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Chapter 8 a large amount of data for these parameters that have been obtained so far can still be used. The κ-function in the iPRSV thermodynamic model is therefore κ=κ0 +κ1[A−D(Tr +B)]2 +E+A−D(Tr +B)Tr +C, (8) wherethevalueofthecoefficientsareA=1.1,B=0.25,C=0.2,D=1.2andE=0.01. The accuracy of the iPRSV thermodynamic model is similar or better than that of the model from which is derived. The derivatives of κ with respect to the temperature, that are required for the implemen- tation of a complete thermodynamic model into a computer program, are given in Ref. [69] together with a thorough discussion on the limits of the thermodynamic model. Wong and Sandler developed a set of mixing rules which satisfy the theoretically correct quadratic composition dependence of the second virial coefficient [70]. The mixing rule is derived by equating the excess Helmholtz energy AE of an activity coefficient model describing molecular interaction in the liquid phase to that obtained from the EoS at the so-called infinite-pressure state, namely, in the limit of a specific volume approaching the co-volume. The mixing rule contains one additional binary interaction parameter kij in the cross second virial coefficient, see Eq. 11. The binary interaction parameter can be determined by various approaches, see e.g. Ref. [88]. The Wong-Sandler mixing rule (WSMR) is used extensively in conjunction with the PRSV EoS. For the activity coefficient model, a so-called “solely energetic” model is usually preferred (i.e., a model which does not have an explicit free-volume term). As it is common practice for the PRSV EoS, the NRTL model introduced in Ref. [89] is used here to compute the activity coefficient, see also Ref. [90]. According to the WSMR, the a and b coefficients in (5) are substituted by respectively, where (9) √ 2 − 1 ≈ −0.62323. (10) aM =RTDbM, and bM = NC NC Q 1−D , NC D=AE∞+xiai, Q=xixjb−a. CEoS i=1 RTbi i=1 j=1 RT ij The parameter CEoS depends upon the equation of state. For the PRSV EOS, it reads ln The following combining rule has been used CEoS = √2 2 b− a = bi +bj −ai +aj 1−kij. (11) RT ij 2RT where a and b are the energy and the co-volume parameter. The subscript M refers to mixture properties while i and j refer to the components in the mixture. NC is the number of components. From the pressure EoS, a complete thermodynamic model can be finally obtained by specifying the relation between the temperature and the specific heat at constant pressure cP in the dilute gas limit, see e.g. [91]. In the present study, the following functional form of cP ψ(T)= limcP(T,v)=C0 +C1 T +C2 T2 +C3 T3 (12) v→∞ with C0 , C1 , C2 and C3 constants. The values of the parameters C0 , C1 , C2 and C3 are given in Ref. [69] for the fluids of interest here. From the cP definition (12) and the pressure EoS (5) a 220PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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