During the course of simulation, the particle number density can assume values that span several orders of magnitude. For example, starting from 0 initial particles/cm3 there can be 1012 particles/cm3 during a nucleation burst and then 106 particles/cm3 when agglomeration or oxidation dominate. There is no intrinsic/natural scale (such as usage of mole fractions for gas-phase species) to "normalize" these numbers. Choice of division by Avogadro number and using mole/cm3 for number density can result in small numbers that may not get resolved to sufficient precision. For example, if the number density is 1012 particles/cm3, usage of mole/cm3 would mean that the value of the variable solved for is 10-11. This is too small for typical "double precision" numbers.

Ansys Chemkin therefore solves for "scaled molar density". That is, the variable solved for is phi*molar number density where phi is a user-prescribed scaling factor. For a typical Chemkin gas-particle simulation the particle number density is roughly of the order of 1012. Hence, the default value of the scaling factor is 1012 which makes the variable solved for of the order of 10.

For the method of moments, in addition to the scaling factor Ansys Chemkin solves for (Mr - Mr-1) for r > 0. The corresponding equations can be derived using equation 18-88.