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Chapter 2Coupled mass transfer and sol-gel reaction in atwo-phase bulk system ∗NMR imaging and relaxation time measurements were employed to monitor the masstransfer of TMOS from the oleic to the aqueous phase in a two-phase bulk system.The longitudinal relaxation time (T 1 ) was calibrated and used to determine the concentrationof TMOS in n-hexadecane during the transfer. In the aqueous phase asharp decrease in the transverse relaxation time (T 2 ) is observed which is attributedto the gel reaction. The point at which a minimum (or plateau) in T 2 is found,indicates the gelation point.2.1 IntroductionA method to form silica gels commonly applied is the reaction of alkoxy-silanes withwater according to the sol-gel principle [24]. A recent development is the use of these gelformingcompounds in two-phase systems, where the alkoxy-silane is initially mixed witha hydrocarbon phase. The gelation process involves the transfer of the chemical out of theoleic phase into an aqueous phase. Coupled to the mass transfer a heterogeneous reactiontakes place, resulting in gelation of the aqueous phase. An application of this processwas first proposed by Plazanet and Thomere for the consolidation of sand producingformations during oil recovery [25]. The placement and gelation of the chemical in modelporous systems was analyzed by Thompson and Fogler [20, 42]. In a previous workwe presented a Nuclear Magnetic Resonance (NMR) study of the mass transfer and gelreaction of TMOS in two-phase bulk systems and glass bead packs [43].The gelation process of tetra-methyl-ortho-silicate (TMOS) with water can be describedas follows. Initially, the TMOS hardly mixes with water because of its poorsolubility [24, 34], but when TMOS molecules come in contact with water the followinghydrolysis reaction takes placeSi(OCH 3 ) 4 + 4H 2 O ⇋ Si(OH) 4+ 4CH 3 OH. (2.1)The reaction products, silicic acid and methanol, are easily miscible with water and thepresence of methanol results in an enhanced solubility of TMOS in water. The secondstep is the polymerization or condensation of silicic acid:≡ Si - OH + HO - Si ≡ ⇋ ≡ Si - O - Si ≡ + H 2 O. (2.2)* Adapted from Castelijns et al. , J. Appl. Phys. 100, 024961 (2006)9
10 2. Coupled mass transfer and sol-gel reaction in a two-phase bulk systemThe rate and extent of both reactions are mainly dependent on temperature, pH, andconcentrations [24, 35, 44–46]. The gelation process results in a homogeneous gel consistingof a branched silica network together with (free) water and methanol molecules. Thegel network can be regarded as a percolation of smaller silica clusters that cover a certain(bounded) domain.The gel time of a sol-gel solution can be determined from NMR relaxation measurements(see Appendix A for a short introduction to NMR). Dokter et al. [47] studied thegel reaction in alkaline silica solutions which start to gel after adding acid. They observeda decay in the time-dependent T 2 and the occurrence of a minimum in T 2 near the gelpoint. 2 H-NMR measurements of gelling solutions using deuterated TMOS, water andmethanol were carried out by Wonorahardjo et al. [48]. The longitudinal relaxation timein the rotating frame T 1ρ of the solvents showed a transition in decay rate before and aftergelation.This chapter presents the results of a series of experiments as a detailed extension ofthe previous work [43]. The mass transfer and gelation process were studied in an idealizedsetting, namely in small, two-phase bulk systems. TMOS is mixed with n-hexadecane andplaced in a cylinder together with water, after which the reactive transfer occurs. Theprocess is monitored by means of NMR imaging and relaxation time measurements. Withthis technique the liquids and their spatial distribution are visualized inside the cylinderduring the experiment. The method of NMR imaging is non-intrusive, so that the processis not disturbed by the analysis. The NMR signal obtained in the experiments is sensitiveto the presence of hydrogen nuclei in the liquids. Since the hydrogen densities for theliquids and gels considered are almost equal, the discrimination among the componentsand the contrast in the images cannot be derived from the hydrogen density. SpectroscopicNMR imaging [39] is a useful tool to quantify chemical species, based on chemical shift,but this tool was not used, except for a few test measurements. The reason for this is thatthe magnetic field homogeneity in the set-up was not sufficient to allow for discriminationamong the different -CH species. Secondly, when studying the reactive transport in porousmaterials, the presence of pore-scale magnetic gradients [49] would cause an additionalline broadening. Instead, we developed an approach which is based on the relaxation timesT 1 and T 2 of the hydrogen nuclei. It is noted that in our methods the NMR signal andrelaxation times result from the combined NMR response of all hydrogen nuclei, i.e. thechemical shift [39] was not resolved in the frequency domain.It was found empirically [43] that the relaxation times depend on the composition andtemperature of the fluids. The relaxation times are related to the molecular mobilities.Since the viscosity is related to the molecular mobilities, the relaxation times can be correlatedto the viscosity [43], at least for the pure components. By measuring the relaxationtimes of the liquid phases the concentration of TMOS in n-hexadecane can be determined,and also the rate of gelation in water can be characterized. To this end, the relaxationtimes were measured for a series of calibration samples, i.e. n-hexadecane/TMOS mixturesand a set of prepared gel samples.The experiments with the two-phase systems were done at various temperatures, andwith different concentrations of TMOS in n-hexadecane. Typical mass transfer ratesand gel times are derived for each experiment. The gel times acquired with the NMR
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Part IIGel placement in porous mate
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160 Bibliography[12] B. Vinot, R. S
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172 Summaryand gelation rates. The
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