Program (or subroutine) fb_parms provides the values of the alpha parameters that appear in the dimensionless differential equations. There are five parameters...three for radial dispersion and two for intraphase heat and mass transfer. The definitions of the parameters are shown below.
Parameters affected by fluid density variations
The two highlighted parameters contain the fluid density in their definitions. For gas phase reactions, the density will vary with the extent of reaction for systems that involve a change in the number of moles. The density will also be affected by temperature variations.
To account for the changes in density, the terms in the difference formulas involving the two mass transfer groups are multiplied by the ratio of the local density to the inlet density. The local density is computed via a function that includes the local molecular weight of the fluid, which in turn is computed from the local weight fractions of the fluid.
Some reactor models include the affect of molar change on the velocity. Usually, this is accomplished by writing the mass balances in terms of extents of reaction. This method (usually?) doesn't make corrections for temperature variations.
Too frequently, the affect of molar change on the velocity (i.e. density) is ignored (see my previous post, 7/24/2013).
What about liquids?
Models involving liquids often include the assumption that density of the fluid remains constant, regardless of molar change or temperature. This assumption is probably valid in most cases. In my model, I still compute the local density regardless of the fluid state. This was done for simplicity and for more generality.
Computing the density
The density can be computed using the molar volume function, mc_StrVv, shown in my Prode Physical Properties test file. This function computes the molar volume as a function of fluid state, temperature, pressure, and composition, i.e. the state variables. The density is computed by dividing the fluid molecular weight by this molar volume. The functions needed are shown below. Mw is the vector of component molecular weights.
Don't have Prode Physical Properties?
If you don't have the Prode program, you may assume ideal gas law or constant density for gases and liquids, respectively. Of course, the assumption of ideal gas needs to be checked for validity.