Continuing with the methane reforming system, compute the equilibrium coefficients as a function of temperature. These coefficients will be needed for reaction rate expressions if the reactor composition is near the equilibrium.
Component free energies of formation
As with the enthalpy of formation, the free energy of formation can be obtained from reference tables or from the Prode program:
Free energy changes for reactions at standard condition
van't Hoff equation
Integrate the above equation to obtain ln(Keq) as a function of temperature.
In the Mathcad worksheet, the above equation is used in the form below, where rj is the reaction index.
Two versions of the formula are supplied in the above assignment. The first is for multi reaction systems and the second is for single reaction systems. The former case requires vector variables and the latter requires scalars. In Mathcad, a scalar can't be referred to as the only element of a vector.
Note that I have used a temperature dependent heat of reaction in the formula. When exploring a large temperature range as shown in the plot below, this is a good practice. When the temperature range for the reactor has been selected, a constant value for the heat of reaction may be used. This will speed up the calculation of Keq. Thus far, I continue to use the temperature dependent method because computation times are satisfactory.
Selecting the reactor temperature region
We desire Keq > 1 in order to produce significant conversion of methane to hydrogen. Thus, the ln(Keq) should be > 0. The plot shows that a temperature > 900 K is needed for the main reaction. The shift reaction (Reaction 1) is not greatly affected by temperature above 600 K.
Wasn't that easy?
I hope everyone is noticing how easy it is to get results with Mathcad. This post and the previous look just like pages in a textbook on reactor engineering. There has been no "computer code". The closest to a code statement are the statements that retrieve the physical properties from PPP. When we get to more complicated problems that require if-then-else, or for and while loops, we will see a more "code like" program. However, those programs will just assemble statements like those shown above.