Theory
Like reference equations, state-of-the-art technical equations of state are formulated in terms of the Helmholtz energy, which is split into an ideal gas part and a residual part. Instead of the specific volume, the density is used as a variable:
2.104
with
To calculate
3.69
The resulting expressions for
2.105
For eq. 3.70 the following antiderivatives are given:
C.197
C.198
For eq. 3.69 the antiderivatives are:
C.195
C.196
The residual part is different
For polar fluids (R11, R12, R22, R32, R113, R123, R125, R134a, R143a, R152a, carbon dioxide, ammonia, acetone, nitrous oxide, sulfur dioxide, R141b, R142b, R218 and R245fa):
References:
R. Span; W. Wagner; Int. J. Thermophys. 24(1), 41-109 (2003).
E. W. Lemmon; R. Span; J. Chem. Eng. Data 24(1), 41-109 (2006).
R. Span; W. Wagner; Int. J. Thermophys. 24(1), 111-162 (2003).
E. C. Ihmels; E. W. Lemmon; Fluid Phase Equilib. 207, 111-130 (2003).
Parameter vectors for the ideal gas heat capacity (cid) and for the real part of the Helmholtz energy (c) are stored in separate files and are imported as references. In the ideal heat capacity parameter vector, the first element denotes the equation to be used (1 - 3.70, 2 - 3.69).
cP
id function 3.70 and the two different integrals required for calculation of
cP
id function 3.69 and the two different integrals required for calculation of
Set the correct functions for cP id and the two different integrals depending on the function used.
Auxiliary functions:
pressure
A starting value close above the hardcore volume is usually possible and ensures finding the liquid root. As P(v) covers several orders of magnitude, the objective of the root function should be the relative deviation in pressure.
h as function of T and v
Solution:
Conditions:
a)
The heat stream to be supplied by the heat exchanger can then be calculated via:
b)
Although in the supercritical state, the root function does not succeed to find a real solution when starting from the ideal gas volume. The second function usually used to find the liquid volume starts at a very low liquid volume and converges to the correct solution.
In the next step the molar and total enthalphy difference between inlet and outlet stream is calculated: