Les propriétés d'équilibre entre phases et masses volumiques

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1 Les propriétés d'équilibre entre phases et masses volumiques Christophe COQUELET Mines ParisTech, PSL Research University, CTP - Centre Thermodynamique des Procédés, 35 rue St Honoré, Fontainebleau Cedex, France Christophe.coquelet@mines-paristech.fr Centre of Thermodynamics of Processes

2 MOTIVATIONS Example of work done for Edf Chatou (Fluid selection) Franck David The selection of the fluids is mainly based on their energetic performances evaluated on energetic machines. The performance (COP) is generally evaluated from a process simulator and confirmed after several tests on existing machines. Example of ORC (Bo LIU, 04) Simulated using Thermoptim TM TS diagram of two stage ORC Journée SFT-SFGP-AFF-IIF 5 March 07

3 MOTIVATIONS Developement of equations of state and phase diagrams understanding Objectives Phase diagrams representation Knowledge of phase diagram is essential (azeotrope, critical point, relative volatility, conditions of apparition of liquid liquid equilibrium, solubility in lubricant Density predictions Estimation of the densities of both vapor and liquid phasse with the maximimum of accuracy Scott and van Konynenburg classification. Journée SFT-SFGP-AFF-IIF 5 March 07 3

4 Properties Phase equilibrium measurements What can we measure? Temperature Pressure Composition Volume (variation of volume) or density Speed of sound Flow Luminosity Hardness Etc Goal: do not disturb the system during experiments Research on techniques and experimental procedures Size of the equilibrium cell Development of sensors Journée SFT-SFGP-AFF-IIF 5 March 07 4

5 Experimental Approach Selection of the best experimental technique Definition of the objective (number of data, accuracy, number of chemicals, etc..) Knowledge of phase diagram is recommended Prediction using GC EoS or MS are welcome Purity of the chemicals Required time for the measurements Utilization of the data Calibration and uncertainties Journée SFT-SFGP-AFF-IIF 5 March 07 5

6 Calibration Calibration: process of finding a relationship between the physical property and the output signal Required: New instrument After an insturment has been repaired or modified Before and/or after measurement After an event (shock, sudden shutdown, etc) Calibration and errors: process = (measure standard measure) + errors Journée SFT-SFGP-AFF-IIF 5 March 07 Material Equipment Method Operator Environment 6

7 Two types of uncertainties Uncertainty related to repeatability: type A Ex: u rep ( P) = N ( N ) N ( Pk P) k= Standard deviation: type B The uncertainty is supposed to be ±a Different distribution laws: Normal distribution Uniform distribution Arcsine distribution u ref = u ref = u ref = a a 3 a Journée SFT-SFGP-AFF-IIF 5 March 07 7

8 Experimental Approach Experimental methods Closed Circuit methods Open circuit methods Isothermal Synthetic Isochoric Static stirred Analytic Static cirulated Forced circulation of one compound of the mixture Forced circulation of the mixture Bubble point Dew point VLE/VLLE/LLE Enthalpy Density Journée SFT-SFGP-AFF-IIF 5 March 07 8

9 Vapor Liquid Equilibrium Measurement Static Analytic method Temperature is maintained constant Component are added using gas cylinder SD GC PC TR Phase sampling (ROLSI ) PT SC LS VS V4 V6 Gas Chromatography for the determination of the composition of each phase Determination of experimental uncertainty using NIST standard Order of magnitude: u(t)=0.05k, u(p)=0.005 MPa, u(z)=0.005 LB PP PP EC EC TR MS LV LV ST EC: equilibrium cell; LV: loading valve; PP: platinum resistance thermometer probe; PT: pressure transducer; C: more volatile compound; C: less volatile compound; GC: gas chromatograph; LS: liquid sampler; VS: vapor sampler; SC: sample controlling; PC: personal computer; VP: vacuum pump. VP VP V TR TR PT TP TP V V5 C C V3 Journée SFT-SFGP-AFF-IIF 5 March 07 9

10 Vapor Liquid Equilibrium Measurement Relative volatility Graphic treatment: relative volatility α = y x x y Example: Ethane C4F Pressure/MPa 3 alpha C H 6 mole fraction C H 6 mole fraction Solid lines: PR Dashed lines: PSRK Journée SFT-SFGP-AFF-IIF 5 March 07 0

11 Vapor Liquid Equilibrium Measurement Example of results: CO + R3 Pressure as a function of CO mole fraction in the CO () R3 () mixture at different temperatures VLE Data. o : 83. K, : 93. K, : K, * : K, : K, + : K, : K, : K. solid lines : calculated with PR EoS, Wong Sandler mixing rules and NRTL activity coefficient model Journée SFT-SFGP-AFF-IIF 5 March 07

12 Vapor Liquid Equilibrium Measurement Example of results: CO + R7ea P /MPa x, y Pressure as a function of CO mole fraction in the CO () R7ea () mixture at different temperatures. : 76.0 K, + : 93.5 K, o : K, : K, : 33.5 K, : K, : K, * : K. solid lines : calculated with PR EoS, Wong Sandler mixing rules and NRTL activity coefficient model. Dashes line: mixture critical points line. Journée SFT-SFGP-AFF-IIF 5 March 07

13 Vapor Liquid Equilibrium Measurement Example of results: R3 + propane Azeotropic behavior VLE for the R3 () + propane () system at K. solid lines, calculated with PR EoS and Wong Sandler mixing rules Journée SFT-SFGP-AFF-IIF 5 March 07 3

14 Vapor Liquid Equilibrium Measurement Example of results: R34a + DME P /MPa x, y Azeotropic behaviour Min P Pressure as a function of R34a mole fraction in the R34a () + DME () mixture at different temperatures. ( ) 93.8 K, ( ) K, (ο) K, ( ) K, ( ) K. Solid lines: calculated with RK EoS, Huron-Vidal mixing rules and NRTL activity coefficient model. Journée SFT-SFGP-AFF-IIF 5 March 07 4

15 Vapor Liquid Equilibrium Measurement Example of results: RE70 + DME α x Left: Pressure as a function of RE70 mole fraction in the RE70 () R30 () binary mixture at different temperatures. ( )33.8 K, ( ) 38.6 K, (+) K, (ο) 357. K, (*) K, ( ) K, ( ) K, ( ) K and ( ) K. Solid lines: calculated with PR EoS, Wong - Sandler mixing rules and NRTL model. Dashed line: calculated critical point line Right: Relative volatility Journée SFT-SFGP-AFF-IIF 5 March 07 5

16 Data Treatment VLE Mixture Estimation of critical point composition Utilisation of scaling law equations and experimental data to predict correctly the phase diagram close to the mixture critical point Equation : Equation : H. Madani, A. Valtz, C. Coquelet, Isothermal vapor liquid equilibrium data for the decafluorobutane (R30) +,,,3,3-pentafluorobutane (R365mfc) system at temperatures from 333 K to 44K, Fluid Phase equilibria, 03, 354, VLE of the binary system at K. ( ) : experimental data, ( ) : mixture critical point Journée SFT-SFGP-AFF-IIF 5 March 07 6

17 PVT measurement Synthetic method Determination of bubble pressure Variable volume cell Possibility to determine density at saturation (after calibration) Journée SFT-SFGP-AFF-IIF 5 March 07 7

18 PVT Measurements Example of results: R3 + R7ea + propane R Vapour Liquidvapour Propane Liquid R7ea Ternary phase diagram: The system R3 () + R90 () + R7ea (3) at T = 300 K and P = 0.9 MPa The system R3 () + R90 () + R7ea (3).Pressure versus temperature diagram for each composition. Mixture : x = 0.3, x = 0.3, : Experimental bubble points, thick line: calculated with RKS EoS and MHV mixing rules. Mixture : x = 0.35, x = 0.74, : Experimental bubble points, solid line: calculated with RKS EoS and MHV mixing rules. Mixture 3: x = 0.493, x = 0.7, : Experimental bubble points, dashed line: calculated with RKS EoS and MHV mixing rules. Journée SFT-SFGP-AFF-IIF 5 March 07 8

Critical point determination Synthetic method Critical points were determined by observing the critical opalescence (dynamic method): ) A mixture of known overall composition is prepared and sent in

19 Critical point determination Synthetic method Critical points were determined by observing the critical opalescence (dynamic method): ) A mixture of known overall composition is prepared and sent in the cell ) The temperature is increased and the flow rate is regulated in order to maintain the meniscus in the middle of the cell 3) At the critical point, the cell becomes orange and the meniscus disappears from the middle of the cell. T C and P C are recorded. Journée SFT-SFGP-AFF-IIF 5 March 07 9

Critical point determination Possibility of density determination around critical point Observation of the vapor liquid interface Accurate calibration of the volume of the cell Measurement of

20 Critical point determination Possibility of density determination around critical point Observation of the vapor liquid interface Accurate calibration of the volume of the cell Measurement of temperature (for the pressure, we consider the pure component vapor pressure) Knowledge of the total mole number using variable volume cell (and density of the fluid in the condition of loading) Journée SFT-SFGP-AFF-IIF 5 March 07 0

21 Critical point determination Possibility of density determination around critical point Exemple: R34a Journée SFT-SFGP-AFF-IIF 5 March 07

22 CO + HFO 34yf Juntaratchat et al. 04 Journée SFT-SFGP-AFF-IIF 5 March 07

23 Density Measurements Synthetic method Vibrating tube densimeter The measurements are based on the indirect synthetic method. The method is based on the relation between the vibrating period of a dimensional resonator and its vibrating mass. The main part of the apparatus is the densimeter cell DMA-5P (Anton Paar KG). Important to control evolution of Z vs pressure Flow diagram of the vibrating tube densimeter. (): loading cell; (a) and (b): regulating and shut-off valves; (3): DMA-5P densimeter; (4): heat exchanger; (5): bursting disk; (6): inlet of the temperature regulating fluid; (7a) and (7b): regulating and shut-off valves; (8): pressure transducers; (9): vacuum pump; (0): vent; (): vibrating cell temperature probe; (): HP 533A data acquisition unit; (3): HP34970A data acquisition unit; (4): bath temperature probe; (5): principal liquid bath. Journée SFT-SFGP-AFF-IIF 5 March 07 3

24 Pure component HFO 6 Comparison between experimental data (vibrating tube densimeter) Estimation of critical properties (Coquelet et al., 0) Journée SFT-SFGP-AFF-IIF 5 March 07 4

25 Data treatment Rectilinear diameter R34yf Coexisting curve Combination of these two expressions ρ = ( ) +( )+ρ ρ = ( ) +( )+ρ Tanaka et Higashi IJR 33, 00, CTP confidential data Parameters are fitted considering both vapor and liquid densities at saturation Journée SFT-SFGP-AFF-IIF 5 March 07 5

26 Mixture Density measurements FX90 (Atofina) R49a R5, R34a, RE70 (DME): in mol% Journée SFT-SFGP-AFF-IIF 5 March 07 6

27 Conclusion Different experimental techniques exist for the measurement of: Vapor Liquid Equilibrium data PTxy PVT Critical point (visual method) Density (vibrating tube or isochoric method) Importance of calibration and uncertainties determination Data are essential for adjustment of equation of state parameters and fluid selection Journée SFT-SFGP-AFF-IIF 5 March 07 7

28 Les propriétés d'équilibre entre phases et masses volumiques Thank you for your attention Centre of Thermodynamics of Processes

29 Journée SFT-SFGP-AFF-IIF 5 March 07 9

30 Example Static analytic method using GC Molar fraction u x n + n ( x ) = u ( x ) + u ( n ) + u ( ) n rep n x + n idem Type A u n S ( n ) = u ( n ) + u ( n ) + u ( ) inj corr rep S n = gas PV RT ( P) u ( T) u ( V ) u u ( ) inj n = n + + P T V Hyp: ±% Type B Journée SFT-SFGP-AFF-IIF 5 March 07 n n + = a + a S a S 0 liquid = ρ V S N k,k = S,k,l N k l= S of component A ρ = N points (k= N) Type B are C T + T c taken for the polynomial B E S max correlation u ( S ) = rep empirical equation { Component Plus, PROSIM France 3 } C C T u u ( n ) n ln B u ( T) inj = + T c T c V ( V ) E( S ),k,l = ( S S ),k,l S,k,k 30

Centre Thermodynamic of Processes

Centre Thermodynamic of Processes MINES ParisTech-PSL-Research University-Armines 35 rue Saint Honoré 77305 Fontainebleau Cedex (France) Tel. : +33 (0)1.64.69.49.63 Fax : +33 (0)1.64.69.49.68 Mail: ctp@mines-paristech.fr