Untitled - Technische Universiteit Eindhoven

More documents

Recommendations

Info

7.4. Results and discussion 109Table 7.3: Properties of the treated sandstone samples. φ Si is the estimated volume fraction ofsilica assuming full hydrolysis and condensation, without correction for shrinkage.The thickness of the plates is given by 2a. The superscript b is used to indicate theduplicate samples prepared with the same gelling solutions as the complementarysamples (see Section 7.3.2). The uncertainties in E p , D and A are based on thequality of the fits.series φ Si pH 2a E p [GPa] D [nm 2 ] A [-][± 0.05 mm]A 0.071 3.1 10.00 9.3 ± 0.3 59 ± 7 0.049 ± 0.0020.071 b 3.1 9.80 8.5 ± 0.1 95 ± 13 0.047 ± 0.0010.084 3.1 8.92 11.3 ± 0.5 112 ± 15 0.110 ± 0.0040.084 b 3.1 8.05 10.1 ± 0.1 20 ± 2 0.097 ± 0.0020.097 3.1 9.40 11.6 ± 0.2 8 ± 1 0.166 ± 0.0050.097 b 3.1 9.70 10.6 ± 0.2 91 ± 12 0.160 ± 0.005B 0.071 8.8 10.00 14.8 ± 0.1 94 ± 9 0.044 ± 0.0010.071 b 8.8 9.70 14.4 ± 0.1 56 ± 5 0.042 ± 0.0010.084 8.8 9.42 15.4 ± 0.2 52 ± 4 0.071 ± 0.0010.097 8.8 8.90 10.7 ± 0.3 14 ± 1 0.226 ± 0.0020.097 b 8.8 10.10 11.1 ± 0.2 50 ± 4 0.153 ± 0.003with increasing (estimated) φ Si . The total amount of hydrodynamic relaxation A, whichis independent of the permeability, can be approximated using Eq. 7.7. Poisson’s ratio isunknown, but we used ν p = 0.25, which is a good estimate for sedimentary rocks [139].The elastic modulus E p is about 10 GPa, so that K p = 6.7 GPa. The solid fraction isρ ≈ 0.8, and therefore K S ≈ 10.5 GPa. Calculation of A then yields a value of 0.04.Using the estimated maximum of A and the measured initial load values, the moduli ofthe treated samples were determined. The results are listed in Table 7.3. The samples inseries A have an average modulus of 10 ± 1 GPa. Three of the samples in series B show ahigher modulus of about 15 GPa, whereas the other two have a modulus of about 11 GPa.Compared to moduli of the untreated rock samples the moduli are at least as high and insome cases almost 50 % higher with respect to the dry rock. However, the treated rocksamples contain a gelled solution. Though the presence of a liquid, especially water, wouldsoften the rock, the relatively high moduli, extracted from the initial load values, indicatethat the gel reinforces the structure. The high degree of VE relaxation observed in mostof the relaxation curves is attributed to inelastic behavior of the combined sandstone-gelsystem upon deflection. The apparent correlation between increasing silica fraction φ Siand the overall magnitude of relaxation may be explained by two mechanisms.First of all, the correlation suggests that the reinforcement effect of the gel becomesweaker with increasing φ Si . Presumably, the gel is more susceptible to syneresis and lossof adhesion during bending of the sample when φ Si is high [24]. The effective moduluswould decrease rapidly and result in an apparent strong VE behavior. Secondly, therecould be a thin layer of gel on the upper surface of the sample, lying between the pushrod
110 7. Permeability reduction in porous materials by in situ formed silica gel1.0510.950.9normalized load0.850.80.750.70.65φ Si= 0.071φ Si= 0.071 bφ Si= 0.084φ Si= 0.084 bφ Si= 0.097φ Si= 0.097 b0.610 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6time [s]Fig. 7.6: Normalized load measured in beam bending experiments on gel treated sandstonesamples (series A, acid-catalyzed gel). The estimated silica fraction of the gels is givenin the legend. The superscript b is used to indicate the duplicate samples preparedwith the same gelling solutions as the complementary samples. The solid curvesrepresent the fits using the combined hydrodynamic and VE relaxation function.1.0510.950.9normalized load0.850.80.750.70.65φ Si= 0.071φ Si= 0.071 bφ Si= 0.084φ Si= 0.097φ Si= 0.097 b0.610 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6time [s]Fig. 7.7: Normalized load measured in beam bending experiments on gel treated sandstonesamples (series B, base-catalyzed gel). The estimated silica fraction of the gels is givenin the legend. The superscript b is used to indicate the duplicate samples preparedwith the same gelling solutions as the complementary samples. The solid curvesrepresent the fits using the combined hydrodynamic and VE relaxation function.
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 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 117: 108 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?