Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. While in previous works (Formaggia et al. 2013, Porta et al., 2014) we assumed a simplified depositional history with only one material, in this work we consider multi-layered basins, in which each layer is characterized by a different material, and hence by different properties. This setting requires several improvements with respect to our earlier works, both concerning the deterministic solver and the stochastic discretization. On the deterministic side, we replace the previous fixed-point iterative solver with a more efficient Newton solver at each step of the time-discretization. On the stochastic side, the multi-layered structure gives rise to discontinuities in the dependence of the state variables on the uncertain parameters, that need an appropriate treatment for surrogate modeling techniques, such as sparse grids, to be effective. We propose an innovative methodology to this end which relies on a change of coordinate system to align the discontinuities of the target function within the random parameter space. The reference coordinate system is built upon exploiting physical features of the problem at hand. We employ the locations of material interfaces, which display a smooth dependence on the random parameters and are therefore amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through two synthetic test cases. In particular, we show that our methodology reproduces with high accuracy multi-modal probability density functions displayed by target state variables (e.g., porosity).Comment: 25 pages, 30 figure

Spectral responses in granular compaction

The slow compaction of a gently tapped granular packing is reminiscent of the low-temperature dynamics of structural and spin glasses. Here, I probe the dynamical spectrum of granular compaction by measuring a complex (frequency-dependent) volumetric susceptibility $\tilde{\chi}_v$. While the packing density $\rho$ displays glass-like slow relaxations (aging) and history-dependence (memory) at low tapping amplitudes, the susceptibility $\tilde{\chi}_v$ displays very weak aging effects, and its spectrum shows no sign of a rapidly growing timescale. These features place $\tilde{\chi}_v$ in sharp contrast to its dielectric and magnetic counterparts in structural and spin glasses; instead, $\tilde\chi_v$ bears close similarities to the complex specific heat of spin glasses. This, I suggest, indicates the glass-like dynamics in granular compaction are governed by statistically rare relaxation processes that become increasingly separated in timescale from the typical relaxations of the system. Finally, I examine the effect of finite system size on the spectrum of compaction dynamics. Starting from the ansatz that low frequency processes correspond to large scale particle rearrangements, I suggest the observed finite size effects are consistent with the suppression of large-scale collective rearrangements in small systems.Comment: 18 pages, 17 figures. Submitted to PR

Macro- and microscale gaseous diffusion in a Stagnic Luvisol as affected by compaction and reduced tillage

Intensification of mechanical agriculture has increased the risk for soil compaction and deformation. Simultaneously, reduced tillage practices have become popular due to energy saving and environmental concerns, as they may strengthen and improve the functioning of structured soil pore system. Soil aeration is affected by both compaction and reduced tillage through changes in soil structure and in the distribution of easily decomposable organic matter. We investigated whether a single wheeling by a 35 000 kg sugar-beet harvester in a Stagnic Luvisol derived from loess near Göttingen, Germany, influenced the gas transport properties (air permeability, gaseous macro- and microdiffusivities, oxygen diffusion rate) in the topsoil and subsoil samples, and whether the effects were different between long-term reduced tillage and mouldboard ploughing. Poor structure in the topsoil resulted in slow macro- and microscale gas transport at moisture contents near field capacity. The macrodiffusivities in the topsoil under conventional tillage were slower compared with those under conservation treatment, and soil compaction reduced the diffusivities by about half at the soil depths studied. This shows that even one pass with heavy machinery near field capacity impairs soil structure deep into the profile, and supports the view that reduced tillage improves soil structure and aeration compared with ploughing, especially in the topsoil

Emerging technologies for the non-invasive characterization of physical-mechanical properties of tablets

The density, porosity, breaking force, viscoelastic properties, and the presence or absence of any structural defects or irregularities are important physical-mechanical quality attributes of popular solid dosage forms like tablets. The irregularities associated with these attributes may influence the drug product functionality. Thus, an accurate and efficient characterization of these properties is critical for successful development and manufacturing of a robust tablets. These properties are mainly analyzed and monitored with traditional pharmacopeial and non-pharmacopeial methods. Such methods are associated with several challenges such as lack of spatial resolution, efficiency, or sample-sparing attributes. Recent advances in technology, design, instrumentation, and software have led to the emergence of newer techniques for non-invasive characterization of physical-mechanical properties of tablets. These techniques include near infrared spectroscopy, Raman spectroscopy, X-ray microtomography, nuclear magnetic resonance (NMR) imaging, terahertz pulsed imaging, laser-induced breakdown spectroscopy, and various acoustic- and thermal-based techniques. Such state-of-the-art techniques are currently applied at various stages of development and manufacturing of tablets at industrial scale. Each technique has specific advantages or challenges with respect to operational efficiency and cost, compared to traditional analytical methods. Currently, most of these techniques are used as secondary analytical tools to support the traditional methods in characterizing or monitoring tablet quality attributes. Therefore, further development in the instrumentation and software, and studies on the applications are necessary for their adoption in routine analysis and monitoring of tablet physical-mechanical properties

Designing A Calibration Set in Spectral Space for Efficient Development of An NIR Method For Tablet Analysis

Designing a calibration set is the first step in developing a spectroscopic calibration method for quantitative analysis of pharmaceutical tablets. This step is critical because successful model development depends on the suitability of the calibration data. For spectroscopic-based methods, traditional concentration based techniques for designing calibration sets are prone to have redundant information while simultaneously lacking necessary information for a successful calibration model. The traditional method also follows the same design approach for different spectroscopic techniques and different formulations, thereby lacks the optimizing capability to be technique and formulation specific. A method for designing a calibration set in the Near Infrared (NIR) spectral space was developed for quantitative analysis of tablets. The pure component NIR spectra of a tablet formulation were used to define the spectral space of that formulation. This method minimizes sample requirements to provide an efficient means for developing multivariate spectroscopic calibration. Multiple comparative studies were conducted between commonly employed experimental design approaches to calibration development and the newly developed spectral space based technique. The comparisons were conducted on single API (Active Pharmaceutical Ingredient) and multiple API formulation to quantify model drugs using NIR spectroscopy. Partial least squares (PLS) models were developed from respective calibration designs. Model performance was comprehensively assessed based on the ability to predict API concentrations in independent prediction sets. Similar prediction performance was achieved using the smaller calibration set designed in spectral space, compared to the traditionally designed large calibration sets. An improved prediction performance was observed for the spectrally designed calibration sets compared to the traditionally designed calibration sets of equal sizes. Spectral space was also used to incorporate physico-chemical information into the calibration design to provide an efficient means of developing robust calibration model. Robust calibration model is critical to ensure consistent model performance during model lifecycle. A weight coefficient based technique was developed for selecting loading vector in PLS model to aid in building robust calibration model. It was also demonstrated that the optimal structures of calibration sets are different between NIR and Raman spectroscopy for the same tablet formulation. The optimum calibration structures are also different between two APIs for the same spectroscopic technique, indicating the criticality of the calibration design to be formulation and technique specific. This study demonstrates that a calibration set designed in spectral space provides an efficient means of developing spectroscopic multivariate calibration for tablet analysis. This study also provides opportunity to design formulation and technique specific calibration sets to optimize calibration capability

Mesoscale Calculations of the Dynamic Behavior of a Granular Ceramic

Mesoscale calculations have been conducted in order to gain further insight into the dynamic compaction characteristics of granular ceramics. The primary goals of this work are to numerically determine the shock response of granular tungsten carbide and to assess the feasibility of using these results to construct the bulk material Hugoniot. Secondary goals include describing the averaged compaction wave behavior as well as characterizing wave front behavior such as the strain rate versus stress relationship and statistically describing the laterally induced velocity distribution. The mesoscale calculations were able to accurately reproduce the experimentally determined Hugoniot slope but under predicted the zero pressure shock speed by 12%. The averaged compaction wave demonstrated an initial transient stress followed by asymptotic behavior as a function of grain bed distance. The wave front dynamics demonstrate non-Gaussian compaction dynamics in the lateral velocity distribution and a power-law strain rate–stress relationship

Assessment and prediction of tablet properties using transmission and backscattering Raman spectroscopy and transmission NIR spectroscopy

This study investigated whether Raman and Near Infrared (NIR) spectroscopy could predict tablet properties. Granules were produced on a continuous line by varying granulation parameters. Tableting process parameters were adjusted to obtain uniform tablet weight and thickness. Spectra were collected offline and tablet properties determined with traditional analyzing methods. Partial Least Squares (PLS) regression was used to correlate spectral information to tablet properties, but predictive models couldn't be established. Principal component analysis (PCA) was effectively used to distinguish theophylline concentrations and hydration levels and multiple linear regression (MLR) analysis allowed insight on how granulation parameters affect granule and tablet properties