Multiphase Multicomponent Isenthalpic Flash Calculations
Authors: Agarwal R.K. , Li Y.K. , Nghiem L.X. , Coombe D.A. 
Published: March 2010

Abstract
Three methods for isenthalpic flash calculations are presented. The first method (Scheme 1) involves a series of isothermal flash calculations at different temperatures until the energy balance equation is satisfied. This scheme cannot easily handle systems for which the number of degrees of freedom from the phase rule equals unity. In the second method (Scheme 2), the energy and material balance equations are updated simultaneously to obtain the temperature and phase splits. These are then used to update the K-values. This process is repeated until convergence is achieved.
All schemes are extensively tested. The results show that Scheme 1 is more robust than Scheme 2 but is about three times slower. A hybrid scheme (Scheme 3) is devised to take advantage of both the robustness of Scheme 1 and the speed of Scheme 2.

Introduction
Isenthalpic flash calculations or flash calculations at a specific pressure and enthalpy have received much less attention than isothermal flash calculations (flash calculations at a specific pressure and temperature), and yet they are the calculations that are predominant in thermal processes.
Typical applications of isenthalpic flash calculations in reservoir engineering include predictions of steam-distillation mechanisms in steamfloods and phase separation in wellbores. The predictions of vaporization and condensation phenomena in these processes entail the determination of phase mole (and volume) fractions and compositions as well as the mixture temperature given the pressure, composition and enthalpy of the feed.
This paper presents the equations for isenthalpic flash calculations and discusses three schemes for solving these equations. The complexities associated with isenthalpic flash calculations that do not exist in isothermal flash calculations are highlighted. Examples showing the performance of these schemes are also given.

Equations for Isenthalpic Flash Calculations

Governing Equations
Isenthalpic flash calculations correspond to finding the temperature, phase splits (phase mole fractions) and phase compositions, given the pressure, composition and enthalpy of the feed, together with the net enthalpy added to the system.
Consider one mole of feed of compositions z in a nc - component, Np-phase system (Fig. 1). After defining the thermodynamic model, there are np independent governing equations for an isenthalpic flash calculation, one energy balance and np — 1 material balance constraint equations.
Let the equilibrium ratios (K-values) be
Equation (1) (Available In Full Paper)
where yij is the mole fraction of Component i in Phase j and R is the reference phase for the K-value definition. Note that R; need not be the same for all components. This gives extra flexibility to define K-values in the cases that components are not always present in all phases. Calculations of these K-values are described in the later sections. By definition KiR = 1.
Let Fj be the mole fraction of phase j in the system, the compositions can be obtained from material balances as follows
Equation (2) (Available In Full Paper)
And
Equation (3) (Available In Full Paper)
In addition, the mole number of Component i in Phase j, nij is given by
Equation (4) (Available In Full Paper)