In the preceding problem, the composition of the feed was assumed to be constant. However, the CO/H₂ ratio in the feed can be manipulated as these streams are usually supplied from different sources. Solve the preceding optimization problem by considering the CO/H₂ ratio as another decision variable. Did you have to consider any additional constraints? Why? Compare the results with the results that you obtained in Problem 16.21.

Problem 16.21

In a process for producing methanol, synthesis gas composed of CO, CO₁, H₁, and H₂O is sent through a heat exchanger, E- 2001, to a plug-flow reactor, R-2001, as shown in Figure P16.21. In addition to the desired methanol synthesis, some undesired reactions also take place:

where C is the concentration of the species i in kmol/m³.

In R-2001, steam is being generated at a temperature of 350°C. Consider an overall heat transfer coefficient of 80 W/m °C between the process stream and the boiling water. The reactor effluent is sent to E-2001 and then further cooled in E-2002 to 40°C before being sent to the flash separator, V-2001. Unconverted reactants are recovered from the top of V-2001. Assume that the feed composition (mole fraction) and rate are

The minimum temperature approach in E-2001 is 15°C. Further assume that the pressure drops in both the shell and tube sides of E-2001 are 0.1 bar. The catalyst particle density is 1800 kg/m and the bed voidage is 0.45. Assume the pressure drop in R- 2001 is 0.2 bar. Maximize the yield of methanol in this process, where the decision variables are the inlet temperature, the pressure of Stream 1, and the dimensions of R-2001 (length and diameter). What bounds on the decision variables did you consider? Why? You can solve this problem with either the SM or EO approach.

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Reactant Gas E-2001 4 3 E-2002 R-2001 steam bfw 6 Unreacted Gas V-2001 Methanol Product