C and sent to a distillation column where 99% of the entering DME exits the top with 1% of the entering methanol and no water. This DME product stream is cooled to 45°C. The bottoms of the first column are sent to a second column where 99% of the entering methanol exits the top at 136°C, along with all the DME and 1% of the entering water, and is recycled. The bottoms of the second column exit at 179°C and are sent for wastewater treatment. Use the method of Example 3.6(b) to complete the following:

(a) Calculate the enthalpy in GJ/h of the feed stream of methanol.

(b) Calculate the enthalpy in GJ/h of the stream entering the first distillation column.

(c) Calculate the enthalpy in GJ/h of the DME product stream.

(d) Calculate the enthalpy in GJ/h of the methanol recycle stream.

(e) Calculate the enthalpy in GJ/h of the aqueous product stream.

(f) Calculate the energy balance in GJ/h of the entire process. Does the process involve a net energy need or surplus?

Data from Example 3.6(b)

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Example 3.6 Reactor energy balances Acetone (A) is reacted in the liquid phase over a heterogeneous acid catalyst to form mesityl oxide (MO) and water (W) at 80C and 0.25 MPa. The reac- tion is 2A MO+W. Conversion is to be 80%. The heat capacity of mes- ityl oxide has been estimated to be C (J/mol-K) = 131.16 +0.27107(K), C (J/mol-K) = 72.429 +0.26457(K), and the acentric factor is estimated to be 0.356. Other properties can be obtained from Appendix E or webbook.nist.gov. Ignore pres- sure corrections and assume ideal solutions. mesityl oxide (a) Estimate the heat duty for a steady-state reaction with liquid feed (100 mol/h) and liquid products. Use the Heat of Reaction method calculated using liquid heats of formation. (b) Estimate the heat duty for the same conditions as (a), but use the Heat of Formation method incorporating heats of formation of ideal gases and Eqn 2.45 to estimate heat of vaporization. (This method is used by process simulators.) (c) Repeat part (b) with the modification of using the experimental heat of vaporization. (d) Estimate the heat duty for the same conditions as (a), but use the Heat of Formation method incorporating the heat of formation of liquids.