When Hirschfelder and Curtis approximation for reactive flows is considered, the RHS of species balance equation does not hold global mass conservation.

Therefore a constant correction velocity is added to the term, V_{k,i} ,so that the constraint,

\sum_{k=1}^{N} Y_k V_{k,i} = 0, is satisfied.

My doubt relates to which balance equations this correction must be applied, it is clear to me that it must be applied into species balance equation, but it is not that clear:

Why it is added in the energy equation diffusive term but not into the momentum equation?