In this thesis, PN simulations of drying are compared with experimentally obtained data fromdrying of a representative 2D microfluidic network in SiO2 under varying thermal conditions withthe aim to identify governing physical pore scale effects. Gravity and viscous effects aredisregarded in this thesis. Instead drying with slight local temperature variation and drying withimposed thermal gradients are studied. Based on this investigation, a powerful non-isothermalPNM is developed. This model incorporates i) the phenomena associated with the temperaturedependency of pore scale invasion, namely thermally affected capillary invasion and vapor flow aswell as ii) the secondary effects induced by wetting liquid films of different morphology. This studyclearly evidences that the macroscopic drying behavior is fundamentally dictated by thetemperature gradient imposed on the PN and moreover by the secondary capillary invasion aswell. In agreement with literature, invasion patterns as in invasion percolation with progressiveevaporation of single clusters are observed in drying with negligible local temperature variation;gradients with temperature decreasing from the surface (negative temperature gradient) canstabilize the drying front, evolving between the invading gas phase and the receding liquid phase,whereas temperature increasing from the surface (positive temperature gradient) leads todestabilization of the liquid phase with early breakthrough of a gas branch and initiation of asecond invasion front migrating in opposite direction to the evaporation front receding from theopen surface of the PN. Special attention is paid on the distinct drying regimes found in thesituation of a positive gradient because they are associated with different pore scale invasionprocesses. More precisely, temperature dependency of surface tension dictates the order ofinvasion as long as the liquid phase is connected in a main liquid cluster (usually found during thefirst period of drying). In contrast to this, detailed study of the vapor transfer mechanismsemphasizes that vapor diffusion through the partially saturated region can control the pore leveldistributions of liquid and gas phase during the period of drying when the liquid phase isdisconnected into small clusters. This is also related to the cluster growth induced by partialcondensation of vapor. It is shown and discussed in detail in this thesis that this effect not onlydepends on direction and height of the temperature gradient for a given pore size distribution butthat moreover the overall evaporation rate influences the cluster growth mechanism. This indicatesthat liquid migration during drying of porous media might be controlled by the interplay of thermalgradients and drying rate. In summary, the study of thermally affected drying of the 2-dimensionalPN reveals complex pore scale mechanisms, usually also expected in drying of real porous media.This leads to the development of a strong mathematical pore scale model based on experimentalfindings. It is demonstrated how this model might be applied to understand and develop moderndrying processes based on the simulation of thermally affected pore scale mass transfer

Pore network models have served as a predictive tool for soil and rock properties with a broad range of applications, particularly in oil recovery, geothermal energy from underground reservoirs, and pollutant transport in soils and aquifers [39]. They rely on the representation of the void space within porous materials as a network of interconnected pores with idealised geometries. Typically, a two-phase flow simulation of a drainage (or imbibition) process is employed, and by averaging the physical properties at the pore scale, macroscopic parameters such as capillary pressure and relative permeability can be estimated. One of the most demanding tasks in these models is to include the possibility of fluids to remain trapped inside the pore space. In this work I proposed a trapping rule which uses the information of neighboring pores instead of a search algorithm. This approximation reduces the simulation time significantly and does not perturb the accuracy of results. Additionally, I included spatial correlation to generate the pore sizes using a matrix decomposition method. Results show higher relative permeabilities and smaller values for irreducible saturation, which emphasizes the effects of ignoring the intrinsic correlation seen in pore sizes from actual porous media. Finally, I implemented the algorithm from Raoof et al. (2010) [38] to generate the topology of a Fontainebleau sandstone by solving an optimization problem using the steepest descent algorithm with a stochastic approximation for the gradient. A drainage simulation is performed on this representative network and relative permeability is compared with published results. The limitations of this algorithm are discussed and other methods are suggested to create a more faithful representation of the pore space.

Pore-scale network modeling has become an effective method for accurate prediction and upscaling of macroscopic properties, such as permeability. Networks are either mapped directly from real media or stochastic methods are used that simulate their heterogeneous pore structure. Flow is then modeled by enforcing conservation of mass in each pore and approximations to the momentum equations are solved in the connecting throats. In many cases network modeling compares favorably to experimental measurements of permeability. However, computational and imaging restrictions generally limit the network size to the order of 1 mm3 (few thousand pores). For extremely heterogeneous media these models are not large enough in capturing the petrophysical properties of the entire heterogeneous media and inaccurate results can be obtained when upscaling to the continuum scale. Moreover, the boundary conditions imposed are artificial; a pressure gradient is imposed in one dimension so the influence of flow behavior in the surrounding media is not included. In this work we upscale permeability in large, heterogeneous media using physically-representative pore-scale network models (domain ~106 pores). High-performance computing is used to obtain accurate results in these models, but a more efficient, novel domain decomposition method is introduced for upscaling the permeability of pore-scale models. The medium is decomposed into hundreds of smaller networks (sub-domains) and then coupled with the surrounding models to determine accurate boundary conditions. Finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the interfaces of the networks boundaries. The results compare favorably to the more computationally intensive (and impractical) approach of upscaling the media as a single model. Moreover, the results are much more accurate than traditional hierarchal upscaling methods. This upscaling technique has important implications for using pore-scale models directly in reservoir simulators in a multiscale setting. The upscaling techniques introduced here on single phase flow can also be easily extended to other flow phenomena, such as multiphase and non-Newtonian behavior. / text

This research addresses a number of fundamental issues concerning convective mass transfer across fluid-fluid interfaces in porous media. Mass transfer to/from distributed sinks/sources is considered for i) the slow dissolution of liquid filaments of a wetting non-aqueous phase liquid (NAPL) held in the corners of angular pores or throats and ii) the fate of gas bubbles generated during the flow of a supersaturated aqueous phase in porous media. 1. Effects of the stability of NAPL films on wetting NAPL dissolution Wettability profoundly affects the distribution of residual NAPL contaminants in natural soils. Under conditions of preferential NAPL wettability, NAPL is retained within small pores and in the form of thick films (liquid filaments) along the corners and crevices of the pore walls. NAPL films in pore corners provide capillary continuity between NAPL-filled pores, dramatically influencing the behaviour of NAPL dissolution to the flowing aqueous phase by convection and diffusion. A pore network model is developed to explore the dissolution behaviour of wetting NAPL in porous media. The effects of initial NAPL distribution and NAPL film stability on dissolution behaviour are studied using the simulator. NAPL phase loses continuity and splits into disconnected clusters of NAPL-filled pores due to rupture of NAPL films. Quasi-state drainage and fingering of the aqueous phase into NAPL-filled pores is treated as an invasion percolation process and a stepwise procedure is adopted for the solution of flow and solute concentration fields. NAPL film stability is shown to critically affect the rate of mass transfer as such that stable NAPL films provide for more rapid dissolution. The network simulator reproduces the essential physics of wetting NAPL dissolution in porous media and explains the concentration-tailing behaviour observed in experiments, suggesting also new possibilities for experimental investigation. 2. Convective Mass Transfer across Fluid Interfaces in Straight Angular Pores Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid-fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (???perfect-slip???) and infinite surface shear (???no-slip???) at the fluid-fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid-fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen [2001]. Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published ???2D-slit??? approximation to the problem at hand is checked and found to be in considerable error. 3. Bubble evolution driven by solute diffusion during the process of supersaturated carbonated water flooding In situ bubble growth in porous media is simulated using a pore network model that idealizes the pore space as a lattice of cubic chambers connected by square tubes. Evolution of the gas phase from nucleation sites is driven by the solute mass transfer from the flowing supersaturated water solution to the bubble clusters. Effects of viscous aqueous phase flow and convective diffusion in pore corners are explicitly accounted for. Growth of bubble clusters is characterised by a pattern of quasi-static drainage and fingering in the gas phase, an invasion percolation process controlled by capillary and gravitational forces. A stepwise solution procedure is followed to determine the aqueous flow field and the solute concentration field in the model by solving the conservation equations. Mobilization of bubbles driven by buoyancy forces is also studied. Results of bubble growth pattern, relative permeability and macroscopic mass transfer coefficient are obtained under different gas saturations and aqueous flow conditions.

Dans cette thèse, des simulations PN de séchage sont comparées à des données expérimentales obtenues dans le séchage d´un réseau de micro-fluidique 2D représentatif dans du SiO2 soumis à des conditions thermiques variables dans le but d’identifier les phénomènes physiques à l´échelle des pores qui sont les plus influents. A partir de cette étude, un PN efficace non-isotherme est développé. Ce modèle incorpore i) les phénomènes associés à la dépendendence en température de l´invasion à l´échelle des pores, c´est à dire l´invasion capillaire sous effet thermique et le flux de vapeur ainsi que ii) le transport secondaire induit par d´épais films liquides observé dans les expériences de microfluidique. Cette étude prouve clairement que le comportement macroscopique du séchage est fondamentalement dirigé par le gradient de température imposé sur le PN ainsi que par le transport capillaire secondaire. En accord avec la littérature, les schémas d´invasion que l´on trouve dans l´invasion percolatrice avec l´évaporation progressive d´amas individuels sont observés dans le séchage à variation de température locale négligeable;des gradients où la température diminue à partir de la surface (gradient de température négatif)peut stabiliser le front de séchage, qui évolue entre la phase gazeuse invasive et la phase liquide qui recule, alors qu´une température qui augmente à partir de la surface (gradient de température positif) amène à la déstabilisation de la phase liquide avec une percée prématurée de la branche gazeuse et l’initiation d´un deuxième front de séchage qui migre dans la direction opposé de celle du front de séchage original. Une attention particulière est prêtée aux régimes distincts que l´on trouve dans le second cas (gradient positif) parce qu´ils sont associés à différents procédés d´invasion à l´échelle des pores. Plus précisément, la dépendance en température de la tension de surface établit l´ordre d´invasion tant que la phase liquide est connectée au groupe liquide principal (que l´on trouve généralement pendant la première période de séchage). En revanche,l´étude détaillée des mécanismes de transfert de la vapeur met l´accent sur le fait que la diffusion de la vapeur à travers la région partiellement saturée peut contrôler les distributions des phases gazeuses et liquides à l´échelle des pores pendant la période de séchage lorsque la phase liquide est déconnectée en petits groupes. Cela est aussi lié à la croissance des amas induite par la condensation partielle de la vapeur. Cette thèse montre et discute en détail que cet effet ne dépend pas seulement de la direction et magnitude du gradient de température pour une distribution de tailles de pores donnée mais qu’en plus le taux d´évaporation influence le mécanisme de croissances des amas. Cela indique que la migration du liquide pendant la phase de séchage de milieux poreux peut être contrôlé par l’interaction des gradients thermiques et du taux de séchage. En somme, l´étude du séchage sous effet thermique des réseaux de pores 2D révèle des phénomènes complexes à l´échelle des pores, généralement aussi anticipés dans le séchage des milieux poreux réels. Cela mène au développement d´un modèle mathématique efficace au niveau des pores basés sur des découvertes expérimentales. Cette thèse démontre la manière dont ce modèle peut être appliqué afin de comprendre et développer des procédés de séchage modernes basés sur la simulation du transfert de masse sous effet thermique à l´échelle des pores / In this thesis, PN simulations of drying are compared with experimentally obtained data fromdrying of a representative 2D microfluidic network in SiO2 under varying thermal conditions withthe aim to identify governing physical pore scale effects. Gravity and viscous effects aredisregarded in this thesis. Instead drying with slight local temperature variation and drying withimposed thermal gradients are studied. Based on this investigation, a powerful non-isothermalPNM is developed. This model incorporates i) the phenomena associated with the temperaturedependency of pore scale invasion, namely thermally affected capillary invasion and vapor flow aswell as ii) the secondary effects induced by wetting liquid films of different morphology. This studyclearly evidences that the macroscopic drying behavior is fundamentally dictated by thetemperature gradient imposed on the PN and moreover by the secondary capillary invasion aswell. In agreement with literature, invasion patterns as in invasion percolation with progressiveevaporation of single clusters are observed in drying with negligible local temperature variation;gradients with temperature decreasing from the surface (negative temperature gradient) canstabilize the drying front, evolving between the invading gas phase and the receding liquid phase,whereas temperature increasing from the surface (positive temperature gradient) leads todestabilization of the liquid phase with early breakthrough of a gas branch and initiation of asecond invasion front migrating in opposite direction to the evaporation front receding from theopen surface of the PN. Special attention is paid on the distinct drying regimes found in thesituation of a positive gradient because they are associated with different pore scale invasionprocesses. More precisely, temperature dependency of surface tension dictates the order ofinvasion as long as the liquid phase is connected in a main liquid cluster (usually found during thefirst period of drying). In contrast to this, detailed study of the vapor transfer mechanismsemphasizes that vapor diffusion through the partially saturated region can control the pore leveldistributions of liquid and gas phase during the period of drying when the liquid phase isdisconnected into small clusters. This is also related to the cluster growth induced by partialcondensation of vapor. It is shown and discussed in detail in this thesis that this effect not onlydepends on direction and height of the temperature gradient for a given pore size distribution butthat moreover the overall evaporation rate influences the cluster growth mechanism. This indicatesthat liquid migration during drying of porous media might be controlled by the interplay of thermalgradients and drying rate. In summary, the study of thermally affected drying of the 2-dimensionalPN reveals complex pore scale mechanisms, usually also expected in drying of real porous media.This leads to the development of a strong mathematical pore scale model based on experimentalfindings. It is demonstrated how this model might be applied to understand and develop moderndrying processes based on the simulation of thermally affected pore scale mass transfer

We study hydrate formation and distribution in two scales. Pore-scale network modeling for drainage and imbibition and 1D field-scale sedimentological model are proposed for such purpose. The network modeling is applied in a novel way to obtain the possible hydrate and fluid saturations in the porous medium. The sedimentological model later uses these results to predict field-scale hydrate distribution. In the model proposed by (Behseresht et al., 2009a), gas charge in the reservoir firstly takes place when BGHSZ (Base of Gas Hydrate Stability Zone) is still above the reservoir. Methane gas migrates from deep source and is contained in the reservoir by the capillary barrier. The gas saturation distribution is determined by gas/water capillary pressure, and is modeled by network modeling of drainage. When gas charge is complete, the gas column in the reservoir is assumed to be disconnected from the deep source, and BGHSZ begins to descend. Hydrate formation is assumed to occur only at BGHSZ. At the microscopic scale it first occurs at the methane/water interface. A review of the possible modes of growth leads to the assumption that hydrate grows into the gaseous phase. It is assumed that the hydrate formation at the pore scale follows the path of imbibition process (displacement of gas phase by aqueous phase), and can be predicted by the network modeling of imbibition. Two scenarios, corresponding to slow and fast influx of water to the BGHSZ, are proposed to give the maximum and minimum hydrate saturations, respectively. The volume of hydrate is smaller than the total volume of gas and water that are converted at fixed temperature and pressure. Therefore, vacancy is created to draw free gas from below the BGHSZ and water into the BGHSZ. BGHSZ keeps descending and converting all the gas at BGHSZ into hydrate. The final hydrate profile has a characteristic pattern, in which a region of high hydrate saturation sits on top of a region with low hydrate saturation. This pattern agrees with the observation in Mount Elbert and Mallik sites. The low hydrate saturation in certain regions with good lithology shows that hydrate distribution is not only controlled by the quality of lithology, but also the gas redistribution during hydrate formation. / text

Fluid flow in porous media is important for a number of fields including nuclear waste disposal, oil and gas, fuel cells, water treatment and civil engineering. The aim of this work is to improve the current understanding of how the pore space governs the fluid flow in porous media in the context of nuclear waste disposal. The effects of biofilm formation on flow are also investigated. The thesis begins with a review of the current porous media characterisation techniques and the means for converting the pore space into pore network models and their existing applications. Further, I review the current understanding of biofilm lifecycle in the context of porous media and its interactions with fluid flow. The model porous media used in this project is Hollington sandstone. The pore space of the material is characterised by X-ray CT and the equivalent pore networks from two popular pore network extraction algorithms are compared comprehensively. The results indicate that different pore network extraction algorithms could interpret the same pore space rather differently. Despite these differences, the single-phase flow properties of the extracted networks are in good agreement with the estimates from a direct approach. However, it is recommended that any flow or transport study using pore network modelling should entail a sensitivity study aiming to determine if the model results are extraction method specific. Following these results, a pore merging algorithm is introduced aimed to improve the over segmentation of long throats and hence improve the quality of the extracted statistics. The improved model is used to study quantitatively the pore space evolution of shale rock during pyrolysis. Next, the extracted statistics from one of the algorithms is used to explore the potential of regular pore network models for up-scaling the flow properties of porous materials. Analysis showed that the anisotropic flow properties observed in the irregular models are due to the different number of red (critical) features present along the flow direction. This observation is used to construct large regular models that can mimic that behaviour and to discuss the potential of estimating the flow properties of porous media based on their isotropic and anisotropic properties. Finally, a long-term flow-through column experiment is conducted aiming to understand the effects of bacterial colonisation on flow in Hollington sandstone. The results show that such systems are quite complex and are susceptible to perturbations. The flow properties of the sandstone were reduced significantly during the course of the experiment. The possible mechanisms responsible for the observed reductions in permeability are discussed and the need for developing new imaging techniques that can allow examining biofilm development in-situ is underlined as necessary for drawing more definitive conclusions.

Firebrand pile ignition of adjacent materials requires an in-depth understanding of heat transfer and flow profile within the firebrand pile. Modeling the firebrand pile as a fibrous porous medium, this study identified a porosity-permeability correlation that accurately describes the transport properties of a firebrand pile. The conduction-based model and Kozeny-Carman model were identified and examined by experiment, where firebrand porosity and permeability were collected with a wind tunnel. The conduction-based model was more stable and more accurate in the porosity range of interest. Pore network models were developed for the simulation of flow profiles utilizing the permeability data collected. The non-uniform network, which better represents a randomly stack firebrand pile, resulted in a more complex multidimensional flow within the pile. / Master of Science / Firebrands are known to be one of the primary ways wildfires can spread. They are mostly small pieces of flammable materials originating from vegetation or wooden structures that can be carried by wind ahead of the fire. The accumulation of firebrands on flammable materials tends to create ignitions, which calls for an in-depth understanding of temperature and airflow within the firebrand pile. Simplifying the firebrand pile as a porous medium, this study identified a relationship between how much void is present in the pile and the resistance of airflow of a firebrand pile. The conduction-based model and Kozeny-Carman model were identified and examined by experiment with a wind tunnel. The conduction-based model was determined to better describe the relationship. Pore network models were developed for the simulation of flow through the firebrand pile utilizing the data collected in the experiment, which provided an understanding of how airflow behaves inside the pile. A non-uniform flow network inside the pile led to a more complex, multidimensional flow through the firebrand pile.

[pt] A formação e o acúmulo de condensado em reservatórios de gás retrógrado, especialmente na vizinhança de poços de produção, obstruem parcialmente o fluxo de gás e afetam negativamente a composição dos fluidos produzidos. Entretanto, a previsão de bloqueio por condensado é comumente imprecisa, visto que experimentos raramente reproduzem as condições extremas e composições complexas dos fluidos dos reservatórios, enquanto a maioria dos modelos em escala de poros simplificam demasiadamente os fenômenos físicos associados à transição de fases entre gás e condensado. Para corrigir essa lacuna, um modelo de rede de poros isotérmico composicional e totalmente implícito é apresentado. As redes de poros propostas consistem em estruturas tridimensionais de capilares constritos circulares. Modos de condensação e padrões de escoamento são atrubuídos aos capilares de acordo com a molhabilidade do meio, as saturações locais e a influência de forças viscosas e capilares. Nos nós da rede, pressão e conteúdo molar são determinados através da solução acoplada de equações de balanço molar e consistênc ia de volumes. Concomitantemente, um cálculo de flash à pressão e à temperatura constantes, baseado na equação de estado de Peng e Robinson, é realizado em cada nó, atualizando as saturações e composições das fases. Para a validação do modelo proposto, análises de escoamento foram executadas baseadas em experimentos de escoamento em testemunho reportados na literatura, usando composição dos fluidos e condições de escoamento correspondentes, e geometria do meio poroso aproximada. Curvas de permeabilidade relativa medidas nos experimentos e previstas pelo modelo mostraram boa concordância quantitativa, para dois valores de tensão interfacial e três valores de velocidade de escoamento de gás. Após a validação, o modelo foi usado para avaliar alteração de molhabilidade e injeção de gás como possíveis métodos de recuperação avançada para reservatórios de gás retrógrado. Os resultados exibiram tendências similares àquelas observadas em experimentos de escoamento em testemunhos, e condições ótimas para melhoramento do escoamento foram identificadas. / [en] Liquid dropout and accumulation in gas-condensate reservoirs, especially in the near wellbore region, hinder gas flow and affect negatively the produced fluid composition. Yet, condensate banking forecasting is commonly inaccurate, as experiments seldom reproduce reservoir extreme conditions and complex fluid composition, while most pore-scale models oversimplify the physical phenomena associated with phase transitions between gas and condensate. To address this gap, a fully implicit isothermal compositional pore-network model for gas and condensate flow is presented. The proposed pore-networks consist of 3D structures of constricted circular capillaries. Condensation modes and flow patterns are attributed to the capillaries according to the medium s wettability, local saturations and influence of viscous and capillary forces. At the network nodes, pressure and molar contents are determined via the coupled solution of molar balance and volume consistency equations. Concomitantly, a PT-flash based on the Peng-Robinson equation of state is performed for each node, updating the local phases saturations and compositions. For the proposed model validation, flow analyses were carried out based on coreflooding experiments reported in the literature, with matching fluid composition and flow conditions, and approximated pore-space geometry. Predicted and measured relative permeability curves showed good quantitative agreement, for two values of interfacial tension and three values of gas flow velocity. Following the validation, the model was used to evaluate wettability alteration and gas injection as prospect enhanced recovery methods for gas-condensate reservoirs. Results exhibited similar trends observed in coreflooding experiments and conditions for optimal flow enhancement were identified.

Le transport réactif des NPs en milieu poreux regroupe trois principaux processus : l’agrégation, le dépôt et le transport des NPs. Le système réel est caractérisé par la complexité et l’interdépendance de ces trois processus. En plus, ces derniers ne possèdent pas forcément la même échelle propre d’étude ou de modélisation. Cela explique la difficulté majeure pour décrire simultanément tous ces processus couplés et interdépendants dans un seul modèle aisément utilisable. Au départ, nous avons simplifié ce système en séparant les différents processus. Ensuite, nous résolvons le problème d’échelle, par l’approche d’homogénéisation ou par l’approche multi-échelles. La séparation du problème, en plusieurs processus et sur plusieurs échelles d’espace, facilite la résolution numérique et la compréhension des processus élémentaires. Dans cette étude, une approche multi-échelles a été développée pour modéliser ces trois processus (l’agrégation, le dépôt et le transport des NPs), chacun dans sa propre échelle. Nous avons considéré deux échelles de taille, l’échelle microscopique ou d’interface (nanométrique), et l’échelle mésoscopique correspondant à la taille des pores (micrométrique). A l’échelle microscopique, les processus d’agrégation et de dépôt ont été modélisés, de manière similaire, avec la théorie DLVO. Les propriétés électrostatiques de surface des NPs ou de la roche sont décrites par un modèle de complexation de surface développé sous PhreeqC. Ce modèle d’interface est testé pour deux types de matériaux, le titane pour les NPs et la silice pour la roche. A l’échelle mésoscopique, le dépôt est quantifié par la théorie classique de la filtration (CFT : Classical Filtration Theory) dans la phase initiale où le filtre est propre. Le processus de transport a été simulé par un modèle de réseau de pores (PNM : Pore Network Model) à l’échelle mésoscopique. Ce modèle de transport est couplé avec le modèle d’agrégation-dépôt et indirectement avec le modèle de complexation de surface en un seul modèle appelé PhreeqC Pore Network Transport(PPNT1.0). / Reactive transport of NPs in porous media involves three main processes: aggregation, deposition and transport of NPs. The natural system is characterized by the complexity and interdependence of these three processes. In addition, these processes do not necessarily have the same study or modeling scale. This explains the extreme difficulty to describe simultaneously all these interdependent processes in one easy-tohandle numerical model. We have simplified the system by separating the different processes. Then, we solve the problem of scale by the homogenization or the multi-scale approach. Dividing the initial problem into different processes on different scales facilitates the numerical solution and the understanding of each process separately. In this study, a multi-scale approach has been developed to model, each mechanism at its own scale. We considered two modeling scales, the microscopic or interfacial scale (nanometric scale), and the mesoscopic scale (micrometric scale). At the microscopic scale, the processes of aggregation and deposition have been modeled in a similar manner with the DLVO theory. Surface electrostatic properties of NPs and rocks are described by a surface complexation model implemented in geochemical modeling program (PHREEQC). This surface complexation model was tested for two types of materials, titanium and silica. At the mesoscopic scale, the deposition is quantified by the classic filtration theory (CFT) in the initial phase when the filter is clean. The transport of NPs in porous media was simulated by a pore network model (PNM) at the mesoscopic scale. This transport model was coupled with the deposition-aggregation model and also indirectly with the surface complexation model. These three models are coupled in a single model called: PhreeqC Pore Network Transport (PPNT1.0).