How do I get saturation densities near but below the EOS critical point temperature

[djvanpeursem]

I am using Fluid "CYCLOPRO". I am unable to get saturation densities near but below the EOS critical temperature. When I call SATTdll() I get an error message saying that the temperature is above the critical temperature. I have a small test program which clearly shows that the temperature is below the EOS critical temperature and hence saturation densities do exist!

I assume that SATTdll() is using an internal correlation which is supposed to closely match the EOS but clearly it is not close enough. Is there another means to get the saturation densities directly from the EOS instead of going through the correlations?

`void ToNIST(REFPROPInstance& RP)
{
int iIn, iOut[200]{}, iFlag = 0, kph = 1, ierr;
char herr[MAX_PATH]{};
double Tctrue, Tc, T, P, Dctrue, den, q, Dl, Dv, dPdD, d2PdD2, z[20]{ 1.0 }, x[20]{}, y[20]{}, Output[200]{};

Tctrue = Tc = T = P = Dctrue = den = q = Dl = Dv = dPdD = d2PdD2 = HUGE_VAL;

iIn = 2;
iOut[0] = 424; // rpEnumFor[TCTRUE];
iOut[1] = 425; // rpEnumFor[DCTRUE];
RP.ALLPROPS0dll(iIn, iOut, iFlag, Tc, den, z, Output, ierr, herr, MAX_PATH);
// ierr: 0
// herr: ""

Tctrue = Output[0]; // 398.69140098377221
Dctrue = Output[1]; // 6.1162146148792953

// Verify that the TCTRUE/DCTRUE point is actually the critical.
iOut[0] = 61; // rpEnumFor[DPDD];
iOut[1] = 67; // rpEnumFor[D2PDD2];
RP.ALLPROPS0dll(iIn, iOut, iFlag, Tctrue, Dctrue, z, Output, ierr, herr, MAX_PATH);
// ierr: 0
// herr: ""

dPdD   = Output[0]; // 6.6245104393966252e-12
d2PdD2 = Output[1]; // 5.5358765256702575e-12

// Now drop the temperature to something close to but below TCTRUE,
// to retrieve the saturation densities
T = 398.6; // < 398.69140098377221 (Tctrue)
RP.SATTdll(T, z, kph, P, Dl, Dv, x, y, ierr, herr, MAX_PATH);
// ierr: 121
// herr: "[SATT error 121] Temperature input is greater than the critical or maxcondentherm temperature: T = 398.600 K, Tc = 398.300 K."

}
`
I am also attaching the Fluid file (as a txt file) I am using.

CYCLOPRO.txt

[nist-aharvey]

I don't know the workings of REFPROP well enough to offer a solution, but I can verify the diagnosis of the problem.
The true critical point of the EOS is around 398.69 K. But the critical temperature given by the EOS developers and used within the EOS is 398.3 K, as can be seen in the fluid file. Saturation calculations in between cause major problems in the current version of REFPROP. There are a few fluids with such mismatches; the situation is described in this 2023 paper:
https://doi.org/10.1007/s10765-023-03261-8

One thing you might try is changing the upper limit of the approximate saturation correlations used within REFPROP (just as initial guesses, I think). If it is just the initial guess giving the error, bypassing that might allow calculations to proceed. To do that, you could change the reducing temperature in the 2 saturation density correlations at the bottom of the Fluid file to the real TC instead of 398.3. This will slightly distort those correlations, but probably not enough to foul up their performance as initial guesses.
I think the odds of that succeeding are <50%, but it is worth a try.
Maybe also try the same change with the approximate vapor pressure equation that is third from the end.