1 / 25

Activity Coefficient Estimation Methods

Activity Coefficient Estimation Methods. Bharat Chandramouli February 5, 2002. Activity Coefficient . The activity coefficient is a measure of the non-ideality of mixing Two components, Enthalpic and Entropic. Estimation/Measurement.

Mia_John
Download Presentation

Activity Coefficient Estimation Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Activity Coefficient Estimation Methods Bharat Chandramouli February 5, 2002

  2. Activity Coefficient • The activity coefficient is a measure of the non-ideality of mixing • Two components, Enthalpic and Entropic

  3. Estimation/Measurement • Activity coefficients in single component/simple mixtures easy to measure • Activity coefficients in water or octanol can be calculated from solubility given sufficiently sensitive methods

  4. Need for estimation • What about complex mixtures? • What about dynamic systems with changing compositions? • It becomes more practical to use estimation methods to approximate g in these cases

  5. Estimation Methods • Group contribution methods are most common because they have predictive ability • There are two group contribution methods commonly used for iom • calculation from solubility parameters • UNIFAC calculation

  6. UNIFAC the UNIversal Functional group Activity Coefficient model • The activity coefficient is calculated from two components Combinational (V, SA) Residual (interactions) (Experiment Fit)

  7. UNIFAC • The group contribution components consist of • volume contributor -Rk • surface area contribution -Qk • interaction parameter between functional groups Amk • To calculate interactions, similar sub-groups are assigned to groups and interactions are between these groups • Calculate activity coefficients by summing all contributions and interactions

  8. UNIFAC-Simple example • Ethanol CH3-CH2-OH

  9. UNIFAC Methods • Interaction parameters are fit from experimental data • This work is still ongoing and many parameters still not available

  10. Hansen Solubility Parameter • This method calculates activity coefficients from the solubility parameter • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding

  11. Hansen Activity Coefficient • The activity coefficient is given by Cohesive energy density Molar Volume Size effect term Enthalpy Entropy

  12. The Size Effect Term • i,omd is a measure of the effect of differing sizes of i and om on their entropy of mixing • This was derived by Flory and Huggins using statistical thermodynamics • For an infinitely dilute solution

  13. Cohesive Energy (Ecoh) • Closely linked to the heat of evaporation • It is a measure of a the ability of a liquid molecule to stay together • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding

  14. Solubility parameter • Solubility parameters are measures of cohesive energy cohesive energy solubility parameter coh. energy density

  15. Calculating solubility parameters • Hansen and others compiled molar attraction constants for functional groups, which are additive contributions to the solubility parameter

  16. Attraction Constants (F) • The product of V was found to vary linearly across homologous series • Additivity of structural sub-groups • F=V values compiled for dispersion and polar components of  • Hansen later compiled additive contributions to Eh

  17. Multi-component Mixtures • How are om parameters calculated? • Parameters weighted using component mole fraction and molar volume to get “average om”

  18. Cohesive Energy Density • i,omA can be derived as • ib is a weighting factor based on dispersive forces, has been tabulated for a variety of compounds • ib corrects for the fact that polar and H bonding forces are localized

  19. Activity Coefficient • Putting the two components together lniom = +

  20. Calculation • First, calculate group contributions for each component in the mixture • Calculate “om” parameters by weighting with mole fraction and molar volume • Calculate parameters for compound of interest • Calculate activity coefficient

  21. Hansen or UNIFAC? • UNIFAC more powerful interaction • UNIFAC not universal–missing parameters • Hansen has certain inconsistencies as certain parameters have to be culled from different sources. Very sensitive to parameter choice • ib not widely available for many compounds, so estimation may be difficult

  22. Where do you use this? • Water solubility estimation • Solvent-Water partitioning (Kow)

  23. gas Compound Thermodynamic Equilibrium? Particle type Temperature Humidity particle Gas/Particle Partitioning • What happens when a semivolatile organic (SOC) encounters a particle??

  24. Partitioning Modes • Mode of SOC-particle interaction depends on the particle • Adsorption Solid particle, no organic liquid layer (dust, inorganic salts) • Absorption Particle either liquid, or has substantial liquid layer (combustion particles, secondary organic aerosol) • SOCs such as PAHs, and alkanes primarily partition to organic or carbonaceous aerosols rather than to mineral-based aerosols

  25. Predictive Partitioning models • Pankow (1994) for absorptive partitioning fom- fraction extractable organic matter igom- activity coefficient of SOC in om MWom-molecular weight of om

More Related