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4.4. Results and discussion 51Table 4.3: Results of the least-square fit on the relaxation time data (for deuterium) of thecalibration gels using Eq. 4.6 and the approximation for f s . The surface relaxationterms, T 2,s , are given for each series at both temperatures.pH T [ ◦ C] T 2,s [ms]no buffer 25 1.33 ± 0.0450 0.70 ± 0.062.95 25 0.57 ± 0.0450 0.31 ± 0.015.50 25 0.41 ± 0.0650 0.33 ± 0.049.48 25 0.21 ± 0.0250 0.18 ± 0.021.21.00 vol%20 vol%40 vol%0.8T 1[s]0.60.40.20.00 5 10 15 20 25 30 35 40 45 50 55Temperature [°C]Fig. 4.5: Average relaxation time T 1 of hydrogen in TMOS/Isopar V (oil) mixtures as a functionof temperature. The concentration of TMOS is indicated in the legend.
52 4. The effect of pH on mass transfer and gelation654no bufferpH = 2.95pH = 5.50pH = 9.48n o[mmol]32100 5 10 15time [h]Fig. 4.6: Concentration of TMOS in the oleic phase as a function of time. The temperaturewas controlled to 25 ◦ C. The type of buffer used is indicated in the legend. The solidcurves are the fitted concentration profiles using the optimization described in Section4.2.initial volume fraction φ T (0) equal to 0.35, are shown in Figure 4.6. For the pH = 9.48 case,initially, the number of molecules n o is close to the initial number (n o (0) = 5.88 mmol) afterwhich it drops gradually to almost zero within 15 hours. The unbuffered system shows asimilar but faster decay, and the concentration is almost zero within 5 hours. The lowerpH system (pH = 2.95) shows the fastest decay, and the mass transfer is complete within2 hours. The lowest mass transfer rate was observed in the intermediate pH system(pH = 5.50). The mass transfer is complete only after 40 hours. Test experiments intransparent vials revealed that a weak and turbid gel was formed quickly within 2 hoursin the intermediate pH systems, despite the limited transfer of TMOS within the initial 2hours. Still, the TMOS transfers completely to the aqueous phase, and the gel does notappear to form an impermeable barrier.The concentration profiles of all bulk experiments were fitted by optimizing the solutionof Eq. 4.5, modified to include an additional offset, and show a good fit, except atsmall times. Due to the instant partitioning in the model the fitted profiles tend tostart below the real initial concentration. From the fits the hydrolysis rate k and theinteraction parameter ε 0 were derived, all of which are listed in Table 4.4. Ideally, thederived hydrolysis rate k and interaction parameter ε 0 should be independent of the initialconcentration of TMOS used in the experiment. For most of the experiments the valuesagree within a factor of 2 with respect to φ T (0) = 0.20, respectively φ T (0) = 0.35. Theresults for the pH = 2.95 system show a bigger discrepancy. Nevertheless, considering thesimplicity of the model, the results are satisfactory and reveal qualitatively the effect ofpH on the hydrolysis rate, which in turn drives the mass transfer. The hydrolysis ratek is on the order of 10 −5 to 10 −3 s −1 . Increasing the temperature always resulted in an
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TWO-PHASE REACTIVE TRANSPORTOF AN O
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Dit proefschrift is goedgekeurd doo
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4. The effect of pH on mass transfe
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102 7. Permeability reduction in po
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114 8. Model of reactive transport
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132 9. Concluding remarks and outlo
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140
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-142 Appendix A, - C D *, - D
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144 Appendix Awhere S 0 is a consta
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146 Appendix AThe 0.95 Tesla scanne
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148 Appendix B
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150 Appendix CwhereΩ A (θ) = −2
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152 Appendix C
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154 Appendix D
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156 Appendix Eand equal to zero in
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158 Appendix EAs the saturations, d
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160 Bibliography[12] B. Vinot, R. S
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162 Bibliography[40] M. D. Mantle a
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164 Bibliography[70] F. J. M. van d
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166 Bibliography[97] K. Yoshida, A.
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168 Bibliography[127] G. W. Scherer
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170 Bibliography
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172 Summaryand gelation rates. The
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174 Samenvattingwaterfase. De T 1 v
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176 List of publications
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178 Dankwoordimmer opgewekte stemmi
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Prior to the speech, Harald Cramér
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