methane carbon isotopes fractionation

[Mr.white]

I am a beginner with PHREEQC, and currently, I am using PHREEQC to study the effects of diffusion on methane carbon isotope fractionation. I would like to learn the simulation method from a paper by Diana B. Loomer and others, but I am encountering some problems.The  literature describes it like this:
Isotopic solubility fractionation was implemented in PHREEQC by adding 13C1to the database as a separate species. The differences in 12C1 and 13C1 log K were based on published fractionation factors (αlogK) in the form:αlogK=([δ13C1]/[δ12C1])aq/([δ13C1]/[δ12C1])g.However, solubility fractionation is temperature dependent, with α decreasing from 1.00062 to 1.00034 between 20℃and 80℃ (Harting et al., 1976). Therefore, the experimental data of Harting et al. (1976) were fit to Equation 1 with two fitting constraints: that α recalculated = α experimental and that log K for 13C1 was greater than or equal to that of 12C1(Equation 1 is temperature dependent equation for solubility: logk=A1+A2*T+A3/T+A4*logT+A5/T2A6*T2).And then the equation of state (EOS) parameters for 13C1 were set equal to those of 12C1. To track small differences in 13C1.
My understanding is that using the research data of predecessors, calculate the logK for 13C and 12C, and then add the data of 12C and 13C to the solution master species and phase in the PHREEQC database. Besides, do I need to add related reactions about 12C and 13C in the solution species? Because I only consider the impact of diffusion on isotopic fractionation, not considering other oxidation-reduction processes (only dissolution and diffusion). After adding the data of 13C and 12C, how do I implement isotopic fractionation in PHREEQC using the fractionation factor? The literature also mentions setting the equation parameters of 13C and 12C consistently, what does this mean?