public subroutine three_phase_line_F(model, Xvars, ns, S, F, dF)

three_phase_line_F

Description

Calculate the function vector and Jacobian for the three-phase line (LLV) of a binary mixture. Phases are defined as x, y and w. Which are two liquid phases and one vapor phase respectively.

The system of equations is defined as: $$\begin{align*} & \ln \phi_i^{(x)} - \ln \phi_i^{(w)} = 0 \\ & \ln \phi_i^{(y)} - \ln \phi_i^{(w)} = 0 \\ & P^{(x)} - P^{(w)} = 0 \\ & P^{(y)} - P^{(w)} = 0 \\ & \text{specification} \begin{cases} y_1 - x_1 - S = 0 & \text{if } ns = 0 \\ \ln v_x - \ln v_y - S = 0 & \text{if } ns = -1 \\ X_{ns} - S = 0 & \text{otherwise} \end{cases} \end{align*}$$

References

[1] M. Cismondi, M.L. Michelsen, Global phase equilibrium calculations: Critical lines, critical end points and liquid–liquid–vapour equilibrium in binary mixtures, The Journal of Supercritical Fluids 39 (2007) 287–295. https://doi.org/10.1016/j.supflu.2006.03.011.

Arguments