Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination
Abstract
1. Introduction
2. Materials and Methods
2.1. Materials and Membrane Preparation
2.2. Gas permeation Tests
2.2.1. Data Analysis by the Tangent Method for Both Instruments
2.2.2. Fitting Method for a Constant Volume/Pressure Increase Instrument
2.2.3. Fitting Method for a Variable Volume/Constant Pressure Instrument
3. Results and Discussion
3.1. Single Gas Transport
3.2. Mixed Gas Transport
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Tangent Method | Fitting Method | Difference % (Fitting-Tangent) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Gas | pFeed | P | Θ | D | S | P | Θ | D | S | P | Θ | D | S |
O2 | 1200 | 3.10 | 888 | 4.22 | 0.551 | 3.09 | 861 | 4.36 | 0.53 | −0.48 | −3.10 | 3.20 | −3.57 |
1000 | 3.11 | 893 | 4.20 | 0.554 | 3.10 | 878 | 4.27 | 0.54 | −0.31 | −1.62 | 1.65 | −1.93 | |
850 | 3.11 | 892 | 4.20 | 0.555 | 3.10 | 878 | 4.27 | 0.54 | −0.28 | −1.62 | 1.65 | −1.90 | |
680 | 3.12 | 893 | 4.20 | 0.557 | 3.11 | 875 | 4.29 | 0.54 | −0.35 | −2.01 | 2.06 | −2.35 | |
520 | 3.14 | 900 | 4.17 | 0.565 | 3.12 | 871 | 4.31 | 0.54 | −0.40 | −3.20 | 3.31 | −3.59 | |
350 | 3.17 | 881 | 4.25 | 0.558 | 3.15 | 855 | 4.39 | 0.54 | −0.40 | −3.00 | 3.09 | −3.39 | |
180 | 3.24 | 851 | 4.41 | 0.552 | 3.23 | 822 | 4.56 | 0.53 | −0.34 | −3.42 | 3.55 | −3.75 | |
100 | 3.36 | 838 | 4.47 | 0.563 | 3.52 | 788 | 4.76 | 0.55 | 4.61 | −5.96 | 6.34 | −1.63 | |
N2 | 1200 | 1.16 | 1514 | 2.48 | 0.351 | 1.15 | 1449 | 2.59 | 0.33 | −0.51 | −4.27 | 4.46 | −4.75 |
1000 | 1.15 | 1533 | 2.45 | 0.353 | 1.15 | 1496 | 2.51 | 0.34 | −0.34 | −2.46 | 2.52 | −2.79 | |
850 | 1.16 | 1542 | 2.43 | 0.356 | 1.15 | 1494 | 2.51 | 0.34 | −0.39 | −3.10 | 3.20 | −3.48 | |
680 | 1.16 | 1549 | 2.42 | 0.359 | 1.15 | 1487 | 2.52 | 0.34 | −0.43 | −4.06 | 4.23 | −4.47 | |
520 | 1.17 | 1556 | 2.41 | 0.365 | 1.17 | 1483 | 2.53 | 0.35 | −0.53 | −4.67 | 4.90 | −5.18 | |
350 | 1.20 | 1554 | 2.41 | 0.372 | 1.19 | 1454 | 2.58 | 0.35 | −0.67 | −6.45 | 6.90 | −7.08 | |
180 | 1.29 | 1554 | 2.41 | 0.400 | 1.27 | 1364 | 2.75 | 0.35 | −1.05 | −12.3 | 14.0 | −13.2 | |
100 | 1.48 | 1258 | 2.98 | 0.373 | 1.45 | 1072 | 3.50 | 0.31 | −2.34 | −14.8 | 17.3 | −16.8 | |
CH4 | 1200 | 3.79 | 1924 | 1.95 | 1.46 | 3.71 | 1654 | 2.27 | 1.23 | −2.11 | −14.0 | 16.3 | −15.8 |
1000 | 3.80 | 1972 | 1.90 | 1.50 | 3.72 | 1698 | 2.21 | 1.26 | −2.18 | −13.9 | 16.1 | −15.8 | |
850 | 3.80 | 1998 | 1.88 | 1.52 | 3.75 | 1796 | 2.09 | 1.35 | −1.36 | −10.1 | 11.3 | −11.3 | |
680 | 3.81 | 2054 | 1.83 | 1.57 | 3.72 | 1737 | 2.16 | 1.29 | −2.58 | −15.5 | 18.3 | −17.6 | |
520 | 3.83 | 2088 | 1.80 | 1.60 | 3.77 | 1857 | 2.02 | 1.40 | −1.5 | −11.1 | 12.5 | −12.4 | |
350 | 3.88 | 2219 | 1.69 | 1.72 | 3.75 | 1793 | 2.09 | 1.35 | −3.36 | −19.2 | 23.8 | −21.9 | |
180 | 4.04 | 2352 | 1.59 | 1.90 | 3.88 | 1869 | 2.01 | 1.45 | −3.84 | −20.5 | 25.8 | −23.6 | |
100 | 4.20 | 2366 | 1.59 | 1.99 | 4.12 | 2064 | 1.82 | 1.70 | −1.94 | −12.8 | 14.6 | −14.5 | |
H2 | 1200 | 7.73 | 56.8 | 66.0 | 0.088 | 7.71 | 53.9 | 69.6 | 0.083 | −0.24 | −5.06 | 5.33 | −5.28 |
1000 | 7.73 | 58.6 | 63.9 | 0.091 | 7.72 | 58.1 | 64.5 | 0.09 | −0.09 | −0.91 | 0.92 | −1.00 | |
850 | 7.75 | 59.7 | 62.8 | 0.093 | 7.74 | 58.8 | 63.8 | 0.091 | −0.18 | −1.52 | 1.55 | −1.70 | |
680 | 7.76 | 61.1 | 61.3 | 0.095 | 7.75 | 59.4 | 63.1 | 0.092 | −0.18 | −2.82 | 2.9 | −2.99 | |
520 | 7.77 | 60.7 | 61.8 | 0.094 | 7.72 | 58.1 | 64.5 | 0.09 | −0.60 | −4.25 | 4.44 | −4.83 | |
350 | 7.80 | 60.5 | 61.9 | 0.094 | 7.75 | 57.1 | 65.7 | 0.089 | −0.63 | −5.67 | 6.01 | −6.26 | |
180 | 7.87 | 61.8 | 60.7 | 0.097 | 7.83 | 57.5 | 65.2 | 0.09 | −0.50 | −6.91 | 7.42 | −7.38 | |
100 | 8.30 | 57.3 | 65.5 | 0.095 | 8.27 | 51.5 | 72.9 | 0.085 | −0.40 | −10.2 | 11.3 | −10.5 | |
He | 1200 | 5.27 | 18.7 | 200 | 0.020 | 5.21 | 18.6 | 201 | 0.019 | −1.19 | −0.46 | 0.46 | −1.64 |
1000 | 5.29 | 18.9 | 198 | 0.020 | 5.22 | 18.8 | 200 | 0.02 | −1.42 | −0.83 | 0.83 | −2.24 | |
850 | 5.27 | 18.6 | 202 | 0.020 | 5.26 | 19.3 | 195 | 0.02 | −0.14 | 3.64 | −3.52 | 3.50 | |
680 | 5.11 | 19.7 | 190 | 0.020 | 5.14 | 20.3 | 185 | 0.021 | 0.56 | 2.81 | −2.73 | 3.39 | |
520 | 5.18 | 17.5 | 214 | 0.018 | 5.34 | 19.8 | 190 | 0.021 | 2.98 | 12. 7 | −11.2 | 16.0 | |
350 | 5.57 | 19.7 | 190 | 0.022 | 5.46 | 18.3 | 205 | 0.02 | −2.05 | −7.03 | 7.56 | −8.94 | |
180 | 5.49 | 19.7 | 191 | 0.022 | 5.63 | 18.7 | 200 | 0.021 | 2.61 | −4.87 | 5.11 | −2.38 | |
100 | 6.33 | 19.0 | 197 | 0.024 | 6.17 | 20.0 | 188 | 0.025 | −2.56 | 4.94 | −4.71 | 2.26 | |
CO2 | 1200 | 65.8 | 784 | 4.78 | 10.3 | 66.0 | 801 | 4.68 | 10.6 | 0.38 | 2.22 | −2.18 | 2.61 |
1000 | 65.3 | 838 | 4.48 | 10.9 | 65.5 | 870 | 4.31 | 11.4 | 0.27 | 3.88 | −3.74 | 4.16 | |
850 | 65.3 | 891 | 4.21 | 11.6 | 65.4 | 917 | 4.09 | 12.0 | 0.13 | 2.93 | −2.85 | 3.07 | |
680 | 65.1 | 944 | 3.97 | 12.3 | 65.2 | 973 | 3.85 | 12.7 | 0.22 | 3.16 | −3.06 | 3.39 | |
520 | 65.1 | 1023 | 3.66 | 13.3 | 65.2 | 1048 | 3.58 | 13.7 | 0.13 | 2.45 | −2.39 | 2.58 | |
350 | 65.1 | 1123 | 3.34 | 14.6 | 64.7 | 1142 | 3.28 | 14.8 | −0.49 | 1.65 | −1.63 | 1.15 | |
180 | 64.8 | 1308 | 2.87 | 16.9 | 64.5 | 1325 | 2.83 | 17.1 | −0.41 | 1.32 | −1.31 | 0.91 | |
100 | 64.6 | 1513 | 2.48 | 19.5 | 64.0 | 1515 | 2.48 | 19.4 | −0.83 | 0.10 | −0.10 | −0.73 | |
C2H6 | 1000 | 9.15 | 154 | 24.4 | 0.28 | 9.07 | 142 | 26.3 | 0.26 | −0.87 | −7.79 | 7.79 | −7.14 |
Appendix B
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Tangent Method | Fitting Method | ||||||||
---|---|---|---|---|---|---|---|---|---|
Gas | P | D | S | P1 | P2 | D1 | D2 | S1 | S2 |
CH4 | 3.79 | 1.95 | 1.46 | 1.66 | 2.11 | 13.5 | 1.19 | 0.09 | 1.32 |
C2H4 | 14.4 | 0.87 | 12.4 | 6.49 | 7.93 | 15.6 | 0.48 | 0.31 | 12.3 |
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Fuoco, A.; Monteleone, M.; Esposito, E.; Bruno, R.; Ferrando-Soria, J.; Pardo, E.; Armentano, D.; Jansen, J.C. Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination. Computation 2020, 8, 28. https://doi.org/10.3390/computation8020028
Fuoco A, Monteleone M, Esposito E, Bruno R, Ferrando-Soria J, Pardo E, Armentano D, Jansen JC. Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination. Computation. 2020; 8(2):28. https://doi.org/10.3390/computation8020028
Chicago/Turabian StyleFuoco, Alessio, Marcello Monteleone, Elisa Esposito, Rosaria Bruno, Jesús Ferrando-Soria, Emilio Pardo, Donatella Armentano, and Johannes Carolus Jansen. 2020. "Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination" Computation 8, no. 2: 28. https://doi.org/10.3390/computation8020028
APA StyleFuoco, A., Monteleone, M., Esposito, E., Bruno, R., Ferrando-Soria, J., Pardo, E., Armentano, D., & Jansen, J. C. (2020). Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination. Computation, 8(2), 28. https://doi.org/10.3390/computation8020028