Saturated liquid calculation route

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

For this calculation route, you must define both the reference temperature in the Ref T column and the reference enthalpy in the Ref H column for that component. The Ref H value is dependent on the Ref T value and you may need to calculate its value outside of AVEVA Process Simulation. See Changes to the enthalpy basis and reference state for components for more information on how to change the reference temperature and enthalpy.

All the calculations are based on the enthalpy of the liquid at the reference temperature, that is, the Ref H value. We use this value in all the equations that AVEVA Process Simulation uses to calculate the enthalpy of the liquid. AVEVA Process Simulation calculates the enthalpy of the vapor directly from the enthalpy of the liquid by using the latent heat of vaporization.

The calculations require temperature-dependent correlations for the saturated liquid heat capacity (cp,iL), the latent heat of vaporization (DHivap), and the ideal gas heat capacity (cp,iIG). 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 below the critical temperature, TC, on the temperature-dependent correlation for the saturated liquid heat capacity, cp,iL.

where

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

Tref,i is the Ref T value in the Fluid Editor for component i.

Hiref(Tref,i) is the Ref H value in the Fluid Editor for component i.

However, for Henry's solutes, we assume that a Henry's solute exists as dissolved vapor in the liquid phase and no phase change occurs. To account for the Henry's solute contributions to the liquid enthalpy, we include the heat of absorption:

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

If the range of the correlation for the liquid heat capacity does not extend to the required temperature, AVEVA Process Simulation extrapolates the liquid enthalpy according to the following equation:

where

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

Habs,i is zero for all components except Henry's solutes.

Ions use a specialized liquid enthalpy calculation that does not support changes to the reference temperature (Ref T), reference enthalpy (Ref H), or phase-change temperature (Phase Ch T). Therefore, ions always use the system enthalpy calculations. 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):

If you include the heat 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 the critical temperature, TC, on the liquid heat capacity correlation and the latent heat correlation:

where

DHivap(T) is the latent heat of vaporization of component i at the required temperature. The System:SIMSCI data bank contains a default correlation for this variable. You can also supply your own correlation by using AVEVA Thermodynamic Data Manager or the thermodynamic data overrides in the Fluid Editor.

If the range of these correlations does not extend to the required temperature, AVEVA Process Simulation extrapolates the values for both cp,iL(T) and DHivap(T) when it calculates the vapor enthalpy.

The latent heat value must be zero at the critical temperature so that HV,i(TC) equals HL,i(TC). If the latent heat correlation does not extend to TC, AVEVA Process Simulation extrapolates the latent heat value to zero at this temperature.

If you specify a phase-change temperature (that is, you enter a value in the Phase Ch T column), AVEVA Process Simulation performs the phase change at the specified temperature and uses the value of the latent heat of vaporization at the phase-change temperature in the calculations. It also uses the ideal gas heat capacity to determine the enthalpy change from the phase-change temperature to the required temperature (T).

where

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 correlation by using AVEVA Thermodynamic Data Manager or the thermodynamic data overrides in the Fluid Editor.

Tphc,i is the Phase Ch T value in the Fluid Editor for component i.

We base all calculations above TC on the correlation for the ideal gas heat capacity:

If the range for the correlation for the ideal gas heat capacity, cpIG, 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.