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

Analytical and finite element modelling of the dynamic interaction between off-road tyres and deformable terrains

Automotive tyres are one of the main components of a vehicle and have an extremely complex structure consisting of several types of steel reinforcing layers embedded in hyperelastic rubber materials. They serve to support, drive – accelerate and decelerate – and steer the vehicle, and to reduce transmitted road vibrations. However, driving is associated with certain types of pollution due to CO2 emissions, various particles due to tyre wear, as well as noise. The main source of CO2 emissions is the tyre rolling resistance, which accounts for roughly 30% of the fuel consumed by cars. The phenomenon becomes more pronounced in off-road conditions, where truck vehicles are responsible for about a quarter of the total CO2 emissions. Appropriate legislation has been introduced, to control all of these pollution aspects. Therefore, tyre simulation (especially in off-road conditions) is essential in order to achieve a feasible design of a vehicle, in terms of economy and safety. [Continues.

Inverse Dynamics Problems

The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems

Influence of Rock Heterogeneity on Fracture Pattern Formation

Imperial Users onl

Numerical Modelling of Melt Segregation Within and Around Sill Intrusions

The continental crust has an observed stratification from mafic lower crust to granitic shallow crust. How this stratification arises is one of the key unanswered questions in igneous petrology. For this thesis a general coupled model of heat and mass transport during buoyancy driven melt segregation has been developed and employed to simulate the intrusion and subsequent evolution of sills in regions termed deep crustal hot zones. A system of governing equations describing the conservation of heat, mass and momentum in a two phase media undergoing buoyancy driven melt segregation has been developed. Suitable numerical methods have been employed to solve the governing equations and a computer code developed for their solution. As sills are emplaced into the crust they cool and crystallise with the release of latent heat warming and then melting the surrounding country rock. It is shown that contributions from both the crust and intrusion are significant. Subsequent melt migration leads to the development of high melt fraction layers able to fluidise and form mobile magmas in geologically short time periods. The model can predict temperature and melt fraction of these mobile magmas and from this the composition can be inferred. Low temperature, evolved magmas are shown to develop which are able to leave the hot zone and ascend to the shallow crust, driving crustal stratification. The model is then extended to discuss the transport of major components during melt migration and applied to several geologically significant systems. Binary systems have been chosen due to their relative simplicity and the importance of several two component phase diagrams in igneous systems. Mixing in a heterogeneous crust is shown to lead to previously unobserved effects such as the formation of mobile magmas at the interface between compositionally distinct layers. Finally trace element transport during melt migration is investigated for both compatible and incompatible elements. Large deviations from the current paradigms of trace element fractionation are observed when the migration of species is modelled explicitly. This thesis shows that melt migration is an important process in geological systems and is a major influence during the formation of mobile magmas and their resultant temperature, composition and trace element concentration

DUAL-MODALITY (NEUTRON AND X-RAY) IMAGING FOR CHARACTERIZATION OF PARTIALLY SATURATED GRANULAR MATERIALS AND FLOW THROUGH POROUS MEDIA

Problems involving mechanics of partially saturated soil and physics of flow through porous media are complex and largely unresolved based on using continuum approach. Recent advances in radiation based imaging techniques provide unique access to simultaneously observe continuum scale response while probing corresponding microstructure for developing predictive science and engineering tools in place of phenomenological approach used to date. Recent developments with X-ray/Synchrotron and neutron imaging techniques provided tools to visualize the interior of soil specimen at pore/grain level. X-ray and neutron radiation often presents complementary contrast for given condensed matter in the images due to different fundamental interaction mechanisms. While X-rays mainly interact with the electron clouds, neutrons directly interact with the nucleus of an atom. The dual-modal contrasts are well suited for probing the three phases (silica, air and water) of partially saturated sand since neutrons provide high penetration through large sample size and are very sensitive to water and X-rays of high energy can penetrate moderate sample sizes and clearly show the particle and void phases. Both neutron and X-ray imaging techniques are used to study microstructure of partially saturated compacted sand and water flow behavior through sand with different initial structures. Water distribution in compacted sand with different water contents for different grain shapes of sand was visualized with relatively coarse resolution neutron radiographs and tomograms. Dual-modal contrast of partially saturated sand was presented by using high spatial resolution neutron and X-ray imaging. Advanced image registration technique was used to combine the dual modality data for a more complete quantitative analysis. Quantitative analysis such as grain size distribution, pore size distribution, coordination number, and water saturation along the height were obtained from the image data. Predictive simulations were performed to obtain capillary pressure – saturation curves and simulated two fluid phase (water and air) distribution based image data. In-situ water flow experiments were performed to investigate the effect of initial microstructure. Flow patterns for dense and loose states of Ottawa sand specimens were compared. Flow patterns and water distribution of dense Ottawa and Q-ROK sand specimens was visualized with high resolution neutron and X-ray image data

Insights into cardiac remodelling by multi-modal magnetic resonance imaging and spectroscopy

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