Second Order Accuracy Algorithm For Calculation Of VT-Flash

Phase Equilibrium Thermodynamics plays an important role in many scientific fields,such as chemical and chemical engineering,and the equilibrium coexistence of multi-component systems in industry mainly is the coexistence of gas and liquid phases.Flash calculation is an important application of two-phase equilibrium.The computa-tion problems of phase equilibria often depend on given conditions;the conventional phase equilibria is calculated at constant pressure,temperature,and chemical compo-sition,which is called PT-flash.Although PT flash has been widely used in many applications,the PT-based formulations of the phase stability and phase equilibria has at some limitations.For specified pressure,temperature,and overall molar fractions,the equilibrium state of the system might not be uniquely determined,and the P-V-T relationship of the fluid is usually represented by the pressure equation of state,so it is more convenient to calculate the thermodynamic properties by variables V and T.Therefore it is necessary to study the phase equilibria under constant volume,temper-ature,and moles(VT-flash).In this paper,we propose an second order accuracy algorithm for calculation of two-phase equilibria at constant temperature,moles and volume(VT-flash).An evolution equation for describing the dynamics of two phase fluid system is based on Fick' s law of diffusion for multi-component fluids and the Peng-Robinson equation of state.The evolution equation for moles of each component is derived using the discretization of diffusion equations,while the volume evolution equation is constructed based on the mechanical mechanism and the Peng-Robinson equation of state.We discretize this evolution system by using the adams method.We develop an energy stable and second order accuracy algorithm with an adaptive choice strategy of time steps,which allows us to calculate the suitable time step size to guarantee the correct definition of the Helmhotz free energy function,and physical properties of moles and volumes,including positivity,maximum limits.Numerical examples are tested to demonstrate efficiency of the proposed method.