Uncertainty in Enthalpy Values/Calculations for R454B

[Steph-Huu]

Dear NIST REFPROP Team,

I am a researcher working in the field of next-generation low-GWP refrigerant system modeling and analysis. In my scientific research, I am utilizing REFPROP to obtain thermodynamic properties of R454B.

To ensure the rigor and reliability of my research, I need to account for the uncertainty in the calculated enthalpy values (or enthalpy differences) for this fluid. Specifically, I would like to know:

1. What is the estimated expanded uncertainty (k=2, or 95% confidence level) associated with the calculated mass enthalpy (h) for R454B, across its typical application ranges (e.g., for saturated liquid/vapor, and superheated vapor states common in vapor-compression cycles)?

2. Alternatively, if available, what is the uncertainty associated with enthalpy differences (Δh), which is crucial for calculating cooling capacity or compressor work?

I have consulted the REFPROP documentation but could not find explicit uncertainty estimates for this property. Could you please:

• Provide the uncertainty information, or point me to the relevant technical note or publication where this data is published?
• Briefly explain the main contributors to the uncertainty for this blend (e.g., uncertainties in the equation of state, mixing rules, or the underlying experimental data for its components R32/R1234yf)?

Thank you very much for your time and for maintaining this invaluable resource for the scientific and engineering community.

[nist-aharvey]

This is not a complete answer to your question, but it is not meaningful to talk about an uncertainty in enthalpy itself, because the reference state that defines the zero of enthalpy is arbitrary. The only physically meaningful quantities are differences in enthalpy between states, so it only makes sense to talk about the uncertainty of enthalpy differences.

The relative uncertainty in an enthalpy difference due to a temperature change at roughly constant pressure (assuming no phase change) will be approximately the relative uncertainty in the isobaric heat capacity. Most equation of state publications will describe the uncertainty in Cp. I am not immediately aware of any similarly simple way to estimate the uncertainty of an enthalpy of compression. Enthalpy of vaporization is also physically relevant, and again the EOS publications may give information about how well that quantity is known for each pure component.

As a rule of thumb, if you are mixing components that mix nearly ideally (small enthalpy and volume of mixing, like hexane + heptane), the uncertainty in mixture quantities would be mostly due to the uncertainty of the pure component properties, but if you have a more nonideal system the mixing effects would dominate the uncertainty (unless there is a lot of good data on the mixture to constrain the mixing rules). Some information about uncertainty in the pure-component EOS can be found in REFPROP under "Fluid Information" for each component, and also in the underlying publication documenting the EOS.
In some cases there is a publication describing the optimization for the mixture; in the case of your mixture I find this paper from 2023:
https://doi.org/10.1063/5.0135368
Since that paper was published after the most recent version of REFPROP was released, you may want to update your mixture model to the model in that paper.

[nist-aharvey]

I should add that, since the release of REFPROP 10.0, a new EOS for pure R1234yf has been published (in 2022):
https://doi.org/10.1007/s10765-022-03015-y
The corresponding REFPROP Fluid file is available as Supplementary Material to the paper (and the new EOS is used for the mixture modeling in the 2023 paper I cited above).

[Steph-Huu]

I should add that, since the release of REFPROP 10.0, a new EOS for pure R1234yf has been published (in 2022): https://doi.org/10.1007/s10765-022-03015-y The corresponding REFPROP Fluid file is available as Supplementary Material to the paper (and the new EOS is used for the mixture modeling in the 2023 paper I cited above).

Thank you very much for your prompt and highly informative reply. Your explanation regarding the meaning of enthalpy uncertainty, the role of isobaric heat capacity (Cp), and the distinction between ideal and non-ideal mixing systems was exceptionally clear and helpful. It provides a solid conceptual framework for my understanding.

To apply this guidance specifically to my work with R454B (R32/R1234yf), I would be grateful if you could offer some further clarification on the following points:

1. Is the uncertainty information available in REFPROP's "Fluid Information" for the pure components (R32 and R1234yf) considered sufficient and representative for estimating mixture property uncertainties under typical vapor-compression cycle conditions?

2. Practical Application of the Cp Guideline: For calculating the uncertainty in enthalpy difference due to temperature change (e.g., in a superheater or condenser), could you advise on a typical or conservative range for the relative uncertainty in Cp for modern refrigerant blends like R454B? Would a range of 1-3% be reasonable, or is it likely higher? Any rule-of-thumb or reference would be invaluable.

3. Addressing Compression Enthalpy & Mixing Effects: You mentioned the uncertainty in the enthalpy of compression is less straightforward. For a zeotropic blend like R454B undergoing compression, would the dominant source of uncertainty still stem from the Cp uncertainty integrated over the temperature/pressure path, or do mixing rule uncertainties become significant even for this single-phase process?
   Given that R454B is a non-azeotropic mixture with some non-ideality, following your advice, should I understand that the largest contributions to enthalpy difference uncertainty in a cycle will likely come from: a) the vaporization enthalpy (if its uncertainty is high), and b) the mixing effects in the state determination itself, especially near the two-phase region?

Thank you again for your time and expertise. Your guidance is crucial for ensuring the scientific rigor of my work.

Sincerely

[nist-aharvey]

Those are all good questions, but I may not have good answers. You might have gotten better guidance from Ian Bell (who wrote that 2023 paper I mentioned), but unfortunately he left NIST about a year ago and thus far we have not been able to replace his expertise on modeling refrigerant mixtures. But here goes some comments that I hope are at least slightly helpful:

1. The information that you can see within REFPROP is, at least in principle, a reasonable summary of the uncertainty estimates from the underlying archival paper. But sometimes it is simplified for conciseness -- it might say some property is good to 1% in the liquid but if you looked in the paper you might see that it is really 0.5% for the liquid near ambient conditions and 1% elsewhere. So it is always best to consult the original paper to be sure you pick up good uncertainty estimates for the conditions of particular interest to you, since in some cases the paper will have a more fine-grained picture of uncertainties than what you see in REFPROP.
   And just a note that you should pick up the new EOS for 1234yf that I mentioned, which should have tighter (and maybe better documented) uncertainties than the older EOS that is in REFPROP 10.
2. Here's where I wish we had Ian to help us. I think there might be a somewhat different answer for vapor and liquid. For a vapor, there are a lot fewer molecular interactions so I would expect uncertainty in Cp to be roughly the same as for the pure components in the vapor (maybe a mole-weighted average of the pure-component relative uncertainties if they differ). For the liquid, nonideality is more important, and in the absence of mixture Cp data to validate against it might be reasonable to assume double the same sort of weighted average for a moderately nonideal mixture. On a quick skim of that 2023 paper it looks like they had only one-liquid-phase Cp data point, which they hit within 2%. If mixture sound-speed data are reproduced as well as the pure-component sound speeds (which I haven't looked at in detail for this mixture), that would suggest that the mixture model is not adding a lot of extra error to the caloric properties (including Cp).
3. There is additional uncertainty besides the sources you name from the pressure derivative of enthalpy at constant temperature (often called the isothermal throttling coefficient). So if you imagine a compression it could be modeled as an isothermal step and an isobaric step, where the constant-pressure step would be uncertain according to uncertainty in Cp but the isothermal step is uncertain according to the uncertainty in that throttling coefficient, which is tough to estimate because it is hardly ever measured. Probably that isothermal throttling uncertainty in relative terms would be roughly similar to the uncertainty in Cp.
   A final comment is that vaporization enthalpy for a mixture can't really be defined (unless you are right at an azeotrope), since you are getting a mix of vaporization and composition change with any change. But if a mixture model describes the vapor-liquid equilibrium well over a range of temperatures, that suggests that the model isn't adding much extra uncertainty beyond the degree to which the pure-component EOS are uncertain in their enthalpies of vaporization (which is also hard to estimate).

[Steph-Huu]

Thank you very much for your detailed and thoughtful reply. I truly appreciate the time and effort you took to explain the background and limitations so clearly.

I am sorry to hear that Ian Bell has left NIST. His work has been extremely influential in this field, and it is indeed a great loss for the refrigerant modeling community.

I hope that in the future, improved models, new experimental data, or renewed expertise will make it possible to address these kinds of questions more rigorously. Thank you again for your kind help and professional guidance.

Best regards.