System enthalpy calculation route

The following diagram summarizes the enthalpy calculations that AVEVA Process Simulation performs when you use the system calculation route.

For this calculation route, all the calculations are based on the enthalpy of the vapor at 25°C, which equals the heat of formation in the gas state at this temperature. We use this value in all the equations that AVEVA Process Simulation uses to calculate the enthalpy of the vapor. AVEVA Process Simulation calculates the enthalpy of the liquid directly from the enthalpy of the vapor by using the latent heat of vaporization.

The calculations require temperature-dependent correlations for the latent heat of vaporization (DHvap), the ideal gas heat capacity (cpIG), and the departure function (DdepH). The System:SIMSCI data bank contains default correlations for these variables. You can also supply your own correlations by using AVEVA Thermodynamic Data Manager.

Liquid enthalpy calculations

We base all calculations on the enthalpy of the vapor phase and the latent heat of vaporization:

However, for Henry's solutes, the latent heat of vaporization is not included (DHivap(T) = 0) in the liquid enthalpy calculations, because we assume that a Henry's solute exists as dissolved vapor in the liquid phase and no phase change occurs. Similarly, the calculation for the departure function does not include Henry's solutes when we calculate the liquid enthalpy. Instead, we include the heat of absorption:

See Heat of absorption for more information on how we calculate the heat of absorption.

Ions use a specialized liquid enthalpy calculation. For ions in the standard state (that is, infinite dilute aqueous solution), the heat capacity changes with temperature. We use the following three-parameter correlation from Thomsen[5] (Correlation 96 in AVEVA Thermodynamic Data Manager) to calculate the standard-state heat capacity for ion i (C¥p,i):

where

C1, C2, C3, and C4 are ion-specific parameters

According to Thomsen[5], C4 is a constant value of 200 K for all components.

If data for an ion is not available in Thomsen[1], we use Correlation 1 (the polynomial equation) instead of Correlation 96 to calculate Cp for that ion. See Equation forms for temperature-dependent properties in AVEVA Thermodynamic Data Manager for more information.

We obtain the liquid enthalpy for ions (H¥i) from the heat capacity according to the following equation:

where

DfH¥i is the heat of formation of ion i at infinite dilution

If you choose to include the pressure adjustment in the liquid enthalpy calculations (select the Include Liquid Enthalpy Pressure Adjustment checkbox in the Fluid Editor), then we use the following equation to calculate the liquid enthalpy for any components that are not Henry's solutes, solids, or ions:

where

P is the pressure of the system

Pisat is the saturation pressure of component i

viL,sat is the liquid molar volume of component i at saturation conditions

At low and medium pressures, the contribution of the pressure adjustment is minimal. However, at high pressures, the pressure adjustment may significantly impact your enthalpy results.

We use the following mixing rule to calculate the enthalpy of the liquid phase (HL):

where

i iterates over the set of all components in the liquid phase

j iterates over the set of Henry's solvents in the liquid phase

k iterates over the set of Henry's solutes in the liquid phase

If you include the enthalpy of mixing in the liquid enthalpy calculations (select the Include Heat of Mixing (Excess Enthalpy) in Liquid Enthalpy Calculations checkbox in the Fluid Editor), the mixing rule includes the heat of mixing (HE):

See Heat of mixing for more information on how we calculate the heat of mixing.

If you include the non-equilibrium solids in the composition calculations of the liquid phase (select the Include non-equilibrium solid components checkbox in the Fluid Editor), the mixing rule becomes a weighted average between the liquid enthalpy calculated on a solids-free basis and the enthalpy of the solids:

where

xL is the composition fraction of the liquid components in the liquid phase

xS is the composition fraction of the solid components in the liquid phase

HLSF(T) is the liquid enthalpy calculated on a solids-free basis

HS(T) is the enthalpy of the solids

xiSF is the component fraction of component i calculated on a solids-free basis

See Enthalpy calculations for solids for more information on how we calculate the enthaply of the solids.

If you include both the heat of mixing and the non-equilibrium solids in the liquid enthalpy calculations, the mixing rule includes both HE and the weighted average adjustment for HS(T).

Vapor enthalpy calculations

We base all calculations below Tmax,i on the correlation for the ideal gas heat capacity:

where

DdepHiV is the departure function that computes the difference between the enthalpy of the real gas and the enthalpy in the ideal gas state. If you are using the ideal gas law as the vapor phase equilibrium method, the departure function becomes zero. See Departure function for more information.

cp,iIG is the correlation for the ideal gas heat capacity for component i as a function of temperature. The System:SIMSCI data bank contains a default correlation for the ideal gas heat capacity. You can also supply your own correlations by using AVEVA Thermodynamic Data Manager or the thermodynamic data overrides in the Fluid Editor.

Tmax,i is the maximum temperature for which the correlation for the ideal gas heat capacity is valid.

If the range for the correlation for the ideal gas heat capacity, cp,iIG, does not extend to the required temperature, AVEVA Process Simulation linearly extrapolates the value at the required temperature:

Note: The summary diagram does not show the portion of the calculations for temperatures greater than Tmax.

We use the following mixing rule to calculate the enthalpy of the vapor phase (HV):

References

1. Thomsen, K. Aqueous Electrolytes: Model Parameters and Process Simulation. Ph.D. Thesis, Technical University of Denmark, Lyngby, Denmark, 1997.