Methanol Synthesis Using Gibbs Free Energy Minimization
Consider the two reactions taking place simultaneously during the synthesis of methanol:[more]
R1: (primary reaction: methanol synthesis from syngas) and R2: (secondary reaction: reverse water-gas shift reaction).
The feed for reactions R1 and R2 comes from a steam reformer and generally contains , , , and . In all calculations, assume that: (1) the total feed to the reactor is equal to 1 mole; (2) the amount of present in the feed is negligible; and (3) the feed composition is 15.47 mol , 76.29 mol , and 8.24 mol .
The Demonstration computes the equilibrium composition of the five species involved (, , , , and ) versus pressure (in bars) for user-set values of the temperature (in ). To do so, the program minimizes the total Gibbs free energy of the gas mixture. Here, the residual Gibbs free energy is calculated using the Peng–Robinson equation of state , while the pure components Gibbs free energies are obtained from experimental values .
The calculation method is benchmarked against the results obtained using the reaction coordinate method for and various values of . Good agreement is found between both methods.
The reaction coordinate results were obtained using a separate program, and the methodology used is explained in . For the equilibrium constants, the following expressions and , for reactions 1 and 2, are used:
 S. I. Sandler, Chemical and Engineering Thermodynamics, 3rd ed., New York: John Wiley & Sons, 1999.
 I. Barin and G. Platzki, Thermochemical Data of Pure Substances, 3rd ed., New York: VCH Publishers, Inc., 1995.
 T. Chang, R. W. Rousseau, and P. K. Kilpatrick, "Methanol Synthesis Reactions: Calculations of Equilibrium Conversions Using Equations of State," Industrial & Engineering Chemistry Process Design and Development, 25(2), 1986 pp. 477–481. doi:10.1021/i200033a021.