This thesis presents an important step towards a deeper understanding of naturally fractured carbonate reservoirs (NFCRs). It demonstrates the various kinds of discontinuities using geological evidence, mathematical kinematics model and computed tomography and uses this as a basis for proposing a new classification for NFCRs. Additionally, this study takes advantage of rock mechanics theory to illustrate how natural fractures can collapse due to fluid flow and pressure changes in the fractured media. The explanations and mathematical modeling developed in this dissertation can be used as diagnostic tools to predict fluid velocity, fluid flow, tectonic fracture collapse, pressure behavior during reservoir depleting, considering stress-sensitive and non-stress-sensitive, with nonlinear terms in the diffusivity equation applied to NFCRs. Furthermore, the book presents the description of real reservoirs with their field data as the principal goal in the mathematical description ofthe realistic phenomenology of NFCRs.

Inhalt
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 propo sal considerations 

3.3 Ternary classification of NFCRs 

3.4 Ternary classification parameters 

3.5 Geological discontinuities lines  3.5.1 Line of tectonic-sedimentary breccias

3.5.2 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 m odel 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: = 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...