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90 6. Coupled mass transfer and gelation of TMOS in porous materialsTable 6.3: Fit results for the mass transfer rate α T and the gelation rate κ.label buffer (pH) T [ ◦ C] α T [h −1 ] κ [h −1 ]A01 no buffer 25 0.61 ± 0.03 1.78± 0.05A02 no buffer 50 1.17 ± 0.03 4.3 ± 0.1A03 no buffer 25 0.50 ± 0.02 2.92 ± 0.09A04 no buffer 50 0.89 ± 0.02 2.8 ± 0.2A05 2.84 25 8.1 ± 0.8 0.21 ±0.01A06 2.84 50 > 20 1.51 ± 0.07A07 6.20 25 0.54 ± 0.01 4.8 ±0.3A08 6.20 50 0.94 ± 0.04 9 ± 2A09 9.48 25 0.75 ± 0.02 1.34 ± 0.09A10 9.48 50 2.9 ± 0.3 1.8 ± 0.3B01 no buffer 25 0.33 ± 0.02 0.52 ± 0.01B02 no buffer 50 > 20 0.50 ± 0.02which would correspond to a concentration of φ T = 0.03. The final plateaus observed inthe uncorrected concentration profiles of φ T , for all experiments, lie between φ T = 0.02and φ T = 0.07. It was found in two-phase bulk experiments (see Chapters 2 and 4) thatthe TMOS continues to transfer from the oleic to the aqueous phase even when gelationof the aqueous phase has already occurred. Assuming that the transfer of the TMOS inthe porous material also tends to a complete transfer the high plateaus of φ T are causedby apparently high values of T 1 due to the contribution of hydrogen in the aqueous phase.Mass transfer ratesIn order to characterize the mass transfer rate of TMOS during the shut-in period theobtained time dependences of the concentration profiles for all slices were combined to asingle time dependence and smoothed. This yields a profile that represents an averageprofile for the experiment. Subsequently, the average profile is fitted with a first-orderexponential decay function, given byφ T (t) = A exp(−α T t) + B, (6.3)where A is the initial concentration, α T is the mass transfer rate, and B is an offset. Theaverage profiles for experiments A03, A05, A07 and A09 (which were done at 25 ◦ C) aregiven in Figure 6.10. Again, the concentration profiles show a non-zero plateau, due tothe presence of 1 H in the aqueous phase, which affects the measurement of φ T . Exceptfor experiment A07 the initial points of the concentration profiles are well below φ T =0.20, which is probably due to a high mass transfer rate during injection of the chemicalbefore the shut-in period. For now we focus on the typical mass transfer rate duringshut-in. The profiles are adequately fitted with the exponential decay function (Eq. 6.3).The resulting mass transfer rates α T for all experiments are listed in Table 6.3. At 25◦ C the mass transfer rate is on the order of 0.5 h −1 for all experiments except A05, forwhich the mass transfer rate is 8.1 ± 0.8 h −1 . The mass transfer is driven by the degree