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7.4. Results and discussion 103application of the gel in natural reservoirs, since the water found in most reservoirs issaline. The properties of the gel rods are listed in Table 7.1.Table 7.1: Properties of the gel rods and beam bending results. φ Si is the estimated volumefraction of silica assuming full hydrolysis and condensation, and corrected for thevolume contraction of the gel. The pH listed is the pH of the water used in thehydrolysis reaction. The parameter C S represents the amount of sodium-chloride(NaCl) added to the gelling solution.series φ Si pH C S aging time E p [MPa] D [nm 2 ][mMolal]I 0.113 ± 0.007 3.1 0 43 h 5.9 ± 0.2 1.04 ± 0.060.131 ± 0.008 3.1 0 43 h 12.2 ± 0.5 0.67 ± 0.030.149 ± 0.009 3.1 0 43 h 22.8 ± 0.9 0.38 ± 0.02II 0.123 ± 0.007 3.1 0 91 h 18.6 ± 0.7 0.66 ± 0.030.123 ± 0.007 3.1 40 91 h 15.9 ± 0.6 0.72 ± 0.040.123 ± 0.007 3.1 60 91 h 15.1 ± 0.6 0.76 ± 0.050.123 ± 0.007 3.1 80 91 h 15.5 ± 0.6 0.72 ± 0.04III 0.098 ± 0.005 9.25 0 72 h 6.9 ± 0.3 14.8 ± 0.70.098 ± 0.005 9.25 40 72 h 7.3 ± 0.3 18.2 ± 0.80.098 ± 0.005 9.25 60 72 h 7.0 ± 0.3 26 ± 2IV 0.078 ± 0.004 8.8 0 72 h 1.4 ± 0.1 40 ± 20.092 ± 0.005 8.8 0 72 h 2.9 ± 0.1 28 ± 20.100 ± 0.005 8.8 0 72 h 4.0 ± 0.2 20 ± 1The parameter φ Si is a measure for the total silica content of the alcogels based onthe initial TMOS content and on the assumption that hydrolysis and condensation arecomplete. However, complete condensation implies the silica network would condense intonon-porous quartz, which is not the case. Neither does the estimate account for possiblewashing out of polysiloxane molecules in the exchange process. Still, this measure is usedto indicate the silica content of the gels. The values for φ Si were corrected for volumecontraction effects due to syneresis. Especially the gels prepared with the acid solution(pH = 3.1) showed a significant degree of radial contraction after aging. Because thegels are prone to breaking or cracking when exposed to air or any physical contact thedimensions were not checked rigorously. Instead, the diameter was measured for one ortwo rods per series. The diameter of the acid-catalyzed gels was found to be 10.40 ± 0.10mm after aging, whereas the diameter of the molds was 11.5 ± 0.1 mm. The dimensionswere measured with a digital caliper having an accuracy of ± 10 µm. The diameter ofthe base-catalyzed gels reduced to 11.20 ± 0.10 mm (pH = 9.25), respectively, 11.15 ±0.10 mm (pH = 8.8). The higher degree of shrinkage for the low pH gels compared to thehigh pH gels was also observed by Hdach et al. [124] for similar gels. Although the lengthof the gel rods could not be checked, due to the type of molds used, it is assumed that
104 7. Permeability reduction in porous materials by in situ formed silica gel1.0510.950.9normalized load0.850.80.750.7data0.65 fitVEelastic0.610 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6time [s]Fig. 7.3: Results of beam bending experiment on a gel rod (φ Si = 0.123 ± 0.007, pH = 3.1,no extra salt, aging time 91 hours). The total fit is the product of hydrodynamicrelaxation (dotted line) and viscoelastic (VE) relaxation (dashed line). The numberdensity of the data points of the normalized load, indicated by the circles, is reducedto one-fourth for the sake of clarity.the shrinkage occurred uniformly in all three dimensions. The volume contraction factoris therefore equal to (d final /d initial ) 3 .Relaxation analysisThe data obtained from the beam bending measurements was analyzed in terms of theapplied load versus time. The normalized load of each measurement was plotted andfitted with Eq. 7.9 using the hydrodynamic relaxation expression for cylinders (Eq. 7.1)and the stretched exponential function (Eq. 7.10) for the viscoelastic contribution. Themeasured relaxation and the fit were in excellent agreement for each gel rod. Figure 7.3shows the results for one of the gel rods (φ Si = 0.123 ± 0.007, pH = 3.1, no extra saltadded, aging time 91 hours). It can be observed in this figure that the gel exhibits asignificant degree of VE relaxation, but the effect is only important on a time scale muchlonger than the time scale of the hydrodynamic relaxation and both relaxation effectsare well separated. Similar VE behavior was exhibited by all other gel rods. The VErelaxation is attributed to the presence of water in the pores, and chemical attack of thewater on the present siloxane bonds in the network [126, 135]. Therefore, the exchange ofthe mother liquid with ethanol appears to be incomplete, nevertheless the hydrodynamicrelaxation could readily be extracted from the relaxation data.For the gels the fit yields the following parameters. First, Poisson’s ratio ν p wasdirectly calculated from the amount of hydrodynamic relaxation A resulting from thefit. The average ν p was found to be 0.20 ± 0.02. The modulus E p follows from A and
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TWO-PHASE REACTIVE TRANSPORTOF AN O
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2 1. Introductionproducerbarrierlow
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4 1. IntroductionTwo inter-European
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Part ITwo-phase bulk systems7
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154 Appendix D
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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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