Untitled - Technische Universiteit Eindhoven

More documents

Recommendations

Info

7.4. Results and discussion 111and the rock sample, that is crushed during bending, leading to a decrease in deflectionof the sample and relaxation of the load. In case the gel layer is weak and compliant withrespect to the rock then the pre-loading method applied in the experiments should preventthis problem. The high loads obtained in the experiments also suggest that the load isnot borne by a weak gel layer. However, if the layer is dense and has a modulus similarto the rock the pushrod would still effectively bend the rock sample and produce the highloads. Since the gel layer is thin, it would not directly contribute to the total stress, henceload, in terms of the elastic and hydrodynamic effects. Still, the fast relaxation of the loadmay be due to a fast deformation of the gel layer in contact with the pushrod and thesupports, resulting in a decreasing strain in the rock sample. The effect of this apparentslip mechanism or real slip at the surface is analyzed theoretically in Appendix C.In the ideal situation the gel would completely fill the pore space of the rock. Theoverall permeability of the rock sample would be equal to or smaller than the intrinsicpermeability of the gel. To a first-order approximation the permeability would equal theintrinsic permeability of the gel times the porosity (about 0.2) of the rock. Ideally, uponbending the hydrodynamic relaxation would be described by Eq. 7.4 with an A value ofabout 0.04. Given the intrinsic permeability of the gels, the corresponding relaxation timeτ R would be about 1×10 4 s for the rock samples treated with acid-catalyzed gel (seriesA) and τ R would be about 1×10 3 s for the rock samples treated with base-catalyzed gel(series B). The inflection point, demarcating the final plateau of R, is found at t ≈ 0.2τ R .The relaxation data of the rock samples in series B (see Figure 7.7) show a clearinflection point between 10 and 100 seconds. Despite the high degree of relaxation atthe inflection points for the samples with φ Si = 0.084 or φ Si = 0.097, the relaxationcurves were successfully fitted with the common expressions for hydrodynamic and VErelaxation (Eqs. 7.4 and 7.10), which is demonstrated in Figure 7.7. The extractedparameters D and A are given in Table 7.3. For the two samples with φ Si = 0.071 theamount of hydrodynamic relaxation A corresponds well with the estimated value of 0.04.The extracted permeability varies between 14 to 94 nm 2 without a clear correlation tothe estimated silica concentration of the gel inside the rock samples. The estimated silicaconcentration is based on the initial TMOS concentration as it was for the gel rods, butnot corrected for shrinkage. TMOS concentrations were similar for the gels rods as forthe treated rock samples. The overall permeability of the rock samples treated with basecatalyzedgel appears to be at least equal or slightly higher than the intrinsic permeabilityof the corresponding gel rods. Therefore, the gel does not completely fill all of the pores.Also the relaxation data of the rock samples in series A were fitted with the expressionsfor hydrodynamic and VE relaxation. Again, for the two samples with φ Si = 0.071 thecurve fit was adequate yielding values for A of about 0.05, and a permeability of 59 ±7 nm 2 , respectively, 95 ± 13 nm 2 . For the higher concentration samples the fit of therelaxation curves was less accurate. As can be observed in Figure 7.6 the inflection pointsin the fitted curves do not agree well with the inflection points in the measured loadcurves. The extracted permeability for these samples ranges between 8 and 112 nm 2 ,but these values can only indicate the order of magnitude. Compared to the intrinsicpermeability of the acid-catalyzed gel rods the overall permeability of the rock samples ishigher. However, at a given TMOS concentration the gel rods exhibited a high degree of
112 7. Permeability reduction in porous materials by in situ formed silica gelcontraction and pore size reduction. The order of magnitude of the permeability foundin series B is comparable to the values found in series A.7.5 ConclusionThe intrinsic permeability and elastic modulus of various TMOS-based silica alcogelswere successfully measured with the method of beam bending. Addition of sodiumchloride,up to 80 mMolal, and the pH of the solution had no significant effect on themodulus, whereas increasing curing and aging times resulted in increased moduli. Thepermeabilities decreased with increasing silica fraction and aging time. The permeabilityof the acid-catalyzed gels was on the order of 1 nm 2 . The base-catalyzed gels yieldedpermeabilities 10 to 100 times higher in magnitude than the acid-catalyzed gels, which isnot exclusively attributed to the lower silica fractions of the acid-catalyzed gels, but alsoto the difference in pore structure of the network. Untreated Bentheim sandstone exhibitsa significant viscoelastic behavior upon bending, which is due to slip between the grainsand the low amount of siliceous cement. The permeability of rock samples treated withbase-catalyzed gel is on the order of 10 to 100 nm 2 without a clear correlation to the silicadensity of the gel, and is at least as high as the intrinsic permeability of the correspondinggel samples. The permeability of the rock samples treated with acid-catalyzed gel wasdetermined less accurately, but is on the same order of magnitude as for the alkaline series.The findings imply that the gel is not uniformly distributed in the pore space, and thatthe effectiveness of the treatment varies between the samples, but is insensitive to thepH and concentration of the gelling solution. Compared to the untreated rock the overallpermeability is reduced by a factor of at least 10 4 , so that the gel adequately blocks thepores.
Page 2:
TWO-PHASE REACTIVE TRANSPORTOF AN O
Page 5 and 6:
Dit proefschrift is goedgekeurd doo
Page 7 and 8:
4. The effect of pH on mass transfe
Page 9 and 10:
Samenvatting . . . . . . . . . . .
Page 11 and 12:
2 1. Introductionproducerbarrierlow
Page 13 and 14:
4 1. IntroductionTwo inter-European
Page 16:
Part ITwo-phase bulk systems7
Page 19 and 20:
10 2. Coupled mass transfer and sol
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
32 3. Interfacial effects during re
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
0+,44 4. The effect of pH on mass t
Page 55 and 56:
46 4. The effect of pH on mass tran
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
58 5. Cross-linking of silica with
Page 69 and 70: 60 5. Cross-linking of silica with
Page 71 and 72: 0+,62 5. Cross-linking of silica wi
Page 84: Part IIGel placement in porous mate
Page 87 and 88: 78 6. Coupled mass transfer and gel
Page 107 and 108: 98 7. Permeability reduction in por
Page 109 and 110: 100 7. Permeability reduction in po
Page 119: 110 7. Permeability reduction in po
Page 123 and 124: 114 8. Model of reactive transport
Page 141 and 142: 132 9. Concluding remarks and outlo
Page 149 and 150: 140
Page 151 and 152: -142 Appendix A, - C D *, - D
Page 153 and 154: 144 Appendix Awhere S 0 is a consta
Page 155 and 156: 146 Appendix AThe 0.95 Tesla scanne
Page 157 and 158: 148 Appendix B
Page 159 and 160: 150 Appendix CwhereΩ A (θ) = −2
Page 161 and 162: 152 Appendix C
Page 163 and 164: 154 Appendix D
Page 165 and 166: 156 Appendix Eand equal to zero in
Page 167 and 168: 158 Appendix EAs the saturations, d
Page 169 and 170: 160 Bibliography[12] B. Vinot, R. S
Page 171 and 172:
162 Bibliography[40] M. D. Mantle a
Page 173 and 174:
164 Bibliography[70] F. J. M. van d
Page 175 and 176:
166 Bibliography[97] K. Yoshida, A.
Page 177 and 178:
168 Bibliography[127] G. W. Scherer
Page 179 and 180:
170 Bibliography
Page 181 and 182:
172 Summaryand gelation rates. The
Page 183 and 184:
174 Samenvattingwaterfase. De T 1 v
Page 185 and 186:
176 List of publications
Page 187 and 188:
178 Dankwoordimmer opgewekte stemmi
Page 189:
Prior to the speech, Harald Cramér
show all

Untitled - Technische Universiteit Eindhoven

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?