Adaptive Equalisation for Impulsive Noise Environments

This thesis addresses the problem of adaptive channel equalisation in environments where the interfering noise exhibits non–Gaussian behaviour due to impulsive phenomena. The family of alpha-stable distributions has proved to be a suitable and flexible tool for the modelling of signals with impulsive nature. However,non–Gaussian alpha–stable signals have infinite variance, and signal processing techniques based on second order moments are meaningless in such environments. In order to exploit the flexibility of the stable family and still take advantage of the existing signal processing tools, a novel framework for the integration of the stable model in a communications context is proposed, based on a finite dynamic range receiver. The performance of traditional signal processing algorithms designed under the Gaussian assumption may degrade seriously in impulsive environments. When this degradation cannot be tolerated, the traditional signal processing methods must be revisited and redesigned taking into account the non–Gaussian noise statistics. In this direction, the optimum feed–forward and decision feedback Bayesian symbol–by–symbol equalisers for stable noise environments are derived. Then, new analytical tools for the evaluation of systems in infinite variance environments are presented. For the centers estimation of the proposed Bayesian equaliser, a unified framework for a family of robust recursive linear estimation techniques is presented and the underlying relationships between them are identified. Furthermore, the direct clustering technique is studied and robust variants of the existing algorithms are proposed. A novel clustering algorithm is also derived based on robust location estimation. The problem of estimating the stable parameters has been addressed in the literature and a variety of algorithms can be found. Some of these algorithms are assessed in terms of efficiency, simplicity and performance and the most suitable is chosen for the equalisation problem. All the building components of an adaptive Bayesian equaliser are then put together and the performance of the equaliser is evaluated experimentally. The simulation results suggest that the proposed adaptive equaliser offers a significant performance benefit compared with a traditional equaliser, designed under the Gaussian assumption. The implementation of the proposed Bayesian equaliser is simple but the computational complexity can be unaffordable. However, this thesis proposes certain approximations which enable the computationally efficient implementation of the optimum equaliser with negligible loss in performance

Multiscale Characterization of Wettability in Porous Media

Wettability is one of the key controlling parameters for multiphase flow in porous media, and paramount for various geoscience applications. While a general awareness of the importance of wettability was established decades ago, our fundamental understanding of how wettability influences transport and of how to characterize wettability has improved tremendously in recent years through breakthroughs in imaging technology and modeling techniques. Numerical modeling studies clearly show not only that macroscopic two-phase flow is influenced by the average wettability, but also that the spatial distribution of wetting significantly impacts the macroscopic parameters. Herein, we explore the thermodynamics for porous multiphase systems, and recent breakthroughs in wettability characterization. Our view is that bridging the multiscale characterization of wetting must consider two fundamental perspectives: geometry and energy. Advancing the overall description requires an improved understanding of the operative mechanisms that dominate at various scales, and the development of quantitative approaches to capture these effects. We take a multistage approach, looking at these fundamental perspectives from the sub-pore-to-pore length scales, followed by the pore-to-core length scales using various analytical techniques and numerical simulations. Within this context, there remain many open-ended questions, and we therefore highlight these issues to provide guidance on future research directions. Our overall aim is to provide comprehensive guidance on the multiscale characterization of wettability in porous media, in order to facilitate novel research

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments and in-situ micro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106 times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale

From connected pathway flow to ganglion dynamics

During imbibition, initially connected oil is displaced until it is trapped as immobile clusters. While initial and final states have been well described before, here we image the dynamic transient process in a sandstone rock using fast synchrotron-based X-ray computed microtomography. Wetting film swelling and subsequent snap off, at unusually high saturation, decreases nonwetting phase connectivity, which leads to nonwetting phase fragmentation into mobile ganglia, i.e., ganglion dynamics regime. We find that in addition to pressure-driven connected pathway flow, mass transfer in the oil phase also occurs by a sequence of correlated breakup and coalescence processes. For example, meniscus oscillations caused by snap-off events trigger coalescence of adjacent clusters. The ganglion dynamics occurs at the length scale of oil clusters and thus represents an intermediate flow regime between pore and Darcy scale that is so far dismissed in most upscaling attempts