For reactor models, the molar enthalpy or heat capacity of all compounds are needed in order to compute the heat of reaction and Gibbs free energy for the reactor temperature range. The Prode Physical Properties software (PPP) contains the component heat capacities of the gases in the form of parameters for a function that has been fitted to the raw data. The form of the fitting function can vary with the compound, but the most common form used in PPP appears to be the one shown below.
PPP provides no function to obtain the value of the component heat capacity at a given temperature. Nor can the parameters for the curve fit be obtained via a PPP function. Instead, the function form and the constants can be obtained manually from the PPP window.
Obtaining the heat capacity parameters manually would be time consuming and reading and typing the long constants invites error. As an alternative, PPP has a function that obtains the molar enthalpy of a compound. The heat of reaction and free energy at elevated temperatures can be computed using these enthalpies instead of heat capacity. However, when I converted one of my reactor models to use these component enthalpies, the computation time became unacceptably long. I believe the cause was the need to numerically integrate Cp dT to each temperature needed, repeatedly. A symbolic expression for the enthalpy would greatly reduce the computation time, but Mathcad could not find a symbolic integration of Cp dT.
My eventual solution was to refit the heat capacity to a cubic polynomial in temperature. This form can be easily integrated to a temperature quadratic for enthalpy. In the next post, I will show how the refitting was accomplished in Mathcad. For now, l will show the results.
The PPP window indicated that the heat capacity data covered the temperature range between 300 and 1500 K. Thus, I fit the cubic equation to that range also. Notice in the plot above that the original PPP curve and the cubic curve are nearly identical in that temperature range. Above 1500 K, the two curves deviate from one another as expected. Also note that the PPP curves appear to continue the fitted trajectory into the extrapolated region. This feature may be why Prode uses the cosh-sinh function, but I'm only guessing.
Using the cubic polynomial, the computation time returned to normal. If you are using the Prode-Mathcad combination and you experience long computation times, look for this problem with the component enthalpies. As you will see in the next post, the "fix" is easy.