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IAPWS_IF97 functional form with no slip

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IAPWS_IF97 functional form with no slip


Mark Mikofski (view profile)


18 Mar 2012 (Updated )

Water and steam properties and derivatives based on the IAPWS IF97. Functional form. No slip.

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IAPWS_IF97(FUN,IN1,IN2) is 27 functions of water properties and derivatives, based on the International Association on Properties of Water and Steam ( Thermodynamic, hydrodynamic and non-linear modeling often requires thermodynamic derivatives, therefore IAPWS_IF97 can calculate most property derivates as functions of pressure and enthalpy, e.g.: dT/dp_ph, cp_ph, dv/dp_ph and dv/dh_ph. Since modeling often involves multiple dimensions that are discretized or meshed to form a set of either finite-difference or finite-element equations, IAPWS_IF97 is vectorized even across regions (subcooled/compressed-liquid, saturated, superheated and supercritical). For arrays is an order of magnitude faster than XSteam and is multithreaded if your computer is capable.
This is the functional form. I will submit a class & package versions definition soon, that also offer slip correction using Zivi's correlation (1964) for 2-phase flow.

Please report bugs here or at Github:

Reference Documents:
Industrial Formulation 1997 (IF97-Rev, IAPWS-IF97), IAPWS-IF97-S01, IAPWS-IF97-S03rev, IAPWS-IF97-S04, IAPWS-IF97-S05, Revised Advisory Note No. 3 Thermodynamic Derivatives from IAPWS Formulations 2008, Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance, 2008 Revised Release on the IAPWS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance.

Thermal Conductivity [W/m/K]:
    'k_pT', 'k_ph'
Viscosity [Pa*s]:
    'mu_pT', 'mu_ph', 'dmudh_ph', 'dmudp_ph'
Enthalpy [kJ/kg]:
    'h_pT', 'hL_p', 'hV_p', 'dhLdp_p', 'dhVdp_p'
Specific Volume [m^3/kg]:
    'v_pT', 'v_ph', 'vL_p', 'vV_p', 'dvLdp_p', 'dvVdp_p', 'dvdp_ph', 'dvdh_ph'
Temperature [K]:
    'T_ph', 'dTdp_ph', 'cp_ph'
Saturation Pressure [MPa] and Temperature [K]:
    'psat_T', 'Tsat_p', 'dTsatdpsat_p'


X Steam, Thermodynamic Properties Of Water And Steam. inspired this file.

This file inspired Water And Steam Refractive Index and A Simple Finite Volume Solver For Matlab.

Required Products MATLAB
MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (31)
15 Dec 2016 Leonardo Paoli

Hi, Amazing work!

However I am having an issue, with temperatures above 800 C.
For example: IAPWS_IF97('T_ph',20,4300) = NaN
when its supposed to simply give 1164.20 K

I had the same problem with XSteam

19 Oct 2016 Mark Mikofski

Mark Mikofski (view profile)

Peter, good catch! The issue is not actually with k_pT, but with psat_T(Tsat_p(p)) is not exactly equal to p, due to floating point errors.

Unfortunately, not sure of the best fix for it, but probably a tolerance maybe based on eps(p)

I think the culprit is on line 159:

valid1 = p>=psat & p<=pmax & T>=Tmin & T<=TB13; % valid range for region 1, include B13 in region 1

since psat is defined as psat_T(T), it should return exactly what was put in for p, ie: linspace(3, 4, 10), but floating point errors are confounding this, and we get::

K>> p>=psat

ans =

false, false, true, true, false, true, false, false, false, false

K>> format long

K>> err = abs(p-psat)

err =

1.0e-13 *

0.297539770599542 (fails)
0.124344978758018 (fails)
0.093258734068513 (fails)
0.031086244689504 (fails)
0.532907051820075 (fails)
0.275335310107039 (fails)
0.266453525910038 (fails)

You can see that the numbers, due to floating point errors are off by less than 1e-12, but eps(p) is ~ 1e-15, so if I use 100*eps(p) it works:

K>> abs(p-psat) < eps(p*100)

returns all true. If you think this is a good fix, submit it as a PR on GitHub, I will merge it add you as author and push it up to MATLAB FEX. Thanks for your contribution!

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19 Oct 2016 Mark Mikofski

Mark Mikofski (view profile)

Hi Peter, thanks for your comment. This MATLAB IAPWS97 implementation is on GitHub here:

Can you please submit an issue on GitHub:

Also feel free to hack on the code and send a PR. I will update the MATLAB FEX version with your changes and credit them to you.

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19 Oct 2016 Peter Cook

This is a magnificent package, though I've got a small quirk to report for 'k_pT' calcs on the 1-2 boundary (region 4) - it appears the function is only correctly identifying the saturation line about 70% of the time. I know this isn't a big deal physically because for most heat transfer problems here most energy is lost through latent heat, but I thought it was worth reporting. Here's an example:

>> P = linspace(3,4,10); k = IAPWS_IF97('k_pT',P,IAPWS_IF97('Tsat_p',P))

k =


28 Jun 2016 Peter Pauska

29 Nov 2015 Kymbat Atamuratova

Mark, good day.
I have problem with this program...
When compiling says
Error in ==> IAPWS_IF97_example at 10
h = IAPWS_IF97('h_pT',p,T); % [kJ/kg] enthalpy = f(p,T)
How may it be corrected? "Pressure and temperature ranges" work,but enthalpy is not determined. Thanks!

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15 Oct 2015 Nahla

Nahla (view profile)

Many thanks Mark

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14 Oct 2015 Mark Mikofski

Mark Mikofski (view profile)

So Sorry @Nahla. You are absolutely correct! I'm sorry I keep inverting Cp by mistake!

It is defined exactly as you have stated it and as it should be according to thermodynamics, the IAPWS and the wikipedia link I originally pasted:

cp = (dh/dT)|p

So, so, so sorry for the confusion!

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14 Oct 2015 Nahla

Nahla (view profile)

Oh ok, then probably it is the way you defined it in the program, because the heat capacity definition is


Thank you Mark, I appreciate it.

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13 Oct 2015 Mark Mikofski

Mark Mikofski (view profile)

@Nahla - yes exactly, I am using the relation:

Cp(p, h) = (dT(p, h)/dh)|p

everywhere in IAPWS_IF97

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13 Oct 2015 Nahla

Nahla (view profile)

Thank you again Mark, sorry if my question sounds silly, but do you mean cp_ph is the reciprocal of the derivative of the temperature of steam wrt enthalpy? because this is what it is according to the thermodynamic relations.

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13 Oct 2015 Mark Mikofski

Mark Mikofski (view profile)

@Nahla, thank you very much, I'm glad you've found this MATLAB implementation of IAPWS-IF97 useful.
The derivative of the temperature of steam wrt enthalpy is equivalent to cp_ph. Hope that helps!
See and

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12 Oct 2015 Nahla

Nahla (view profile)

This is a very useful code that I have been using now for years, many thanks Mark.
I have a question, is there a way I can find the derivative of the temperature of steam wrt enthalpy?

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25 Mar 2015 Mark Mikofski

Mark Mikofski (view profile)

Charlie Hansen: sorry for not seeing your message here. I'm sorry you are running into an issue, but it will be difficult for me to debug it without more info. Can you please post an issue on GitHub here: describing in detail what exact code you have tried, what the exact stack trace was use lasterror MATLAB builtin and exactly how you have IAPWS_IF97 on your path?

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24 Mar 2015 Mark Mikofski

Mark Mikofski (view profile)

Fernando Bello: In order to use `pT_uv()`, which is a reverse function, you will need my `newtonraphson()` solver from the FEX: Once downloaded either add it to your path or extract to your main MATLAB working folder.
AFAIK `pT_uv()` is the only function that depends on `newtonraphson()`. Note it is *not* an official IAPWS-IF97 function, although it does use the IAPWS-IF97 correlations.
Glad you are finding it useful. Please don't hesitate to report any other issues! --Mark

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24 Mar 2015 Fernando Bello

I have doubts with this program... When you use

pT_uv(41990.5,1/999.794) it says this error:

Undefined function 'newtonraphson' for input arguments of type

Error in pT_uv (line 66)
[x,resnorm,F,exitflag,output,jacob] = newtonraphson(fun,x0,options);

What is it? do i need the newton-raphson solver that is not included in this program.

About the rest of the program, it works great! it is a really good and fine job! Thank you for sharing

08 Jan 2015 Charlie Hansen


This seems to be an extremely useful functionality (especially because it is not self-referencing), but I am unable to run it in even a simple test. Trying to run the example file (IAPWS_IF97_example.m) and making my own simple call to the function both result in the same error:

Error using IAPWS_IF97
Too many input arguments.

Is there some incompatibility that you know of that may be causing this issue? I did not alter the main IAPWS_IF97.m file and also tried to download it again but saw no change.

Thanks for your help.

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20 Sep 2014 Nahla

Nahla (view profile)

Thank you Mark, it is working now. I appreciate it.

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20 Sep 2014 hgghh

hgghh (view profile)

19 Sep 2014 Mark Mikofski

Mark Mikofski (view profile)

ok Nahla, I found the bugs and fixed them enough so that you should get the correct derivatives for specific volume along the saturated liquid and vapor lines, but you will need to use the new dvLdp_p and dvVdp_p functions. There are 2 new tests included which will plot the derivatives together with finite difference approximations. For more details please see IAPWS "Revised Advisory Note #3, Thermodynamic Derivatives from IAPWS Formulations" ( which details how derivatives are found. To get the derivatives on the liquid and vapor lines, since the specific volume and enthalpy are functions of p or T only then a Taylor expansion, dhL/dp = (dh/dp)_T + (dh/dT)_p * dT_sat/dp_sat is used where the partial derivatives (dh/dp)_T and (dh/dT)_p are found using the advisory note separately for regions 1, 2 and 3. Ditto for specific volume. I made some silly sign errors, and I also switched cv accidentally for cv+p*v*alphap - I think my eyes wandered to internal energy, u, in the table instead of enthalpy, h, which is right below it. Sorry for the inconvenience! Thanks for noticing the error!

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19 Sep 2014 Mark Mikofski

Mark Mikofski (view profile)

Nahla, I think you may have discovered a typo in IAPWS_IF97. If I change the signs of the region 4b terms in dhLdp on line 914 to ...

dhLdp(valid4b) = (v3L - Tsat4b.*alphap3L./betap3_rhoT(rho3L,Tsat4b).*(1 - p4b.*alphap3L.*dTsatdpsat4b))/conversion_factor + cv3_rhoT(rho3L,Tsat4b).*dTsatdpsat4b;

I get a curve that matches a finite difference approximation of dhLdp. This function is also used in dvdp_ph(). Can you please post an issue on Github, and try to correct the error and validate it versus the IAPWS_IF97 documentation. Thanks!

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19 Sep 2014 Nahla

Nahla (view profile)

I have a question regarding the derivatives. I need the derivative of density wrt saturation pressure. However when I use the derivative of sp. volume wrt to p and multiply it with -rho^2, it does not give me accurate answers. Is there another way around this?

19 Jun 2014 Ehsan

Ehsan (view profile)

17 Oct 2013 Zoe

Zoe (view profile)

fast nice... parallel computing :)

14 Oct 2013 Mark Mikofski

Mark Mikofski (view profile)

The documentation is online here:

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13 Dec 2012 Thomas Clark

Nice vectorisation, thank you for this Mark.

15 May 2012 Peter Sugimura

26 Mar 2012 Mark Mikofski

Mark Mikofski (view profile)

until implemented, quality can be calculated from either enthalpy or specific volume and from either psat or Tsat as follows:

x_ph = @(p,h)(h - hL_p(p))./(hV_p(p) - hL_p(p))

then use x = x_ph(p,h)


x_hT = @(h,T)(h - hL_p(psat_T(T)))./(hV_p(psat_T(T)) - hL_p(psat_T(T)))

then use x = x_hT(h,T)

and the very similar for specific volume:

x_pv = @(p,v)(v - vL_p(p))./(vV_p(p) - vL_p(p))

then use x = x_pv(p,v)


x_vT = @(v,T)(v - vL_p(psat_T(T)))./(vV_p(psat_T(T)) - vL_p(psat_T(T)))

then use x = x_vT(h,T)

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26 Mar 2012 Mark Mikofski

Mark Mikofski (view profile)

Great suggestions Jonathan. I have added them to the issues list on Github here:
Also, I cp is available as a function of p & h (but not p & T as you pointed out), if that would suit your needs.

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26 Mar 2012 Jonathan Currie

Good implementation and the vectorization works really well. However would suggest adding:

- Entropy calculations
- Cp, Cv calculations as a function of P,T (not constrained by region)
- Inverse calculations for P
- Quality calculations
- More property pairings (e.g. P,T, P,S, P,H, H,S)
- Customizable units?

Not sure on the implementation question. I've always found classes too slow, there seems to be a bit of getting started overhead in every method call.

22 Mar 2012 Mark Mikofski

Mark Mikofski (view profile)

I've thought of a couple of other ways to present this code:
1. as a "+folder package", each function in it's own file; use namespace or import to use functions; e.g. IAPWS_IF.h_pT(0.1,298)
2. a @class folder, consolidate constants as hidden constant properties, functions as methods or static methods, method to set slip if slip is desired for 2-phase flow
3. "+folder package" for class, same as #2 but in a package for import.
Each has pros and cons. What works best for users?

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19 Mar 2012 1.2

revise/format description, add more tags

23 Mar 2012 1.3

add link to github

23 Mar 2012 1.4

show units, categorize and format functions

26 Mar 2012 1.5

acknowledge Magnus Holmgren's XSteam

14 Oct 2013 1.6

add quality, update help, add assertions

22 Sep 2014 1.7

fix bugs in dhL/dp and dhV/dp, and add dvL/dp and dvV/dp functions

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