Analysis of Dynamic NMR Data

Abstract

An analysis of one and two-dimensional data sets using the so-called inverse Laplace transforms (ILT) and a discrete approach called Anahess is presented. Actually, the ILT is in mathematical terms an ill posed numerical inversion of Fredholm integrals with smooth kernels, meaning that several and very different solutions may fit the experimental data equally well. This inversion is referred to as an ILT in this book. The ILT and Anahess are fundamentally different methods for analysing the data, and the two methods are evaluated against each other on synthetic data sets. These data sets will represent the NMR data typically found from analysing real systems such as cheese or fluid saturated porous rock core plugs. Singular components and distribution are represented in the synthetic data sets. While the ILT algorithm fits the experimental data to a large set of fixed points in a grid, the Anahess algorithm minimizes the number of points, which are not fixed due to user defined grid as for the ILT algorithm. From the comparison, it will become obvious that both approaches have their benefits and drawbacks. Ultimately, user interpretation is required to decide which particular model fits the system better, either the Anahess algorithm, which fits a limited number of discrete components that are continuously variable, or the ILT algorithm, which assigns a larger set of components from a fixed grid.The analysis of NMR data arising from measurements of dynamic parameters such as diffusion and relaxation in heterogeneous systems is a challenging task. As discussed in Chap. 3 there are several factors besides the dynamic parameters that influence the attenuation of the NMR signal while incrementing the applied magnetic field gradient. The most important ones are the restricting geometries experienced during the prepare and read intervals in the PFG NMR sequence and the possible existence of internal magnetic field gradients. Due to these influences, it is not straightforward to assign a deviation from the mono exponential to a multi exponential behaviour in the measured diffusivity, thus being indistinguishable from experimental artefacts [1][2][3][4][5][6].In the following section a method will be provided to analyse one-dimensional data sets that minimises the afore mentioned artefacts. Afterwards, an analysis of one and two-dimensional data sets using the so-called inverse laplace transforms

Demulsification of Crude Oil Emulsions Tracked by Pulsed Field Gradient (PFG) Nuclear Magnetic Resonance (NMR). Part I: Chemical Demulsification

“…The smallest droplets appearing is likely due to an artifact that sometimes results from the inverse Laplace transformation, depending on signal-to-noise and the curve smoothing factor applied. 39 The smoothing factor has a tendency to stretch the DSD toward smaller and bigger droplets when decreased, which is not real, especially considering that the final DSD shows smaller droplets (Figure 3) than the initial DSD (Figure 2). However, there is a real possibility of small droplets appearing, because Yeung et al 40 showed that micrometer-sized droplets can detach from the surface of larger droplets when covered by high concentrations of bitumen.…”

“…The DSD has a shift both towards smaller and larger droplets. The smallest droplets appearing is likely due to an artefact that sometimes results from the inverse Laplace transformation, depending on signal-to-noise and the curve smoothing factor applied 39 . The smoothing factor has a tendency to stretch the DSD towards smaller and bigger droplets when decreased, which is not real, especially considering that the final DSD shows smaller droplets (Fig 3 .) than the initial DSD (Fig.…”