PROBLEMS
In solving the problems that follow, cite all sources of data not given in the process description and clearly state all assumptions.
1. Construct a detailed flowchart of the process, showing known compositions, flow rates, pressures, and temperatures. Use this chart to keep track of your calculations and as a basis for a final flowchart to be prepared when you have finished the case study.
2. Assume there are no side reactions in the synthesis of methanol, methyl acetate, and acetic anhydride, and calculate the molar flow rates of reactants (kmol/h) in the fresh feeds to each of the reactors. Where fresh feed must be supplied from a source external to the process, calculate the feed rates of these materials in kg/h.
3. Estimate the amount of oxygen fed to the gasification reactor in kmol and standard cubic meters per kg of coal fed to the process.
4. Suppose that air, rather than pure oxygen, were fed to the reactor. What would be the flow of air in kmol and standard m3 per kg of coal fed to the process? What would be the composition of the gas leaving the gasifier under these conditions? Suggest reasons based on these calculations for the use of O2 instead of air.
5. If all of the sulfur in the coal reacts to form H2S, determine the air requirements for the Claus plant in kmol and standard m3 per kg of coal fed to the process.
6. Estimate the mole fraction of water in the gas exiting the scrubber. What is the rate (kg/kg coal) at which water exits the scrubber in the product gas?
7. Determine the fraction of the gas leaving the scrubber that must be sent to the water gas shift reactor. Calculate the composition of the stream resulting from mixing the product from the water-gas shift reactor and the stream bypassing the reactor.
8. Determine the coal feed rate (kg/h), and calculate the rates at which oxygen is fed to the gasifier (kmol/h) and air is fed to the Claus plant (kmol/h).
9. Estimate the composition of the product gas leaving the acid gas removal system. What fraction of this gas is sent to the cryogenic separator? What is the composition of the gas resulting from blending the H2-rich product from the cryogenic separator with the stream bypassing the separator?
10. Using the equilibrium constants for Reactions 8 and 11, determine the composition of the effluent from the methanol synthesis reactor. What is the single-pass conversion of carbon monoxide? (A trial-and-error solution is required.)
11. Based on the equilibrium constant given for Reaction 13, calculate the composition of the product stream leaving the methyl acetate synthesis reactor and the single-pass conversion of methanol to methyl acetate. Determine the recycle rates of methanol and acetic acid.
12. Propose a modification of the methyl acetate reactor that would involve recycle of primarily one reactant. (Hint: Consider the effect of feeding an excess of one of the reactants on product composition.) Estimate the recycle rate for the proposed modification. Summarize features of this mode of operation that could make it more economical than the mode requiring recycle of both reactants.
13. What fraction of the elemental sulfur leaving the Claus plant reactor is condensed? (The dependence of the vapor pressure of sulfur on temperature is given in Table 3-7 of Perry’s Chemical Engineers’ Handbook.) A suggestion has been made to burn the residual sulfur in the gas stream exiting the sulfur condenser, forming SO2 and discharging this material into the atmosphere. Estimate the emission rate of SO2 (kg/h) if this suggestion is followed.
14. The plant has a methanol storage tank with a capacity of 2,000,000 liters. The average temperature of the liquid in the tank is 400 C and the tank is padded with nitrogen at a pressure of 1 atm (absolute) to reduce explosion hazards. The vapor space in the tank can be assumed saturated with methanol. The volume of methanol stored in the tank increases from 800,000 to 1,200,000 liters twice a day, and in the process a portion of the vapor space is displaced by liquid methanol. What would be the methanol vapor emission to the atmosphere (kg/day) if there were no emission control devices? Propose two different schemes to reduce vapor emissions.
15. Determine the relationship between flow rate and temperature of the water fed to the scrubber. Is the rate at which heat must be removed from the water as it is pumped 5. If all of the sulfur in the coal reacts to form H2S, determine the air requirements for the Claus plant from the wash tank to the scrubber affected by the flow rate of water? Explain.
16. Assume that the temperature of the gases and slag leaving the gasifier is 1100°C. Estimate the total rate at which heat must be removed from the wash tank-scrubber system. (Note: The actual temperature of such streams in commercial entrained-flow gasifiers is closer to 1350°C.) The following properties of ash and slag may be used: for ash, Cp(kJ/kg °C ) = 0.604 + 0.586 x 10-3T(K), ?Hm= 710 kJ/kg; for slag, Cp(kJ/kg °C ) = 0.767 + 0.744 x 10-3T(K),
17. The portion of the gas from the scrubber that is not sent to the water-gas shift reactor and the product gas from the water-gas shift reactor are used to generate steam in waste-heat boilers. Steam can be generated and used at three absolute pressures - 2858 kPa, 790 kPa and 205 kPa. The relative worths of steam at these pressures are 1.3, 1.2 and 1.0. Given that the gas fed to the acid gas removal system must be cooled to 100°C and that gas fed to a boiler can be cooled to within 5°C of the temperature of the steam it generates, propose a bank of waste-heat boilers that maximizes the value of the generated steam, How much of each steam is generated in the optimum configuration? Why do the respective steams have different values?
18. How much low-pressure steam (205kPa) in kg/h can be generated by heat recovered the Claus plant?