Fractured reservoirs have been traditionally idealized using dual-porosity models. In these models, all matrix and fractures systems have identical properties. However, it is not uncommon for naturally fractured reservoirs to have orthogonal fractures with different properties. In addition, for hydraulically fractured reservoirs that have preexisting natural fractures such as shale gas reservoirs, it is almost certain that these types of fractures are present. Therefore, a triple-porosity (dual-fracture) model is developed in this work for characterizing fractured reservoirs with different fractures properties. The model consists of three contiguous porous media: the matrix, less permeable micro-fractures and more permeable macro-fractures. Only the macro-fractures produce to the well while they are fed by the micro-fractures only. Consequently, the matrix feeds the micro-fractures only. Therefore, the flow is sequential from one medium to the other. Four sub-models are derived based on the interporosity flow assumption between adjacent media, i.e., pseudosteady state or transient flow assumption. These are fully transient flow model (Model 1), fully pseudosteady state flow model (Model 4) and two mixed flow models (Model 2 and 3). The solutions were mainly derived for linear flow which makes this model the first triple-porosity model for linear reservoirs. In addition, the Laplace domain solutions are also new and have not been presented in the literature before in this form. Model 1 is used to analyze fractured shale gas horizontal wells. Non-linear regression using least absolute value method is used to match field data, mainly gas rate. Once a match is achieved, the well model is completely described. Consequently, original gas in place (OGIP) can be estimated and well future performance can be forecasted.

The state of the art of modeling fluid flow in shale gas reservoirs is dominated by dual porosity models that divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano- pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual porosity models and Darcy’s Law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of complex flow mechanisms occurring in these reservoirs. Through the use of a unique simulator, this research work establishes a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three separate porosity systems: organic matter (mainly kerogen); inorganic matter; and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In the organic matter or kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of smaller pores (mainly nanopores and picopores) and larger pores (mainly micropores and nanopores) in kerogen are incorporated in the simulator. The separate inorganic sub-blocks mainly contribute to the ability to better model dynamic water behavior. The multiple porosity model is built upon a unique tool for simulating general multiple porosity systems in which several porosity systems may be tied to each other through arbitrary transfer functions and connectivities. This new model will allow us to better understand complex flow mechanisms and in turn to extend simulation to the reservoir scale including hydraulic fractures through upscaling techniques

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There have been many attempts to use mathematical method in order to characterize shale gas/oil reservoirs with multi-transverse hydraulic fractures horizontal well. Many authors have tried to come up with a suitable and practical mathematical model. To analyze the production data of a shale reservoir correctly, an understanding and choosing the proper mathematical model is required. Therefore, three models (the homogeneous linear flow model, the transient linear dual porosity model, and the fully transient linear triple porosity model) will be studied and compared to provide correct interpretation guidelines for these models. The analytical solutions and interpretation guidelines are developed in this work to interpret the production data of shale reservoirs effectively. Verification and derivation of asymptotic and associated equations from the Laplace space for dual porosity and triple porosity models are performed in order to generate analysis equations. Theories and practical applications of the three models (the homogeneous linear flow model, the dual porosity model, and the triple porosity model) are presented. A simplified triple porosity model with practical analytical solutions is proposed in order to reduce its complexity. This research provides the interpretation guidelines with various analysis equations for different flow periods or different physical properties. From theoretical and field examples of interpretation, the possible errors are presented. Finally, the three models are compared in a production analysis with the assumption of infinite conductivity of hydraulic fractures.

Different methods have been proposed for history matching production of shale gas/oil wells which are drilled horizontally and usually hydraulically fractured with multiple stages. These methods are simulation, analytical models, and empirical equations. It has been well known that among the methods listed above, analytical models are more favorable in application to field data for two reasons. First, analytical solutions are faster than simulation, and second, they are more rigorous than empirical equations. Production behavior of horizontally drilled shale gas/oil wells has never been completely matched with the models which are described in this thesis. For shale gas wells, correction due to adsorption is explained with derived equations. The algorithm which is used for history matching and forecasting is explained in detail with a computer program as an implementation of it that is written in Excel's VBA. As an objective of this research, robust method is presented with a computer program which is applied to field data. The method presented in this thesis is applied to analyze the production performance of gas wells from Barnett, Woodford, and Fayetteville shales. It is shown that the method works well to understand reservoir description and predict future performance of shale gas wells. Moreover, synthetic shale oil well also was used to validate application of the method to oil wells. Given the huge unconventional resource potential and increasing energy demand in the world, the method described in this thesis will be the "game changing" technology to understand the reservoir properties and make future predictions in short period of time.

Les réservoirs de type "tight oil" et "shale gaz" ont une partie importante de leur volume poreux occupée par des micropores (< 2nm) et des mesopores (entre 2 et 50 nm). Ce type d'environnement crée de fortes forces d’interaction dans le fluide confiné avec les parois du pores et entre ses propres molécules, ce qui change fortement la thermodynamique du fluide. Un travail important doit donc être effectué sur le développement de méthodes de mise à l'échelle de la distribution de pore pour effectuer des simulations réservoir à grande échelle. Premièrement, des simulations moléculaires sont effectuées sur des fluides confinés afin d'obtenir des propriétés thermodynamiques de référence à l'équilibre liquide/vapeur pour différentes tailles de pore. Ensuite, une comparaison des données de simulation moléculaire avec les résultats issus des équation d'état utilisées dans la littérature a permis de mettre en valeur la méthode de flash avec pression capillaire et changement du point critique comme la meilleure méthode existante pour décrire la physique du fluide confiné. Des simulations fines d'écoulement matrice/fracture ont donc été effectuées pour différentes tailles de pore. Des modèles de mise à l'échelle en maillage grossier ont été ensuite construits à partir du même cas synthétique et les résultats ont été comparés avec ceux des simulations de référence en maillage fin. Un nouveau modèle de triple porosité considérant fracture, petit pores et grand pores avec une approche MINC a donné des résultats très proches du maillage fin. Finalement un réservoir stimulé hydrauliquement à grande échelle a été simulé pour différentes distributions de pores avec le modèle développé. / Tight oil and shale gas reservoirs have a significant part of their pore volume occupied by micro (below 2nm) and mesopores (between 2 and 50nm). This kind of environment creates strong interaction forces in the confined fluid with pore walls as well as between its own molecules and then changes dramatically the fluid phase behavior. An important work has therefore to be done on developing upscaling methodology of the pore size distribution for large scale reservoir simulations. Firstly, molecular simulations are performed on different confined fluids in order to get reference thermodynamic properties at liquid/vapor equilibrium for different pore sizes. Then, the comparison with commonly used modified equation of state (EOS) in the literature highlighted the model of flash with capillary pressure and critical temperature and pressure shift as the best one to match reference molecular simulation results. Afterwards fine grid matrix/fracture simulations have been built and performed for different pore size distributions. Then, coarse grid upscaling models have then been performed on the same synthetic case and compared to the reference fine grid results. A new triple porosity model considering fracture, small pores and large pores with MINC (Multiple Interacting Continua) approach, has shown very good match with the reference fine grid results. Finally a large scale stimulated reservoir volume with different pore size distribution inside the matrix has been built using the upscaling method developed here.