PFG NMR and Bayesian analysis to characterise non-Newtonian fluids

Thomas W Blythe,Andrew J Sederman,E Hugh Stitt,Andrew P.E York,Lynn F Gladden

doi:10.1016/j.jmr.2016.11.003

Abstract

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.

Highlights

Many fluids encountered in everyday life, such as mayonnaise, toothpaste and shaving foam, exhibit both solid- and liquid-like behaviour
In this work we extend current methodologies to enable the estimation of Herschel-Bulkley rheological parameters using PFG nuclear magnetic resonance (NMR), where y^ corresponds to the measured signal in q-space, SðqÞ, and h corresponds to n and r0=R describing the flow under study
A Bayesian NMR approach has been developed to enable the rheological characterisation of fluids demonstrating HerschelBulkley rheological behaviour in a pipe flow geometry using PFG NMR, requiring only single-axis gradient hardware

Summary

Introduction

Many fluids encountered in everyday life, such as mayonnaise, toothpaste and shaving foam, exhibit both solid- and liquid-like behaviour. This non-Newtonian behaviour may be explained by considering the concept of yield stress, a parameter that quantifies the minimum shear stress that is required to be applied to a fluid before deformational flow can begin to occur. The rheological behaviour of many fluids can be accurately described using the Herschel-Bulkley constitutive equation: sðc_ Þ 1⁄4 s0 þ kc_ n; ð1Þ where s is shear stress, c_ is shear rate, s0 is the yield stress of the fluid, and k and n represent the consistency factor and flow behaviour index, respectively. A major weakness of the HerschelBulkley constitutive equation is its inability to unambiguously establish the rheological parameters, since different sets of these parameters can provide equivalent fits to the experimental data [4]

Methods

Results

Conclusion