Methanol is synthesized from carbon monoxide and hydrogen in the reaction

A process flowchart is shown below.

The fresh feed to the system, which contains only CO and H₂, is blended with a recycle stream containing the same species. The combined stream is heated and compressed to a temperature (K) and a pressure (kPa) and fed to the reactor. The percentage excess hydrogen in this stream is H_xs. The reactor effluent—also at T and P—goes to a separation unit where essentially all of the methanol produced in the reactor is condensed and removed as product. The unreacted CO and H₂ constitute the recycle stream blended with fresh feed.

Provided that the reaction temperature (and hence the rate of reaction) is high enough and the ideal gas equation of state is a reasonable approximation at the reactor outlet conditions (a questionable assumption), the ratio

approaches the equilibrium value

In these equations, p_i is the partial pressure of species in kilopascals (i = CH₃OH, CO, H₂) and is in Kelvin.

a. Suppose P = 5000 kPa, T = 500 K, and H_xs = 5 0%. Calculate ṅ₄, ṅ₅, and ṅ₆, the component flow rates (kmol/h) in the reactor effluent. Use the known value of H_xs, atomic balances around the reactor, and the equilibrium relationship, K_pc = K_p(T), to write four equations in the four variables to ṅ₃; use algebra to eliminate all but ṅ₆; and use trial and error to solve the remaining nonlinear equation for ṅ₆. Then calculate component fresh feed rates (ṅ₁ and ṅ₂) and the flow rate (SCMH) of the recycle stream.

b. Write a spreadsheet program to perform the calculations of part (a) for the same basis of calculation (100 kmol CO/h fed to the reactor) and different specified values of (kPa), (K), and H H_xs(%). The spreadsheet should have the following columns:

When the correct formulas have been entered, the value in Column I should be varied until the value in Column L equals 0.

Run the program for the following nine conditions (three of which are the same):

Summarize the effects of reactor pressure, reactor temperature, and excess hydrogen on the

yield of methanol (kmol M produced per 100 kmol CO fed to the reactor).

c. You should find that the methanol yield increases with increasing pressure and decreasing temperature. What cost is associated with increasing the pressure?

d. Why might the yield be much lower than the calculated value if the temperature is too low?

e. If you actually ran the reaction at the given conditions and analyzed the reactor effluent, why might the spreadsheet values in Columns F–M be significantly different from the measured values of these quantities? (Give several reasons, including assumptions made in obtaining the spreadsheet values.)

Transcribed Image Text:

CO + 2 H2 = CH;OH