Extending the use of Earth's Field NMR using Bayesian methodology: application to particle sizing

PFG NMR and Bayesian analysis to characterise non-Newtonian fluids

Many industrial flow processes are sensitive to changes in the rheological behaviour of process fluids, and there therefore exists a need for methods that provide online, or inline, rheological characterisation necessary for process control and optimisation over timescales of minutes or less. Nuclear magnetic resonance (NMR) offers a non-invasive technique for this application, without limitation on optical opacity. We present a Bayesian analysis approach using pulsed field gradient (PFG) NMR to enable estimation of the rheological parameters of Herschel-Bulkley fluids in a pipe flow geometry, characterised by a flow behaviour index n, yield stress τ₀, and consistency factor k, by analysis of the signal in q-space. This approach eliminates the need for velocity image acquisition and expensive gradient hardware. We investigate the robustness of the proposed Bayesian NMR approach to noisy data and reduced sampling using simulated NMR data and show that even with a signal-to-noise ratio (SNR) of 100, only 16 points are required to be sampled to provide rheological parameters accurate to within 2% of the ground truth. Experimental validation is provided through an experimental case study on Carbopol 940 solutions (model Herschel-Bulkley fluids) using PFG NMR at a ¹H resonance frequency of 85.2MHz; for SNR>1000, only 8 points are required to be sampled. This corresponds to a total acquisition time of <60s and represents an 88% reduction in acquisition time when compared to MR flow imaging. Comparison of the shear stress-shear rate relationship, quantified using Bayesian NMR, with non-Bayesian NMR methods demonstrates that the Bayesian NMR approach is in agreement with MR flow imaging to within the accuracy of the measurement. Furthermore, as we increase the concentration of Carbopol 940 we observe a change in rheological characteristics, probably due to shear history-dependent behaviour and the different geometries used. This behaviour highlights the need for online, or inline, rheological characterisation in industrial process applications.

Magnetic resonance signal moment determination using the Earth's magnetic field

We demonstrate a method to manipulate magnetic resonance data such that the moments of the signal spatial distribution are readily accessible. Usually, magnetic resonance imaging relies on data acquired in so-called k-space which is subsequently Fourier transformed to render an image. Here, via analysis of the complex signal in the vicinity of the centre of k-space we are able to access the first three moments of the signal spatial distribution, ultimately in multiple directions. This is demonstrated for biofouling of a reverse osmosis (RO) membrane module, rendering unique information and an early warning of the onset of fouling. The analysis is particularly applicable for the use of mobile magnetic resonance spectrometers; here we demonstrate it using an Earth's magnetic field system.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.