1. Construction of Global Phase Equilibrium Diagrams Martín Cismondi Universidad Nacional de Córdoba - CONICET

2. Introduction A real binary system show one of 5 (or 6) different types of phase behaviour. EOS modelling leads to the same possible types (+ other). Correspondence between real and predicted type depends on the model and parameters.

3. Type I: Unique Critical Line (LV) Pv2 A Pv1

4. Type II: Also a LL critical line and LLV B A LLV Ps2 Ps1

5. Type IV: Discontinuity in the LV critical line and second LLV region B D E D E UCEP LCEP LLV

6. Type IV: T-x projection BD E UCEP LCEP UCEP

7. Type III: “rearrangement” of critical lines C D UCEP

8. Type III: T-x projection C D UCEP

9. Type V: Just like type IV but without LL immiscibility at low T D E D E UCEP LCEP LLV

10. Azeotropic lines and… Azeotropic End Points (AEP) PAEP (Pure, meeting a vapour pressure line) CAEP (Critical, meeting a critical line) HAEP (Heterogeneous, meeting a LLV line)

11. One example of azeotropic line (P-T) CAEP HAEP

12. The same example in T-x CAEP HAEP

13. Cases with two azeotropic lines! P H C H

14. Objectives Identification of predicted type Automated calculation of global phase equilibrium diagrams Automated calculation of Pxy, Txy and isoplethic diagrams from limiting points

15. What do we need? Strategy for construction of a GPED without knowing the type in advance. General method for CRIT lines calculation. Location of isolated LL critical lines. General methods for LLV and AZE lines. Detection of CEP ’ s and AEP ’ s (critical and azeotropic end points). Classifications of Pxy, Txy and isoplethic diagrams in terms of limiting points. Methods for calculation of Pxy, Txy and isoplethic segments.

16. Algorithm: Basic Structure

17. Some remarks about the methods… Formulation in T, v and x, y, w… Solve using Newton J ΔX = -F ; F n = X S - S Michelsen’s procedure for tracing lines J (dX/dS) = (dF/dS) → X new = X old + (dX/dS) ΔS ΔS new = min (4 ΔS old / N iter, ΔS max ) The variable to be specified depends on dX/dS

18. Calculation of critical points: Criticality conditions tpd 2 =0b = smallest eigenvalue λ 1 =0 tpd 3 =0c = = 0 n1 = z1 + s u1; n2 = z2 + s u2

19. How to locate an isolated LL critical line? Must be 0 and min at (T, P)

20. LLV equilibrium and CEP’s

21. Use of stability analysis in the search for a Critical End Point (CEP)

22. Calculation of a Critical End Point

23. Calculation of LLV lines

24. Examples: type II minimum composition

25. Split of LV critical line in type IV or V

26. Transition III IV II

27. Our Classification for Adding Azeotropy

28. Detection of AEP’s PAEP: compute along each vapour pressure line CAEP: Pseudocritical point compute 1 st derivative along the LV critical line HAEP: crossing between L and V composition compute y 1 – x 1 along LLV line

29. Calculation of azeotropic lines: variables and equations

30. Illustration: Negative Azeotropy

31. Double Azeotropy: Minimum T in the azeotropic line

32. PAEP Tmin Bancroft point (Pv 1 = Pv 2 )

33. Automated construction of complete Pxy and Txy diagrams Reading and storing the lines and points of the Global Phase Equilibrium Diagram. Identification of type. Detection of local temperature and pressure minima or maxima in critical lines. Determination of the pressures (or temperatures) at which the different lines intersect at the specified temperature (or pressure). Deduction, from the points obtained, of how many and which zones there will be. Calculation of each zone or two-phase region.

34. T specified (NVP=2, NC=2, NLLV=1)

35. Translating from limiting points to diagrams

36. variables and equations…

38. Examples: Closed loops in Pxy diagrams

39. Detection of composition local minima or maxima in critical lines, as well as in vapour or liquid branches of LLV lines. Location of intersection points at specified composition. Deduction of the number and nature of the segments the isopleth will be constituted of. Calculation of each segment of the isopleth. Generation of Complete Isopleths

40. Location of intersection points

41. Number and nature of segments

42. Calculation of each segment Numerical continuation method Sensitivities are used to –Choose which variable to specify for next point –Estimate values for all variables

43. Global Diagram: P-T projection

44. Global Diagram: T-x projection

45. Ethane-Methanol. RK-PR EOS.

49. Modular Approach One general subroutine for calculation of P, and derivatives wrt T, V and n (given T, V and n) Model specific subroutines for calculation of A r and derivatives wrt T, V and n

50. Conclusions We have provided strategies for constructing GPED’s from scratch. Types I to V, with or without azeotropy. Pxy, Txy and Isopleths can be derived. Strength: based on the GPED Weakness: everything is based on the GPED www.gpec.plapiqui.edu.ar www.gpec.efn.uncor.edu

51. References Global phase equilibrium calculations –Cismondi, M., Michelsen, M. “Global Phase Equilibrium Calculations: Critical Lines, Critical End Points and Liquid-Liquid-Vapour Equilibrium in Binary Mixtures”. The Journal of Supercritical Fluids, Vol. 39, 287-295. 2007. –Cismondi, M., Michelsen, M. “Automated Calculation of Complete Pxy and Txy Diagrams for Binary Systems”. Fluid Phase Equilibria, Vol. 259, 228-234. 2007. –Cismondi, M., Michelsen, M. L., Zabaloy, M.S. “Automated generation of phase diagrams for binary systems with azeotropic behavior”. Industrial and Engineering Chemistry Research, Vol. 47 Issue 23, 9728–9743. 2008. GPEC (the program) –Cismondi, M., Nuñez, D. N., Zabaloy, M. S., Brignole, E. A., Michelsen, M. L., Mollerup, J. M. “GPEC: A Program for Global Phase Equilibrium Calculations in Binary Systems” (Oral Presentation). EQUIFASE 2006. Morelia, Michoacán, México. October 21-25, 2006. Models and their pure compound parameters –Cismondi, M., Mollerup, J. “Development and Application of a Three-Parameter RK-PR Equation of State”. Fluid Phase Equilibria, Vol. 232, 74-89. 2005. –Cismondi, M., Brignole, E. A., Mollerup, J. “Rescaling of Three-Parameter Equations of State: PC-SAFT and SPHCT”. Fluid Phase Equilibria, Vol. 234, 108-121. 2005.