Despite the large potential of unconventional resources, many unknowns still exist regarding the physics controlling the extraction processes in these settings. These include accurate representation of phase equilibrium in tight formations and effective implementation of relevant models in simulation tools. When a fluid is confined in pore spaces of nanometer size, significant interfacial curvatures may occur that can result in large capillary pressures between the liquid and vapor phases: The pressure difference between the two phases will likely affect the vapor-liquid equilibrium state. Previous efforts have shown that this effect is negligible for conventional reservoirs (with pores in the micron range) and current commercial' reservoir simulators commonly ignore the effect of capillary pressure in the VLE calculations. However, experimental and modeling efforts have shown that ignoring capillary pressure in the VLE calculations will not be a valid approximation for unconventional (tight) reservoirs. In this work, we analyze the numerical aspects of including capillarity phenomena in VLE calculations in an effort to arrive at robust and efficient algorithms for stability analysis that can be used in compositional modeling/simulation of unconventional reservoirs. While the equality of chemical potentials is a necessary condition for equilibrium, it is not a sufficient one. A sufficient condition for equilibrium is the minimization of Gibbs energy, and the latter can be tested using the tangent plane distance (TPD) criteria. We show that stability analysis based on the TPD criteria remains valid for systems with large capillary pressures and propose effective/robust algorithms for stability testing. The proposed algorithms are tested for multicomponent reservoir fluid systems over a range of relevant temperatures, pressures and pore radii. (C) 2016 Elsevier B.V. All rights reserved.