Volume-based phase stability analysis including capillary pressure

The effect of capillary pressure on phase equilibrium is very important in tight formations, such as shale oil and gas reservoirs. In confined fluids, the capillary pressure induced by highly curved interfaces causes bubble points suppression and an inflated dew point locus, with a shift of cricondentherm points towards higher temperatures, as compared to the bulk fluid. In the conventional phase stability testing including capillary pressure, the problem is solved using the classical tangent plane distance (TPD) function (related to the Gibbs free energy surface) and mole numbers as primary variables. In this work, a volume-based approach (in which the equation of state needs not to be solved for volume) is used to solve this problem, as a bound and linear inequality constrained minimization of a TPD function with respect to the component molar densities. A modified Cholesky factorization (to ensure a descent direction) and a two-stage line search procedure (to ensure that iterates remain in the feasible domain and the objective function is decreased) are used in Newton iterations; a proper change of variables strengthens the robustness. The Weinaug-Katz equation (widely used in chemical and petroleum industry), which is a function of molar densities only, is used for interfacial tensions; the additional partial derivatives in the gradient vector and Hessian matrix have very simple expressions, unlike in conventional formulations. The proposed method is tested for two hydrocarbon mixtures (an oil and a gas condensate) in a wide range of pressures, temperatures and curvature radii, with a special attention paid to the convergence behavior near the singularities, that is, the stability test limit locus (SILL) and the spinodal. The method proves to be highly robust and exhibits fast convergence, showing a similar convergence behavior and almost the same computational effort as in the case of a bulk fluid. The results are only slightly different from conventional methods (except at high curvatures near the cricondentherm and at low pressures); differences are due to the fact that the dependence of capillary pressure on composition is taken into account in deriving the stationarity conditions, unlike in the conventional approach. The proposed method is not dependent on the thermodynamic model and can be used with any capillary pressure representation in which the interfacial tension model is explicit in molar densities. (C) 2019 Elsevier B.V. All rights reserved.