Solvation analysis is one of the most important tasks in chemical and biological modeling. Implicit solvent models are some of the most popular approaches. In this work, based on differential geometry theory, we defines the solvent-solute boundary via the variation of the nonpolar solvation free energy. The solvation free energy functional of the system is constructed based on a continuum description of the solvent and the discrete description of the solute. The first variation of the energy functional gives rise to the governing Laplace- Beltrami equation. The present model predictions of the nonpolar solvation energies are in an excellent agreement with experimental data. Moreover, the existence of a global minimizer for the nonpolar solvation model has been proved.