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Contents Abstract Acknowledgments 1 Introduction 1.1 Problem Statement 1.2 Methodology  1.3 Scope 1.4 Outline of the thesis   2 Phenomenology and Contradictions in Carbonate Reservoirs  2.1 First Contradiction: Tectonic Fracture or Nonplanar Discontinuity?   2.2 Second Contradiction: How Do Different Discontinuities Impact? 2.3 Analogs Reservoirs and Outcrops for a Flow Analytical Model   2.4 Geological and Tomography Features of Tectonic Fractures   2.5 Analytical Model for the Profile Velocity of Tectonic Fractures 2.6 Kinematic Analytical Modeling for Tectonic Fractures  2.7 Third Contradiction: Darcy’s Flow or Couette General Flow for Planar Discontinuity (Tectonic Fracture)2.8 Geological and Tomography Features of Fault Breccias  2.9 Kinematic Analytical Modeling for Fault Breccias   2.10 Geological and Tomography Features of Chicxulub Impact Breccias and Cantarell Reservoir 2.11 Kinematic Analytical Modeling for Impact Breccias  2.12 Fourth Contradiction: Fluid Flow of the Cantarell Reservoir Modeled without Considerer Chicxulub Impact 2.13 Geological and Tomography Features of Sedimentary Breccias 2.14 Kinematic Analytical Modeling for Sedimentary Breccia  2.15 Geological and Tomography Features of Vugs  2.16 Kinematic Analytical Modeling for Vugs 2.17 Fifth Contradiction: Liquids Retention Paradox for Vugs  2.18 Application Examples  2.18.1 Behavior of Fluid Velocities 2.18.2 Carbonate Reservoir Characteristics: Cardenas Field Application. 2.19 Mathematical models summary 2.20 Nomenclature 3 A Ternary, Static, and Dynamic Classification of NFCRs 3.1 Classification proposal  3.2 Ternary classification proposal considerations  3.3 Ternary classification of NFCRs  3.4 Ternary classification parameters  3.5 Geological discontinuities lines  3.5.1 Line of tectonic-sedimentary breccias3.5.2 Line of impact breccias  3.5.3 Dissolution line 3.5.4 Interception of geological discontinuities lines 3.5.5 Classifying Fractured Carbonate Reservoirs   3.6 Generalized ternary classification   3.6.1 Classification of Naturally Fractured Reservoirs. Author: Ronald Nelson 3.6.2 Classification for naturally fractured reservoir, by Gilman et al. 3.6.3 Types of Naturally Fractured Reservoirs. Author: Héber CincoLey 3.6.4 Reservoirs classification, by Soto et al 3.6.5 Similarities between classifications available in literature and ternary classification 3.7 Examples of NFCRs 3.8 Nomenclature  4 Analytical model for Non Stress Sensitive Naturally Fractured Carbonate Reservoirs (NFCRs) 4.1 Overview  4.2 Analytical considerations for model  4.3 Couette and Darcy’s equation  4.4 Analytical model 4.5 Mathematical model and solution for constant rate radial flow in an infinite reservoir 4.6 Solution of the Nonlinear Partial Differential Equation without stresssensitive 4.6.1 Case without transfer function 5 Analytical model for Stress Sensitive Naturally Fractured Carbonate Reservoirs (NFCRs) 5.1 Analytical considerations for model 5.2 Analytical model 5.3 Solution Nonlinear Partial Differential Equation 5.3.1 Case 1: γ = cf  6 Westergaard’s solution applied to Carbonate Reservoirs 6.1 Westergaard’s solution 6.1.1 Airy Stress Function  6.1.2 Displacement in the horizontal direction, u 6.1.3 Displacement in the vertical direction, v  6.2 Westergaard’s application for tectonic fractures 6.3 Westergaard’s solution applied to a limestone reservoir with tectonic fractures 6.3.1 Field geological aspects  6.3.2 Paleontological description  6.3.3 Petrography  6.3.4 Permeability and porosity 6.3.5 X-ray diffraction for the identification and analysis of carbonates rocks 6.3.6 Computed tomography, CT 6.3.7 Fluid Pore Pressure 6.4 Carbonate rock mechanical properties 6.4.1 Overburden stress, Sv 6.4.2 Maximum and minimum horizontal stresses magnitudes  6.4.3 Elastic parameters: Young’s modulus and Poisson’s ratio 6.5 Closed or open natural horizontal fractures 7 Applicability and benefits of doctoral thesis for hydrocarbons industry 8 Conclusions and recommendations8.1 Conclusions  Recommendations