Reactive transport and gel formation in two-phase systems and porous media

    Introduction

Reactive transport phenomena occur in a wide variety of scientific and engineering fields. Coupled mass transfer and chemical reactions are found in chemical reactors, biological cells, soils, etc. An interesting example of reactive flow is found in the application of gel systems in porous rocks, in order to modify the fluid flow properties in the rock, with respect to oil or water. High water-cut during oil and gas production is a world-wide problem, especially in maturing oil fields, and leads to a decline in hydrocarbon production and to water disposal problems. Gel treatments can be applied in the near-well bore region to reduce or block the flow of water into the well.  Gels have also been considered for their potential use as a barrier to contaminant transport in groundwater.

A novel type of gelant was introduced by Thompson and Fogler,that can be mixed with oil, and reacts upon contact with water to form a gel in the water phase. This gelant, TMOS or Si(OCH3)4, reacts with water as according to the sol-gel principle:

With respect to the application of the gelant in two-phase systems (in bulk or in porous media) the gelant TMOS is initially mixed with oil or a hydrocarbon. Near the oil-water interface the gelant will transfer to the water phase and react with water to form a gel. This process is shown in Figure 1.

Fig. 1. Schematic view of the mass transfer of the gelant from the oil to the water phase
and the subsequent gelation in a bulk system.


    NMR bulk experiments

The coupled mass transfer and gel reactions were studied in bulk systems containing both oil and water. Two series of experiments were performed. The first one was done using n-hexadecane (for the oil phase) and normal water (for the water phase). The reactive transport was monitored using a 4.7 Tesla NMR scanner. The second series was done using a mineral oil and heavy water (D2O) with or without a buffer. In this series the effect of pH on the reactive transport mechanisms was analyzed. These experiments were done using a 0.95 Tesla NMR scanner equipped with a binuclear rf insert. The hardware was custom made to allow for fast toggling between both components.
2D images were acquired, using the 4.7 Tesla scanner, to obtain a qualitative view on the process and to obtain a measure for the rate of mass transfer that is directly indicated by the shift of the oil-water interface. The images are T1-weighted to yield an adequate contrast between water and oil/TMOS (see Figure 2). From these 2D images the interfacial tension between both phases can be determined by employing a detailed image analysis and optimization procedure. Our analysis showed that the interfacial tension changes during the reactive transport. This is relevant with respect to the two-phase flow processes in porous media.


Fig. 2. NMR images of the two-phase bulk system (vertical slice of a cylindrical sample),
acquired at the beginning of the   experiment (left frame), and after 15 hours (right frame).
The upper phase represents the oil/TMOS phase (initial f  = 40 vol%),
and the lower phase represents the (gelled) water  phase.

Additionally, in the bulk systems the concentration of the gelant can be monitored by measuring the T1 of the mixture. For this a calibration of the relaxation time T1 for different concentrations was obtained (see Figure 3). In the second series (with the D2O buffers) it was observed that the change in concentration, i.e. the mass transfer, is driven by the hydrolysis reaction, the rate of which is a strong function of pH and temperature. Figure 4 shows the concentration plots for different pH systems.


Fig. 3. Longitudinal relaxation times (T1) of TMOS/n-hexadecane calibration mixtures
as a function of temperature and volume  fraction.


Fig. 4. Average concentration, no, of TMOS in oil  as a function of time. The experiments were done
with or without a buffer. The pH is indicated in the legend.
The heterogeneous gel reaction in the aqueous phase causes a distinct decline in the transversal relaxation time T2 of the water. This is attributed to the formation of methanol and the formation of the silica network. The T2 decreases and levels off within hours. The time at which the minimum or plateau is reached corresponds to the gelation time of the aqueous phase. Also the gelation rate and gel time appeared to be strongly dependent on the pH and temperature (see Figure 5).


Fig. 5. T2 of the aqueous phase (2H-NMR) in the bulk experiments.. The experiments were done
with or without a buffer. The pH is indicated in the legend.

    NMR experiments on reactive transport in porous materials

Bentheim sandstone cores were prepared to contain oil and water well-distributed throughout the porous network. At residual water or residual oil conditions a few pore volumes of mixture, consisting of TMOS and oil, were injected in the core within minutes. Then during shut-in the concentration of TMOS in the oleic phase is determined at several positions along the core (see Figure 6) for about 48 hours. Simultaneously, the T2 of the aqueous phase is measured, which indicates the rate of gelation. Preliminary results were obtained from some experiments in which the phases and components were separated on the basis of chemical shift. However, the 1H spectra suffer from a significant line-broadening in the natural rocks, which hinders the separation of the components in the NMR signal.


Fig. 6. Schematic of core holder and fluid injection set-up. The slice positions of the NMR measurements are shown in the graph.

A clear distinction between the oleic phase and the aqueous phase in the porous systems is realized by using D2O for the aqueous phase. The signal of the aqueous phase and the relaxation time T2 were measured with 2H-NMR (like in the bulk experiments described above). As an example, the T2 of the 2H content at several positions in a sandstone core is shown in Figure 7. The water-wet core was prepared at  residual oil saturation, such that the oleic phase consisted mainly of oil/TMOS droplets surrounded by D2O.  During shut-in the TMOS transfers from the oleic phase to the aqueous phase. The heteregeneous reaction causes a decrease of T2 of the D2O within the core. Like in bulk, the mass transfer appears to be driven by the hydrolysis reaction. Again, both the hydrolysis and the gel reaction were found to be strongly dependent on the pH and temperature. 


Fig. 7. T2 of the aqueous phase in the sandstone core measured with 2H NMR. The core was  prepared at residual
   oil conditions. The oil initially contains 20 vol% of TMOS. The heteregenous gel reactions result in a marked decline of T2.


    Effect of gel placement on the permeability

Parallel to the NMR experiments with the sandstone cores, as described above, the effect of the gel on the relative permeabilities was determined. This was done by monitoring the differential pressure (see Figure 6) over the cores, while injection oil or water. The results showed that the relative permeability to oil was reduced up to a factor of 3.2. The relative permeability to water was reduced by a factor between 1.9 and 27. For each experiment, the relative permeability to water was reduced more than that to oil. No clear dependence of the reduction on the parameters (pH, temperature) was observed within the range considered. The disproportionate permeability reduction is advantageous for the water shut-off treatments.
A series of beam-bending experiments was performed to study the effect of in situ formed gel (under single phase) conditions on the overall permeability of the sandstone. Beam bending (see Figure 8) is an excellent method to measure the permeability in low-permeable media, such as gels, concrete etc.


Fig. 8. Principle of three-point beam bending.


 First, a series of bending experiments was done on gel rods prepared from TMOS-methanol-water. An example of the load relaxation curve, which is measured in the experiment, is shown in Figure 9. The gels, prepared with an acid buffer and a TMOS concentration of about 10%, have a permeability of about 1 nm2, whereas the base-catalyzed gels have a permeability of about 10-100 nm2. When the sandstone is treated with the gel, under single phase conditions, the permeability of the rock is reduced by a factor of about 10,000. The magnitude of the reduction appeared to be insensitive to the pH and concentration used.

Fig. 9. Example of beam-bending experiment on gel rod. The graph shows the relaxation of the load required to sustain a certain deflection of the beam.
 The hydrodynamic relaxation part exhibits an inflection. The permeability follows from this relaxation time.


Darwish, M.I.M., R.K. Rowe, J.R.C. van der Maarel, L. Pel, H. Huinink, P.L.J. Zitha, Contaminant containment using polymer gel barriers, Canadian Geotechnical J. 41, 106-117 (2004).

Castelijns, H.J., L. Pel, H.P. Huinink, P.L.J. Zitha, Investigation of reactive transport phenomena for modification of two-phase flow  using NMR, conference paper SPE 94559 presented at the 6th SPE European Formation Damage Conference, held in  Scheveningen, the Netherlands, 25-27 May 2005.

Castelijns, H.J., L. Pel, H.P. Huinink, P.L.J. Zitha, Mass transfer and gelation in sandstone cores of a novel water shut-off chemical, conference paper SPE 99684 presented at the 2006 SPE/DOE Symposium on Improved Oil Recovery, held in Tulsa, Oklahoma, USA, 22-26 April 2006. 

Castelijns, H.J., H.P. Huinink, L. Pel, P.L.J. Zitha, Analysis of coupled mass transfer and sol-gel reaction in a two phase system, J. of Applied Physics 100, 024916 (2006).

Castelijns, H.J., H.P. Huinink, P.L.J. Zitha, Characterization of interfacial effects during reactive transport with MRI methods, Colloids & Surfaces A, in press (2007).

Castelijns, H.J., H.P. Huinink, L. Pel, P.L.J. Zitha, The effect of pH on the couples mass transfer and sol-gel reaction in a two-phase system, J. of Physical Chemistry B, accepted (2007).

Castelijns, H.J., G.W. Scherer, L. Pel, P.L.J. Zitha, Permeability reduction in porous materials by in situ formed silica gel, J. of Applied Physics, accepted (2007).