29
wider range of MeOH concentrations, up to 40%, were extrapolated to lower intermediate concentrations and compared to density data from REFPROP at the same compositions and temperature.
Experimental
Figure 2. a. The effect of methanol concentration on the retention of theobromine at 3 different BPR pressures. b. The average density in the column as a function of methanol concentration at 3 different BPR settings. 4.6x150mm, 5µm RX-Sil. Conditions: 2mL/min, 40°C.
A few approaches have appeared for calculating viscosities, but the results are somewhat inconsistent. Tarafder [5] used REFPROP to generate constant density (isopycnic) lines as a reference, and compared the calculated density of CO2
Fekete [3] took a completely different approach in calculating dynamic viscosity of MeOH/CO2
mixtures. He used some
empirical data [14] on the viscosity/density of CO2
/
MeOH mixtures to old empirical density measurements and found fairly signifi cant deviations near the critical points but relatively good agreement elsewhere. Tarafder then calculated and plotted all the temperatures and pressures that gave the same density with the same composition. These plots contain the ratio of ρ/η, where η is dynamic viscosity, and ρ is density. This ratio is proportional to kinematic viscosity. To convert such data to actual values for kinematic viscosity required another estimation, in this case of column porosity, the only non-constant in the differential version of Darcy’s Law [5]. With an estimation of column porosity, values were assigned to each kinematic viscosity curve. Mixtures ranged from 5% to 20%. There are many assumptions, approximations, and estimations in these numbers that make the results questionable.
/MeOH mixtures where a liquid phase was in contact with a vapor phase at low pressures (<80 bar). He then extended correlations to conditions at higher pressures and temperatures, between 0% and 40% MeOH. Extrapolating the low pressure data to much higher pressures (through the critical points) is a bit of a stretch since there is a poor relationship between density and viscosity in fl uids where the modifi er is much less dense than the CO2
at higher pressures. Surprisingly, this is actually a fairly common approach [15] using the same underlying assumptions and similar data. The authors [3] claim to have checked the calculated values with a few measured values with good agreement, without providing details. These results were reported as dynamic viscosity in centi-Poise.
The 2 sets of data don’t quite fi t, but are close, when Fekete’s [3] results are divided by density (to generate kinematic viscosity) or when Tarafder’s [5] data is multiplied by density (to generate dynamic viscosity). The differences are not very large and the curves have the same general shape.
Figure 3. Dynamic viscosity vs methanol concentration in CO2 at 5 pressures. Bottom circles 100 bar; squares, 150 bar; triangles, 200 bar, diamonds, 300 bar; and top circles, 400 bar.
In a recent report, from this laboratory [11], the changes in density, with high modifi er concentrations and high pressures were briefl y characterised with respect to retention, effi ciency, and pressure drops, using density data from REFPROP. A missing link in understanding effi ciency, pressure drops, and optimum fl ow rate has been the lack of accurate viscosity values and the relationship between viscosity, density, and pressure drops at pressures > ≈ 200 bar, and methanol concentrations > ≈ 20%. In the present work, the viscosity results from Fekete [3], which covers a
Equipment Chromatograms were collected using a Model 4301A 1260 Infi nity II SFC, controlled by a Model C.01.08 (210) Chemstation, all from Agilent Technologies, Waldbronn, DE (Germany). The instrument consists of a SFC conversion module, a binary pump, a Multisampler, thermostated column compartment, and a 120 Hz diode array detector (DAD). Standard 170µm tubing, including 2 heat exchangers was used throughout, except for a 50 cm piece of 120µm tubing serving as the inlet tube of the fl ow cell. The fl ow cell volume was 13µL with a 10mm fl ow path length. The column was 4.6 x 150mm packed with 5µm RX-Sil from Agilent Technologies, Little Falls, DE, USA.
The Agilent SFC is fairly unique in that the
binary pump does not compress the CO2 signifi cantly. It is pre-compressed to 8 bar below the delivery pressure by the SFC conversion module. The binary pump only meters the fl ow. Since the CO2
half of the
binary pump does not compress, there is almost no heat of compression and no
ambiguity about the temperature of the CO2 that is being delivered. Knowing the pump temperature, and the delivery pressure, one can obtain the density of each pure fl uid from REFPROP. The pump delivers v/v%. If one knows the density of each fl uid, and the volumetric displacement of each pump vs. time, one then knows the actual Mole%. Conversely, it is fairly easy to convert Mole% to v/v%. With other SFC’s it is more diffi cult due to high heats of compression. With signifi cant pump compression, the temperature of the fl uid is not the temperature of the pump head.
Chemicals
Theobromine was obtained from Sigma- Aldrich, St. Louis MO, USA (> 98%, used as received). The CO2
was beverage
grade, from Terry Supply Co., Bradenton, FL, USA, in 50 lb cylinders, without a DIP tube. The HPLC grade MeOH and IPA was purchased from SECO, Aston, PA, USA. The samples were dissolved in methanol. The ‘feed’ solvent used in the autosampler was isopropyl alcohol.
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