A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization

This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements

Uniform multi-penalty regularization for linear ill-posed inverse problems

This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems

Sequential coupled numerical simulations of an air/ground-source heat pump: Validation of the model and results of yearly simulations

Numerical simulations are important tools for the assessment of exploiting geothermal energy in heat pump applications. They can be used to evaluate the performance of the system, the long-term production scenarios and the sustainability of the geothermal reservoir. The present work introduces and describes a numerical model, in which a dedicated Matlab script has been realized to allow sequentially coupled simulations of a shallow geothermal reservoir and of a heat pump system. A mathematical model of a dual-source heat pump, working alternatively with the ground or the air as heat source/sink, has been developed in Matlab environment. The heat exchangers of the heat pump have been modelled considering the equations that govern the physical phenomena. The dynamic numerical simulator FEFLOW, based on the finite element method, has been used to simulate the behaviour of the geothermal reservoir, subjected to heat extraction/reinjection by a closed loop vertical heat exchangers field. This methodological approach is useful to evaluate the performance of the coupled system in the long term, and it is important for understanding the advantages and limits of the dual-source heat pump in assuring sustainability over time avoiding the depletion of geothermal resources. The models and their coupling have been calibrated and validated with experimental data from a shallow geothermal plant located in Tribano (Padova, IT). It consists of eight coaxial borehole heat exchangers 30 m deep, connected to a 16 kW dual-source heat pump prototype. The heat pump system provides heating and cooling to an office area. The coupled model has been used to compare the performance of the heat pump when working in air-mode only or in ground-mode only. This allowed the development of a switching control strategy between the two thermal sources. Yearly simulations with the switching strategy have shown that the seasonal performance factor of the dual-source heat pump during the heating mode can be 13.8 % higher compared to the one obtained with a conventional air source heat pump and 3.8 % higher with respect to a ground source heat pump

TOUGH2Viewer tutorial

TOUGH2Viewer is a Java program capable of displaying unstructured (Voronoi complying) grids, locally refined and structured grids (complying with the MESHMAKER iTOUGH2 format). In particular, TOUGH2Viewer allows to navigate through a 3D grid compatible with the iTOUGH2 data file format and see: (1) the thermodynamic variables and the material (namely, petrophysical properties) of each block; (2) maps of isovalues (2D) of all thermodynamic variables; (3) isosurfaces (3D) of all thermodynamic variables; (4) flows of mass and heat between blocks; (5) spatial profiles of thermodynamic variables, of a selected set of blocks, long a Cartesian directions; (6) time plot of thermodynamic variables of a selected block. All commands to manage a 3D visualization (zooming, pan, rotations) are CAD complying

Macro-Scale Underground Geomechanical and Thermal Mapping for Very Shallow Geothermal Applications

The document is an extended abstract presented at "GeoENV 2016", the 11th International Conference on Geostatistics for Environmental Application Conference, 6-8 July 2016, Lisbon, Portugal

The search for negative amplitude components in quasi-continuous distributions of relaxation times: the example of 1H magnetization exchange in articular cartilage and hydrated collagen

When inverting nuclear magnetic resonance relaxation data in order to obtain quasi-continuous distributions of relaxation times for fluids in porous media, it is common practice to impose a non-negative (NN) constraint on the distributions. While this approach can be useful in reducing the effects of data distortion and/or preventing wild oscillations in the distributions, it may give misleading results in the presence of real negative amplitude components. Here, some examples of valid negative components for articular cartilage and hydrated collagen are given. Articular cartilage is a connective tissue, consisting mainly of collagen, proteoglycans and water, which can be considered, in many aspects, as a porous medium. Separate T1 relaxation data are obtained for low-mobility ('solid') macromolecular 1H and for higher-mobility ('liquid') 1H by the separation of these components in free induction decays, with α denoting the solid/liquid 1H ratio. When quasi-continuous distributions of relaxation times (T1) of the solid and liquid signal components of cartilage or collagen are computed from experimental relaxation data without imposing the usual NN constraint, valid negative peaks may appear. The features of the distributions, in particular negative peaks, and the fact that peaks at longer times for macromolecular and water protons are at essentially the same T1, are interpreted as the result of a magnetization exchange between these two spin pools. For the only-slightly-hydrated collagen samples, with α>1, the exchange leads to small negative peaks at short T1 times for the macromolecular component. However, for the cartilage, with substantial hydration or for a strongly hydrated collagen sample, both with α1, the behavior is reversed, with a negative peak for water at short times. The validity of a negative peak may be accepted (dismissed) by a high (low) cost of NN in error of fit. Computed distributions for simulated data using observed signal-to-noise ratios also verify the need for some negative components. Observed relaxation times and signal ratios can be fitted formally by a simple two-site exchange model that gives the exchange times and the uncoupled relaxation times of the liquid and solid components, with significant trends of these parameters with increasing 1H ratio, α. The solid-to-liquid exchange times are found to be in the range from 10 ms to a few tens of ms at all hydration levels. The results may be of interest for the application of magnetization exchange contrast in the imaging of articular cartilage to determine changes associated with pathologies and ageing. Other important porous media exist where exchange phenomena and negative relaxation components cannot be disregarded

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L2 regularization; (2) MF-L1, based on L1 penalties; and (3) a hybrid approach combining locally adapted L2 and global L1 penalties. Each method’s regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a “dispersion analysis” technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios

Propagator Resolved Transverse Relaxation Exchange Spectroscopy

We use the propagator resolved transverse relaxation exchange technique to look at the movement of fluid in three different types of rock samples. The two pore model previously used to fit molecular exchange simulations to the experimental data is expanded to accommodate the three site exchange seen in two of the samples. Estimated values for pore space characteristics from the simulations were compared to values calculated from X‐Ray CT data of the samples. While discrepancies exist between the NMR and X‐Ray CT results, the molecular exchange behavior estimated from the three samples reflects well with their morphology