New NMR Methods for Studying Mass Transport Through Porous Media

Abstract

This thesis reports on the use of Pulsed Gradient Spin Echo NMR (PGSE NMR) to study dispersion and flow in porous media. In each of the experiments the medium consists of random bead packs through which water, and other fluids were pumped. Using two pairs of position-encoding pulses in the PGSE experiment gives the possibility of examining velocity fluctuations, by comparing displacements, during the two encoding intervals. In particular Velocity Exchange Spectroscopy (VEXSY) experiments can reveal the gradual transition to asymptotic behaviour as the ratio of the exchange time to the correlation time is increased. Furthermore, the off-diagonal of the VEXSY experiment can be used to directly measure the Velocity Autocorrelation Function (VACF). This can be performed in 1D mode using the compensated Double PGSE encoding. The thesis investigates the use of stimulated echoes for variety of the PFG NMR techniques. This technique results in a superposition of signals arising from different magnetisation pathways. Phase cycle schemes that select desired encoding as required are demonstrated. The temporal correlations of velocities for both water and a water-glycerol mixture flowing through a bead packs have been investigated using the 2D NMR VEXSY methods. By combining various flow rates (from 10 ml/h up to 10 l/h), fluid viscosities, and bead sizes (100, 400 and 500 μm), a wide range of flow parameters has been covered, Péclet numbers ranging from 9.4 x 101 to 8.6 x 104. A detailed investigation of flow through porous media by the Velocity Exchange NMR method allows us to draw some conclusions regarding dispersion in random bead packs. First, it is clear that both the Péclet number and the reduced mixing time Tlm/Tvc are needed to define the conditional probability. Second, we observe the existence of three “pools” of molecules: a slow moving uncorrelated sub-ensemble whose displacement is dominated by Brownian motion, an intermediate sub-ensemble whose velocities change little over Tlm, and a fast flowing sub-ensemble whose correlations diminish due to mechanical dispersion. Third, we note that the approach to asymptotic dispersion depends strongly on the Péclet number, and not just on the reduced mixing time Tlm/Tvc. The VEXSY technique has been applied to a bead pack system undergoing two-phase flow. A glass tube of 12 mm inner diameter with two symmetrically positioned inlets on one side used in all experiments was filled with glass beads of (400 ± 50)μm. Liquids were pumped through with total volume flow rates between about 1.0 and 1.5 l/h. The chemical shift difference between water and methyl protons of silicone oil has been exploited to simultaneously determine probability of displacements of both components in a water/silicone oil mixture flowing through a glass bead pack. The joint two-time probability densities as well as the conditional probabilities of velocities show a clearly distinct dispersion behaviour of both fluids which as a consequence of the different wetting properties of the fluids with respect to the glass surface of the bead pack. 1D Double PGSE NMR has been used to examine the approach to asymptotic dispersion for flow in randomly packed array of 500 μm latex spheres in a cylindrical tube of inner diameter 10 mm. Measurement of VACF were performed in directions both transverse to and co-linear with the flow direction, Péclet numbers covering a range from 2.8 x 103 to 8.64 x 103. A study of flow shows that Double PGSE NMR provides a highly effective means of measuring the Velocity Auto-correlation Function. The correlation times obtained by this method for the random spherical bead packs agree remarkably well with the calculated values for Tvc. A comparison of the Double and Single PGSE NMR measurements indicates the presence of a sub-ensemble with a very slowly fluctuating velocity distribution, which agrees well with the observations of VEXSY NMR studies mentioned previously. The presence of such a slowly fluctuating component is consistent with the idea that asymptotic conditions will only be reached when the fluid particles have travelled over a length scale several orders of magnitude larger than the bead diameters. From the longitudinal dispersion experiments a range of correlation times is found, and also the division of the ensemble into two distinct sub-ensembles, one with apparently uniform fluctuations at the idealised rate, (Tvc)-1, and one with a rate over an order of magnitude greater.