Some care needs to be taken in using the mixture-averaged diffusion coefficients as described here. The mixture formulae are approximations, and they are not constrained to require that the net species diffusion flux is zero, that is, the condition,

(5–82)

is not automatically satisfied. Therefore, applying these mixture diffusion relationships in the solution of a system of species conservation equations may lead to some nonconservation, that is, the resultant mass fractions will not sum to one. Therefore, one of a number of corrective actions must be invoked to ensure mass conservation. These corrections are implemented within Ansys Chemkin.

One attractive method is to define a " conservation diffusion velocity" as Coffee and Heimerl [49] recommend. In this approach we assume that the diffusion velocity vector is given as

(5–83)

where is the ordinary diffusion velocity Equation 5–43 and is a constant correction factor (independent of species, but spatially varying) introduced to satisfy Equation 5–82 . The correction velocity is defined by

(5–84)

This approach is the one used in Oppdif, for example.

An alternative approach is attractive in problems having one species that is always present in excess. Here, rather than solving a conservation equation for the one excess species, its mass fraction is computed simply by subtracting the sum of the remaining mass fractions from unity. A similar approach involves determining locally at each computational cell which species is in excess. The diffusion velocity for that species is computed to require satisfaction of Equation 5–82 . Ansys Chemkin includes both this trace-species approach and the correction-velocity approach as user options.

Even though the multicomponent formulation is theoretically forced to conserve mass, the numerical implementations can cause some slight nonconservation. Depending on the numerical method, even slight inconsistencies can lead to difficulties. Methods that do a good job of controlling numerical errors, such as the differential/algebraic equation solver DASSL, [50] for example, are especially sensitive to inconsistencies, and can suffer computational inefficiencies or convergence failures if mass is not strictly conserved. Therefore, even when the multicomponent formulation is used, it is often advisable to provide corrective measures such as those described above for the mixture-averaged approach. In the case of multicomponent formulations, however, the magnitude of any such corrections will be significantly smaller.