Solved: Methanol is synthesized from carbon monoxide and

Chapter 5, Problem 5.51

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Methanol is synthesized from carbon monoxide and hydrogen in the reaction CO + 2H2 CH3 0H A process flowchart is shown below. M =CH 30H n5(kmol H2/h) t REACTOR SEPARATOR nj(kmol CO/h) 100 kmol CO/h n4(kmol CO/h) n6(kmol M/h) n2(kmol H2/h) n3(kmol H2ih) n5(kmol H2/h) T(K), P(kPa) H,!",(% excess H2) n6(kmoi M/h) T(K), P(kPa) 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 T (K) and a pressure P(kPa) and fed to the reactor. The percentage excess hydrogen in this stream is Hxs 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 Kp(T) = 1.390 X 10-4exp (21.225 + 91~.6 - 7.492 In r + 4.076 x 1O-3r - 7.161 x 1O-8r 2) In these equations, Pi is the partial pressure of species i in kilopascals (i = CH30H, CO, H2) and T is in Kelvin. (a) Suppose P = 5000 kPa, r = 500 K, and Hxs = 5.0%. Calculate n4, n5, and n6, the component flow rates (kmol/h) in the reactor effluent. [Suggestion: Use the known value of Hxs , atomic balances around the reactor, and the equilibrium relationship, Kpc = Kp(T), to write four equations in the four variables n3 to n6; use algebra to eliminate all but n6; and use trial and error to solve the remaining nonlinear equation for n6'] Then calculate component fresh feed rates (nj and n2) 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 COlh fed to the reactor) and different specified values of P(kPa), T(K), and *Computer problem. 228 Chapter 5 Single-Phase Systems Hxs(%)' The spreadsheet should have the following columns: A, P(kPa) B. T(K) C. Hxs(%) D. Kp(T) X 108 . (The given function of T multiplied by 108 . Wht'ID = 500 K, the value in this column should be 91.113.) E. Kppz F. ;"3. The rate (kmol/h) at which Hz enters the reactor. G. ;"4. The rate (kmol/h) at which CO leaves the reactor. H. ;"5. The rate (kmol/h) at which Hz leaves the reactor. 1. ;"6. The rate (kmol/h) at which methanol leaves the reactor. 1. ;"tot. The total molar flow rate (kmol/h) of the reactor effluent. K. Kpc X 108 . The ratio YM/(YCOY~,) mUltiplied by 108 . When the correct solution has been attained, this value should equaf the one in Column E. L. Kppz - Kpcpz. Column E - Column K, which equals zero for the correct solution. M. ;"1' The molar flow rate (kmol/h) of CO in the fresh feed. N. ;"2. The molar flow rate (kmol/h) of H2 in the fresh feed. O. Vrec(SCMH). The flow rate of the recycle stream in m3 (STP)/h. When the correct formulas have been entered, the value in Column I should be varied until the value in Column L equals O. Run the program for the following nine conditions (three of which are the same): T = 500 K, H xs = 5%, and P = 1000 kPa, 5000 kPa, and 10,000 kPa. P = 5000 kPa, Hxs = 5%, and T = 400 K, 500 K, and 600 K. T = 500 K, P = 5000 kPa, and Hxs = 0%,5%, and 10%. Encyclopedia batch Equipment reactor 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.)