Discontinuous Galerkin methods for convection-diffusion equations and applications in petroleum engineering

This dissertation contains research in discontinuous Galerkin (DG) methods applying to convection-diffusion equations. It contains both theoretical analysis and applications. Initially, we develop a conservative local discontinuous Galerkin (LDG) method for the coupled system of compressible miscible displacement problem in two space dimensions. The main difficulty is how to deal with the discontinuity of approximations of velocity, u, in the convection term across the cell interfaces. To overcome the problems, we apply the idea of LDG with IMEX time marching using the diffusion term to control the convection term. Optimal error estimates in Linfinity(0, T; L2) norm for the solution and the auxiliary variables will be derived. Then, high-order bound-preserving (BP) discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacements on triangular meshes will be developed. There are three main difficulties to make the concentration of each component between 0 and 1. Firstly, the concentration of each component did not satisfy a maximum-principle. Secondly, the first-order numerical flux was difficult to construct. Thirdly, the classical slope limiter could not be applied to the concentration of each component. To conquer these three obstacles, we first construct special techniques to preserve two bounds without using the maximum-principle-preserving technique. The time derivative of the pressure was treated as a source of the concentration equation. Next, we apply the flux limiter to obtain high-order accuracy using the second-order flux as the lower order one instead of using the first-order flux. Finally, L2-projection of the porosity and constructed special limiters that are suitable for multi-component fluid mixtures were used. Lastly, a new LDG method for convection-diffusion equations on overlapping mesh introduced in [J. Du, Y. Yang and E. Chung, Stability analysis and error estimates of local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes, BIT Numerical Mathematics (2019)] showed that the convergence rates cannot be improved if the dual mesh is constructed by using the midpoint of the primitive mesh. They provided several ways to gain optimal convergence rates but the reason for accuracy degeneration is still unclear. We will use Fourier analysis to analyze the scheme for linear parabolic equations with periodic boundary conditions in one space dimension. To investigate the reason for the accuracy degeneration, we explicitly write out the error between the numerical and exact solutions. Moreover, some superconvergence points that may depend on the perturbation constant in the construction of the dual mesh were also found out

Viscoplastic displacement flows in narrow channels

Les écoulements à déplacement se produisent fréquemment dans les applications naturelles et industrielles. Bien que les déplacements Newtoniens aient été pris en considération dans une grande variété d’études théoriques et expérimentales dans les dernières décennies, un nombre considérable de fluides pratiques présentent des caractéristiques viscoplastiques, rendant la prévision du comportement des écoulements plus difficile. Les écoulement de déplacement viscoplastiques sont généralement contrôlés par un équilibre entre diverses forces, y compris la force visqueuse, la force de flottabilité, la force d’inertie, contrainte d’écoulement, etc., en plus de caractéristiques miscibles et non miscibles. Une compétition entre ces forces peut conduire à des comportements imprévisibles et exotiques de déplacement. Permettant une compréhension approfondie de ces écoulements, dans cette thèse de doctorat nous avons étudié l’écoulement à déplacement d’un fluide viscoplastique par un fluide Newtonien dans une géométrie simple, c.-à-d. un canal étroit et confiné. Dans la première partie de cette thèse (chapitres 1 à 3), nous étudions expérimentalement les écoulements à déplacement non-miscibles d’un fluide viscoplastique par un fluide Newtonien. En particulier, nous analysons le mouvement d’air dans un gel de Carbopol, dans une cellule de Hele-Shaw de section rectangulaire. Cette géométrie est composée de deux plaques parallèles rigides. Nous étudions les résultats en termes d’efficacité de déplacement et de morphologie des modèles d’écoulement. Nous démontrons que les comportements complexes du gel Carbopol, c.-à-d. les fortes propriétés viscoplastiques et les faibles propriétés viscoélastiques, affectent les caractéristiques d’écoulement de déplacement. Ensuite, nous étendons cette étude au déplacement d’un gel de Carbopol par une huile de silicone afin de considérer les effets de la mouillabilité sur l’écoulement. Nous observons qu’une combinaison de comportements viscoplastiques et de mouillabilité exerce un impact significatif sur les modèles d’écoulement à déplacement, pour lesquels quatre régimes d’écoulement différents sont identifiés : un régime capillaire, un régime de contrainte d’écoulement, un régime visqueux et un régime élastoinertiel. Enfin, nous étudions les impacts du rapport d’aspect de la section transversale de la cellule sur les caractéristiques de déplacement viscoplastique. Dans la deuxième partie de cette thèse (chapitres 4 à 5), nous étudions numériquement les écoulements à déplacement miscibles d’un fluide viscoplastique par un fluide Newtonien dans un long canal plan 2D. Pour un déplacement «heavy-light», l’analyse des modèles d’écoulement en fonction de divers paramètres sans dimension nous permet d’identifier trois régimes d’écoulement distincts : déplacements «center-type»/«slump- type», «back flow»/«no-back flow» et déplacement «stable/instable». Nous décrivons les effets du rapport de viscosité des fluides, de la flottabilité, de la contrainte d’écoulement et de l’inclinaison du canal sur les régimes d’écoulement susmentionnés.Displacement flows frequently occur in natural and industrial applications. Although Newtonian displacements have been considered in a wide range of theoretical and experimental studies in the recent decades, a considerable number of practical fluids exhibit viscoplastic features, making it hard to predict the flow behaviors. Viscoplastic displacement flows are generally controlled by a balance between a variety of forces, including viscous, buoyant, inertial, yield stress, etc., in addition to miscible and immiscible features. A competition between these forces may lead to exotic, unpredictable displacement flow behaviors. To provide a deep understanding of these flows, in this Ph.D. thesis we investigate the displacement flow of a viscoplastic fluid by a Newtonian fluid in a simple flow geometry, i.e., a narrow confined channel. In the first part of this thesis (Chapters 1-3), we experimentally study immiscible displacement flows of a viscoplastic fluid by a Newtonian fluid. In particular, we analyze the invasion of air into a Carbopol gel in a rectangular cross-section Hele-Shaw cell. This flow geometry is composed of two rigid parallel plates with a small gap. We study the results in terms of the displacement efficiency and morphology of the flow patterns. We demonstrate that the complex behaviors of the Carbopol gel, i.e., strong viscoplastic properties and weak viscoelastic properties, affect the displacement flow features. We then extend this study to the displacement of a Carbopol gel by silicon oil in order to consider the effects of wettability on the flow. We observe that a combination of viscoplastic behaviors and wettability exerts a significant impact on the displacement flow patterns, for which four different flow regimes are identified a capillary regime, a yield stress regime, a viscous regime and an elasto-inertial regime. Finally, we investigate the impacts of the cell cross-section aspect ratio on viscoplastic displacement flow features. In the second part of this thesis (Chapters 4-5), we numerically study miscible displacement flows of a viscoplastic fluid by a Newtonian fluid in a long 2D plane channel. For a heavy-light displacement, analyzing the displacement flow patterns as a function of various dimensionless parameters allows us to identify three distinct flow regimes center/slump-type, back/no-backflow and stable/unstable displacements. We describe the effects of the viscosity ratio of fluids, buoyancy, yield stress and channel inclination on the aforementioned flow regimes

Modeling capillarity and two-phase flow in granular media: from porescale to network scale

Numerical simulations at the pore scale are a way to study the behavior of multiphase flows encountered in many natural processes and industrial applications. In this work, liquid morphology and capillary action are examined at the pore-scale by means of the multicomponent Shan-Chen lattice Boltzmann method (LBM). The accuracy of the numerical model is first contrasted with theoretical solutions. The numerical results are extended to complex microstructures beyond the pendular regime. The LBM has been employed to simulate multiphase flow through idealized granular porous media under quasi-static primary drainage conditions. LBM simulations provide an excellent description of the fluid-fluid interface displacement through the grains. Additionally, the receding phase trapped in the granular media in form of pendular bridges or liquid clusters is well captured. Unfortunately, such simulations require a significant computation time. A 2D model (Throat-Network model) based on analytical solutions is proposed to mimic the multiphase flow with very reduced computation cost, therefore, suitable to replace LBM simulations when the computation resources are limited. The approach emphasizes the importance of simulating at the throat scale rather than the pore body scale in order to obtain the local capillary pressure - liquid content relationships. The Throat-Network model is a starting point for a hybrid model proposed to solve 3D problems. The hybrid model combines the efficiency of the pore-network approach and the accuracy of the LBM at the pore scale to optimize the computational resources. The hybrid model is based on the decomposition of the granular assembly into small subsets, in which LBM simulations are performed to determine the main hydrostatic properties (entry capillary pressure, capillary pressure - liquid content relationship and liquid morphology for each pore throat). Despite the reduction of computation time, it is still not negligible and not affordable for large granular packings. Approximations by the Incircle and the MS-P method, which predict hydrostatic properties, are contrasted with the results provided by LBM and the hybrid model. Relatively accurate predictions are given by the approximations.Per tal d’estudiar els fluxos multifàsics presents a molts processos naturals i industrials és indispensable entendre les propietats físiques dels sistemes multifàsics a escala microscòpica. La morfologia dels fluids i les forces capil·lars s’investiguen a l’escala del porus mitjançant el ”multicomponent Shan-Chen lattice Boltzmann method (LBM)”. La precisió del model numèric ha estat contrastada amb solucions teòriques. Els resultats numèrics s’han estès a microestructures líquides complexes més enllà del règim pendular. El LBM ha estat emprat per simular fluxos multifàsics a través de medis porosos sota condicions quasi-estàtiques de drenatge. Les simulacions dutes a terme mitjançant el LBM proporcionen una descripció excel·lent del moviment de la interfície entre fluids a través de les partícules sòlides. Durant el drenatge, les simulacions numèriques són capaces de reproduir l’efecte del fluid atrapat dins el medi granular en forma de ponts o estructures líquides complexes. Malauradament, aquestes simulacions requereixen un temps de computació molt elevat. Per tal d’optimitzar els recursos de computació, proposem un model 2D (model Throat-Network) basat en solucions analítiques que permet reproduir fluxos multifàsics a través d’un conjunt de discs amb un temps de computació molt reduït. Per tant, aquest mètode és una alternativa que pot substituir les simulacions LBM quan els recursos de computació són escassos. El model Throat-Network destaca la importància de tractar el problema a l’escala de la gola del porus per tal d’obtenir les relacions pressió capil·lar - volum locals. Aquest enfocament és un punt de partida pel model híbrid que es presenta per resoldre els problemes en 3D. El model híbrid combina l’eficàcia del model ”Pore-Network” i la precisió del LBM a l’escala del porus. El model híbrid es basa en la descomposició d’una mostra granular en subdominis més petits, els quals corresponen a les goles dels porus (la gola dels porus és l’espai que connecta dos porus adjacents). Les simulacions LBM s’executen per a cada un dels subdominis per tal de determinar les propietats hidroestàtiques més rellevants (pressió capil·lar d’entrada, la corba de pressió capil·lar - grau de saturació i la morfologia líquida per cada una de les goles del porus). Malgrat la reducció significativa en el cost computacional del model híbrid, els temps de càlcul no són menyspreables i poc realistes per mostres granulars de grans dimensions. Les aproximacions donades pels mètodes de l’”Incircle” i el MS-P, que permeten estimar les propietats hidroestàtiques, han estat contrastades amb els resultats obtinguts amb LBM i el model híbrid.Les simulations numériques à l’échelle du pore sont fréquemment utilisées pour étudier le comportement des écoulements multiphasiques largement rencont des structures liquides et l’actiorés dans phénomènes naturels et applications industrielles. Dans ce travail, la morphologien capillaire sont examinées à l’échelle des pores par la méthode de Boltzmann sur réseau (LBM) à plusieurs composants selon le modèle de Shan-Chen. Les résultats numériques obtenus sont en bon accord avec les solutions théoriques. Les simulations numériques sont étendues à microstructures complexes au-delà du régime pendulaire. La LBM a été utilisée pour modéliser l’écoulement multiphasique à travers un milieu poreux idéalisé dans des conditions de drainage primaire quasi-statique. Les simulations LBM ont fourni une excellente description du déplacement de l’interface fluide-fluide à travers les grains. Pendant le drainage, les simulations LBM sont capables de reproduire la déconnexion d’une phase dans le milieu granulaire sous la forme de ponts pendulaires ou structures liquides complexes. Malheureusement, le temps de calcul nécessaire pour ce type de simulations est assez élevé. Afin d’optimiser les ressources de calcul, nous présentons un modèle 2D (modèle Throat-Network) basé sur des solutions analytiques pour décrire l’écoulement biphasique à travers un ensemble de disques dans un temps de calcul très réduit, donc le modèle 2D est susceptible de remplacer les simulations LBM lorsque les ressources de calcul sont limitées. L’approche souligne l’importance de simuler le problème a l’échelle de la gorge du pore pour obtenir les relations volume - pression capillaire locales. Le modèle Throat-Network est un point de départ pour le modèle hybride proposé pour résoudre les problèmes en 3D. Le modèle hybride combine l’efficacité de l’approche réseau de pores et la précision du LBM à l’échelle des pores. Le modèle hybride est basé sur la décomposition de l’échantillon en petits sous-domaines, dans lesquels des simulations LBM sont effectuées pour déterminer les propriétés hydrostatiques principales (pression capillaire d’entrée, courbe de drainage primaire et morphologie du liquide pour chaque gorge du pore). Malgré la réduction significative des temps de calcul obtenus avec le modèle hybride, le temps n’est pas négligeable et les modélisations numériques d’échantillons de grandes tailles ne sont pas réalistes. Les approximations données par les méthodes Incircle et MS-P, qui prédisent les propriétés hydrostatiques, sont comparées à celles de LBM et du modèle hybride

Asphaltene deposition simulation in porous media during CO₂ injection using Lattice Boltzmann Method

Carbon dioxide (CO₂) injection in oil reservoirs is a potential means of Enhanced Oil Recovery (EOR) and reducing greenhouse gas. Change in the thermodynamic condition and composition due to the CO₂ injection process may trigger the asphaltene precipitation and deposition which directly affects the efficiency of the EOR process. Predicting the possibility of the asphaltene issue under different operating conditions can help the oil industry for better process design, handle the potential operational problems and estimate the production cost. In spite of, the existence of different modeling approaches based on conventional numerical methods, the lack of a flexible and more comprehensive modeling approach is inevitable. The new and advanced numerical method, called the Lattice Boltzmann Method (LBM) covers the limitations of the conventional numerical methods in dealing with complex boundary conditions and incorporating the microscopic interactions. This study is aiming at the modeling of the Asphaltene deposition, and it’s effect on the fluid flow in porous media during an immiscible injection of CO₂ with applying the LBM as the main simulator engine that gets fed by the given phase behavior to take the asphaltene deposition into account as well. Porosity and CO₂ injection velocity are the changing factors in this study. Applying the same condition on two mediums, it has been seen that the recovery factor is 22.5% higher and deposited asphaltene is 2.56% lower in a more porous medium that is attributed to uniform pore size distribution and higher absolute permeability of the more porous case. Furthermore, the fingering phenomena seem to be high in a less porous medium which causes an early breakthrough. Studies on the CO₂ injection velocity effect showed that by increasing CO₂ injection velocity by 2 times and 3 times, the recovery factor increases 4% and decreases 6%, respectively. A decrease in recovery factor is attributed to the asphaltene deposition at which the deposited asphaltene is two times higher at injection velocity of

Modeling capillarity and two-phase flow in granular media: from porescale to network scale

Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i Université Grenoble Alpes. Resums extesos en francès i català a l'apendeix de la tesi.Numerical simulations at the pore scale are a way to study the behavior of multiphase flows encountered in many natural processes and industrial applications. In this work, liquid morphology and capillary action are examined at the pore-scale by means of the multicomponent Shan-Chen lattice Boltzmann method (LBM). The accuracy of the numerical model is first contrasted with theoretical solutions. The numerical results are extended to complex microstructures beyond the pendular regime. The LBM has been employed to simulate multiphase flow through idealized granular porous media under quasi-static primary drainage conditions. LBM simulations provide an excellent description of the fluid-fluid interface displacement through the grains. Additionally, the receding phase trapped in the granular media in form of pendular bridges or liquid clusters is well captured. Unfortunately, such simulations require a significant computation time. A 2D model (Throat-Network model) based on analytical solutions is proposed to mimic the multiphase flow with very reduced computation cost, therefore, suitable to replace LBM simulations when the computation resources are limited. The approach emphasizes the importance of simulating at the throat scale rather than the pore body scale in order to obtain the local capillary pressure - liquid content relationships. The Throat-Network model is a starting point for a hybrid model proposed to solve 3D problems. The hybrid model combines the efficiency of the pore-network approach and the accuracy of the LBM at the pore scale to optimize the computational resources. The hybrid model is based on the decomposition of the granular assembly into small subsets, in which LBM simulations are performed to determine the main hydrostatic properties (entry capillary pressure, capillary pressure - liquid content relationship and liquid morphology for each pore throat). Despite the reduction of computation time, it is still not negligible and not affordable for large granular packings. Approximations by the Incircle and the MS-P method, which predict hydrostatic properties, are contrasted with the results provided by LBM and the hybrid model. Relatively accurate predictions are given by the approximations.Per tal d’estudiar els fluxos multifàsics presents a molts processos naturals i industrials és indispensable entendre les propietats físiques dels sistemes multifàsics a escala microscòpica. La morfologia dels fluids i les forces capil·lars s’investiguen a l’escala del porus mitjançant el ”multicomponent Shan-Chen lattice Boltzmann method (LBM)”. La precisió del model numèric ha estat contrastada amb solucions teòriques. Els resultats numèrics s’han estès a microestructures líquides complexes més enllà del règim pendular. El LBM ha estat emprat per simular fluxos multifàsics a través de medis porosos sota condicions quasi-estàtiques de drenatge. Les simulacions dutes a terme mitjançant el LBM proporcionen una descripció excel·lent del moviment de la interfície entre fluids a través de les partícules sòlides. Durant el drenatge, les simulacions numèriques són capaces de reproduir l’efecte del fluid atrapat dins el medi granular en forma de ponts o estructures líquides complexes. Malauradament, aquestes simulacions requereixen un temps de computació molt elevat. Per tal d’optimitzar els recursos de computació, proposem un model 2D (model Throat-Network) basat en solucions analítiques que permet reproduir fluxos multifàsics a través d’un conjunt de discs amb un temps de computació molt reduït. Per tant, aquest mètode és una alternativa que pot substituir les simulacions LBM quan els recursos de computació són escassos. El model Throat-Network destaca la importància de tractar el problema a l’escala de la gola del porus per tal d’obtenir les relacions pressió capil·lar - volum locals. Aquest enfocament és un punt de partida pel model híbrid que es presenta per resoldre els problemes en 3D. El model híbrid combina l’eficàcia del model ”Pore-Network” i la precisió del LBM a l’escala del porus. El model híbrid es basa en la descomposició d’una mostra granular en subdominis més petits, els quals corresponen a les goles dels porus (la gola dels porus és l’espai que connecta dos porus adjacents). Les simulacions LBM s’executen per a cada un dels subdominis per tal de determinar les propietats hidroestàtiques més rellevants (pressió capil·lar d’entrada, la corba de pressió capil·lar - grau de saturació i la morfologia líquida per cada una de les goles del porus). Malgrat la reducció significativa en el cost computacional del model híbrid, els temps de càlcul no són menyspreables i poc realistes per mostres granulars de grans dimensions. Les aproximacions donades pels mètodes de l’”Incircle” i el MS-P, que permeten estimar les propietats hidroestàtiques, han estat contrastades amb els resultats obtinguts amb LBM i el model híbrid.Les simulations numériques à l’échelle du pore sont fréquemment utilisées pour étudier le comportement des écoulements multiphasiques largement rencont des structures liquides et l’actiorés dans phénomènes naturels et applications industrielles. Dans ce travail, la morphologien capillaire sont examinées à l’échelle des pores par la méthode de Boltzmann sur réseau (LBM) à plusieurs composants selon le modèle de Shan-Chen. Les résultats numériques obtenus sont en bon accord avec les solutions théoriques. Les simulations numériques sont étendues à microstructures complexes au-delà du régime pendulaire. La LBM a été utilisée pour modéliser l’écoulement multiphasique à travers un milieu poreux idéalisé dans des conditions de drainage primaire quasi-statique. Les simulations LBM ont fourni une excellente description du déplacement de l’interface fluide-fluide à travers les grains. Pendant le drainage, les simulations LBM sont capables de reproduire la déconnexion d’une phase dans le milieu granulaire sous la forme de ponts pendulaires ou structures liquides complexes. Malheureusement, le temps de calcul nécessaire pour ce type de simulations est assez élevé. Afin d’optimiser les ressources de calcul, nous présentons un modèle 2D (modèle Throat-Network) basé sur des solutions analytiques pour décrire l’écoulement biphasique à travers un ensemble de disques dans un temps de calcul très réduit, donc le modèle 2D est susceptible de remplacer les simulations LBM lorsque les ressources de calcul sont limitées. L’approche souligne l’importance de simuler le problème a l’échelle de la gorge du pore pour obtenir les relations volume - pression capillaire locales. Le modèle Throat-Network est un point de départ pour le modèle hybride proposé pour résoudre les problèmes en 3D. Le modèle hybride combine l’efficacité de l’approche réseau de pores et la précision du LBM à l’échelle des pores. Le modèle hybride est basé sur la décomposition de l’échantillon en petits sous-domaines, dans lesquels des simulations LBM sont effectuées pour déterminer les propriétés hydrostatiques principales (pression capillaire d’entrée, courbe de drainage primaire et morphologie du liquide pour chaque gorge du pore). Malgré la réduction significative des temps de calcul obtenus avec le modèle hybride, le temps n’est pas négligeable et les modélisations numériques d’échantillons de grandes tailles ne sont pas réalistes. Les approximations données par les méthodes Incircle et MS-P, qui prédisent les propriétés hydrostatiques, sont comparées à celles de LBM et du modèle hybride.Postprint (published version

Hydromechanical Frameworks for Assessing the Occurrence of Wellbore Bridging and Fracture Broaching During Blowouts

Rigorous hydromechanical frameworks needed for modeling wellbore bridging and broaching during uncontrolled production of oil and gas are developed in this work. First, two sources of sand production are identified: borehole breakout and erosion of the producing formation. Theoretical framework for predicting the morphology of type B breakout mode is developed for the first time in this study; both fracture mechanics and shear failure theories are used in predicting the breakout geometry. Furthermore, a framework for estimating the size of caving produced during breakout (type A or B) is presented. Using asymptotic analysis of crack-boundary interactions, the state of damage around the borehole during the breakout process is determined, and the limiting buckling lengths of the resulting wing-cracks are predicted based on plate buckling theory. Third, a three-phase erosion kinetic equations, coupled with an erosion constitutive law, which is based on virtual power principle, are used in modeling radial and axial erosion in the reservoir and along the wellbore respectively. The proposed erosion constitutive law identifies the limitation of the pressure-gradient phenomenological model, which is currently being used. For a rigorous investigation into the self-killing of the well, a thermodynamically multiphase field model is developed for the gas-liquid-solid flow. The model, which is the combination of Navier-Stokes and Cahn-Hilliard type equations, incorporates the hydrodynamic interactions among the different species of the mixture. Lastly, this work considers a faster means for estimating fracture propagation in heterogeneous media (layered or naturally fractured) in the event the well is shut-in

Coupled geomechanics and transient multiphase flow at fracture-matrix interface in tight reservoirs.

Fractured hydrocarbon reservoirs play a significant role in the world economy and energy markets. Fluid injection (normally water) forces the hydrocarbons out of the reservoirs. Geomechanics, externally applied stress on the rock, play a significant role in the oil recovery from fractured reservoirs. Subsurface fluid injection modifies pore pressure and in-situ stresses locally. In response to the pressure/stress combined effects, the pores and fracture regions undergo deformation. Similarly, it is a well-known fact that pore volume significantly impacts the absolute and relative permeability of fractured tight reservoirs. The governing factors that characterize multiphase fluid flow mechanisms in naturally-fractured tight reservoirs - such as wellbore stability, CO2 sequestration and improved hydrocarbon recovery - are relative permeability and capillary pressure. Although the effects of geomechanical parameters on single-phase fluid flow in naturally-fractured tight reservoirs are well documented, the interdependence between geomechanical and multiphase flows are severely lacking. This study aims to bridge this knowledge gap using advanced numerical techniques, focusing on accurately capturing complex flow phenomena at the fracture-matrix interface to enhance the accuracy of predicting oil recovery from naturally-fractured tight reservoirs, leading towards more efficient operations and reduced costs. Extensive sets of numerical investigations have been carried out in the present study, using an advanced Computational Fluid Dynamics (CFD) solver, to accurately capture transient multiphase flow (oil and water) phenomena within naturally-fractured tight reservoirs. Special attention has been paid towards accurate multiphase flow modelling and characterisation at the fracture-matrix interface. The numerical models have been validated against Berea Sandstone experimental data. Two separate numerical models have been developed with the aim to identify the most appropriate modelling technique for accurate numerical predictions of multiphase flow in naturally-fractured tight reservoirs. These two models are based on duct flow theory and flow through porous medium theory, respectively, while the Brooks and Corey method has been utilised to compute fluid saturation, relative permeability and capillary pressure at the fracture-matrix interface. The results obtained show that the difference between the numerical and experimental results is 30% when duct flow model is considered, while it is 2.57% when porous medium is considered. In order to critically evaluate the dependence of multiphase flow on the geomechanical parameters of naturally-fractured tight reservoirs, a one-way FEACFD coupling scheme has been implemented in the present study, not taking into consideration the pore pressure. The effects of externally applied stress loading on the geomechanical (porosity and fracture aperture) and multiphase flow characteristics (permeability, capillary pressure, relative permeability and fluid saturation) at the fracture-matrix interface have been thoroughly analysed. For accurate modelling and numerical predictions in naturally-fractured tight reservoirs, a viscous loss term has been incorporated in the momentum-conservation equations. The numerical predictions from the one-way coupled model matches well with Clashach core flooding experimental data, with 9% average difference between the two. The results obtained clearly indicate that external stress loading has significant impact on the geomechanical and multiphase flow characteristics at the fracture-matrix interface. Finally, a novel numerical model has been developed based on the full coupling scheme, with the aim to enhance the accuracy of the numerical predictions regarding oil recovery from naturally-fractured tight reservoirs for efficient and cost effective operations. The porous elasticity interface is coupled with multiphase flow in porous media where the mass conservation of each phase, and an extended Darcy's equation, underpin multiphase flow characteristics. The fully coupled model takes into consideration the pore pressure and has been validated against Clashach core flooding experimental data. The developed model has been shown to significantly enhance the prediction accuracy from 9%, for one-way coupled model, to 4%, and has the ability to capture complex multiphase flow phenomena at the fracture-matrix interface. Moreover, the novel model accurately predicts the effects of geomechanical parameters on multiphase flow characteristics. It is envisaged that the novel fully coupled model developed in this study will pave the way for future scientific research in the area of geomechanical-fluid flow coupling for enhanced oil recovery in naturally-fractured tight reservoirs

Hydro-mechanical analysis of expansive clays : constitutive and numerical modelling.

Bentonite-based materials are being currently considered in several countries as a backfill component in the multi-barrier concept for deep geological disposal of radioactive waste. The bentonite barrier fulfils several important functions: i) high swelling capacity to fill gaps and compress the excavation damaged zone and ii) very low hydraulic conductivity and important retention capacity which retards significantly radionuclides transport. Small-scale testing in geotechnical laboratories and in-situ experiments in underground research laboratories (URL) have demonstrated that initial state, water supply conditions and volume constrictions are the main aspects affecting the behaviour of bentonites. In this context, the main objective of the present study is the numerical simulation of the hydro-mechanical behaviour of expansive clays. For this purpose, a constitutive model has been developed to characterise the bentonite-based materials. The modelling of these materials is a quite challenging task. They exhibit a marked double-porosity system in which the swelling/shrinkage mechanism occurs at clay aggregate level and the collapsible behaviour comes from granular-like skeleton formed by the aggregates. In addition, several material configuration, with even more intricate fabric, have been proposed for the emplacement works of seals and plugs. The explicit consideration of two structural levels for the constitutive model seems to be suitable. Mechanical interaction and water mass exchanges between them can explain the short- and long-term behaviour. The model has been formulated using concepts of elasto-plasticity for strain hardening materials and generalized plasticity theory. The formulation has been implemented in the finite element code program CODE-BRIGHT and has been used to solve a variety of problems. The results provide relevant insights into the hydro-mechanical behaviour of double structure porous media, and they indicated the main aspects affecting the responses of expansive barriers. In particular, the relevance of the structural levels interaction has been demonstrated.Postprint (published version

Alternating Injection of Steam and CO2 For Thermal Recovery of Heavy Oil

A combination of rising oil demand and declining supply from the conventional sources is drawing global attention to the vast heavy-oil resources. These are commonly developed with steam-based processes which, in most cases, burn fossil fuel to generate the required steam. However, tightening constraints on fuel, water, and the environment are some of the factors currently fuelling the interests in enhancements to the traditional steaming operations. To mitigate some of the steam-related issues, we introduce two new thermal recovery methods, namely: (i) alternating-injection of steam and CO2 (SAC), and (ii) alternating-injection of steam and flue-gas (SAF). The primary objective of this research is to assess the technical and commercial feasibility of these new processes. To achieve this objective, we employ a combination of analytic modelling, numerical simulations and experimental studies, investigating the reservoir heat-transport aspects of steam-based processes, asphaltene-induced formation impairment, as well as the key controls on reservoir dynamics and project economics. In this work, the concepts of first-contact condensation (FCC) and multiple-contact condensation (MCC) have been introduced as additional mechanisms of heat-transport in steam-based processes. Hence, the traditional conductive-convective heat equations have been extended. Solutions of these equations indicate that laboratory and field observations are better rationalised, hence eliminating the current practice of employing unrealistic effective permeability and thermal diffusivity to explain these observations. We also provide conditions under which petroleum reservoirs may be analysed as adiabatic systems, and establish the relative influence of reservoir and operating parameters on reservoir heat-transport. Considering the asphaltene-precipitation potentials of CO2 and flue-gas, new models have been formulated for describing asphaltene-induced impairment of the permeability of porous media which, in turn, have been analysed as either closed (non-flowing) or open (flowing) systems. Application of the models to rationalise the experimental results from common porous media, which include sandstone, carbonate and glass-bead, validates their robustness. As a further test on the robustness of the proposed models, their main underlying assumptions have been validated with a set of capillary-flow experiments, which approximate asphaltene deposition at pore scale. As a case study for reservoir simulations, the Nigerian heavy-oil deposit has been examined. The sensitivity of reservoir response to reservoir, geometric (number and design of wells) and operating parameters has been quantified. From these results, a realistic set of dynamic-simulation models has been constructed for the Nigerian deposit. Within the parameter-space explored, the main subsurface uncertainties are reservoir geometry, permeability distribution as well as fluid and relative-permeability models. In addition, all the processes, namely steam-alone, SAC and SAF, are vulnerable to geometric and operating parameters. On the net effect of in-situ asphaltene removal, the alternating-injection processes would only yield higher oil recovery than the steam-alone process if there is significant in-situ deasphalting such that the oil-viscosity reduction effect overrides the permeability impairment effect. Otherwise, the miscibility of these gases in the oil-phase is not sufficiently high to take advantage of the reduction of crude viscosity by dilution. Finally, within the range of parameters evaluated, the three processes are technically and commercially feasible for the Nigerian deposit investigated. However, in terms of economics and robustness against commercial risks, the order is SAC > steam-alone > SAF. The reservoir model, oil price and costs are found to be the main determinants of project risks. Given the limitations of this research and the uncertainties in the input data used for analyses, we complete the work by outlining the scope for further studies