Water and steam properties and derivatives based on the IAPWS IF97. Functional form. No slip.
IAPWS_IF97(FUN,IN1,IN2) is 27 functions of water properties and derivatives, based on the International Association on Properties of Water and Steam (http://www.iapws.org). Thermodynamic, hydrodynamic and nonlinear 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 finitedifference or finiteelement equations, IAPWS_IF97 is vectorized even across regions (subcooled/compressedliquid, 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 2phase flow.
Please report bugs here or at Github:
https://github.com/mikofski/IAPWS_IF97/issues
Reference Documents:
Industrial Formulation 1997 (IF97Rev, IAPWSIF97), IAPWSIF97S01, IAPWSIF97S03rev, IAPWSIF97S04, IAPWSIF97S05, 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.
Functions:
Quality:
'x_ph','x_hT','x_pv','x_vT'
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'
1.7  fix bugs in dhL/dp and dhV/dp, and add dvL/dp and dvV/dp functions 

1.6  add quality, update help, add assertions 

1.5  acknowledge Magnus Holmgren's XSteam 

1.4  show units, categorize and format functions 

1.3  add link to github 

1.2  revise/format description, add more tags 
Inspired by: X Steam, Thermodynamic properties of water and steam.
Inspired: Water and Steam Refractive Index, A Simple Finite Volume Solver for Matlab
vaya putra (view profile)
hi
i am using Matlab R2017a
when i try this, some mistake, anyone help me
Not enough input arguments.
Error in XSteam (line 221)
fun=lower(fun);
Peter Cook (view profile)
Mark,
I did some forking of your package last week  nothing major but I made the following properties available as lowlevel calls:
'd2gammadtau2_pT','d2gammadpi2_pT','d2gammadtautau2_pT','d2gammadpipi2_pT','d2gammadpitau2_pT',...
'w1_pT','w2_pT','u1_pT','u2_pT','cv1_pT','cv2_pT',...
'gamma1_pT','gamma2_pT','s1_pT','s2_pT','phi3_rhoT'
The updated region 2 dimensionless Gibbs derivatives (d2gammad...) return the ideal and residual derivatives separately  I'd like to discuss if this is actually necessary as IAPWS IF97 Table 13 leads me to believe some of these calls are redundant.
w1_pT & w2_pT return the region 1 & 2 sonic velocities. I have an outside function that computes a retarded 2 phase/equilibrium sonic velocity that uses the same approximation as FLUENT, but that property (2phase speed of sound) is not supported by the IAPWS  let me know if you are interested in that as well.
u1 & u2 return the region 1 & 2 internal energy.
cv1 & cv2 return the region 1 & 2 isochoric heat capacity.
gamma1 & gamma2 return the region 1 & region 2 dimensionless Gibbs energy.
s1 & s2 return the region 1 & region 2 entropy.
phi3_pT returns the region 3 dimensionless Helmholtz energy. I stopped here because I realized I very rarely use region 3 properties in my own work.
Send me an email and we can discuss a couple of these  I can add this to the Git for the code as well if you'd like.
Maroua Rou (view profile)
Great job!
Please, can this program be extended for calculating thermodynamic properties of ice VII (from 2 to 20GPa) beyond 1000 bar?
Haben Ghebremedhin (view profile)
@ Mark Mikofski Outstanding job on vectoring the Xsteam file, I was wondering if you have any suggestion on how to calculate Internal energy, Isotherm bulk modulus and coefficient of thermal expansion using your function?
It there is a way to calculate these values using your function, it would be a perfect fit for the Thermal Liquid Settings module in simscape.
Leonardo Paoli (view profile)
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
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:
https://github.com/mikofski/IAPWS_IF97/blob/master/IAPWS_IF97.m#L159
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(ppsat)
err =
1.0e13 *
0.297539770599542 (fails)
0.124344978758018 (fails)
0.133226762955019
0.013322676295502
0.093258734068513 (fails)
0.008881784197001
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 1e12, but eps(p) is ~ 1e15, so if I use 100*eps(p) it works:
K>> abs(ppsat) < 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!
Mark Mikofski (view profile)
Hi Peter, thanks for your comment. This MATLAB IAPWS97 implementation is on GitHub here:
https://github.com/mikofski/IAPWS_IF97.
Can you please submit an issue on GitHub:
https://github.com/mikofski/IAPWS_IF97/issues
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.
Peter Cook (view profile)
This is a magnificent package, though I've got a small quirk to report for 'k_pT' calcs on the 12 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 =
0.046698
0.047223
0.63122
0.62921
0.048767
0.62522
0.049777
0.050277
0.050774
0.051268
Peter Pauska (view profile)
Kymbat Atamuratova (view profile)
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!
http://www.mathworks.com/matlabcentral/fileexchange/35710iapwsif97functionalformwithnoslip/content/html/IAPWS_IF97_example.html
Nahla (view profile)
Many thanks Mark
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!
Nahla (view profile)
Oh ok, then probably it is the way you defined it in the program, because the heat capacity definition is
Cp=(dH/dT)p
Thank you Mark, I appreciate it.
Mark Mikofski (view profile)
@Nahla  yes exactly, I am using the relation:
Cp(p, h) = (dT(p, h)/dh)p
everywhere in IAPWS_IF97
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.
Mark Mikofski (view profile)
@Nahla, thank you very much, I'm glad you've found this MATLAB implementation of IAPWSIF97 useful.
The derivative of the temperature of steam wrt enthalpy is equivalent to cp_ph. Hope that helps!
See http://mikofski.github.io/IAPWS_IF97/ and https://en.wikipedia.org/wiki/Heat_capacity#Thermodynamic_relations_and_definition_of_heat_capacity
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?
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: https://github.com/mikofski/iapws_if97/issues 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?
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: http://www.mathworks.com/matlabcentral/fileexchange/43097newtonraphsonsolver. 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 IAPWSIF97 function, although it does use the IAPWSIF97 correlations.
Glad you are finding it useful. Please don't hesitate to report any other issues! Mark
Fernando Bello (view profile)
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
'function_handle'.
Error in pT_uv (line 66)
[x,resnorm,F,exitflag,output,jacob] = newtonraphson(fun,x0,options);
What is it? do i need the newtonraphson 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
Charlie Hansen (view profile)
Mark,
This seems to be an extremely useful functionality (especially because it is not selfreferencing), 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.
Nahla (view profile)
Thank you Mark, it is working now. I appreciate it.
hgghh (view profile)
https://www.drupal.org/u/hd.clemson.vs.florida.state.live.stream.
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" (http://www.iapws.org/relguide/Advise3.pdf) 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!
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!
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?
Thanks
Ehsan (view profile)
Zoe (view profile)
fast nice... parallel computing :)
Mark Mikofski (view profile)
The documentation is online here:
http://mikofski.github.io/IAPWS_IF97/
Thomas Clark (view profile)
Nice vectorisation, thank you for this Mark.
Peter Sugimura (view profile)
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)
or:
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)
or:
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)
Mark Mikofski (view profile)
Great suggestions Jonathan. I have added them to the issues list on Github here:
https://github.com/mikofski/iapws_if97/issues
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.
Jonathan Currie (view profile)
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.
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 2phase 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?