public subroutine ar_consistency(eos, n, V, T, eq31, eq33, eq34, eq36, eq37)

ar_consistency

$A^r$ models consistency tests.

Description

The evaluated equations are taken from Fundamentals & Computational Aspects 2 ed. by Michelsen and Mollerup Chapter 2 section 3. The “eq” are evaluations of the left hand side of the following expressions:

Equation 31:

$$\sum_i n_i ln \hat{\phi}_i - \frac{G^r(T,P,n)}{RT} = 0$$

Equation 33:

$$\left(\frac{\partial ln \hat{\phi}_i}{\partial n_j} \right)_{T,P} - \left(\frac{\partial ln \hat{\phi}_j}{\partial n_i} \right)_{T,P} = 0$$

Equation 34:

$$\sum_i n_i \left(\frac{\partial ln \hat{\phi}_i}{\partial n_j} \right)_{T,P} = 0$$

Equation 36:

$$\left(\frac{\partial}{\partial P} \sum_i n_i ln \hat{\phi}_i \right)_{T,n} - \frac{(Z - 1)n}{P} = 0$$

Equation 37:

$$\sum_i n_i \left(\frac{\partial ln \hat{\phi}_i}{\partial T} \right)_{P,n} + \frac{H^r(T,P,n)}{RT^2} = 0$$

The consistency test could be applied to any instantiated ArModel as shown in the following example.

Examples

 use yaeos, only: pr, SoaveRedlichKwong, ArModel
 use yaeos__consistency_armodel, only: ar_consistency

 class(ArModel), allocatable :: model
 real(pr) :: tc(4), pc(4), w(4)

 real(pr) :: n(4), T, V

 real(pr) :: eq31, eq33(size(n), size(n)), eq34(size(n)), eq36, eq37

 n = [1.5, 0.2, 0.7, 2.3]
 tc = [190.564, 425.12, 300.11, 320.25]
 pc = [45.99, 37.96, 39.23, 40.21]
 w = [0.0115478, 0.200164, 0.3624, 0.298]

 T = 600_pr
 V = 0.5_pr

 model = SoaveRedlichKwong(tc, pc, w)

 call ar_consistency(&
    model, n, V, T, eq31=eq31, eq33=eq33, eq34=eq34, eq36=eq36, eq37=eq37 &
    )

All eqXX variables should be close to zero.

References

1. Michelsen, M. L., & Mollerup, J. M. (2007). Thermodynamic models: Fundamentals & computational aspects (2. ed). Tie-Line Publications.

Arguments