In the Kiselev crossover procedure, the renormalized temperature and volume distance was utilized. The parameters were functions of both temperature and pressure, which would bring in much extra complication in the derivative against volume when calculating pressure expression. However, the issue seems to be completely mathematical, since the renormalized distances should be treated as variables, rather than functions. I was quite confused here whether to treat it as variables or functions, i.e., whether to take derivatives of them when calculating pressure.

Furthermore, when calculating fugacities, the renormalized distances involved more than two variables, as they are functions of volume, temperature and component. The component variable was introduced by the mixture critical property correlations, which also appeared in other parts of the correlation. As the procedure required much derivatives against component, was the critical parameters also taken derivatives? If considered as part of the correlation, they should be. However, if taken that the mixture critical point was "already there", they should not. I was also quite confused here.