Two-Phase Flow in Chromatographic Processes
- Experimental and Theoretical Analysis
Franziska Ortner and Marco Mazzotti
Institute of Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
[email protected]
Motivation
Model Equations and Assumptions
Interaction of adsorbing components can result in a
Experimental evidence of LLPS
considerable enrichment in the liquid phase. As a
consequence, these components can exceed their
solubility limits, and phase separation occurs within the
chromatographic column.
Liquid-liquid phase separation (LLPS) has been observed
for the system phenetole (PNT), 4-tert-Butylphenol (TBP)
in the solvent methanol:water 63:37 (v:v) and on a Zorbax
300SB-C18 column[1].
Standard chromatographic models only consider a single
convective phase, and thus fail to describe a spontaneous
phase split, as well as hydrodynamic effects and
adsorption behavior in the presence of multiple
convective phases[1,2].
In this contribution, we develop a model accounting for the mentioned effects, and apply it
to the experimental system PNT, methanol and water with the adsorbent Zorbax 300SB-C18.
Characterization of System Properties
Thermodynamic equilibrium between liquid phases
Component mass balances
Assumptions
Variable porosity
Volume additivity
Thermodyn. equ. between liquid phases
Thermodyn. equ. between liquid phases and adsorbed phase
see below
Hydrodynamic behavior
Hydrodynamic behavior
• Pressure drop described by extended Darcy’s law:
• Neglecting pressure difference of phases due to interfacial tensions
Fractional flow[3] with wetting phase w and nonwetting phase nw:
equal velocities (simplified approach)
different velocities
Liquid-liquid equilibria: experimental
data and fitted UNIQUAC model
• PNT almost completely immiscible
with water
Experimental
UNIQUAC model
• Miscibility increases with increasing
methanol content
• Accurate description with UNIQUAC
model
• Fitted parameter values:
Simulated Profiles
Different velocities
• Concentration and flow profiles are not
identical
Comparison with equal velocities
Significant differences visible concerning:
•Concentration levels (Ci profile)
• Differences depend on the determined
fractional flow function
•Elution times of transitions
(Ci and Fi profile)
•Types of transitions (Ci and Fi profile)
Adsorption behavior
Adsorption isotherms
based on activities
Adsorption isotherms
based on concentration
Adsorption
Flow profile
Desorption
Adsorption
Desorption
experimentally accessible
• Determined by breakthrough experiments in the soluble region at different solvent ratios
(mass fraction of methanol in solvent)
experimentally not accessible
Concentration profile
Validation Experiments
UNIQUAC model
• Transforming liquid phase concentrations to activities with the established UNIQUAC
model, the experimental adsorption data falls on one curve
• Description by an anti-Langmuir isotherm, being a function of liquid phase activities
Two-phase flow
• Displacement of two phases
in thermodyn. equ.: decoupling of hydrodynamic effects
from adsorption effects
Experimental
conditions
Experimental pressure
and flow profiles
Experimental conditions
quantitative agreement
qualitative agreement
• All initial and feed states are single phase states,
but immiscible → high chance of two-phase flow
within the column
• Entire chromatographic cycles (adsorption and
desorption steps) considered
• Quantitative description by model accounting for
different velocities.
Validation experiments
• Relative permeabilities determined from pressure and
outlet flow profiles based on
mass balance and equilibrium theory equations[4]
Relative permeability functions
• Displacement of a pure solvent mixture (initial
states A) by a mixture of PNT with methanol (feed
states B).
Adsorption
Desorption
Adsorption
A1 - B1
Desorption
A2 – B2
Fractional flow functions
References: [1] Jermann, S. et al. J. Chrom. A, 1425 (2015), 116-28
[2] Ortner, F. et al. Ind. Eng. Chem. Res., 54 (2015), 11420−37
[3] Buckley S., Leverett M., Trans. AIME, 146 (1942), 107-16
[4] Marle, C. M. (1981), Multiphase Flow in Porous Media, Gulf Publishing, Houston