Matthias Appel

Fast measurements of average flow velocity by Low-Field 1H NMR

In this paper, we describe a method for measuring the average flow velocity of a sample by means of Nuclear Magnetic Resonance. This method is based on the Carr-Purcell-Meiboom-Gill (CPMG) sequence and does not require the application of any additional static or pulsed magnetic field gradients to the background magnetic field. The technique is based on analyzing the early-time behavior of the echo amplitudes of the CPMG sequence. Measurements of average flow velocity of water are presented. The experimental results show a linear relationship between the slope/y-intercept ratio of a linear fit of the first echoes in the CPMG sequence, and the average flow velocity of the flowing fluid. The proposed method can be implemented in low-cost Low-Field NMR spectrometers allowing a continuous monitoring of the average velocity of a fluid in almost real-time, even if the flow velocity changes rapidly.

Fast imaging of laboratory core floods using 3D compressed sensing RARE MRI.

Three-dimensional (3D) imaging of the fluid distributions within the rock is essential to enable the unambiguous interpretation of core flooding data. Magnetic resonance imaging (MRI) has been widely used to image fluid saturation in rock cores; however, conventional acquisition strategies are typically too slow to capture the dynamic nature of the displacement processes that are of interest. Using Compressed Sensing (CS), it is possible to reconstruct a near-perfect image from significantly fewer measurements than was previously thought necessary, and this can result in a significant reduction in the image acquisition times. In the present study, a method using the Rapid Acquisition with Relaxation Enhancement (RARE) pulse sequence with CS to provide 3D images of the fluid saturation in rock core samples during laboratory core floods is demonstrated. An objective method using image quality metrics for the determination of the most suitable regularisation functional to be used in the CS reconstructions is reported. It is shown that for the present application, Total Variation outperforms the Haar and Daubechies3 wavelet families in terms of the agreement of their respective CS reconstructions with a fully-sampled reference image. Using the CS-RARE approach, 3D images of the fluid saturation in the rock core have been acquired in 16min. The CS-RARE technique has been applied to image the residual water saturation in the rock during a water-water displacement core flood. With a flow rate corresponding to an interstitial velocity of vi=1.89±0.03ftday(-1), 0.1 pore volumes were injected over the course of each image acquisition, a four-fold reduction when compared to a fully-sampled RARE acquisition. Finally, the 3D CS-RARE technique has been used to image the drainage of dodecane into the water-saturated rock in which the dynamics of the coalescence of discrete clusters of the non-wetting phase are clearly observed. The enhancement in the temporal resolution that has been achieved using the CS-RARE approach enables dynamic transport processes pertinent to laboratory core floods to be investigated in 3D on a time-scale and with a spatial resolution that, until now, has not been possible.

Interpretation of restricted diffusion in sandstones with internal field gradients

We report on experiments to characterize internal magnetic field gradients that are caused by magnetic susceptibility differences between the solid phase and the fluids filling the pore space. Our measurements focus on low-field relaxometry of brine and oil in sandstones from various reservoirs around the world. Our results show the need to understand the dependence of internal field gradients on diffusion length, pore size- and fluid distribution in order to predict the impact of internal gradients on the interpretation of NMR experiments.

Liquid polyethylene glycol dispersed in a poly(styrene)-b-poly(ethylene/butylene)-b-poly(styrene) elastomer: determination of morphology and molecular mobility by light and electron microscopy as well as nuclear magnetic resonance self-diffusion andT2 measurements

An emulsion of liquid polyethylene glycol (PEG) in a rubbery poly(styrene)-b-poly(ethylene/butylene-b-poly-(styrene) (SEBS) matrix was prepared using a poly-(butadiene-b-poly(ethylene oxide) (PB-b-PEO) diblock copolymer as emulsifier. In addition to its emulsifying effect, it was shown that a block copolymer containing a crystalline PEO sequence has a tendency to form micelles as well as supramolecular structures in form of square platelets when they are solubilized in nonpolar solvent such as methylcyclohexane. The filmification of the emulsion by solvent evaporation and the film morphology were examined by light and electron microscopy and by nuclear magnetic resonance (NMR) T2 and self-diffusion measurements. Microscopic evaluations have shown cavities having an average size, depending on the copolymer content, of a few micrometers and filled with liquid PEG. Additionally, smaller structures typically in the range of 30–50 nm have been observed by transmission electron microscopy and are attributed to crystalline lamellae formed by the copolymer in the matrix. The T2 measurements reveal three contributions to the transverse magnetization decay: one of the SEBS matrix, one of the liquid within the cavities and one of the liquid dissolved in the smaller structures formed by the copolymer in the matrix. In the pulsed field gradient NMR self-diffusion experiments two self-diffusion coefficients were found, one of the liquid in the cavities and one of the liquid dissolved in the matrix within the smaller structures. Generally, a restricted diffusion is observed in that latter case owing to confining structures for the diffusing liquid molecules.

Acquisition of spatially-resolved displacement propagators using compressed sensing APGSTE-RARE MRI

A method is presented for accelerating the acquisition of spatially-resolved displacement propagators via under-sampling of an Alternating Pulsed Gradient Stimulated Echo - Rapid Acquisition with Relaxation Enhancement (APGSTE-RARE) data acquisition with compressed sensing image reconstruction. The method was demonstrated with respect to the acquisition of 2D spatially-resolved displacement propagators of water flowing through a packed bed of hollow cylinders. The q,k-space was under-sampled according to variable-density pseudo-random sampling patterns. The quality of compressed sensing reconstructions of spatially-resolved propagators at a range of sampling fractions was assessed using the peak signal-to-noise ratio (PSNR) as a quality metric. Propagators of good quality (PSNR 33.2 dB) were reconstructed from only 6.25% of all data points in q,k-space, resulting in a reduction in the data acquisition time from 4 h to 14 min. The spatially-resolved propagators were reconstructed using both the total variation and nuclear norm sparsifying transforms; use of total variation resulted in a slightly higher quality of the reconstructed image in most cases. To illustrate the power of this method to characterise heterogeneous flow in porous media, the method is applied to the characterisation of flow in a vuggy carbonate rock.

Fast spatially-resolved T2 measurements with constant-gradient CPMG

Speed of acquisition is paramount for the application of magnetic resonance to flow experiments through porous rocks. One popular method for imaging core floods is the spatially resolved T2 experiment which can separate fluids either by their viscosity contrast or by doping one fluid with a relaxation agent. Existing techniques for spatial-T2 may suffer from long acquisition times and eddy currents due to the pulsing of magnetic field gradients. Here, we propose a constant gradient method for 1d spatially-resolved T2 which embraces the speed of frequency encoding techniques and avoids eddy currents by the absence of any gradient ramps during the radio frequency (r.f.) pulse train. We provide the operating envelope for this kind of experiment, which is restricted due to the slice selectivity of the r.f. pulses in the presence of the magnetic field gradient. Additionally, we show that the effects of self-diffusion and the mixing of T1 and T2 contributions are manageable. As an illustration, we have applied this technique to an enhanced oil recovery experiment. The two fluid phases were tracked without any doping and with a time resolution of 40 s. In this case, the increased time resolution allowed us to observe dynamic flow phenomena such as fluid fingering and the calculation of the velocity of the fluid displacement fronts.

Under-sampling and compressed sensing of 3D spatially-resolved displacement propagators in porous media using APGSTE-RARE MRI

A method for under-sampling and compressed sensing of 3D spatially-resolved propagators is presented and demonstrated for flow in a packed bed and a heterogeneous carbonate rock. By sampling only 12.5% of q,k-space, the experimental acquisition time was reduced by almost an order of magnitude. In particular, for both systems studied, a 3D image was acquired at 1 mm isotropic spatial resolution such that 134,400 local propagators were obtained. Data were acquired in ~1 h and ~11 h for the packed bed and rock, respectively. It is shown that spatial resolution and under-sampling using this implementation retains the quantitative nature of the propagator measurement, and differences between implementation of this measurement in two and three dimensions are identified. The potential for 3D spatially-resolved propagators to provide new insights into transport processes in porous media by characterisation of the statistical moments of the propagators is discussed.