Three test systems were chosen for which limiting activity coefficients have already been determined by Krummen et al. (2004) using the IGS technique. The three test systems were n- heptane (1) in N-methyl-2-pyrrolidone (NMP) (2), cyclohexane (1) in N-methyl-2-pyrrolidone (2) and n-hexane (1) in N-methyl-2-pyrrolidone (2). (1 refers to the solute while 2 refers to the solvent). The limiting activity coefficients obtained from experiments using the IGS technique were compared to literature data published by Krummen et al. (2004) obtained from experiments using the same technique. Once it was established that the data was good and reliable, unknown systems were attempted and the results of which can be found in Part 2 of this chapter.
7.1 Limiting Activity Coefficients -Krummen et al. (2000)
The double cell technique was used for the analysis of all test systems, but for the n-hexane (1) + NMP (2) system the single cell technique was also used and the results for the two techniques were compared. The limiting activity coefficients were evaluated for all the equations outlined in the previous chapter. The results for the Krummen et al. (2000) proposed equation (EquaUon 6.55) are reported, followed by that for leroi et al. (1977) based equations (Equations 6.23, 6.24, 6.29 and 6.33) and lastly for the Hovorka and Dohnal (1997) derived equation (Equation 6.65).
7.1.1 Test System 1: Cyclohexane (1) + NMP (2)
Before one can forge ahead with the experimental determination of activity coeffICients a suitable inert gas flow rate needs to be determined. The higher the flow rate, the less likely it is that the system will reach equilibrium. There is a maximum flow rate that must not be exceeded when using the IGS technique for a particular system. If experiments are performed at flow rates beyond this maximum flow rate there will be large errors in the limiting activity coeffiCients as equilibrium conditions will not be obtained. There would be a loss of accuracy and precision which would lead to inconclusive results. At the same time, operating at a very low flow rate would result in a poor variation of solute peak areas with time. It would not be possible to obtain a good representation of data for slope in a short period of time especially for non-volatile solutes, but for highly volatile solutes low flow rates are ideal. As a result there needs to be a suitable balance between flow rate and experimental time with regard to solute volatility.
Chapter 7 Part I
The solute peak areas and residence times were obtained from the GC program Clarity which is an integration program that analyses the signal coming from the FIO detector of the Varian 3300 gas chromatograph. This was done with the aid of a computer. The solute peak areas and residence times are used to determine the slope (a). The peak areas need to be represented before a plot can be made. The peak areas AI are divided by the initial area Ao and the logarithm of the resultant ratio is plotted against time to give a straight line. The gradient
a
ofthe line is used in Equation 6.55 to determine
1 7.
All plots and data manipulations were done in Microsoft Excel unless otherwise stated. MATLAB was used to determine vapour pressures and fugacity coefficients.The system cyclohexane (1) + NMP (2) was used in order to determine the inert gas flow rate range necessary for accurate results. Five flow rates between 4 and 50 millilitres per minute were chosen to determine a suitable operating range for the system. Nitrogen was the chosen inert gas used for all experiments. A plot showing the slopes for the system cyclohexane (1) + NMP (2) at different nitrogen gas flow rates (0) is illustrated in Figure 7-1. Experiments were done in order to find a suitable range for the flow rate. The equipment was not able to handle flow rates greater than 50 mVmin and the bubbles formed by the capillaries were becoming large.
Profiles to determine slope a for the system cyclohexane (1) + NMP (2)
'"
200".
300".
Time (minute.)
'"
Figure 7-1: Straight line plots showing slope 8. The slope was used to determine limiting activity coefficients at constant temperature from Equation 6.55.
It is recommended that higher flow rates be used for systems wnere the solute volatility is very low in order to reduce experimental time. Temperature. time between injections. solute volatility and inert gas flow rate effect the variation of solute in the dilutor cell. with Ume. A good variation of solute peak areas with time is required for a reasonable plot to determine the slope. High temperatures, longer stripping times, high volatility solutes and high inert gas flow rates contribute to larger variations of the solute peaks with time. High temperatures and gas flow rates as well as long stripping times between injections work against highly volatile solutes as most of the solute is stripped before a well represented plot can be made. Therefore. a balance between these variables must be found, usually by logical deduction or trial and error.
From Figure 7-1 the profound effect that the inert gas flow rate has on the slope can be seen. As the flow rate increases the slope also increases. This shows that the higher the inert gas flow rate, the higher the stripping rate which will be expected. The resulting limiting activity coefficients due to varying flow rate and keeping temperature constant is shown in Table 7-1.
Flowrate (D) Temperature (T) Limiting Activity Coefficients Deviation (ml/min)
rC )
Y ~ E"Pt~" .. t"DI~
Y L/l#:~QI"~" %
5.83 50.16 6.67 6.7 -0.48
12.65 50.16 6.67 6.7 -0.45
24.43 50.23 6.65 6.7 -0.72
34.59 50.17 6.68 6.7 -0.30
47.47 50.30 6.64 6.7 -0.89
Table 7-1: Activity coefficients at infinite dilution for the system cyclohexane (1) + NMP (2) at a temperature of approximately SO 'C and at different inert gas flow rates chosen in the
range 4 to 50 mllmin.
The literature value for the yot> for cyclohexane in NMP at SO.2 ·C is 6.7 as determined by Krummen et a1. (2004) using the IGS technique with flow rates between 30 and 40 mllmin. It can be seen that the values obtained using the newly designed equipment gives values close to the value obtained by Krummen et a1. (2004). Even with inert gas flow rates as high as 47 mllmin the deviation from the literature value is small. However it was then decided to operate the equipment at flow rates in the range 10 to 30 ml/min. This was done in order to minimize the pressure build-up in the pre-saturator as the ~O~-ring seals were not able to keep the Tetlon plug in place. The effect of temperature on the limiting activity coefficients for the system cyclohexane (1) + NMP (2) was then investigated.
Chapter 7 Part I
Plots to determine slope a for cyclohexane (1) + NMP (2) system
0
'" . , ..
20'''''
300''''
."". ""
. .,
•
"30·• T .. 40·C
~., .. T"5()"C
)(T"60'C
~
~...
~ ~2..0.25
~
.
. "
Time (minutes)Figure 7-2: GC solute peak areas that have been represented to give straight line plots for the determination of slope a, at different temperatures for the system cyclohexane (1)
+ NMP (2).
Figure 7-2 shows the effect that temperature has on the slope and thus the stripping rate. As temperature increases the slopes increase, which means that the stripping rate increases. This means that more solute is going into the bubble phase. This makes sense due to the fact that the volatilities of the solute and solvent in the equilibrium cells are a function of temperature. The higher the temperature the more volatile the components in the cell become and thus readily move into the gas phase. The effect that temperature has on the limiting activity coefficients at constant nitrogen gas flow rate is shown in Table 7-2.
literature Data Experimental Values Deviation
T rC) Y ~ L/ter"tuH
o
(ml/mln) T rC) 'Y ~ Experlmentll 1%)30.1 7.8 14.89 30.08 7.77 -0.43
40.2 7.19 11.77 40.03 7.21 0.32
50.1 6.7 12.65 50.16 6.73 0.42
60.2 6.23 11.77 60.06 6.20 -0.49
Table 7-2: Experimental limiting activity coefficients for cyclohexane (1) + NMP (2) evaluated at different temperatures. Also tabulated are literature values at similar
temperatures, determined by Krummen et at (2004).
The calculated deviation shown in Table 7·2 is not a true measure of the accuracy of the results because the temperatures at which the experiments have been performed are not exactly the same as the literature temperatures. Instead a plot of the experimental results and literature values gives a better indication of the accuracy and is a far better comparison. Deviations will not be shown in tables; instead a plot, such as that in Figure 7·3 shows clearly the accuracy of the results when compared to literature.
•
literature versus Experimental limiting activity coefficients for the cyclohexane (1) + NMP (2) system
_L~erature
_ ExperImental
.,L.---~»c---~~~---.3C---~~---cc---~C---".·3
lem perature rC)
Figure 7·3: Comparison of experimental and literature values of limiting activity coefficients for the system cyclohexane (1) + NMP (2) from Equation 6.55.
The flow rate is not consistent for the four experimental runs for this system because at the time of the measurements a pressure regulator was not in place at the gas inlet to the system. This resulted in the flow rate changing due to others using nitrogen gas from the same tank on different days. However, the flow rate during the experimental run was the same throughout the run. The actual value of the limiting activity coefficients is not significantly affected by inert gas flow rate as long as it is constant throughout the entire period of analysis and equilibrium conditions are maintained in the cells. Once the regulator was in place disturbances in the nitrogen gas line did not affect the flow of nitrogen out of the regulator. This was true only if these disturbances did not result in a pressure that was below the set pressure on the regulator.
The results show that the experimental setup is well suited for the determination of activity coefficients at infinite dilution for the cyclohexane (1) + NMP (2) system. The obtained results
Chapter 1 Part I
are in strong agreement with already published literature data. The trend for y«> as a function of temperature confirms the general trend for these types of systems. The results for this system determined from other proposed equations follow later in the chapter.
7.1.2 Test System 2: n-heptane (1) + NMP (2)
The next test system studied was n-heptane (1) in NMP (2). The limiting activity coefficients for the system n-heptane in NMP evaluated from Equation 6.55 can be found in this section. The results for other equations are reported later in the chapter. The various plots to determine slope a, is shown in Figure 7-4.
.. ,
~.65
Straight line plots for the determination of slope afor the system n- heptane (1) + NMP (2)
f ~~~~~~~ ",~;;;: ~~~~,~oo~~~,;~~--~ ,~,,~--~,;~~:::.oo::::~.~
_ .. lO·
_T_40'C _T-S:rC _ T-60'C
Time (minutes)
Figure 7-4: Temperature effect on the straight line plots for the system n-heptane (1) + NMP (2) for use with Equation 6.55 to determine limiting activity coefficients.
The effect of temperature on the slope a, for this system is similar to that for the system cyclohexane (1) + NMP (2). The slope gradually increases as temperature increases, but this has an opposite effect on the limiting activity coefficient itself. The limiting activity coefficient has an inverse relationship with temperature Le. as temperature increases the solute limiting activity coefficient decreases. This is true for most systems and the effect can be cleany seen in the table below.
Literature Values Experimental Values
Tee)
Y ~ LilertJlUr£ o (ml/min)T ee)
Y ~ &perj"..",,/30 14.9 11.06 30.12 14.92
40.2 13.7 11.13 39.83 13.72
50.2 12.4 11.08 50.51 12.43
60.2 11.5 11.46 60.19 11.46
Table 7-3: Calculated limiting activity coefficients for the system n-heptane (1) + NMP (2) with corresponding literature values at similar temperatures obtained from Equation 6.55.
The experimental values are in strong agreement with recently published literature values by Krummen et al. (2004). After installing the pressure regulator the nitrogen gas flow rate was constant for the different runs done on different days. despite use from the same source by other researchers. This is clearly depicted in Table 7-3 for the four runs done over four days. The flow rate is very difficult to set at a specific value using a simple needle valve. An electronic mass flow device can be used to control the inert gas flow rate but this equipment is very expensive.
A clear indication of the effect of temperature on y'lO is seen in Figure 7-5.
.! E
~
0"
, . .
, . ,
,.
"
Uterature versus Experimental limiting activity coefficients for the n-heptane (1) + NMP (2) system
_ Ueqotute
_ Experimental
'.',:---~----:-:---::----:-:----::,---,.
2a 43 48 Sl 58 63
Temperature rC)
Figure 7-5: limiting activity coefficients for the system n-heptane (1) + NMP (2) as a function of temperature and comparison with published literature data by Krummen et al.
(2004).
Chapter 7 Part I
The limiting activity coefficient is strongly affected by temperature, as seen by the results of the two test systems.
7.1.3 Test System 3: n~hexane (1) + NMP (2)
For the third test system the effect of using one cell (SCT) and two cells (DCT) was investigated.
The nature of the components determines which technique to use. Due to the low volatility (less than 1 mm Hg) of the solvent NMP in these systems the SeT can be successfully used. Another prerequisite is that the solvent must be a single component and not a mixture of components otherwise the concentration might change considerably in the dilutor cell due to the fact that the rate at which each component is stripped may vary. In that case the DCT must be used to ensure accurate results. The DCT slope plots for the system n-hexane (1) + NMP (2) is shown in Figure 7-6.
Straight line profUes for the determination of slope a for the system n-hexane (1) + NMP (2) using the ocr
Time (minutes)
Figure 7-6: Plots for the determinaUon of slope (a) at different temperatures and constant flow rate for the system n-hexane (1) + NMP (2) using the double cell technique
The affect of temperature on the system n-hexane (1) + NMP (2) is similar to the other two test systems. Since the slope (a) greatly influences the limiting activity coefficient it is expected that the affect of temperature on
y'"
should be similar to that of the other two test systems as shown in Table 7-4.Double Cell Technique
Literature Data Experimental Data
T ("C) Y ~ Llr~r"r"re D (ml/min) T ("C) Y ~ ~ri ... ~"rd
30.1 12.7 19.42 30.13 12.65
40.2 11.6 19.91 40.12 11.59
50.2 10.7 19.95 50.34 10.64
60.2 9.9 19.93 60.61 9.88
Table 7-4: Comparison of literature and experimental data for the system n·hexane (1) + NMP (2) obtained using the double cell technique.
A higher flow rate than for the other two test systems was used for the detennination of y<lO in order to check the effect it would have on the activity coefficient for this system. The higher flow rate of 20 mllmin still allows for equilibrium in the dilutor cell as determined with the cyclohexane (1) + NMP (2) system for flow rates up to 47 mllmin. The double cell technique clearly works well for systems will low solvent volatility and high solute volatility and to check if the single cell technique works just as well as the DCT, it was used to determine limiting activity coefficients at similar temperatures. The slopes obtained for the detennination of y<lO for such an analysis is shown in Figure 7-7.
·u
Straight line profiles for the determination of slope a for the system n-hexane (1) + NMP (2) using the SCT
• SCT T-30'C . SCTT""O·C .SCT T-5Q'C xSCTTooSO'C
Time (minutes)
" . '" ".
Figure 7-7: Plots for the determination of slopes a, for the evaluation of limiting activity coefficients using Equation 6,55 and for the SCT.
Chapter 7 Part I
The slopes for the single cell technique have a similar trend to that for the double cell technique with the effect of temperature. The flow rates of inert gas for both techniques are similar and the limiting activity coefficients with their corresponding temperatures and flows are shown in Table 7-5.
Single Cell Technique
o
(mlfmin) T rC) Y•
E:JpeTi",ennl
20.23 30.15 12.69
20.62 39.93 11.55
20.64 50.23 10.64
19.38 60.62 9.89
Table 7~5: Limiting activity coefficients at different temperatures for the system n-hexane (1) + NMP (2) obtained using the SCT.
."
• ."
<
~ iE
•
0n'
"
~i '"
tI <
~ c
.. ,
~ ."
V 28
Activity coefficients at infinte dilution for the system n-hexane (1) + NMP (2) at different temperatures
" "
Temperature rC)" "
_ DCT merature data _ DCT experimental data _ SCT experimental data
"
Figure 7·8: Activity coefficients at infinite dilution for the system n-hexane (1) + NMP (2) using the SCT and OCT, and compared to literature data for the DCT by Krummen et al.
(2004).
The limiting activity coefficients determined using the SeT is similar to that for the OCT. This shows that the SCT works just as well as the DCT for systems where solvent volatility is low and solute volatility is high. The difference in the experimental values of y""from published literature
values of Krummen et a1. (2004) is shown in Figure 7-8. These graphs show how close the experimental results are in comparison to published literature data for the OCT.
Both techniques seem to work just as well and have deviations in ...,~ from each other and from literature values of less than 1 %. A sensitivity analysis was performed to check the effect small deviations in the measurable variables would have on the limiting activity coefficient. The results of this are discussed in Chapter 8. Systems involving n-hexene, o-cresol and NMP in different combinations were further attempted and the results of which can be found in Part 2 of Chapter 7. The next
two
sections deal with limiting activity coefficients calculated from equations proposed by other researchers using the same experimental data.7.2 Limiting Activity Coefficients - Leroi et al. (1977), Ouhem and Vldal (1978) and Boa and Han (1995)
In this section activity coefficients at infinite dilution were evaluated using Equations 6.23, 6.24, 6.29 and 6.33 which are the Leroi et al. (1977) based equations. They are used to evaluate limiting activity coefficient for the same test systems as above. All these equations were derived for the determination of limiting activity coefficients for use with the inert gas stripping technique by various researchers already mentioned. Limiting activity coefficients are evaluated for the test systems using the four equations and compared with ...,~ calculated from Equation 6.55 and the literature data of Krummen et al. (2004). Limiting activity coefficients as a result of different inert gas flow rates, evaluated using the four equations for the test system cyc10hexane (1) + NMP (2) can be found in Table 7-6.
7.2.1 Results for the test system: cyclohexane (1) + NMP (2)
Experimental Conditions limiting Activity Coefficients Calculated Using Equation
D (ml/mln) T rC) 6.55 6.23 6.24 6.29 6.33
5.83 50.16 6.67 6.63 6.62 6.62 6.62
12.65 50.16 6.67 6.63 6.62 6.62 6.62
24.43 50.23 6.65 6.61 6.60 6.60 6.60
34.59 50.17 6.68 6.64 6.62 6.63 6.63
47.47 50.30 6.64 )6.60 6.58 6.59 6.59
Table 7-6: Limiting activity coefficients at various inert gas flow rates and at constant temperature for the four Leroi et al. (1977) based equations.
Chapter 7 Part I
Equations 6.23, 6.24, 6.29 and 6.33 predict limiting activity coefficients that are similar to that determined above using Equation 6.55. All the y~ determined using the four Leroi et at (1977) based equations are slightly lower than that determined by Equation 6.55 and the literature value of 6.7 at 50.2 ·C by Krummen et at (2004). The difference between the experimental y~ is however not greater than 0.91 % and not greater than 1.79 % when compared to literature values. The nitrogen gas flow rate appears to have no significant affect on y~ at the experimental conditions concerned. The effect temperature has on the y~ for the system cyclohexane (1) + NMP (2), as predicted by the Equations 6.23, 6.24, 4.6 and 6.33, is shown in Table 7-7.
Experimental Conditions Limiting Activity Coefficients Calculated Using Equation
T ("C) D (ml/mln) 6.55 6.23 6.24 6.29 6.33
30.08 14.89 7.77 7.74 7.74 7.73 7.74
40.03 11.77 7.21 7.15 7.15 7.14 7.15
50.16 12.65 6.73 6.63 6.68 6.68 6.68
60.06 11.77 6.20 6.17 6.14 6.15 6.15
Table 7-7: Limiting activity coefficients calculated using Equations 6.23, 6.24, 6.29 and 6.33 for different temperatures and compared to limiting activity coefficients calculated
using Equation 6.55, derived by Krummen et at (2000).
The limiting activity coefficients calculated using Equations 6.23, 6.24, 6.29 and 6.33 have good agreement with each other and are all lower, although close to the literature values and to those values calculated using Equation 6.55. The greatest deviation in the calculated values from the four Leroi et al. (1977) based equations and Equation 6.55 is 1.48 %. Between the four equations themselves the deviation is only 0.75 %. A clearer indication of how close the values really are is shown in Figure 7-9.
Figure 7 -g shows that the limiting activity coefficients determined using the well known Equations 6.23 and 6.24 derived by Leroi et al. (1977) are very good. Even the simplest of the equations (Equation 6.23) gives values that are in good agreement with the more complex ones.
Duhem and Vidal, and Boa and Han's slightly more complex equations (Equations 6.29 and 6.33) also give acceptable values for the system cyctohexane (1) + NMP (2). Equations 6.24 and 6.33 are for use with volatile solvents, but the results are as justifiable as the more appropriate Equations 6.23 and 6.29 which were derived specifically for non-volatile solvents. A non-volatile solvent is classified here as a solvent whose vapour pressure is less than 1 mmHg under all experimental temperatures and pressures of concern, which was true for all the solvents used.