1st Edition
Tubular String Characterization in High Temperature High Pressure Oil and Gas Wells
High temperature, high oil pressure, oil and gas well completion testing have always been a technical challenge and basic theoretical research is one of the key factors needed to ensure a successful completion test. The completion test basic theory includes: a stress analysis of the completion string, completion string buckling behavior, and temperature and pressure distribution prediction. The completion string is the main bearing and power transmission component for oil and gas well operations and production, and it is required to take on a combination of loads, which result in completion string deformation. Because of these complex relationships, completion string stress analysis has become increasingly more complicated.
This book discusses the characters of tubular strings in HTHP (High Temperature - High Pressure) oil and gas wells. These characters include the mechanical behavior of tubular strings and the temperature and pressure variation of tubular strings in different conditions. Mathematical models are established for different conditions and solution existence and uniqueness of some models is discussed, providing algorithms corresponding to the different models. Numerical experiments are presented to verify the validity of models and the feasibility of algorithms, and the impact of the parameters of models for oil and gas wells is also discussed.
This book is written for production and testing engineers to provide them with the tools to deal more effectively with the numerical decisions they have to take and for researchers and technicians in petroleum and gas testing and production engineering. Finally, it is also intended to serve as a reference book for mathematicians, college teachers and students.
About the book series
Editorial board of the book series
Preface
Acronyms
Symbols
About the authors
1 Background
1.1 Placing the test string
1.2 Seating condition
1.3 Perforation condition
1.4 Injection condition
1.5 Production condition
1.6 Shut-in condition
1.7 Re-opened condition
2 Element theory
2.1 Differential geometry
2.1.1 Frenet frame
2.1.2 Geometric description of the 3D curved borehole
2.1.3 Geometry description of tubular string in 3D inclined well-bore
2.2 Variational methods
3 Tubular string buckling theoretical analysis
3.1 Introduction
3.2 Deformation differential equations modelling
3.2.1 Tubular string differential element force analysis
3.2.2 Static force equilibrium equation for the tubular string infinitesimal
3.2.3 The buckling differential equation for the tubular string
3.3 The equivalent variational problem
3.3.1 Tubular displacement analysis
3.3.2 External force and deformation energy analysis
3.3.3 The equivalent variational problem
3.4 Simplified analysis of the model
3.4.1 The buckling critical load and tubular string deformation solution
3.4.2 The axial buckling deformation analysis of the downhole string
4 Mechanical analysis for the placement of the test string
4.1 Mechanical analysis
4.2 Temperature distribution
4.3 Pressure distribution
4.4 Model calculation
4.4.1 The internal and external pressure calculation
4.4.2 The axial force distribution, the normal pressure and the moment calculation
4.4.3 Calculation procedures
4.5 Example calculation
4.5.1 Simulation parameters
4.5.2 Main results
5 Setting the mechanical analysis
5.1 Hydraulic packer force analysis in deviated HPHT wells
5.1.1 Model building
5.1.2 Computing parameters
5.1.3 Algorithm
5.1.4 Numerical simulation
5.1.5 Discussion
6 Re-opened mechanical analysis
6.1 Introduction
6.2 APDTU-VTPF
6.2.1 HTHP wells characteristics
6.2.2 The packer principle
6.2.3 Theoretical model
6.2.4 Solution methodology
6.2.5 Analysis of field case
7 Predicting pressure and temperature in HTHP injection wells
7.1 Introduction
7.2 PDPT-IW
7.2.1 Physical model
7.2.2 Mathematical model
7.2.3 Solution to the model
7.2.4 Solving model
7.2.5 Numerical simulation
7.2.6 Sensitivity analysis
7.3 PDPT-SIBUHT
7.3.1 Mathematical model
7.3.2 Solution of the model
7.3.3 Solution model
7.3.4 Numerical simulation
7.4 PTPTF-IWLFM
7.4.1 Model building
7.4.2 Model solution
7.4.3 Examples calculation
7.5 PTPD-IGWTE
7.5.1 Mathematical model of heat transmission in the well-bore
7.5.2 Pressure in the well-bore mathematical model 1
7.5.3 Model solution
7.5.4 Numerical simulation
7.6 DFA-SIPVF
7.6.1 The model dryness fraction in the varied (T, P) fields
7.6.2 Varied (T, P) fields analysis
7.6.3 Algorithm steps
7.6.4 Simulation and discussion
7.6.5 Sensitivity analysis
7.7 AASDT-SITP
7.7.1 Force analysis on the tubular string
7.7.2 The tubular axial load and axial stress
7.7.3 Analysis of axial deformation
7.7.4 Varied (T, P) fields analysis
7.7.5 Numerical implementation
7.7.6 Numerical simulation
7.7.7 Main results and analysis
7.8 NMSQ-DWV
7.8.1 Basic assumptions
7.8.2 The steam quality model with variable (T, P) fields
7.8.3 The analysis of the variable (T, P) fields
7.8.4 Numerical implementation
7.8.5 Simulation and discussion
7.8.6 Trend analysis
7.8.7 Sensitivity analysis
7.8.8 Conclusion
8 Predicting of pressure and temperature in HTHP production wells
8.1 Introduction
8.2 PTP-GW
8.2.1 Physical model
8.2.2 Coupled differential equations system model
8.2.3 Model solution
8.2.4 Solving the model
8.2.5 Numerical simulation
8.2.6 Sensitivity analysis
8.3 PTPTV-GW
8.3.1 The coupled system differential equations model
8.3.2 Solution of the model
8.3.3 Solving the model
8.3.4 Numerical simulation
8.3.5 Results and analysis
8.3.6 Error analysis
8.4 PDTPVD-GLTPTF
8.4.1 Prediction model
8.4.2 Model solution
8.4.3 Calculation of some parameters
8.4.4 Example calculation
8.5 NMSOGW-TTBF
8.5.1 The coupled system model
8.5.2 Model analysis
8.5.3 Numerical solution
8.5.4 Calculation of some parameters
8.5.5 Initial condition and boundary condition
8.5.6 Example calculation
8.6 PDPTVD-TBF
8.6.1 The coupled system model
8.6.2 Model analysis
8.6.3 Numerical solution
8.6.4 Numerical simulation
8.6.5 Sensitivity analysis
8.7 PPTHVD-STF
8.7.1 The coupled system model
8.7.2 Model analysis
8.7.3 Numerical solution
8.7.4 Numerical simulation and results discussion
8.7.5 Sensitivity analysis
8.7.6 Comparison analysis
9 Predicting the pressure and temperature in shut-in
9.1 Introduction
9.2 PPT-SPDW
9.2.1 Physical model
9.2.2 The coupled system model
9.2.3 Solution model
9.2.4 Numerical simulation
9.3 PPTVD-TFSP
9.3.1 The coupled system model
9.3.2 Model solution
9.3.3 Numerical simulation
10 Software design and development
10.1 Calculation program
10.1.1 All conditions calculation
10.1.2 Calculation according to conditions
10.2 The database
References
Appendix
Subject index
Book series page
Biography
Jiuping Xu (1962) obtained his Ph.D Applied Mathematics from Tsinghua University, Beijing, China; and a Ph.D in Physical Chemistry from Sichuan University, Chengdu, China, in 1995 and 1999, respectively. Dr. Xu was elected the lifetime academician of the International Academy of Systems and Cybernetic Sciences (IASC) in 2010. He is currently Professor at Sichuan University, the president of International Society for Management Science and Engineering Management, and the vice-president of The Systems Engineering Society of China, the editor in chief of International Journal of Management Science and Engineering Management, the executive-editor in chief of World Journal of Modelling and Simulation. His current research interests include the areas of applied mathematics, physical chemistry, systems science and engineering science. He has published 40 books and over 400 journal papers in Mathematics, Computer and many others. Prof. Xu was awarded the International Federation of Operations Research Societies (IFORS) prize for development at the IFORS XIV Conference, Vancouver, in 1996, and has received numerous prizes in China, including the China Youth Prize of Science and Technology, in 2004.
Zezhong Wu (1970) received his Ph.D in Management Science and Engineering from Sichuan University, China in 2010. Dr. Wu is currently Professor at Chengdu University of Information Technology, director of The Mathematical Model and The Applied Research Institute of Chengdu University of Information Technology. His current research interests include the areas of applied mathematics, petroleum and gas, mathematical modelling and simulation. He has published 30 journal papers.
