Titel
Phase Envelope Calculations with and Without Capillary Pressure using Volume-Based Thermodynamics
Abstract
Standard phase equilibrium calculations are done using pressure and temperature as primary variables. This requires the resolution of the equation of state (EoS) with respect the volume in order to compute the desired thermodynamic properties. Using volume-based thermodynamics the resolution of the EoS is avoided since the volume is the natural variable of the EoS, hence computation of the thermodynamic properties are straightforward. The aim of this work is to present an algorithm for the calculation of the phase envelope using volume-based thermodynamics. The entire phase envelope is traced automatically using sensitivity analysis after solving the system of equations by Newton’s method at each point. Binary and multicomponent systems were studied using the generated algorithm. Additionally, an example of a confined oil mixture under a high capillary pressure difference, typically found in tight and shale reservoris is presented. The Peng-Robinson EoS was employed to describe the fluid properties and the Young-Laplace equation to model de capillary pressure difference. Other thermodynamic models can also be used for the proposed method.
In comparison with the phase envelope calculations using standard pressure-based thermodynamics, advance EoS with multiple volume roots are benefited by the proposed volume-based framework. The algorithm proves to be robust and efficient for tested mixtures. Furthermore, the nature of the system of equations allows the incorporation of capillarity without adding an extra equation. It can easily handle systems with big capillary pressure difference where the liquid pressure can become negative without compromising speed and reliability.