Equations for the PRM method

The Peng-Robinson Modified Panagiotopoulos-Reid (PRM) method uses the same formulation as the Peng- Robinson (PR) equation of state:

Note: This equation is the general two-parameter cubic equation of state when u = 2 and w = -1.

where

xi is the mole fraction of component i

Tc,i is the critical temperature of component i

Pc,i is the critical pressure of component i

For the mixing rule, that is, the a(T) formulation, the PRM method uses two modifications, the Panagiotopoulos-Reid modification and a SimSci modification.

The Panagiotopoulos-Reid modification introduces two adjustable parameters, kij and kji:

where

kij is the binary interaction constant for component i in j

kji is the binary interaction constant for component j in i

When kij = kji, the Panagiotopoulos-Reid mixing rule reduces to that of the PR equation of state.

We have tested this mixing rule for several systems:

• Low-pressure, non-ideal systems

• High-pressure systems

• Three-phase systems

• Systems with supercritical fluids

The results in all reported cases agree well with experimental data.

The SimSci modification introduces an additional two adjustable parameters, cij and cji:

For binary systems, this mixing rule is identical to the the Panagiotopoulos-Reid mixing rule when c12 = c21 = 1.

The four adjustable parameters for this final form of the mixing rule are kij, kji, cij, and cji. For binary, nonpolar systems where the deviations from ideality are not large or are only weakly asymmetric, only the two Panagiotopoulos-Reid parameters (kij and kji) are sufficient to fit the data (that is, c12 = c21 = 1). For non-binary systems for this case, the SimSci mixing rule is identical to the mixing rule proposed by Harvey and Prausnitz2 in 1989. For binary, polar and binary, polar-nonpolar systems where the non-ideality is large or strongly asymmetric, you may need to include the SimSci parameters (c12 and c21). For binary, polar systems, c12 generally equals c21. For binary, polar-nonpolar systems, which have the greatest deviation from ideality, c12 does not equal c21.

The remaining equations depend on your Alpha Selection for your Fluid Type in AVEVA Process Simulation. You can find the Alpha Selection list on the Fluid Editor, in the Equilibrium Options section. It appears only when you select an equation of state in the System list in the System section.

If you select Acentric Factor Formulation in the Alpha Selection list, the remaining equations follow the same formulation as the Soave-Redlich-Kwong (SRK) equation of state:

where

wi = acentric factor for component i

If you select Alpha Databanks in the Alpha Selection list, the remaining equations follow the PR formulation for ai, but the alpha formulation that the software uses is different for each component and depends on the alpha data in the data banks that you add to the Alpha Data Banks box.

where

ai(Tr,i,wi) depends on the data specified in the selected ALPHA data banks

If there is any alpha data missing from the selected ALPHA data banks, the software calculates the alpha value based on the acentric factor formulation.

Warning: If you use a custom ALPHA data bank, you should also use a binary interaction data bank that contains adjusted binary interaction parameters that correspond to the alpha data in your custom ALPHA data bank.

For PRM, the default Alpha Selection is Alpha Databanks. We recommend that you use the default selection.

For both selections in the Alpha Section list, when wi > 0.39849, the software uses the following alpha formulation instead:

Regardless of the selection in the Alpha Selection list, this equation of state uses a specialized alpha formulation for water. See Special adjustments for water: Alpha formulation for the equations of state for more information.