EDP Sciences 1776366616 20260416 fre

laboutique.edpsciences.fr-002663 05 01 01 002663 03 9782759831050 15 9782759831050 00 BA 10 01 02 Current Natural Sciences 01 01 Nonlinear flow and well test analysis in porous media 1 A01 01 A2231 Libing FU FU, Libing Libing FU Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works. Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works.<div ccp_infra_version="3" ccp_infra_timestamp="1701787190870" ccp_infra_user_hash="2520731787" ccp_infra_copy_id="9aa351d5-18e3-4603-9b4c-9ebe567fe0fd" data-ccp-timestamp="1701787190870" style="color: rgb(0, 0, 0); font-size: medium;"></div> 2 A01 01 A2232 Jincai WANG WANG, Jincai Jincai WANG 3 A01 01 A2233 Li CHEN CHEN, Li Li CHEN 4 A01 01 A2234 Fengjun HAO HAO, Fengjun Fengjun HAO 5 A01 01 A2235 Lun ZHAO ZHAO, Lun Lun ZHAO 01 eng 00 190 03 01 24 Izibook:Subject Ingénierie 24 Izibook:SubjectAndCategoryAndTags |Ingénierie| 20 porous media;nonlinear flow;infiltration;low-velocity flow;high-velocity flow;mathematical models;analytical solutions;oil and gas development;reservoir properties;fluid dynamics. 10 2011 SCI085000 01 600 06 05 06 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20231214 01 00 20231214 19 00 20231214 2026 06 3052868830012 01 WORLD 27 03 9782759831067 15 9782759831067 27 03 9782759831074 15 9782759831074 laboutique.edpsciences.fr-R002561 03 01 01 R002561 00 ED E107 00 01 01 Nonlinear flow and well test analysis in porous media 01 eng 08 192 03 22 18467923 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20231214 02 01 002664 03 9782759831067 15 9782759831067 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002664 03 01 01 002664 03 9782759831067 15 9782759831067 10 EA E107 10 00 01 R002561 ED E107 1 10 01 02 Current Natural Sciences 01 01 Nonlinear flow and well test analysis in porous media 1 A01 01 A2231 Libing FU FU, Libing Libing FU Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works. Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works.<div ccp_infra_version="3" ccp_infra_timestamp="1701787190870" ccp_infra_user_hash="2520731787" ccp_infra_copy_id="9aa351d5-18e3-4603-9b4c-9ebe567fe0fd" data-ccp-timestamp="1701787190870" style="color: rgb(0, 0, 0); font-size: medium;"></div> 2 A01 01 A2232 Jincai WANG WANG, Jincai Jincai WANG 3 A01 01 A2233 Li CHEN CHEN, Li Li CHEN 4 A01 01 A2234 Fengjun HAO HAO, Fengjun Fengjun HAO 5 A01 01 A2235 Lun ZHAO ZHAO, Lun Lun ZHAO 01 eng 08 188 03 01 24 Izibook:Subject Ingénierie 24 Izibook:SubjectAndCategoryAndTags |Ingénierie| 20 porous media;nonlinear flow;infiltration;low-velocity flow;high-velocity flow;mathematical models;analytical solutions;oil and gas development;reservoir properties;fluid dynamics. 10 2011 SCI085000 01 600 06 05 06 03 00 Based on the analysis of factors influencing fluid infiltration in porous media, this book systematically summarizes the characteristics and expressions of low-velocity nonlinear flow and high-velocity nonlinear flow infiltration in porous media and provides a set of evaluation methods. Using the exponential formula, the starting pressure gradient formula, and the binomial equation of motion, the authors present a detailed comparison and analysis of the production, pressure, and dimensionless background pressure of the nonlinear flow and Darcy linear flow for steady and unsteady flow. In addition, based on the equation of motion of the starting pressure gradient, a mathematical model of the one-, two-, and three-medium nonlinear seepage flow is established, and approximate analytical solutions are given while the graph of the corresponding well test curve is drawn. Finally, based on the mathematical model of the well test established from the exponential equation of the high-velocity nonlinear flow motion, the atypical well test curve and the relational surface of the time- and space-varying infiltration index are obtained. The authors also discuss the relationship between reservoir and fluid properties and the nonlinear flow test curve. This book is intended to serve as a reference for technical personnel, researchers, teachers, and students involved in oil and gas development. Its research contents provide a theoretical basis for the identification of water flow dominant channels in the long-term water injection development of high-water-cut oilfields, profile control and water shut-off, productivity evaluation of carbonate reservoirs and formation parameters. 02 00 This book comprehensively explores the characteristics and expressions of low-velocity and high-velocity nonlinear flow infiltration in porous media, offering evaluation methods through mathematical models and analytical solutions, with a focus on applications in oil and gas development, reservoir properties, and fluid dynamics. 04 00 Preface..................................................... III<o:p></o:p>CHAPTER 1<o:p></o:p>Mechanism of Nonlinear Flow and Analysis of Characteristics............ 1<o:p></o:p>1.1 Analysis of Factors Affecting Fluid Flow in Porous Media .......... 1<o:p></o:p>1.2 Mechanism of Nonlinear Flowin Low Permeability Reservoirs....... 3<o:p></o:p>1.2.1 Characteristics of Nonlinear Flow in Low Permeability<o:p></o:p>Reservoirs........................................ 4<o:p></o:p>1.2.2 Model of Nonlinear Flow in Low Permeability Reservoirs ..... 6<o:p></o:p>1.3 Mechanisms of Stress Sensitivity in Low-Permeability Reservoirs..... 9<o:p></o:p>1.3.1 Stress Sensitivity Characteristics of Low-Permeability<o:p></o:p>Reservoirs........................................ 9<o:p></o:p>1.3.2 Stress Sensitivity Modelfor Low Permeability Reservoirs ..... 10<o:p></o:p>1.4 Characteristics of High-Velocity Nonlinear Flow ................. 13<o:p></o:p>1.4.1 Introduction....................................... 13<o:p></o:p>1.4.2 Characteristics of High-Velocity Nonlinear Flow ............ 15<o:p></o:p>1.4.3 Judgment Method for High-Velocity Nonlinear Flow ........ 17<o:p></o:p>1.4.4 Equation for Description of High-Velocity Nonlinear Flow .... 19<o:p></o:p>CHAPTER 2<o:p></o:p>Model of Low-Velocity Nonlinear Flow in Single Media ................. 25<o:p></o:p>2.1 Threshold Pressure Gradient Model of Low-Velocity Nonlinear Flow . . 25<o:p></o:p>2.1.1 Stable Flow Model.................................. 26<o:p></o:p>2.1.2 Unstable Flow Model................................ 26<o:p></o:p>2.1.3 Dimensionless Well Test Model Under Unstable Flow ........ 28<o:p></o:p>2.2 Exponential Model of Low-Velocity Nonlinear Flow .............. 34<o:p></o:p>2.2.1 Stable Flow Model.................................. 35<o:p></o:p>2.2.2 Unstable Flow Model................................ 37<o:p></o:p>2.2.3 Dimensionless Well Test Model of Unstable Flow ........... 41<o:p></o:p>CHAPTER 3<o:p></o:p>Theory of Well Test for Low-Velocity Nonlinear Flow in Multiple Media .... 47<o:p></o:p>3.1 Mathematical Model of Low-Velocity Nonlinear Flow in Double<o:p></o:p>Media................................................. 47<o:p></o:p>3.1.1 Motion Equation................................... 48<o:p></o:p>3.1.2 Channeling Equation................................ 48<o:p></o:p>3.1.3 State Equation..................................... 49<o:p></o:p>3.1.4 Continuity Equation................................ 50<o:p></o:p>3.1.5 Simplified Models of Matrix Permeability and Fracture<o:p></o:p>Porosity.......................................... 50<o:p></o:p>3.1.6 Simplified Model of Matrix Permeability ................. 52<o:p></o:p>3.2 Theory of Well Test of Low-Velocity Nonlinear Flow in Double Media 53<o:p></o:p>3.2.1 Mathematical Model of Well Test in Dual-Porosity Reservoir<o:p></o:p>and Its Solution.................................... 53<o:p></o:p>3.2.2 Mathematical Model Considering Wellbore Storage Effect<o:p></o:p>and Skin Factor.................................... 56<o:p></o:p>3.2.3 Characteristics of Well Test Curve of Low-Velocity Nonlinear<o:p></o:p>Flow in Double Media............................... 56<o:p></o:p>3.2.4 Analysis of Factors Affecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow in Double Media Reservoirs . . 59<o:p></o:p>3.3 Mathematical Model of Low-Velocity Nonlinear Flow in Triple<o:p></o:p>Media................................................. 67<o:p></o:p>3.3.1 Ideal Model of Triple Media........................... 68<o:p></o:p>3.3.2 Mathematical Model and Its Solution for Triple Media<o:p></o:p>Reservoirs........................................ 69<o:p></o:p>3.3.3 Well Test Curve Characteristics of Low-Velocity Nonlinear<o:p></o:p>Flow in Triple Media Reservoirs........................ 73<o:p></o:p>3.3.4 Analysis of Factors Affecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow in Triple Media ............ 76<o:p></o:p>CHAPTER 4<o:p></o:p>Well Test of Nonlinear Flow Considering Stress Sensitivity in Low<o:p></o:p>Permeability Reservoirs........................................ 89<o:p></o:p>4.1 Factors Affecting Stress Sensitivity and Mathematical Models ....... 89<o:p></o:p>4.1.1 Change Characteristics of Stress Sensitivity ............... 89<o:p></o:p>4.1.2 Factors Affecting Stress Sensitivity ...................... 92<o:p></o:p>4.1.3 Mathematical Model of Stress Sensitivity ................. 94<o:p></o:p>4.2 Nonlinear Stable and Pseudo-Stable Flow Model Considering Stress<o:p></o:p>Sensitivity.............................................. 97<o:p></o:p>4.2.1 Productivity and Pressure Models of Stable Flow Considering<o:p></o:p>Stress Sensitivity................................... 97<o:p></o:p>4.2.2 Productivity and Pressure Models of Pseudo-Stable Flow<o:p></o:p>Considering Stress Sensitivity.......................... 97<o:p></o:p>4.3 Nonlinear and Unstable Well Test Considering Stress Sensitivity ..... 99<o:p></o:p>4.3.1 Assumptions and the Model........................... 99<o:p></o:p>4.3.2 Solution and Charts for Well Test Model Considering Stress<o:p></o:p>Sensitivity in Low Permeability Reservoirs ................ 101<o:p></o:p>4.4 Well Test in Fracture-Pore Double Media Considering Stress<o:p></o:p>Sensitivity.............................................. 1084.4.1 Sensitivity of Fracture Permeability ..................... 108<o:p></o:p>4.4.2 Well-Test Model of Double Media Considering Stress<o:p></o:p>Sensitivity and Typical Curves......................... 111<o:p></o:p>CHAPTER 5<o:p></o:p>High-Velocity Nonlinear Stable Flow Model ......................... 119<o:p></o:p>5.1 Darcy Linear Radial Flow.................................. 119<o:p></o:p>5.2 Binomial Nonlinear Radial Flow ............................. 120<o:p></o:p>5.3 Exponential Nonlinear RadialFlow ........................... 122<o:p></o:p>5.4 Comparison of the Calculation Results for Darcy’s Linear Flow<o:p></o:p>and Nonlinear Flow...................................... 123<o:p></o:p>5.4.1 Producing in a Constant Production .................... 124<o:p></o:p>5.4.2 Producing at a Constant Bottom-Hole Pressure ............ 129<o:p></o:p>CHAPTER 6<o:p></o:p>Transient Well Test Under High-Velocity Nonlinear Flow ............... 139<o:p></o:p>6.1 Exponential High-Velocity Nonlinear Flow Model ................ 139<o:p></o:p>6.1.1 Exponential High-Velocity Nonlinear Flow Model ........... 139<o:p></o:p>6.1.2 Analytical Solution to the Exponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 141<o:p></o:p>6.1.3 Numerical Solution for the Exponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 144<o:p></o:p>6.1.4 Results and Discussion............................... 148<o:p></o:p>6.2 Binomial High-Velocity Nonlinear Flow Model .................. 152<o:p></o:p>6.2.1 Establishment of Flow Model.......................... 152<o:p></o:p>6.2.2 Solution of the Model................................ 153<o:p></o:p>6.2.3 Results and Discussion............................... 155<o:p></o:p>CHAPTER 7<o:p></o:p>Transient Well Test of Moving Boundary in High-Velocity Nonlinear Flow . . 159<o:p></o:p>7.1 Assumptions............................................ 159<o:p></o:p>7.2 Establishment and Solution ofthe Mathematical Model ........... 160<o:p></o:p>7.3 Results and Discussion.................................... 161<o:p></o:p>Nomenclatures............................................... 167<o:p></o:p>Appendix: Virtual ArgumentInteger Bessel Function .................. 173<o:p></o:p>References.................................................. 177<o:p></o:p> Preface..................................................... III<o:p></o:p>CHAPTER 1<o:p></o:p>Mechanism of Nonlinear Flow andAnalysis of Characteristics............ 1<o:p></o:p>1.1 Analysis of Factors AffectingFluid Flow in Porous Media .......... 1<o:p></o:p>1.2 Mechanism of Nonlinear Flowin Low Permeability Reservoirs....... 3<o:p></o:p>1.2.1 Characteristics ofNonlinear Flow in Low Permeability<o:p></o:p>Reservoirs........................................ 4<o:p></o:p>1.2.2 Model of Nonlinear Flow inLow Permeability Reservoirs ..... 6<o:p></o:p>1.3 Mechanisms of StressSensitivity in Low-Permeability Reservoirs..... 9<o:p></o:p>1.3.1 Stress SensitivityCharacteristics of Low-Permeability<o:p></o:p>Reservoirs........................................ 9<o:p></o:p>1.3.2 Stress Sensitivity Modelfor Low Permeability Reservoirs ..... 10<o:p></o:p>1.4 Characteristics ofHigh-Velocity Nonlinear Flow ................. 13<o:p></o:p>1.4.1 Introduction....................................... 13<o:p></o:p>1.4.2 Characteristics ofHigh-Velocity Nonlinear Flow ............ 15<o:p></o:p>1.4.3 Judgment Method forHigh-Velocity Nonlinear Flow ........ 17<o:p></o:p>1.4.4 Equation for Description ofHigh-Velocity Nonlinear Flow .... 19<o:p></o:p>CHAPTER 2<o:p></o:p>Model of Low-Velocity NonlinearFlow in Single Media ................. 25<o:p></o:p>2.1 Threshold Pressure GradientModel of Low-Velocity Nonlinear Flow . . 25<o:p></o:p>2.1.1 Stable Flow Model.................................. 26<o:p></o:p>2.1.2 Unstable Flow Model................................ 26<o:p></o:p>2.1.3 Dimensionless Well TestModel Under Unstable Flow ........ 28<o:p></o:p>2.2 Exponential Model ofLow-Velocity Nonlinear Flow .............. 34<o:p></o:p>2.2.1 Stable Flow Model.................................. 35<o:p></o:p>2.2.2 Unstable Flow Model................................ 37<o:p></o:p>2.2.3 Dimensionless Well TestModel of Unstable Flow ........... 41<o:p></o:p>CHAPTER 3<o:p></o:p>Theory of Well Test forLow-Velocity Nonlinear Flow in Multiple Media .... 47<o:p></o:p>3.1 Mathematical Model ofLow-Velocity Nonlinear Flow in Double<o:p></o:p>Media................................................. 47<o:p></o:p>3.1.1 Motion Equation................................... 48<o:p></o:p>3.1.2 Channeling Equation................................ 48<o:p></o:p>3.1.3 State Equation..................................... 49<o:p></o:p>3.1.4 Continuity Equation................................ 50<o:p></o:p>3.1.5 Simplified Models of MatrixPermeability and Fracture<o:p></o:p>Porosity.......................................... 50<o:p></o:p>3.1.6 Simplified Model of MatrixPermeability ................. 52<o:p></o:p>3.2 Theory of Well Test ofLow-Velocity Nonlinear Flow in Double Media 53<o:p></o:p>3.2.1 Mathematical Model of WellTest in Dual-Porosity Reservoir<o:p></o:p>and Its Solution.................................... 53<o:p></o:p>3.2.2 Mathematical ModelConsidering Wellbore Storage Effect<o:p></o:p>and Skin Factor.................................... 56<o:p></o:p>3.2.3 Characteristics of WellTest Curve of Low-Velocity Nonlinear<o:p></o:p>Flow in Double Media............................... 56<o:p></o:p>3.2.4 Analysis of FactorsAffecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow inDouble Media Reservoirs . . 59<o:p></o:p>3.3 Mathematical Model ofLow-Velocity Nonlinear Flow in Triple<o:p></o:p>Media................................................. 67<o:p></o:p>3.3.1 Ideal Model of Triple Media........................... 68<o:p></o:p>3.3.2 Mathematical Model and ItsSolution for Triple Media<o:p></o:p>Reservoirs........................................ 69<o:p></o:p>3.3.3 Well Test CurveCharacteristics of Low-Velocity Nonlinear<o:p></o:p>Flow in Triple Media Reservoirs........................ 73<o:p></o:p>3.3.4 Analysis of FactorsAffecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow inTriple Media ............ 76<o:p></o:p>CHAPTER 4<o:p></o:p>Well Test of Nonlinear FlowConsidering Stress Sensitivity in Low<o:p></o:p>Permeability Reservoirs........................................ 89<o:p></o:p>4.1 Factors Affecting StressSensitivity and Mathematical Models ....... 89<o:p></o:p>4.1.1 Change Characteristics ofStress Sensitivity ............... 89<o:p></o:p>4.1.2 Factors Affecting StressSensitivity ...................... 92<o:p></o:p>4.1.3 Mathematical Model ofStress Sensitivity ................. 94<o:p></o:p>4.2 Nonlinear Stable andPseudo-Stable Flow Model Considering Stress<o:p></o:p>Sensitivity.............................................. 97<o:p></o:p>4.2.1 Productivity and PressureModels of Stable Flow Considering<o:p></o:p>Stress Sensitivity................................... 97<o:p></o:p>4.2.2 Productivity and PressureModels of Pseudo-Stable Flow<o:p></o:p>Considering Stress Sensitivity.......................... 97<o:p></o:p>4.3 Nonlinear and Unstable WellTest Considering Stress Sensitivity ..... 99<o:p></o:p>4.3.1 Assumptions and the Model........................... 99<o:p></o:p>4.3.2 Solution and Charts forWell Test Model Considering Stress<o:p></o:p>Sensitivity in Low PermeabilityReservoirs ................ 101<o:p></o:p>4.4 Well Test in Fracture-PoreDouble Media Considering Stress<o:p></o:p>Sensitivity.............................................. 1084.4.1 Sensitivity of FracturePermeability ..................... 108<o:p></o:p>4.4.2 Well-Test Model of DoubleMedia Considering Stress<o:p></o:p>Sensitivity and Typical Curves......................... 111<o:p></o:p>CHAPTER 5<o:p></o:p>High-Velocity Nonlinear StableFlow Model ......................... 119<o:p></o:p>5.1 Darcy Linear Radial Flow.................................. 119<o:p></o:p>5.2 Binomial Nonlinear RadialFlow ............................. 120<o:p></o:p>5.3 Exponential Nonlinear RadialFlow ........................... 122<o:p></o:p>5.4 Comparison of the CalculationResults for Darcy’s Linear Flow<o:p></o:p>and Nonlinear Flow...................................... 123<o:p></o:p>5.4.1 Producing in a ConstantProduction .................... 124<o:p></o:p>5.4.2 Producing at a ConstantBottom-Hole Pressure ............ 129<o:p></o:p>CHAPTER 6<o:p></o:p>Transient Well Test UnderHigh-Velocity Nonlinear Flow ............... 139<o:p></o:p>6.1 Exponential High-VelocityNonlinear Flow Model ................ 139<o:p></o:p>6.1.1 Exponential High-VelocityNonlinear Flow Model ........... 139<o:p></o:p>6.1.2 Analytical Solution to theExponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 141<o:p></o:p>6.1.3 Numerical Solution for theExponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 144<o:p></o:p>6.1.4 Results and Discussion............................... 148<o:p></o:p>6.2 Binomial High-VelocityNonlinear Flow Model .................. 152<o:p></o:p>6.2.1 Establishment of Flow Model.......................... 152<o:p></o:p>6.2.2 Solution of theModel................................ 153<o:p></o:p>6.2.3 Results and Discussion............................... 155<o:p></o:p>CHAPTER 7<o:p></o:p>Transient Well Test of MovingBoundary in High-Velocity Nonlinear Flow . . 159<o:p></o:p>7.1 Assumptions............................................ 159<o:p></o:p>7.2 Establishment and Solution ofthe Mathematical Model ........... 160<o:p></o:p>7.3 Results and Discussion.................................... 161<o:p></o:p>Nomenclatures............................................... 167<o:p></o:p>Appendix: Virtual ArgumentInteger Bessel Function .................. 173<o:p></o:p>References.................................................. 177<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1385/9782759831067/nonlinear-flow-and-well-test-analysis-in-porous-media 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/983/068/original/9782759831050-Nonlinear_Flow_and_Well_Test_Analysis_in_Porous_Media_couv-sofedis.jpg 17 14 20240913T173708+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20231214 01 00 20231214 19 00 20231214 2026 06 3052868830012 01 WORLD 13 03 9782759831050 15 9782759831050 06 03 9782759831074 15 9782759831074 WORLD 08 EDP Sciences & Science Press 04 01 00 20231214 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 51.99 01 5.50 2.71 EUR 04 06 01 02 1 00 182.99 01 5.50 2.71 EUR 01 04 06 01 02 1 00 201.99 01 5.50 10.53 USD 01 laboutique.edpsciences.fr-002665 03 01 01 002665 03 9782759831074 15 9782759831074 10 EA 10 10 01 02 Current Natural Sciences 01 01 Nonlinear flow and well test analysis in porous media 1 A01 01 A2231 Libing FU FU, Libing Libing FU Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works. Fu Libing, Ph.D. graduated from China University of Geosciences (Beijing), is working as a senior engineer in PetroChina Exploration and Development Research Institute, and responsible for the implementation of over 20 national major projects, international cooperation projects and special projects of China National Petroleum Corporation. Fu has been awarded 2 provincial and ministerial-level scientific and technological progress prize and 12 bureau-level scientific and technological prize, and won 6 honors including the honor of Young Talents, Advanced Workers, Youth Civilization, and Top Ten Youth Scientific and Technological Advances of the China Petroleum Exploration and Development Research Institute. Fu has published 28 papers, and written 18 papers of which as the corresponding author/first author, including 10 papers retrieved by SCI/EI and 3 papers retrieved by Chinese core journals. Fu has also applied for 26 patents at home and abroad, 9 of which has been authorized, and 20 of which was applied as the corresponding author/first author. Besides, Fu has been authorized the software copyright as the first author for 4 of his works.<div ccp_infra_version="3" ccp_infra_timestamp="1701787190870" ccp_infra_user_hash="2520731787" ccp_infra_copy_id="9aa351d5-18e3-4603-9b4c-9ebe567fe0fd" data-ccp-timestamp="1701787190870" style="color: rgb(0, 0, 0); font-size: medium;"></div> 2 A01 01 A2232 Jincai WANG WANG, Jincai Jincai WANG 3 A01 01 A2233 Li CHEN CHEN, Li Li CHEN 4 A01 01 A2234 Fengjun HAO HAO, Fengjun Fengjun HAO 5 A01 01 A2235 Lun ZHAO ZHAO, Lun Lun ZHAO 01 eng 08 190 03 01 24 Izibook:Subject Ingénierie 24 Izibook:SubjectAndCategoryAndTags |Ingénierie| 20 porous media;nonlinear flow;infiltration;low-velocity flow;high-velocity flow;mathematical models;analytical solutions;oil and gas development;reservoir properties;fluid dynamics. 10 2011 SCI085000 01 600 06 05 06 03 00 Based on the analysis of factors influencing fluid infiltration in porous media, this book systematically summarizes the characteristics and expressions of low-velocity nonlinear flow and high-velocity nonlinear flow infiltration in porous media and provides a set of evaluation methods. Using the exponential formula, the starting pressure gradient formula, and the binomial equation of motion, the authors present a detailed comparison and analysis of the production, pressure, and dimensionless background pressure of the nonlinear flow and Darcy linear flow for steady and unsteady flow. In addition, based on the equation of motion of the starting pressure gradient, a mathematical model of the one-, two-, and three-medium nonlinear seepage flow is established, and approximate analytical solutions are given while the graph of the corresponding well test curve is drawn. Finally, based on the mathematical model of the well test established from the exponential equation of the high-velocity nonlinear flow motion, the atypical well test curve and the relational surface of the time- and space-varying infiltration index are obtained. The authors also discuss the relationship between reservoir and fluid properties and the nonlinear flow test curve. This book is intended to serve as a reference for technical personnel, researchers, teachers, and students involved in oil and gas development. Its research contents provide a theoretical basis for the identification of water flow dominant channels in the long-term water injection development of high-water-cut oilfields, profile control and water shut-off, productivity evaluation of carbonate reservoirs and formation parameters. 02 00 This book comprehensively explores the characteristics and expressions of low-velocity and high-velocity nonlinear flow infiltration in porous media, offering evaluation methods through mathematical models and analytical solutions, with a focus on applications in oil and gas development, reservoir properties, and fluid dynamics. 04 00 Preface..................................................... III<o:p></o:p>CHAPTER 1<o:p></o:p>Mechanism of Nonlinear Flow and Analysis of Characteristics............ 1<o:p></o:p>1.1 Analysis of Factors Affecting Fluid Flow in Porous Media .......... 1<o:p></o:p>1.2 Mechanism of Nonlinear Flowin Low Permeability Reservoirs....... 3<o:p></o:p>1.2.1 Characteristics of Nonlinear Flow in Low Permeability<o:p></o:p>Reservoirs........................................ 4<o:p></o:p>1.2.2 Model of Nonlinear Flow in Low Permeability Reservoirs ..... 6<o:p></o:p>1.3 Mechanisms of Stress Sensitivity in Low-Permeability Reservoirs..... 9<o:p></o:p>1.3.1 Stress Sensitivity Characteristics of Low-Permeability<o:p></o:p>Reservoirs........................................ 9<o:p></o:p>1.3.2 Stress Sensitivity Modelfor Low Permeability Reservoirs ..... 10<o:p></o:p>1.4 Characteristics of High-Velocity Nonlinear Flow ................. 13<o:p></o:p>1.4.1 Introduction....................................... 13<o:p></o:p>1.4.2 Characteristics of High-Velocity Nonlinear Flow ............ 15<o:p></o:p>1.4.3 Judgment Method for High-Velocity Nonlinear Flow ........ 17<o:p></o:p>1.4.4 Equation for Description of High-Velocity Nonlinear Flow .... 19<o:p></o:p>CHAPTER 2<o:p></o:p>Model of Low-Velocity Nonlinear Flow in Single Media ................. 25<o:p></o:p>2.1 Threshold Pressure Gradient Model of Low-Velocity Nonlinear Flow . . 25<o:p></o:p>2.1.1 Stable Flow Model.................................. 26<o:p></o:p>2.1.2 Unstable Flow Model................................ 26<o:p></o:p>2.1.3 Dimensionless Well Test Model Under Unstable Flow ........ 28<o:p></o:p>2.2 Exponential Model of Low-Velocity Nonlinear Flow .............. 34<o:p></o:p>2.2.1 Stable Flow Model.................................. 35<o:p></o:p>2.2.2 Unstable Flow Model................................ 37<o:p></o:p>2.2.3 Dimensionless Well Test Model of Unstable Flow ........... 41<o:p></o:p>CHAPTER 3<o:p></o:p>Theory of Well Test for Low-Velocity Nonlinear Flow in Multiple Media .... 47<o:p></o:p>3.1 Mathematical Model of Low-Velocity Nonlinear Flow in Double<o:p></o:p>Media................................................. 47<o:p></o:p>3.1.1 Motion Equation................................... 48<o:p></o:p>3.1.2 Channeling Equation................................ 48<o:p></o:p>3.1.3 State Equation..................................... 49<o:p></o:p>3.1.4 Continuity Equation................................ 50<o:p></o:p>3.1.5 Simplified Models of Matrix Permeability and Fracture<o:p></o:p>Porosity.......................................... 50<o:p></o:p>3.1.6 Simplified Model of Matrix Permeability ................. 52<o:p></o:p>3.2 Theory of Well Test of Low-Velocity Nonlinear Flow in Double Media 53<o:p></o:p>3.2.1 Mathematical Model of Well Test in Dual-Porosity Reservoir<o:p></o:p>and Its Solution.................................... 53<o:p></o:p>3.2.2 Mathematical Model Considering Wellbore Storage Effect<o:p></o:p>and Skin Factor.................................... 56<o:p></o:p>3.2.3 Characteristics of Well Test Curve of Low-Velocity Nonlinear<o:p></o:p>Flow in Double Media............................... 56<o:p></o:p>3.2.4 Analysis of Factors Affecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow in Double Media Reservoirs . . 59<o:p></o:p>3.3 Mathematical Model of Low-Velocity Nonlinear Flow in Triple<o:p></o:p>Media................................................. 67<o:p></o:p>3.3.1 Ideal Model of Triple Media........................... 68<o:p></o:p>3.3.2 Mathematical Model and Its Solution for Triple Media<o:p></o:p>Reservoirs........................................ 69<o:p></o:p>3.3.3 Well Test Curve Characteristics of Low-Velocity Nonlinear<o:p></o:p>Flow in Triple Media Reservoirs........................ 73<o:p></o:p>3.3.4 Analysis of Factors Affecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow in Triple Media ............ 76<o:p></o:p>CHAPTER 4<o:p></o:p>Well Test of Nonlinear Flow Considering Stress Sensitivity in Low<o:p></o:p>Permeability Reservoirs........................................ 89<o:p></o:p>4.1 Factors Affecting Stress Sensitivity and Mathematical Models ....... 89<o:p></o:p>4.1.1 Change Characteristics of Stress Sensitivity ............... 89<o:p></o:p>4.1.2 Factors Affecting Stress Sensitivity ...................... 92<o:p></o:p>4.1.3 Mathematical Model of Stress Sensitivity ................. 94<o:p></o:p>4.2 Nonlinear Stable and Pseudo-Stable Flow Model Considering Stress<o:p></o:p>Sensitivity.............................................. 97<o:p></o:p>4.2.1 Productivity and Pressure Models of Stable Flow Considering<o:p></o:p>Stress Sensitivity................................... 97<o:p></o:p>4.2.2 Productivity and Pressure Models of Pseudo-Stable Flow<o:p></o:p>Considering Stress Sensitivity.......................... 97<o:p></o:p>4.3 Nonlinear and Unstable Well Test Considering Stress Sensitivity ..... 99<o:p></o:p>4.3.1 Assumptions and the Model........................... 99<o:p></o:p>4.3.2 Solution and Charts for Well Test Model Considering Stress<o:p></o:p>Sensitivity in Low Permeability Reservoirs ................ 101<o:p></o:p>4.4 Well Test in Fracture-Pore Double Media Considering Stress<o:p></o:p>Sensitivity.............................................. 1084.4.1 Sensitivity of Fracture Permeability ..................... 108<o:p></o:p>4.4.2 Well-Test Model of Double Media Considering Stress<o:p></o:p>Sensitivity and Typical Curves......................... 111<o:p></o:p>CHAPTER 5<o:p></o:p>High-Velocity Nonlinear Stable Flow Model ......................... 119<o:p></o:p>5.1 Darcy Linear Radial Flow.................................. 119<o:p></o:p>5.2 Binomial Nonlinear Radial Flow ............................. 120<o:p></o:p>5.3 Exponential Nonlinear RadialFlow ........................... 122<o:p></o:p>5.4 Comparison of the Calculation Results for Darcy’s Linear Flow<o:p></o:p>and Nonlinear Flow...................................... 123<o:p></o:p>5.4.1 Producing in a Constant Production .................... 124<o:p></o:p>5.4.2 Producing at a Constant Bottom-Hole Pressure ............ 129<o:p></o:p>CHAPTER 6<o:p></o:p>Transient Well Test Under High-Velocity Nonlinear Flow ............... 139<o:p></o:p>6.1 Exponential High-Velocity Nonlinear Flow Model ................ 139<o:p></o:p>6.1.1 Exponential High-Velocity Nonlinear Flow Model ........... 139<o:p></o:p>6.1.2 Analytical Solution to the Exponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 141<o:p></o:p>6.1.3 Numerical Solution for the Exponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 144<o:p></o:p>6.1.4 Results and Discussion............................... 148<o:p></o:p>6.2 Binomial High-Velocity Nonlinear Flow Model .................. 152<o:p></o:p>6.2.1 Establishment of Flow Model.......................... 152<o:p></o:p>6.2.2 Solution of the Model................................ 153<o:p></o:p>6.2.3 Results and Discussion............................... 155<o:p></o:p>CHAPTER 7<o:p></o:p>Transient Well Test of Moving Boundary in High-Velocity Nonlinear Flow . . 159<o:p></o:p>7.1 Assumptions............................................ 159<o:p></o:p>7.2 Establishment and Solution ofthe Mathematical Model ........... 160<o:p></o:p>7.3 Results and Discussion.................................... 161<o:p></o:p>Nomenclatures............................................... 167<o:p></o:p>Appendix: Virtual ArgumentInteger Bessel Function .................. 173<o:p></o:p>References.................................................. 177<o:p></o:p> Preface..................................................... III<o:p></o:p>CHAPTER 1<o:p></o:p>Mechanism of Nonlinear Flow andAnalysis of Characteristics............ 1<o:p></o:p>1.1 Analysis of Factors AffectingFluid Flow in Porous Media .......... 1<o:p></o:p>1.2 Mechanism of Nonlinear Flowin Low Permeability Reservoirs....... 3<o:p></o:p>1.2.1 Characteristics ofNonlinear Flow in Low Permeability<o:p></o:p>Reservoirs........................................ 4<o:p></o:p>1.2.2 Model of Nonlinear Flow inLow Permeability Reservoirs ..... 6<o:p></o:p>1.3 Mechanisms of StressSensitivity in Low-Permeability Reservoirs..... 9<o:p></o:p>1.3.1 Stress SensitivityCharacteristics of Low-Permeability<o:p></o:p>Reservoirs........................................ 9<o:p></o:p>1.3.2 Stress Sensitivity Modelfor Low Permeability Reservoirs ..... 10<o:p></o:p>1.4 Characteristics ofHigh-Velocity Nonlinear Flow ................. 13<o:p></o:p>1.4.1 Introduction....................................... 13<o:p></o:p>1.4.2 Characteristics ofHigh-Velocity Nonlinear Flow ............ 15<o:p></o:p>1.4.3 Judgment Method forHigh-Velocity Nonlinear Flow ........ 17<o:p></o:p>1.4.4 Equation for Description ofHigh-Velocity Nonlinear Flow .... 19<o:p></o:p>CHAPTER 2<o:p></o:p>Model of Low-Velocity NonlinearFlow in Single Media ................. 25<o:p></o:p>2.1 Threshold Pressure GradientModel of Low-Velocity Nonlinear Flow . . 25<o:p></o:p>2.1.1 Stable Flow Model.................................. 26<o:p></o:p>2.1.2 Unstable Flow Model................................ 26<o:p></o:p>2.1.3 Dimensionless Well TestModel Under Unstable Flow ........ 28<o:p></o:p>2.2 Exponential Model ofLow-Velocity Nonlinear Flow .............. 34<o:p></o:p>2.2.1 Stable Flow Model.................................. 35<o:p></o:p>2.2.2 Unstable Flow Model................................ 37<o:p></o:p>2.2.3 Dimensionless Well TestModel of Unstable Flow ........... 41<o:p></o:p>CHAPTER 3<o:p></o:p>Theory of Well Test forLow-Velocity Nonlinear Flow in Multiple Media .... 47<o:p></o:p>3.1 Mathematical Model ofLow-Velocity Nonlinear Flow in Double<o:p></o:p>Media................................................. 47<o:p></o:p>3.1.1 Motion Equation................................... 48<o:p></o:p>3.1.2 Channeling Equation................................ 48<o:p></o:p>3.1.3 State Equation..................................... 49<o:p></o:p>3.1.4 Continuity Equation................................ 50<o:p></o:p>3.1.5 Simplified Models of MatrixPermeability and Fracture<o:p></o:p>Porosity.......................................... 50<o:p></o:p>3.1.6 Simplified Model of MatrixPermeability ................. 52<o:p></o:p>3.2 Theory of Well Test ofLow-Velocity Nonlinear Flow in Double Media 53<o:p></o:p>3.2.1 Mathematical Model of WellTest in Dual-Porosity Reservoir<o:p></o:p>and Its Solution.................................... 53<o:p></o:p>3.2.2 Mathematical ModelConsidering Wellbore Storage Effect<o:p></o:p>and Skin Factor.................................... 56<o:p></o:p>3.2.3 Characteristics of WellTest Curve of Low-Velocity Nonlinear<o:p></o:p>Flow in Double Media............................... 56<o:p></o:p>3.2.4 Analysis of FactorsAffecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow inDouble Media Reservoirs . . 59<o:p></o:p>3.3 Mathematical Model ofLow-Velocity Nonlinear Flow in Triple<o:p></o:p>Media................................................. 67<o:p></o:p>3.3.1 Ideal Model of Triple Media........................... 68<o:p></o:p>3.3.2 Mathematical Model and ItsSolution for Triple Media<o:p></o:p>Reservoirs........................................ 69<o:p></o:p>3.3.3 Well Test CurveCharacteristics of Low-Velocity Nonlinear<o:p></o:p>Flow in Triple Media Reservoirs........................ 73<o:p></o:p>3.3.4 Analysis of FactorsAffecting the Well Test Curves<o:p></o:p>of Low-Velocity Nonlinear Flow inTriple Media ............ 76<o:p></o:p>CHAPTER 4<o:p></o:p>Well Test of Nonlinear FlowConsidering Stress Sensitivity in Low<o:p></o:p>Permeability Reservoirs........................................ 89<o:p></o:p>4.1 Factors Affecting StressSensitivity and Mathematical Models ....... 89<o:p></o:p>4.1.1 Change Characteristics ofStress Sensitivity ............... 89<o:p></o:p>4.1.2 Factors Affecting StressSensitivity ...................... 92<o:p></o:p>4.1.3 Mathematical Model ofStress Sensitivity ................. 94<o:p></o:p>4.2 Nonlinear Stable andPseudo-Stable Flow Model Considering Stress<o:p></o:p>Sensitivity.............................................. 97<o:p></o:p>4.2.1 Productivity and PressureModels of Stable Flow Considering<o:p></o:p>Stress Sensitivity................................... 97<o:p></o:p>4.2.2 Productivity and PressureModels of Pseudo-Stable Flow<o:p></o:p>Considering Stress Sensitivity.......................... 97<o:p></o:p>4.3 Nonlinear and Unstable WellTest Considering Stress Sensitivity ..... 99<o:p></o:p>4.3.1 Assumptions and the Model........................... 99<o:p></o:p>4.3.2 Solution and Charts forWell Test Model Considering Stress<o:p></o:p>Sensitivity in Low PermeabilityReservoirs ................ 101<o:p></o:p>4.4 Well Test in Fracture-PoreDouble Media Considering Stress<o:p></o:p>Sensitivity.............................................. 1084.4.1 Sensitivity of FracturePermeability ..................... 108<o:p></o:p>4.4.2 Well-Test Model of DoubleMedia Considering Stress<o:p></o:p>Sensitivity and Typical Curves......................... 111<o:p></o:p>CHAPTER 5<o:p></o:p>High-Velocity Nonlinear StableFlow Model ......................... 119<o:p></o:p>5.1 Darcy Linear Radial Flow.................................. 119<o:p></o:p>5.2 Binomial Nonlinear RadialFlow ............................. 120<o:p></o:p>5.3 Exponential Nonlinear RadialFlow ........................... 122<o:p></o:p>5.4 Comparison of the CalculationResults for Darcy’s Linear Flow<o:p></o:p>and Nonlinear Flow...................................... 123<o:p></o:p>5.4.1 Producing in a ConstantProduction .................... 124<o:p></o:p>5.4.2 Producing at a ConstantBottom-Hole Pressure ............ 129<o:p></o:p>CHAPTER 6<o:p></o:p>Transient Well Test UnderHigh-Velocity Nonlinear Flow ............... 139<o:p></o:p>6.1 Exponential High-VelocityNonlinear Flow Model ................ 139<o:p></o:p>6.1.1 Exponential High-VelocityNonlinear Flow Model ........... 139<o:p></o:p>6.1.2 Analytical Solution to theExponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 141<o:p></o:p>6.1.3 Numerical Solution for theExponential High-Velocity<o:p></o:p>Nonlinear Flow Model............................... 144<o:p></o:p>6.1.4 Results and Discussion............................... 148<o:p></o:p>6.2 Binomial High-VelocityNonlinear Flow Model .................. 152<o:p></o:p>6.2.1 Establishment of Flow Model.......................... 152<o:p></o:p>6.2.2 Solution of theModel................................ 153<o:p></o:p>6.2.3 Results and Discussion............................... 155<o:p></o:p>CHAPTER 7<o:p></o:p>Transient Well Test of MovingBoundary in High-Velocity Nonlinear Flow . . 159<o:p></o:p>7.1 Assumptions............................................ 159<o:p></o:p>7.2 Establishment and Solution ofthe Mathematical Model ........... 160<o:p></o:p>7.3 Results and Discussion.................................... 161<o:p></o:p>Nomenclatures............................................... 167<o:p></o:p>Appendix: Virtual ArgumentInteger Bessel Function .................. 173<o:p></o:p>References.................................................. 177<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1385/9782759831067/nonlinear-flow-and-well-test-analysis-in-porous-media 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/983/068/original/9782759831050-Nonlinear_Flow_and_Well_Test_Analysis_in_Porous_Media_couv-sofedis.jpg 17 14 20240913T173708+0200 01 P15 EDP Sciences & Science 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