Dynamic simulation of fluids in vessels via entropy maximization

Abstract

This paper proposes a new method to simulate the dynamic behavior of fluids in vessels of known and fixed volume, under the assumption of instantaneous phase equilibrium. The mathematical formulation of the problem leads to a system of differential-algebraic equations, in which the mass and energy balances are ordinary differential equations (ODE) and the phase equilibrium conditions give the algebraic equations. The structure of the problem is such that, at each time step, the internal energy, volume, and number of moles of each component inside the vessel are known. The equilibrium state of the fluid under these specifications maximizes the entropy. An entropy maximization method recently proposed for this problem in the literature was coupled with an ODE solver. The procedure can track the appearance and disappearance of phases in the vessel, adding or removing them as necessary. The examples show applications of the procedure to problems with one, two, or three phases, in different types of dynamic problems. Numerical convergence was easily achieved in all cases, showing the robustness of the proposed procedure.