  We study the non-perturbative superpotential generated by D(-1)-branes in
type IIB compactifications on orientifolds of Calabi-Yau threefold
hypersurfaces. To compute the D-instanton superpotential, we study F-theory
compactification on toric complete intersection elliptic Calabi-Yau fourfolds.
We take the Sen-limit, but with finite $g_s,$ in F-theory compactification with
a restriction that all D7-branes are carrying SO(8) gauge groups, which we call
the global Sen-limit. In the global Sen-limit, the axio-dilaton is not varying
in the compactification manifold. We compute the Picard-Fuchs equations of
elliptic Calabi-Yau fourfolds in the global Sen-limit, and show that the
Picard-Fuchs equations of the elliptic fourfolds split into that of the
underlying Calabi-Yau threefolds and of the elliptic fiber. We then demonstrate
that this splitting property of the Picard-Fuchs equation implies that the
fourform period of the elliptic Calabi-Yau fourfolds in the global Sen-limit
does not contain exponentially suppressed terms $\mathcal{O}(e^{-\pi/g_s})$.
With this result, we finally show that in the global Sen-limit, the
superpotential of the underlying type IIB compactification does not receive
D(-1)-instanton contributions. This result is exact in $g_s.$
