The seepage of fluid through saturated porous media may lead to inner erosion, channelization, preferential flow and transport and deposition of particles. A novel mathematical model was created to describe some of the processes. The model describes a temporal and spatial development of porosity (volume fraction) and permeability (transmissivity) due to erosion and deposition in saturated porous and fractured media. The model calculates the change of permeability and porosity in a direction of different fracture joint sets. The model is based on multi-continua theory, where a region is divided into components (three or more components in this thesis). The components are described by separate differential equations. This approach was used recently by Mahadevan et al. (2012) and Fujisawa et al. (2009) for erosion of porous media. This thesis describes the approaches, assumptions and the equations used in the model. In contrast to the published models, the thesis considers anisotropy. It is characterized by transmissivity tensor (also hydraulic conductivity tensor), which is composed of vectors in the joint sets directions. The model also uses a Dupuit approximation, which allows to approximate flow onto a horizontal plane. The model is also introduced by a numerical simulation using final element...

Les mousses à cellules ouvertes ont diverses applications industrielles, par exemple pour des échangeurs de chaleur, des réacteurs structurés, la filtration, la catalyse, récepteurs solaires volumétriques en raison de leurs propriétés uniques telles qu'une importante porosité et une surface spécifique élevée. Pour déterminer théoriquement la surface spécifique géométrique et les relations entre les paramètres géométriques de mousses, une corrélation mathématique généralisée a été développée. A cet effet, la géométrie de la tetrakaidecahedron a été utilisé et différentes formes de sections transversales de brins de structures en mousse ont été pris en compte de façon explicite. La corrélation dérivée pour prédire les propriétés géométriques peut facilement être étendue à des formes différentes. Des simulations numériques 3-D à l'échelle des pores ont été réalisées pour étudier la perte de charge et la conductivité effective thermique. L'écoulement du fluide à travers la mousse à cellule ouverte a été réalisé dans trois régimes différents: les régimes de Darcy, transitoire et inertiel. L'importance des propriétés géométriques sur les caractéristiques d'écoulement de fluide et leurs inclusions dans les corrélations proposées pour prédire la perte de charge est discutée. La question « Les paramètres d'Ergun peuvent-ils avoir des valeurs numériques constantes ou non ? » est discutée. Trois différentes corrélations étaient dérivées pour prédire la conductivité thermique effective à la fois isotrope et anisotrope des mousses. Les paramètres géométriques de la matrice de mousse étaient introduits dans les corrélations pour prédire la conductivité thermique effective. / Open cell foams have diverse industrial applications e.g. heat exchangers, structured reactors, filtration due to their unique properties such as high porosity and high specific surface area. In order to theoretically determine the geometric specific surface area and relationships between geometrical parameters of isotropic open cell foams, a generalized mathematical correlation was developed. For this purpose the tetrakaidecahedron geometry was used and different shapes of strut cross-sections of foam structures were taken explicitly into account. The derived correlation to predict geometrical properties can be easily extended to different strut shapes. 3-D numerical simulations at pore scale were performed to study the pressure drop characteristics and effective thermal conductivity. Fluid flow through open cell foam was performed in three different regimes: Darcy regime, transition regime and inertia regime. Importance of geometrical properties on fluid flow characteristics and their inclusion in the proposed correlations for predicting pressure drop is discussed. "Can Ergun parameters have constant numerical values or not" is also extensively discussed. Three different correlations were derived to predict the effective thermal conductivity for both, isotropic and anisotropic open cell foams. Geometrical parameters of foam matrix were introduced in the correlations to predict effective thermal conductivity.

Permeable friction course (PFC) is a porous asphalt pavement placed on top of a regular impermeable roadway. Under small rainfall intensities, drainage is contained within the PFC layer; but, under higher rainfall intensities drainage occurs both within and on top of the porous pavement. This dissertation develops a computer model—the permeable friction course drainage code (PERFCODE)—to study this two-dimensional unsteady drainage process. Given a hyetograph, geometric information, and hydraulic properties, the model predicts the variation of water depth within and on top of the PFC layer through time. The porous layer is treated as an unconfined aquifer of variable saturated thickness using Darcy’s law and the Dupuit-Forchheimer assumptions. Surface flow is modeled using the diffusion wave approximation to the Saint-Venant equations. A mass balance approach is used to couple the surface and subsurface phases. Straight and curved roadway geometries are accommodated via a curvilinear grid. The model is validated using steady state solutions that were obtained independently. PERFCODE was applied to a field monitoring site near Austin, Texas and hydrographs predicted by the model were consistent with field measurements. For a sample storm studied in detail, PFC reduced the duration of sheet flow conditions by 80%. The model may be used to improve the drainage design of PFC roadways. / text

An impermeable weir constructed across a stream prevents the longitudinal movement of aquatic life and transportation of physical and chemical substances in water, eventually having a negative impact on river environment. However, a rubble mound weir is considered environmentally friendly, since its permeability allows the streamwise migration of aquatic life. This thesis investigates the performance of this type of weir as a water use facility. The particular objective of the investigation is to study the flow mechanism in terms of water surface profile and discharge through the weir. In the study, flow through the rubble mound weir is considered non-Darcian, steady, and one-dimensional. In the analysis, gradually varied open channel flow algorithm is applied to porous medium flow through the rubble mound weir in which laminar and turbulent components of flow are taken into consideration. Unlike previous studies where Stephenson and Wilkins relations were used, in this thesis Forchheimer equation is used. To verify the validity of numerical solution of governing equation based on Forchheimer relation, an experimental investigation is conducted in the laboratory. The experimentally obtained water surface profiles are compared with the numerical results. It is observed that there is a satisfactory agreement between numerical and experimental results. The water surface profiles obtained by numerical solution are further compared with those based on Stephenson and Wilkins relations. It is concluded that the proposed numerical solution technique for the Forchheimer based governing equation may be used in the analysis of flow through, and design of rockfill weirs.

A pore-scale understanding of fluid flow underpins the constitutive laws of continuum-scale porous media flow. Porous media flow laws are founded on simplified pore structure such as the classical capillary tube model or the pore-network model, both of which do not include diverging-converging pore geometry in the direction of flow. Therefore, modifications in the fluid flow field due to different pore geometries are not well understood. Thus this may translate to uncertainties on how flow in porous media is predicted in practical applications such as geological sequestration of carbon dioxide, petroleum recovery, and contaminant’s fate in aquifers. To fill this gap, we have investigated the role of a spectrum of diverging-converging pore geometries likely formed due to different grain shapes which may be due to a variety of processes such as weathering, sediment transport, and diagenesis. Our findings describe the physical mechanisms for the failure of Darcy’s Law and the characteristics of Forchheimer Law at increasing Reynolds Number flows. Through fundamental fluid physics, we determined the forces which are most responsible for the continuum-scale porous media hydraulic conductivity (K) or permeability. We show that the pore geometry and the eddies associated therein significantly modify the flow field and the boundary stresses. This has important implications on mineral precipitation-dissolution and microbial growth. We present a new non-dimensional geometric factor β, a metric for diverging-converging pore geometry, which can be used to predict K. This model for K based on β generalizes the original and now widely-used Kozeny (1927) model which was based on straight capillary tubes. Further, in order to better quantify the feasibility of geological CO2 sequestration, we have conducted laboratory fluid flow experiments at reservoir conditions to investigate the controls of media wettability and grain shapes on pore-scale capillary trapping. We present experimental evidence for the snap-off or formation of trapped CO2 ganglion. The total trapping potential is found to be 15% of porosity for a water-wet media. We show that at the pore-scale media wettability and viscous-fingering play a critical role in transport and trapping of CO2. Our investigations clearly show that that in single-phase flow pore geometry significantly modifies pore-scale stresses and impacts continuum-scale flow laws. In two-phase flows, while the media wettability plays a vital role, the mobility ratio of CO2 - brine system significantly controls the CO2 capillary trapping potential- a result which should be taken into consideration while managing CO2 sequestration projects. / text

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Of all the strategies to reduce carbon emissions, carbon dioxide (CO₂) geological sequestration is an immediately available option for removing large amounts of the gas from the atmosphere. However, our understanding of the transition behavior between Forchheimer and Darcy flow through porous media during CO₂ injection is currently very limited. In addition, the kinetic mass transfer of SO₂ and CO₂ from CO₂ stream to the saline and the fully coupling between the changes of porosity and permeability and multiphase flow are two significant dimensions to investigate the brine acidification and the induced porosity and permeability changes due to SO₂ co-injection with CO₂. Therefore, this dissertation develops a multiphase flow, contaminant transport and geochemical model which includes the kinetic mass transfer of SO₂ into deep saline aquifers and obtains the critical Forchheimer number for both water and CO₂ by using the experimental data in the literature. The critical Forchheimer numbers and the multiphase flow model are first applied to analyze the application problem involving the injection of CO₂ into deep saline aquifers. The results show that the Forchheimer effect would result in higher displacement efficiency with a magnitude of more than 50% in the Forchheimer regime than that for Darcy flow, which could increase the storage capacity for the same injection rate and volume of a site. Another merit for the incorporation of Forchheimer effect is that more CO₂ would be accumulated in the lower half of the domain and lower pressure would be imposed on the lower boundary of the cap-rock. However, as a price for the advantages mentioned above, the injection pressure required in Forchheimer flow would be higher than that for Darcy flow. The fluid flow and contaminant transport and geochemical model is then applied to analyze the brine acidification and induced porosity and permeability changes due to SO₂ co-injection. The results show that the co-injection of SO₂ with CO₂ would lead to a substantially acid zone near the injecting well and it is important to include the kinetic dissolution of SO₂ from the CO₂ stream to the water phase into the simulation models, otherwise considerable errors would be introduced for the equilibrium assumption. This study provides a useful tool for future analysis and comprehension of multiphase Darcy-Forchheimer flow and brine acidification of CO₂ injection into deep saline aquifers. Results from this dissertation have practical use for scientists and engineers concerned with the description of flow behavior, and transport and fate of SO₂ during SO₂ co-injection with CO₂ in deep saline aquifers.

In this investigation, the flow friction associated with laminar pulsating flows through porous media was numerically studied. The problem is of interest for understanding the regenerators of Stirling and pulse tube cryocoolers. Two-dimensional flow in a system composed of a number of unit cells of generic porous structures was simulated using a CFD tool, with sinusoidal variations of flow with time. Detailed numerical data representing the oscillating velocity and pressure variations for five different generic porous structure geometries in the porosity range of 0.64 to 0.84, with flow pulsation frequency of 40 Hz were obtained, and special attention was paid to the phase shift characteristics between the velocity and pressure waves. Based on these detailed numerical data, the standard unsteady volume-averaged momentum conservation equation for porous media was then applied in order to obtain the instantaneous as well as cycle-averaged permeability and Forchheimer coefficients. It was found that the cycle-averaged permeability coefficients were nearly the same as those for steady flow, but the cycle-averaged Forchheimer coefficients were about two times larger than those for steady flow. Significant phase lags were observed with respect to the volume-averaged velocity and pressure waves. The parametric trends representing the dependence of these phase lags on porosity and flow Reynolds number were discussed. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and flow Reynolds number.

Cette thèse est consacrée à l'étude des équations du Darcy Brinkman Forchheimer (DBF) avec des conditions aux limites non standards. Nous montrons d'abord l'existence de différents type de solutions (faible, forte) correspondant au problème DBF stationnaire dans un domaine simplement connexe avec des conditions portants sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon. Ensuite, nous considérons le système Brinkman Forchheimer (BF) avec des conditions sur la pression dans un domaine non simplement connexe. Nous prouvons que ce problème est bien posé ainsi que l'existence de la solution forte. Nous établissons la régularité de la solution dans les espaces L^p pour p >= 2.L'étude et l'approximation du problème DBF non stationnaire est basée sur une approche pseudo-compressibilité. Une estimation d'erreur d'ordre deux est établie dans le cas o\`u les conditions aux limites sont de types Dirichlet ou Navier.Enfin, une méthode d'éléments finis Galerkin Discontinue est proposée et la convergence établie concernant le problème DBF linéarisé et le système DBF non linéaire avec des conditions aux limites non standard. / This thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions.

Die Trinkwassertalsperre Saidenbach wurde zwischen 1929 und 1933 nordöstlich von Pockau-Lengefeld gebaut. Sie staut mehrere Zuflüsse der Flöha, nämlich Forchheimer Dorfbach, Haselbach, Hölzelbergbach, Lippersdorfer Bach und Saidenbach. Mit über 146 Hektar Wasserfläche ist die Talsperre der größte Stausee im mittleren Erzgebirge und gleichzeitig der größte Trinkwasserspeicher im Verbundsystem Mittleres Erzgebirge. Zusammen mit den Talsperren Neunzehnhain 1 und 2 sowie Einsiedel stellt die Stauanlage Saidenbach Rohwasser für das Wasserwerk Einsiedel bereit, das Trinkwasser nach Chemnitz und Südsachsen liefert. Redaktionsschluss: 27.02.2020