  We apply the standard approach of RG flow for the gauge couplings in N=1 D=4
Supergravity to show how to match its results with the heterotic $Z_3$ orbifold
and Type IIB ${Z_3}$ orientifold-based models. Using only supergravity, anomaly
cancellation and the requirement of unification we determine the part of the
K\"ahler potential of the model invariant under the symmetries of the model.
For heterotic orbifolds/type IIB orientifolds, this shows that the lowest order
K\"ahler term of the dilaton has the structure $-\ln(S+{\bar S})$ in agreement
with string calculations. The structure of the holomorphic coupling is also
found from arguments of unification and anomaly cancellation under the
conjectured $SL(2,Z)_{T_i}$ symmetries of the models. A consequence of the
latter is that in the case of the $Z_3$ orientifold the holomorphic coupling
necessarily contains a part with coefficient proportional to the one loop beta
function, in agreement with string calculations which do not however assume
this symmetry. This gives circumstantial evidence for the existence of this
symmetry at string level in $Z_3$ orientifold. Finally, we comment on the
values of the unification scale and examine the possibility of mirage
unification in which the effective unification scale may be situated far above
the string scale.
