Coupled deformation, fluid flow and fracture propagation in porous media

Polygonal faults are non-tectonic fault systems which are layer-bound (at some vertical scale) and are widely developed in fine-grained sedimentary basins. Although several qualitative mechanisms have been hypothesised to explain the formation of these faults, there is a weak general consensus that they are formed by the coupled deformation and fluid expulsion of the host sediments (consolidation). This thesis presents a numerical framework that can be extended to investigate the role consolidation plays in the development and evolution of these faults. The method is also applicable to reservoir engineering and CO2 storage. An understanding of the coupled mechanical response and fluid flow is critical in determining compaction and subsidence in oil reservoirs and fault-seal integrity during CO2 disposal and storage. The technique uses a fracture mapping approach (FM) and the extended finite element method (XFEM) to modify the single phase FEM consolidation formulation. A key feature of FM-XFEM is its ability to include discontinuities into a model independently of the computational mesh. The fracture mapping approach is used to simulate the flow interaction between the matrix and existing fractures via a transfer function. Since fractures are represented using level set data, the need for complex meshing to describe fractures is not required. The XFEM component of the method simulates the influence of the pore fluid on the mechanical behaviour of the fractured medium. In XFEM, enrichment functions are added to the standard finite element approximation to ensure an accurate approximation of discontinuous fields within the simulation domain. FM-XFEM produces results comparative to the discrete fracture method on relatively coarse meshes. FM-XFEM has also been extended to model the propagation of existing fractures using a mixed-mode criterion applicable to geological media. Stress concentrations at the tips of existing fractures show good agreement with an analytical solution found in literature

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

Application of a porous media model for the acoustic damping of perforated plate absorbers

Perforated panel, or plate, absorbers are commonly employed to reduce sound pressure levels across a broad range of applications including the built environment, industrial installations and propulsion devices. The acoustic performance of a perforated plate absorber depends upon a number of parameters such as physical geometry of the absorber, acoustic spectrum and sound pressure level of the acoustic source. As a consequence, experimental determination of acoustic properties is often required on an individual basis in order to optimise performance.Computational simulation of a perforated plate absorber would alleviate the necessity for experimental characterisation. Fundamentally this can be achieved by the direct numerical solution of the underlying governing equations, the compressible form of the Navier-Stokes equations. The numerical methodology is available and routinely implemented as a Computational Fluid Dynamics solver. However, the numerical simulation of flow through a perforated plate with a large number of very small orifices would require significant computational resource, not routinely available for engineering design simulations.In this paper, a porous media model, implemented as a sub-model within a CFD solver, is investigated and validated against a number of well-acknowledged acoustic experiments undertaken in an impedance tube, for a sound pressure wave incident normal to a perforated plate. The model expresses the underlying governing equations within the perforated plates in terms of a pseudo-physical velocity representation. Comparison between three dimensional, compressible, laminar flow CFD simulations and experimental data, demonstrate that the porous model is able to represent acoustic properties of perforated plate absorbers in linear and non-linear absorption regimes and also the inertial effect in the presence of a mean bias flow.The model significantly reduces the computational resource required in comparison to full geometric resolution and is thus a promising tool for the engineering design of perforated plate absorbers

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above

Development of novel techniques of advanced transport characterization of membranes

Tesi en modalitat de compendi de publicacionsOptimization of membrane separation processes rely on the accurate determination of some parameters related to membrane structure, chemistry, morphology or transport mechanism. Therefore, membrane characterization is fundamental in membrane research and development. This thesis addresses two specific issues of membrane separation processes: the distribution of extent of concentration polarization (CP) over the membrane surface in test cells for pressure-driven membrane processes and the separate information of equilibrium (partitioning) and kinetic (diffusivity) properties of ion-exchange membranes for a better-understanding of ion-transport mechanisms. The implications of CP inhomogeneity for the interpretation of measurements of solute rejection were qualitatively illustrated using a simple model of locally-1D CP combined with a postulated probability distribution of unstirred-layer thickness over the membrane thickness. Disregarding the CP distribution under-estimates the CP of strongly positively-rejected solutes and over-estimates the CP for the negatively-rejected ones. This is especially important in nanofiltration where strong positive and pronounced negative rejections can occur simultaneously for solutes of different charges. Therefore, it is desirable to reduce the inhomogeneity of CP distribution to a minimum in membrane-testing devices. A novel test cell design was developed based on the classical configuration of rotating disk combined with the possibility of setting an operating pressure up to 20 bar. CFD simulations showed that CP was homogeneous over the major part of the membrane surface whereas there were some expectable deviations close to the membrane edge. The approach was also validated experimentally via studying the dependence of observed rejection on the rotation speed and demonstrating that intrinsic rejection was practically independent of it. Then, the cell utility was proved performing different ion rejection studies for several dominant salts (NaCl, MgCl2, Na2SO4 and MgSO4) plus trace ions (Na+, NH4+, Cl- and NO3-) and for electrolyte mixtures of NaCl and MgCl2. The solution-diffusion-electro-migration model was used to obtain ionic membrane permeances from the experimental data. Besides, experiments performed with a cross-flow test cell demonstrated that there was filtration along the membrane porous support even if the membrane is supported by an impermeable surface. This occurs in the peripheral parts of the membrane due to membrane sealing and contribute to CP inhomogeneity. Finally, a novel method based on non-stationary-diffusion of relatively small concentration differences was developed to determine salt diffusion and partitioning coefficients in addition to the ion perm-selectivity, which is the only parameter available from the conventional measurements of stationary membrane potential. An ion-exchange membrane supported by a relatively thick coarse-porous support (glass frit) is placed in a two-compartment stirred cell. The salt concentration in one compartment is kept stationary during the measurement whereas in the other compartment, the initial solution is rapidly replaced by a solution of different concentration. Thus, there is a time-dependent electrical response due to a progressive redistribution of applied concentration difference between the membrane and the porous support and the different ion perm-selectivities of those media. Experimental data was fitted to a mathematical model that describes transient transport phenomena including osmosis, which was found to contribute notably on the measurements. The osmotic permeability was determined in separate measurements. The rate of signal relaxation is primarily controlled by the diffusion permeability of the membrane but is also affected by the salt partitioning. The results were validated by comparison with the literature data and using conventional techniques. Systematic studies were also carried out under different conditionsL'optimització dels processos de separació amb membranes depèn d'una combinació de factors relacionats amb les propietats fisicoquímiques, l'estructura o la morfologia. Per tant, una caracterització acurada és fonamental en la investigació i desenvolupament de membranes. Aquesta tesi aborda dos problemes específics dels processos de separació amb membranes: la distribució de l'abast de la polarització per concentració (PC) sobre la superfície de la membrana als mòduls de membrana on la força impulsora és la pressió i l'obtenció d'informació diferenciada de les propietats cinètiques i d'equilibri en membranes de bescanvi iònic per a una millor comprensió dels mecanismes de transport d'ions. Les conseqüències de la inhomogeneïtat de la PC a l'hora d'interpretar les mesures del rebuig del solut es van il·lustrar qualitativament mitjançant un senzill model que descriu la PC localment en 1D combinat amb una distribució de probabilitats pel gruix de la capa límit. Ignorar la distribució a la PC subestima la PC dels soluts rebutjats positivament i sobreestima la PC per als rebutjats negativament. Aquest fet és especialment important en la nanofiltració, on es poden produir simultàniament rebuigs positius i negatius pronunciats per a soluts de diferents càrregues. Per tant, és desitjable reduir al màxim la inhomogeneïtat de la distribució de la PC als mòduls de membrana. Es va desenvolupar un nou disseny de mòdul per membranes basat en la clàssica configuració de disc rotatiu. Simulacions de dinàmics de fluids van demostrar que la PC es homogènia a la major part de la superfície de la membrana mentre que es van obtenir algunes desviacions esperables a prop de la vora de la membrana. A més, es va validar experimentalment estudiant la dependència del rebuig observat amb la velocitat de rotació i demostrant que el rebuig intrínsec es pràcticament independent. Posteriorment, es van obtenir les permeances iòniques mitjançant el model "Solution-diffusion-electro-migration" realitzant diferents estudis amb salts dominants (NaCl, MgCl2, Na2SO4 i MgSO4) més ions traça (Na+, NH4+, Cl- i NO3-) i amb mescles binàries de NaCl i MgCl2. D'altra banda, alguns experiments amb una cel·la de flux tangencial van demostrar que hi ha una filtració al llarg del suport porós de la membrana, fins i tot si aquesta esta recolzada per una superfície impermeable. Això es produeix a les zones perifèriques de la membrana, a causa de la pressurització del mòdul i contribueix a la inhomogeneïtat de la PC. Finalment, es va desenvolupar un nou mètode basat en la difusió no estacionària en condicions de diferències de concentració relativament petites per determinar la difusió i els coeficients de partició, a més de la permselectivitat iònica, que és l'únic paràmetre disponible a partir de les mesures convencionals del potencial de membrana en estat estacionari. Una membrana de bescanvi iònic recolzada per un suport relativament gruixut i porós es col·loca en una cel·la agitada de dos compartiments. La concentració de sal en un compartiment es manté estacionària durant l'experiment mentre que a l'altre compartiment, la solució inicial és substitueix ràpidament per una solució de concentració diferent. Així, hi ha una resposta elèctrica depenent de temps a causa d'una redistribució progressiva de la diferència de concentració aplicada entre la membrana i el suport porós degut a les diferents selectivitats iòniques entre ambdós medis. Les dades experimentals es van ajustar a un model matemàtic que descriu els fenòmens de transport en estat transitori, incloent la osmosis, ja que es va observar que contribueix significativament en les mesures. La permeabilitat osmòtica es va determinar paral·lelament. La velocitat de relaxació de la senyal obtinguda està controlada principalment per la difusió de la membrana, tot i que també es veu afectada pel coeficient de particióPostprint (published version

Numerical Analysis of Water Coning for the Recovery of Petroleum: an Enriched BEM Approach

The scope of this thesis focuses on enrichment techniques applied to the water coning problem, a numerical simulation solved with the enriched Boundary Element Method (BEM) for potential problems. The problem consists on a time dependent two-zone model with a pumping sink causing the extraction of hydrocarbons. A time dependent two-zone model implicates a moving interface between the zones and since a numerical simulation is performed, a refined discretization of the interface is necessary thus a high amount of Degrees of Freedom (DoF) are needed for its solution. Enrichment schemes reduce the numbers of DoF on the interface, in theory optimising computer effort. The Boundary Integral Equation (BIE) solved for this problem. In this work, the physical aspects of the model and the enrichment scheme are described in order to perform tests that would result in the best enrichment function possible that captures reliable results regardless of the conditions of the model. The enrichment scheme is compared to the classical (unenriched) BEM that is used as a reference solution. The change of scheme results in achieving the same accuracy with 8% of the original number of equations. The results allow us to predict the computational improvements that might be achieved when this technique is applied to 3D or the conditions of the model change. These results suggest that simulations would be over 20,000 times faster without loss in accuracy. This presents industry with a strategy to prevent water to be drawn into an oil well, eliminating an expensive oil-water separation process

Sorption and Transport Behaviour of Hydrophobic Organic Compounds in Soils and Sediments of Bangladesh and Their Impact on Groundwater Pollution : Laboratory Investigations and Model Simulations

*** Zugleich als Dissertation an der Univ. Tübingen erschienen, 2002 *** This thesis focuses on the elucidation of the sorption and related transport processes controlling the fate of hydrophobic organic compounds (HOCs) (contaminants and pesticide) in the subsurface environment. For a variety of organic compounds (phenanthrene, 1,2-DCB, TCE and carbofuran) batch and column experiments were carried out with different geosorbents (deltaic, floodplain and residuum soils, aquifer sediments and peat) to simulate the effect in Bangladesh top soils and sediments and the ultimate impact on groundwater. Overall, the results reported here so far indicate that sorption in these samples for the chemicals investigated is dominated by the partitioning processes. A nonlinear type sorption isotherm is described by the combination of the partitioning and pore-filling mechanisms. The solubility normalized Freundlich model predicts an inverse linear relationship between the sorption coefficient measured at a given relative concentration vs. S which facilitate the prediction of sorption of a variety of pollutants based on measured data of one probe compound. An effect of preferential solute transport coupled with diffusion into the surrounding matrix region has been examined by conducting macropore flow column experiments. A new analytical solution was developed to model the breakthrough curves. The model accounts for advection in the macropore region, diffusion into the matrix region and linear sorption in both regions. From the experimental results and the model assumptions it was concluded that sorption equilibrium was not achieved during matrix diffusion at the time scale of the macropore flow experiment. The combination of batch and column experimental results together with materials (solids) and environmental properties and a use of solute transport model, can provide tools for cost-effective soil and groundwater risk assessment.*** Published as printed thesis at Tuebingen University, 2002 **

A POROUS MEDIA APPROACH TOWARDS A DYNAMIC MECHANISTIC MODEL OF DRUG ELIMINATION BY THE LIVER

Hepatic drug elimination is a major PK process contributing to loss of drug concentration in the body. The prediction of hepatic clearance (and hence drug concentrations in the body) requires an understanding of the physiology and mechanisms of the hepatic elimination process and their compilation into a mechanistic model. Several physiological models including well-stirred model, parallel tube model and dispersion model have been developed to describe the hepatic elimination process and to determine how physiological variables such as blood flow, unbound fraction and enzyme activity may influence the hepatic clearance. However, each model has distinguishing advantages and limitations, which lead sometimes to very disparate prediction outcomes. Although hepatic drug elimination has been mathematically described by different physiological models, the mass transfer phenomena in the liver has not been described from a porous media viewpoint using local volume averaging method. The inherently porous structure of the liver allows us to describe the hepatic drug elimination process based on a porous media approach such that structural properties of the liver tissue, physico-chemical properties of the drug as well as transport properties associated with the hepatic blood perfusion are included in the model. Applying local volume averaging method and local equilibrium to the liver as a porous medium, a governing partial differential equation which takes into account liver porosity, tortuosity, permeability, unbound drug fraction and hepatic tissue partition coefficient, drug-plasma diffusivity, axial/radial dispersion and hepatocellular metabolism parameters was developed. The governing equation was numerically solved using implicit finite difference and Gauss-Seidel iterative method in order to describe changes in dug concentration with time and position across the liver following an intravenous drug administration. The model was used to predict hepatic clearance and bioavailability, which were then compared to reported observations. The predicted values of hepatic clearance and bioavailability had good agreement with the reported observations for high and low clearance drugs. As well, the model was able to successfully predict an unsteady state of hepatic drug elimination with concentration dependent intrinsic clearance. When statistically compared to the well-stirred, parallel tube and dispersion models the proposed model suggested a smaller mean squared prediction error and very good agreement to reported observations for eight drugs. A sensitivity analysis revealed that an increase in liver porosity results in a slight decrease in the drug concentration gradient across the liver while higher tissue partition coefficient values increase the concentration gradient. The model also suggested that the bioavailability was sensitive to the interaction between unbound fraction and intrinsic clearance. This study indicates that the liver and hepatic drug elimination can be successfully explored from a porous media viewpoint and may provide better mechanistic predictions of drug elimination processes by the liver