Filtration modelling in wall-flow particulate filters of low soot penetration thickness

A filtration model for wall-flow particulate filters based on the theory of packed beds of spherical particles is presented to diagnose the combined response of filtration efficiency and pressure drop from a reliable computation of the flow field and the porous media properties. The model takes as main assumption the experimentally well-known low soot penetration thickness inside the porous wall. The analysis of soot loading processes in different particulate filters shows the ability of the proposed approach to predict the filtration efficiency as a function of the particle size distribution. Nevertheless, pressure drop and overall filtration efficiency are determined by the mode diameter of the raw particulate matter emission. The results reveal the dependence of the filtration efficiency in clean conditions on the sticking coefficient. However, the dynamics of the pressure drop and filtration efficiency as the soot loading varies is governed by the soot penetration thickness. This parameter is closely related to the porous wall Peclet number, which accounts for the porous wall and flow properties influence on the deposition process. The effect of the transition from deep bed to cake filtration regime on the pressure drop is also discussed underlying the importance of the macroscale over microscale phenomena.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through Grant No. TRA2013-40853-R. Additionally, the Ph.D. student E. Angiolini has been funded by a grant from Conselleria de Educacio, Cultura i Esport of the Generalitat Valenciana with reference GRISOLIA/2013/036. These supports are gratefully acknowledged by the authors.Serrano Cruz, JR.; Climent, H.; Piqueras, P.; Angiolini, E. (2016). Filtration modelling in wall-flow particulate filters of low soot penetration thickness. Energy. 112:883-898. https://doi.org/10.1016/j.energy.2016.06.121S88389811

High resolution modeling of transport in porous media

This dissertation presents research on the pore-level modeling of transport in porous media. The focus of this work is on high-resolution modeling, a rigorous approach that represents detailed geometry and first-principle physics at the streamline scale. Three major topics are presented in this dissertation: an efficient approach for solving Stokes flow in essentially arbitrary disordered porous media, high-resolution versus network simulations of dispersion phenomena, and a stochastic model for solving interfacial mass transfer from source spheres in porous media. First an approach was developed for solving the Stokes flow problem in a comparatively large, very heterogeneous two-dimensional porous media with high efficiency using a combined domain decomposition and boundary element method. The second topic discussed in this dissertation is the high-resolution and network simulation of dispersion in the porous media for the purpose of evaluating network discretization effects for the hydrodynamic model and the nodal mixing assumption for the solute transport model. It was found that molecular diffusion is not resolved properly with the nodal mixing assumption in the high Peclet number range. The third topic was the development of a stochastic model for simulating interfacial mass transfer from the surface of a single source sphere in a heterogeneous porous medium, which is valid in both low and high Peclet number range

Contribution to the understanding of filtration and pressure drop phenomena in wall-flow DPFs

From the last decades of the 20th century, internal combustion engines have undergone a continuous improvement process aimed to the increase of their efficiency and decrease of the pollutants emissions. The reduction of the availability of fossil fuel and the increase of human-made pollution observed in the last decades is leading worldwide to more stringent emission standards that make the engine manufacturers to constantly look for fuel consumption and emission reductions while keeping engine performance. To comply with current and incoming emission regulations, the exhaust line of internal combustion engines has been gradually complicated by the presence of aftertreatment systems. Among them, the particulate filter is the device in charge of abating the emission of soot in the atmosphere. Concerning compression ignition engines, diesel particulate filters (DPF) were first commercially utilized in significant numbers in passenger car and heavy-duty engines since the beginning of the 21st century. Euro 6 emission standards limits the emitted particulate matter from direct injection engines, thus extending the use of particulate filters also to direct injection gasoline engines. A deep knowledge of the phenomena happening inside the DPF is required for the correct understanding of the behaviour of this system and its interaction with the engine. The precise knowledge of the filtration and pressure drop processes is mandatory for the design of the particulate filter and is also essential to wisely think up and analyse solutions aimed to limit the negative impact of the filter on the fuel consumption maintaining its capability of retaining soot particles. Thus, the present work pretends to provide a contribution to the understanding of these phenomena in wall-flow DPFs. The problem has been faced on a computational and experimental basis. A notable part of the work was dedicated to the development and validation of a one-dimensional DPF filtration model to be coupled with the existing pressure drop model. The model was implemented in OpenWAM¿, the open-source gas dynamics software for internal combustion engines and components computation developed at CMT - Motores Térmicos. The developed computational tool was applied to the assessment of the aftertreatment (DOC&DPF) volume downsizing potential in post- and pre-turbo aftertreatment configuration. The study is completed with experimental analysis to support theoretical insights discussing how the soot deposition profile and the particulate layer properties impact on the DPF pressure drop.Desde las últimas décadas del siglo XX, se ha producido un proceso de mejora continua de los motores de combustión interna alternativos con el fin de aumentar su eficiencia y reducir las emisiones contaminantes. La reducción de la disponibilidad de combustibles fósiles y el incremento de la polución de origen antropogénico observados en las ultimas décadas ha provocado el progresivo endurecimiento de las normativas anticontaminación a nivel mundial obligando a los fabricantes de motores a buscar la reducción continua del consumo de combustible y emisiones, manteniendo las prestaciones del motor. El cumplimiento de las actuales y futuras normativas anticontaminación requiere de la instalación de diversos sistemas de postratamiento de gases en la línea de escape de los motores de combustión interna alternativos, aumentando su complejidad. Entre estos sistemas, el filtro de partículas es el equipo encargado de la reducción de la emisión de hollín a la atmósfera. Con respeto a los motores de encendido por compresión, los filtros de partículas diésel se implementaron por primera vez de forma masiva en vehículos de pasajeros y vehículos pesados a principio del siglo XXI. La normativa anti contaminación Euro 6 limita las emisiones de partículas de los motores de inyección directa, extendiendo el uso de filtros de partículas a los motores de inyección directa de gasolina. Es necesario tener un conocimiento profundo de los fenómenos que tienen lugar en el DPF para comprender el comportamiento de este sistema y su interacción con el motor. El conocimiento de los procesos de filtrado y perdida de presión es vital para el diseño del filtro de partículas y resulta esencial para encontrar y analizar soluciones que ayuden a limitar el impacto negativo del DPF sobre el consumo de combustible sin perder la capacidad de retener partículas de hollín. En este contexto, este trabajo pretende aportar una contribucción a la comprensión de estos fenómenos en filtros de partículas de flujo de pared. Esta tarea se ha planteado desde un punto de vista computacional y experimental. Parte importante de este trabajo ha consistido en el desarrollo y validación de un modelo de filtrado unidimensional de DPF que se ha acoplado con el modelo de caida de presión ya existente. El modelo se ha implementado en OpenWAM¿, el software de libre acceso para el cálculo fluidodinámico de motores de combustión interna y sus componentes desarrollado en CMT - Motores Térmicos. La herramienta computacional desarrollada se ha aplicado a la evaluación del potencial de reducción de volumen de sistemas de postratamiento (DOC&DPF) en configuraciones post- y pre-turbo. Este estudio se ha completado con un análisis experimental para dar respaldo a los conceptos teóricos empleados discutiendo como el perfil de deposición del hollín y las propiedades de la capa de partículas afectan a la perdida de presión del DPF.Des les últimes dècades del segle XX, s'ha produït un procés de millora contínua dels motors de combustió interna alternatius amb l'objectiu d'augmentar la seua eficiència i reduir les emissions contaminants. La reducció de la disponibilitat de combustibles fòssils i l'increment de la polució d'origen antropòlogic observats en les últimes dècades ha provocat que les normatives anticontaminació s'han fet més rígides a nivell mundial, obligant als fabricants de motors a buscar la reducció contínua del consum de combustibles i emissions, mantenint les prestacions dels motors. El cumpliment de les normes anticontaminació actuals i futures, requereixen de l'instalació de diversos sistemes de post-tractament de gasos a l'eixida dels motors de combustió interna alternatius, llavors augmentant la complexitat. Entre aquestos sistemes, el filtre de partícules es l'equip encarregat de la reducció de les partícules de sutge a l'atmosfera. Respecte als motors d'encès per compressió, els filtres de partícules van instalar-se de manera massiva als vehicles de passatgers i vehicles pesats al principi del segle XXI. La normativa anti contaminació Euro 6 limita les emissions de partícules dels motors d'inyecció directa, estenent l'ús del filtre de partícules als motors d'injecció directa de gasolina. És necessari tindre un coneixement dels fenòmens que tenen lloc al DPF per a comprendre el comportament del sistema i la seua interacció amb el motor. El coneixement dels processos de filtrat i la pèrdua de pressió és vital per al diseny del filtre de partícules i resulta essencial per a trobar i analitzar les solucions que ajuden a limitar l'impacte negatiu del DPF sobre el consum de combustible sense perdre la capacitat de retenir partícules de sutge. En aquest context, el projecte pretén aportar una contribució a la comprensió d'aquestos fenòmens en els filtres de partícules de flux de paret. Aquesta feina s'ha plantejat des d'un punt de vista computacional i experimental. Part important d'aquest treball ha consistit en el desenvolupament i validació d'un model de filtrat unidimensional de DPF que s'ha acoplat a un model de pèrdua de pressió existent. El model s'ha implementat en OpenWAM¿, el software de lliure accés per al cálcul fluidodinámic de motors de combustió interna i els seus components desenvolupats al CMT - Motores Térmicos. La ferramenta computacional desenvolupada s'ha aplicat a la evaluació del potencial de reducció del volum de sistemes de post tractament (DOC&DPF) en les configuracions post- i pre-turbo. Aquest estudi s'ha completat amb una anàlisi experimental per a donar suport als concepts teòrics emprats discutint com el perfil de la disposició de sutge i les propietats de la capa de partícules que afecten a la pèrdua de pressió del DPF.Angiolini, E. (2017). Contribution to the understanding of filtration and pressure drop phenomena in wall-flow DPFs [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86157TESI

Direct Simulation of Transport in Open-Cell Metal Foams

Flows in porous media may be modeled using two major classes of approaches: (a) a macroscopic approach, where volume-averaged semiempirical equations are used to describe flow characteristics, and (b) a microscopic approach, where small-scale flow details are simulated by considering the specific geometry of the porous medium. In the first approach, small-scale details are ignored and the information so lost is represented in the governing equations using an engineering model. In the second, the intricate geometry of the porous structures is accounted for and the transport through these structures computed. The latter approach is computationally expensive if the entire physical domain were to be simulated. Computational time can be reduced by exploiting periodicity when it exists. In the present work we carry out a direct simulation of the transport in an open-cell metal foam using a periodic unit cell. The foam geometry is created by assuming the pore to be spherical. The spheres are located at the vertices and at the center of the unit cell. The periodic foam geometry is obtained by subtracting the unit cell cube from the spheres. Fluid and heat flow are computed in the periodic unit cell. Our objective in the present study is to obtain the effective thermal conductivity, pressure drop, and local heat transfer coefficient from a consistent direct simulation of the open-cell foam structure. The computed values compare well with the existing experimental measurements and semiempirical models for porosities greater than 94%. The results and the merits of the present approach are discussed

Longitudinal dispersion in nonuniform isotropic porous media

A theoretical and experimental investigation has been made of the longitudinal dispersion of chemically and dynamically passive solutes during flow through nonuniform, isotropic porous media. Both theoretical and experimental results are limited to the high Peclet number, low Reynolds number flow regime. The goal of the theoretical investigation is to provide a quantitative method for calculating the coefficient of longitudinal dispersion using only measurable structural features of the porous medium and the characteristics of the carrying fluid and solute. A nonuniform porous medium contains variations in grain scale pore structure, but is homogeneous at the macroscopic level for quantities such as the permeability or porosity. A random capillary tube network model of nonuniform porous media is developed which uses a pore radius distribution and pore length distribution to characterize the grain scale structure of porous media. The analysis gives the asymptotic longitudinal dispersion coefficient in terms of integrals of kinematic properties of solute particles flowing through individual, random capillary tubes. However, shear dispersion within individual capillary tubes is found to have negligible impact on the overall longitudinal dispersion in porous media. The dispersion integrals are evaluated using a Monte Carlo integration technique. An analysis of the permeability in nonuniform porous media is used to establish a proper flow field for the analysis of longitudinal dispersion. The experimental investigation of longitudinal dispersion is carried out by measuring (with conductivity probes) the development of an initially sharp miscible displacement interface. The experimentally determined longitudinal dispersion coefficients are found to be greater in nonuniform media than in uniform media when compared using Peclet numbers based on the geometric mean grain diameter. The experimental breakthrough curves also display highly asymmetrical shapes, in which the "tail" of the breakthrough is longer than would be expected from advection-diffusion theory. Although the theoretical model does not predict the tailing behavior, it is found that the leading portion of the breakthrough curve is described by advection-diffusion theory. The theoretically determined longitudinal dispersion coefficients lie roughly within a factor of 1.35 of the measured values. The material presented in this report is essentially the same as the thesis submitted by the author in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Pore-scale simulation of micro and nanoparticle transport in porous media

The transport and deposition of colloidal particles in saturated porous media are processes of considerable importance in many fields of science and engineering, including the propagation of contaminants and of microorganisms in aquifer systems and the use of micro- and nano-particles as reagents for groundwater remediation interventions. Colloid transport is a peculiar multi-scale problem: pore-scale phenomena and inter granular dynamics have an important impact on the larger-scale transport. In this thesis a microscale approach was used to gain a better understanding of the mechanisms underlying colloidal processes, such as deposition and aggregation. The research activity was carried out by performing numerical simulations through the FEM software, COMSOL Multiphysics®. The first part of the study focuses on the development of a new correlation equation to predict single collector efficiency, a key concept in filtration theory, which allows predicting particle deposition on a single spherical collector. By performing Eulerian and Lagrangian simulations in a simple geometry and by using an innovative approach to interpret the results, a new correlation equation to predict single collector efficiency has been formulated. A hierarchical approach to interpret the results was exploited. The proposed correlation equation presents innovative features, such as the validity for a wide range of parameters (also at very small Peclet numbers), the prediction of efficiency values always lower than unity, the total flux normalization and the analysis of the mutual interactions between the main transport mechanisms (advection, gravity and diffusion) and the steric effect. The final formula was also extended to include porosity and a reduced model was proposed. The second part of the study focuses on more realistic systems, characterized by a column of spherical collectors in series. The numerical simulations performed show the limits of the existing models to interpret the experimental data. Therefore, a more rigorous procedure to evaluate the filtration processes in presence of a series of collectors was developed

Direct Pore Level Simulation of Heat Transfer in Open Cell Reticulated Porous Ceramics

The project involved in studying the fluid transport, heat and mass transport inside various ceramic porous inserts by Direct Pore Level Simulations (DPLS). The geometric grid data required for the simulations are reconstructed from the computer tomographic scan images of the real porous media. The simulation results are used to study the influence of the structural properties of porous media on the fluid flow, heat transfer and mass transfer

Homogenization of two fluid flow in porous media

The macroscopic behavior of air and water in porous media is often approximated using Richards’ equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e., constant gas pressure, this model is shown to reduce to the simpler form of Richards’ equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media to the underlying geometrical and material properties

Investigation of local mixing and its influence on core scale mixing (dispersion)

textLocal displacement efficiency in miscible floods is significantly affected by mixing taking place in the medium. Laboratory experiments usually measure flow-averaged ("cup mixed") effluent concentration histories. The core-scale averaged mixing, termed as dispersion, is used to quantify mixing in flow through porous media. The dispersion coefficient has the contributions of convective spreading and diffusion lumped together. Despite decades of research there remain questions about the nature and origin of dispersion. The main objective of this research is to understand the basic physics of solute transport and mixing at the pore scale and to use this information to explain core-scale mixing behavior (dispersion). We use two different approaches to study the interaction between convective spreading and diffusion for a range of flow conditions and the influence of their interaction on dispersion. In the first approach, we perform a direct numerical simulation of pore scale solute transport (by solving the Navier Stokes and convection diffusion equations) in a surrogate pore space. The second approach tracks movement of solute particles through a network model that is physically representative of real granular material. The first approach is useful in direct visualization of mixing in pore space whereas the second approach helps quantify the effect of pore scale process on core scale mixing (dispersion). Mixing in porous media results from interaction between convective spreading and molecular diffusion. The converging-diverging flow around sand grains causes the solute front to stretch, split and rejoin. In this process the area of contact between regions of high and low solute concentrations increases by an order of magnitude. Diffusion tends to reduce local variations in solute concentration inside the pore body. If the fluid velocity is small, diffusion is able to homogenize the solute concentration inside each pore. On the other hand, in the limit of very large fluid velocity (or no diffusion) local mixing because of diffusion tends to zero and dispersion is entirely caused by convective spreading. Flow reversal provides insights about mixing mechanisms in flow through porous media. For purely convective transport, upon flow reversal solute particles retrace their path to the inlet. Convective spreading cancels and echo dispersion is zero. Diffusion, even though small in magnitude, causes local mixing and makes dispersion in porous media irreversible. Echo dispersion in porous media is far greater than diffusion and as large as forward (transmission) dispersion. In the second approach, we study dispersion in porous media by tracking movement of a swarm of solute particles through a physically representative network model. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes' equation. In the absence of diffusion the paths of all solute particles are completely determined and reversible. We track the movement of solute particles on these paths to investigate dispersion caused by purely convective spreading at the pore scale. Then we superimpose diffusion and study its influence on dispersion. In this way we obtain for the first time an unequivocal assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion through porous media. Alternative particle tracking algorithms that use a probabilistic choice of an out-flowing throat at a pore fail to quantify convective spreading accurately. For Fickian behavior of dispersion it is essential that all solute particles encounter a wide range of independent (and identically distributed) velocities. If plug flow occurs in the pore throats a solute particle can encounter a wide range of independent velocities because of velocity differences in pore throats and randomness of pore structure. Plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading causing dispersion to be simply the sum of convective spreading and diffusion. In plug flow hydrodynamic dispersion varies linearly with the pore-scale Peclet number. For a more realistic parabolic velocity profile in pore throats particles near the solid surface of the medium do not have independent velocities. Now purely convective spreading is non-Fickian. When diffusion is non-zero, solute particles can move away from the low velocity region near the solid surface into the main flow stream and subsequently dispersion again becomes asymptotically Fickian. Now dispersion is the result of an interaction between convection and diffusion and it results in a weak nonlinear dependence of dispersion on Peclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data. We conclude that the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (i) stream splitting of the solute front at every pore, thus causing independence of particle velocities purely by convection, (ii) a velocity gradient within throats and (iii) diffusion. Taylor's dispersion in a capillary tube accounts for only the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts for the only the first and third phenomena, resulting in a linear dependence of dispersion upon Peclet number.Petroleum and Geosystems Engineerin