Optimising sampling patterns for bi-exponentially decaying signals.

A recently reported method, based on the Cramér-Rao Lower Bound theory, for optimising sampling patterns for a wide range of nuclear magnetic resonance (NMR) experiments is applied to the problem of optimising sampling patterns for bi-exponentially decaying signals. Sampling patterns are optimised by minimizing the percentage error in estimating the most difficult to estimate parameter of the bi-exponential model, termed the objective function. The predictions of the method are demonstrated in application to pulsed field gradient NMR data recorded for the two-component diffusion of a binary mixture of methane/ethane in a zeolite. It is shown that the proposed method identifies an optimal sampling pattern with the predicted objective function being within 10% of that calculated from the experiment dataset. The method is used to advise on the number of sampled points and the noise level needed to resolve two-component systems characterised by a range of ratios of populations and diffusion coefficients. It is subsequently illustrated how the method can be used to reduce the experiment acquisition time while still being able to resolve a given two-component system

Inhibitory effect of oxygenated heterocyclic compounds in mesoporous catalytic materials: A pulsed-field gradient NMR diffusion study

Oxygenated heterocyclic compounds are often used as solvents in liquid-phase catalytic reactions, such as hydrogenation and oxidation over porous oxide-based catalysts. It has often been reported that such compounds inhibit catalyst activity relative to the use of hydrocarbons as the solvent media. In this work we use $^{1}$H pulsed-field gradient (PFG) NMR diffusion studies to study diffusion properties of binary mixtures 1,4-dioxane/cyclohexane in mesoporous TiO$_{2}$ over the whole composition range in order to understand the effect of the solid surface on molecular transport and molecular interactions within the pore space. The results reveal that whilst the diffusion of the hydrocarbon is only affected by geometrical restrictions, the diffusion profile of 1,4-dioxane is highly influenced by interactions within the catalyst pore, which is thought to be due to the presence of lone electron pairs on the oxygen atoms of 1,4-dioxane, allowing the molecule to act as a Lewis base when in contact with the solid surface. This agrees with findings on the inhibitory capacity of oxygenated heterocyclic compounds when used either as solvent in catalysis or present as impurities in some chemical feedstocks. The work shows that it is possible to use $^{1}$H PFG NMR in order to characterise the effect of surfaces on molecular transport and hence understand catalytic behaviour in liquid-phase catalytic reactions.Carmine D’Agostino would like to acknowledge Wolfson College, Cambridge, for supporting his research. The authors would also like to acknowledge the EPSRC (EP/G011397/1) for funding

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Operando magnetic resonance studies of phase behaviour and oligomer accumulation within catalyst pores during heterogeneous catalytic ethene oligomerization

Two-dimensional 1H magnetic resonance imaging and spatially-resolved 1H magnetic resonance spectroscopy and diffusion measurements were recorded as a function of time-on-stream within a fixed-bed reactor to provide direct measurements of the progress of the heterogeneous catalytic oligomerization of ethene occurring over a 1 wt% Ni-Al2O3-SiO2 catalyst. The catalyst bed was of internal diameter 2 cm; magnetic resonance measurements were recorded over a bed length of 5.5 cm. Experiments were conducted at a temperature and pressure of 110 °C and 29 bara, respectively, with continuous downflow of ethene at a flowrate of 0.78 L h-1. During conversion the accumulation of 1H-containing species within the catalyst pellets was imaged, and spatially-resolved 1H NMR spectra were recorded at 1 mm intervals along the length of the reactor. Diffusion-filtered 1D chemical shift imaging was used to discriminate between gas- and liquid-phase species along the length of the reactor at 1 mm intervals. Finally, spectrally-encoded pulsed field gradient measurements of molecular diffusion were employed to infer the molecular composition of the gas and liquid phases and to identify populations of these phases inside and external to the pore space of the catalyst pellets; these measurements were spatially-resolved along the length of the reactor, with data being averaged over sections of height 4 mm. The results are consistent with oligomers of carbon number C20 and greater existing within the pores of the catalyst pellets which act to block the pore space, thereby deactivating the catalyst

Adsorption of pyridine from aqueous solutions by polymeric adsorbents MN 200 and MN 500. Part 1: Adsorption performance and PFG-NMR studies

The removal of pyridine from aqueous solutions was carried out using Macronet polymeric adsorbents MN 200 and MN 500. The optimal pyridine uptakes were in approximately neutral solutions as a result of optimal effect of π -π hydrophobic and attractive electrostatic interactions between pyridine and the adsorbents. These adsorbents showed superior pyridine uptake capacities than some apatite and activated carbons in isotherm studies. Thermodynamic analysis showed that pyridine adsorption is exothermic on MN 200 and endothermic on MN 500, implying that the adsorption on MN 500 is an activated process, which is attributed to the presence of sulfonic acid groups. Pseudo-first and second order rate models were used to fit the adsorption kinetics for the adsorbents. Translational dynamics of guest molecules within the porous polymers was analysed by PFG-NMR diffusion technique and the diffusion behaviour was characterised by two distinctive diffusion regions. PFG-NMR derived self-diffusion coefficients of pyridine in MN 500 were much slower than the expected diffusion coefficients based on a purely geometrical confinement effect, which suggests the interaction of pyridine with the sulfonic acid groups on MN 500 and their stronger effect on diffusivity also enhances the adsorption performance of this adsorbent. These studies reveal new insights into adsorption properties of pyridine in porous polymers in relation to the structural and surface properties probed by PFG-NMR and account for the effectiveness of these adsorbents in the treatment of waste water containing the aromatic N-heterocyclic compound.Carmine D’Agostino would like to acknowledge Wolfson College, Cambridge, for supporting his research activities.This is the author accepted manuscript. The final version is available from Elsevier at http://dx.doi.org/10.1016/j.cej.2016.07.039

In Situ Chemically-Selective Monitoring of Multiphase Displacement Processes in a Carbonate Rock Using 3D Magnetic Resonance Imaging.

Accurate monitoring of multiphase displacement processes is essential for the development, validation and benchmarking of numerical models used for reservoir simulation and for asset characterization. Here we demonstrate the first application of a chemically-selective 3D magnetic resonance imaging (MRI) technique which provides high-temporal resolution, quantitative, spatially resolved information of oil and water saturations during a dynamic imbibition core flood experiment in an Estaillades carbonate rock. Firstly, the relative saturations of dodecane ( S o ) and water ( S w ) , as determined from the MRI measurements, have been benchmarked against those obtained from nuclear magnetic resonance (NMR) spectroscopy and volumetric analysis of the core flood effluent. Excellent agreement between both the NMR and MRI determinations of S o and S w was obtained. These values were in agreement to 4 and 9% of the values determined by volumetric analysis, with absolute errors in the measurement of saturation determined by NMR and MRI being 0.04 or less over the range of relative saturations investigated. The chemically-selective 3D MRI method was subsequently applied to monitor the displacement of dodecane in the core plug sample by water under continuous flow conditions at an interstitial velocity of 1.27 × 10 - 6 m s - 1 ( 0.4 ft day - 1 ) . During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of 0.31 mm × 0.39 mm × 0.39 mm were acquired on a timescale of 16 min per image. Using this technique the spatial and temporal dynamics of the displacement process have been monitored. This MRI technique will provide insights to structure-transport relationships associated with multiphase displacement processes in complex porous materials, such as those encountered in petrophysics research.The authors would like to thank Royal Dutch Shell plc for funding this work. LFG, MDM and AJS also wish to thank EPSRC for financial support (EP/K039318/1)

Assessing the use of NMR chemical shifts for prediction of VLE in non-ideal binary liquid mixtures

A method of estimating vapour liquid equilibrium (VLE) using NMR chemical shift data has been proposed by Xu et al. (2012). This method is based on the concept that the average local composition around each species is determined by the thermodynamics of the system, and also determines the screening of the NMR active groups within that molecule, and so their NMR chemical shifts. Xu et al.‘s method has been replicated and verified; results are confirmed to be accurate for alcohol + hydrocarbon mixtures, giving VLE predictions of comparable accuracy to the UNIFAC, generally considered the best predictive activity coefficient model available. However, for more strongly non-ideal mixtures, the method becomes less reliable, giving significantly less accurate predictions of total pressure than UNIFAC. Several causes for this are identified. The model proposed by Xu et al. (2012) is unable to fit minima or maxima in chemical shifts, which are observed experimentally in some binary mixtures. Different NMR resonances within the same molecule lead to different predictions of VLE, clearly an un-physical result. The thermodynamics of strongly non-ideal mixtures are determined by more complex interactions than a simple description of average local composition around each component in the mixtures, for example strong and directional hydrogen bonds. Different groups within the same molecule may have different local compositions in their immediate vicinity; for example in the case of alcohol + water mixtures, one would expect a clustering of water molecules around the hydroxyl group but not the aliphatic group. Hence, the concept of a simple local composition model is not valid for these more complex cases, and it is therefore not surprising that a model based on this simple concept is often not effective in predicting VLE.C. D’Agostino would like to acknowledge Wolfson College, Cambridge, for supporting his research activities.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0009250914004461

Water-wax behaviour in porous silica at low temperature Fischer-Tropsch conditions

© 2018 Water is a major product of Fischer-Tropsch synthesis, and hence the behaviour of water within Fischer-Tropsch synthesis catalysts and its potential influence on catalyst rate and selectivity are questions of long-standing interest. The present work applies three different magnetic resonance techniques to study how water interacts with a model wax, n-octacosane, within the pore space of a porous silica of mean pore size ∼18 nm. 1H magnetic resonance spectroscopy, spin-lattice relaxation time and pulsed-field gradient measurements were performed at 195 °C, and for water pressure in the range 3–13.6 bar, conditions relevant to low temperature Fischer-Tropsch synthesis. The uptake of water within this system is shown to be very similar to that observed for capillary condensation of water within the empty pore space of the same porous silica under the same experimental conditions; suggesting that capillary condensation of water within the wax-saturated pores is occurring. The behaviour of water is characterised by two regimes. At low water relative pressures of ∼0.3 ≤ P/P0 ≤ ∼0.8 water moves into the pore space, displacing wax from the pore surface and existing as a water-rich layer between the pore surface and an oil-rich phase in the centre of the pore; the strong interaction with the pore surface is evidenced by the short nuclear spin relaxation time values of water at the lowest pressures which then increase slightly as multi-layer adsorption at the pore surface occurs with increase in pressure. In the water relative pressure range ∼0.8 ≤ P/P0 ≤ ∼0.97, condensation of water within the pores is observed, characterised by increases in both spin-lattice relaxation time and molecular diffusivity. Analysis of the data suggests that as much as ∼40% of the pore surface is occupied by condensed water after condensation has occurred. It is suggested that these two regimes of water behaviour inside initially wax-filled pores might explain previously reported aspects of the behaviour of Fischer-Tropsch catalyst performance as a function of pore size and amount of co-fed water

Assessing the effect of reducing agents on the selective catalytic reduction of NO<inf>x</inf> over Ag/Al<inf>2</inf>O<inf>3</inf> catalysts

The selective catalytic reduction (SCR) of NOx in the presence of different reducing agents over Ag/Al2O3 prepared by wet impregnation was investigated by probing catalyst activity and using NMR relaxation time analysis.We gratefully acknowledge funding for this work from the EPSRC CASTech grant (EP/G012156/1). Carmine D’Agostino would like to acknowledge Wolfson College, Cambridge, for supporting his research activities. The authors would also like to thank Dr Jonathan Mitchell for useful discussions.This is the final version of the article. It first appeared from RSC via http://dx.doi.org/10.1039/C5CY01508

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.Royal Dutch Shell plc; Engineering and Physical Sciences Research Council (EP/K039318/1, EP/M00483X/1)This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jmr.2016.07.01