Preface
In recent years, advanced production decline analysis（production analysis or rate transient analysis）has become one of the hottest topics in reservoir engineering. Based on the transient filtration theory, this analysis leads to novel match type curves by taking advantages of reservoir engineering method and pressure transient analysis. It uses daily production data to quantitatively analyze the fluid flow in porous media, determine the reservoir parameters, and calculate the OOIP(OGIP). Methods for this analysis include empirical ones represented by Arps, classic ones such as Fetkovich method, advanced LOG-LOG analysis ones represented by Blasingame method, and reservoir engineering ones represented by FMB.This analysis method, together with lifecycle well test analysis method, have become the main methods for reservoir dynamics characterization, for which the corresponding analysis softwares have been widely used in oil-gas fields. However, to the best of our knowledge, there is no book which provides a systematic introduction on this analysis.
This book entitled Advanced Production Decline Analysis and Application aims to bridge this gap, which is a summarization of recent literature as well as the experience of the author in reservoir dynamics characterization. This book will introduce the method of the decline curve analysis by hand. As indicated by Professor Liu Nengqiang,“Well test interpretation has been operated on computers nowadays. However, it would be better if operators can learn how to carry out the analysis by hand. This will help them to better understand programs, instructions, and procedures so as to use computer-aid programs to deliver the best interpretation. Even if they put hands on it just for one time, they could get a good impression.” The methods described in this book helps in the same way.
This book is composed of two parts, i.e., main text and appendix. The main text starts from the basic concept of advanced production decline analysis. It gives a comprehensive introduction on Arps, Fetkovich, Blasingame, Agarwal-Gardner, NPI, transient, long linear flow, and FMB by using a well in a bounded circle reservoir as an example, and by combining with field applications. It also introduces in details how to use this analysis method in practice. The appendix explains the nomenclature and major equations in the main text and the computer programs for Blasingame decline type curves and normorized pseudo-pressure of gas well. The appendix helps the readers re-generate the decline type curves in the main text, or induce new decline type curves for different reservoirs.
The author would like to thank Professor Gao Chengtai,Xi’an Petroleum University, Professor Zhou Fangde , Xi’an Jiaotong University, who supervised the author during Master and PhD studies, respectively. The author would also like to thank Professor Liu Yuewu, Institute of Mechanics, Chinese Academic of Science, who supervised his post-doc study. Without their guidance, the author may not have made these achievements. The author would like to thank Professor Wang Xiaodong of China University of Geosciences, Professor Chen Junbin and Lin Jiaen,Xi’an Petroleum University, who provided a lot of useful suggestions for improving the book. The author would like to thank Professor Jiang Tongwen, Pan Wenqing，Luo Chunshu，Deng xingliang，Shi Ying，Xiao Xiangjiao，Yang Jianping of Tarim oil field，Senior Engineer Fan Jiwu and Jia Lianchao of Changqing oil field, Wang Bin of Xinjiang oil field, Sun Hu and Duan Jianting of Chuanqing Drilling Engineering Co.,Ltd.,CNPC，who provided support and help in various projects. The author would like to thank Dr.Luo Mingliang，Wang Weiyang and Chen Huijuan of China University of Petroleum (East China) for providing useful literature. The author would also like to thank Professor Li Xizhe，Chen Jianjun，Lu Jialiang，Long Daojiang, Wan Yujin，Han Yongxin，Cao Wen and Yang Xifei of Exploration and Development Research Institute of Petrochina, Langfang Branch for their valuable help.
The work presented in this book was supported in part by China Postdoctoral Science Foundation (No.2011M500403), China Postdoctoral Science Foundation-the Fifth Special (No.2012T50140), China Petroleum Exploration and Development Research Institute of youth innovation fund (No.2009A1715).
Due to the limited knowledge and experience, the author could not avoid inappropriate statements in this book, and therefore he welcomes any suggestions and criticisms.
2012．12．2
Sun Hedong
Contents
1 FUNDAMENTALS OF ADVANCED PRODUCTION DECLINE ANALYSIS (1)
1.1 INTRODUCTION (1)
1.2 DIFFERENCES AND SIMILARITIES BETWEENT PRODUCTION ANALYSIS AND WELL TEST ANALYSIS (2)
1.3 BASIC CONCEPTS OF PRODUCTION ANALYSIS (3)
1.3.1 Wellbore storage (3)
1.3.2 Skin (4)
1.3.3 Effective wellbore radius (4)
1.3.4 Line source solution of infinite reservoir (5)
1.3.5 Stable state flow、pseudosteady state flow、boundary dominated flow (5)
1.3.6 Radius of investigation (8)
1.3.7 Dimensionless variables (8)
1.3.8 Shape factor and time of pseudosteady state flow (10)
1.3.9 Principle of superposition (11)
1.3.10 Pseudopressure、pseudotime (13)
1.3.11 Material balance time (14)
1.3.12 Typical flow regime (14)
1.3.13 Principle of log-log analysis (17)
1.3.14 Recoverable reserves (18)
1.3.15 Dynamical reserves (19)
2 ARPS DECLINE CURVES ANALYSIS (21)
2.1 ARPS EQUATIONS (21)
2.1.1 Exponential decline equation (21)
2.1.2 Hyperbolic decline equation (22)
2.1.3 Harmonic decline equation (24)
2.1.4 Comparison of Arps equation (25)
2.1.5 Modified hyperbolic decline equation (25)
2.1.6 OOIP(OGIP)and well spacing (27)
2.2 FUNDAMENTALS OF ARPS DECLINE CURVES (27)
2.2.1 Rate equation of water drive reservoir (27)
2.2.2 Exponential decline equation of water drive reservoir (28)
2.2.3 Hyperbolic decline equation of water drive reservoir (28)
2.2.4 Harmonic decline equation of water drive reservoir (29)
2.2.5 Decline equation of constant volume reservoir (30)
2.2.6 Decline equation of stratified reservoir (31)
2.2.7 Decline equation of constant volume gas reservoir (31)
2.3 ARPS TYPE CURVES (32)
2.3.1 Gentry-Arps type curves (32)
2.3.2 Arps dimensionless decline rate curves (33)
2.3.3 Arps dimensionless decline cumulative production curves (33)
2.3.4 Arps dimensionless decline rate integral curves (34)
2.3.5 Arps dimensionless decline rate integral derivative curves (35)
2.3.6 Arps dimensionless decline type curves (36)
2.4 POWER LAW DECLINE ANALYSIS (38)
2.4.1 ILK method (38)
2.4.2 Mattar method (38)
2.5 EXAMPLE OF ARPS DECLINE ANALYSIS (39)
2.5.1 Discriminant analysis (40)
2.5.2 Arps exponential decline analysis (40)
2.5.3 Arps harmonic decline analysis (42)
2.5.4 Comparison of results (42)
3 FETKOVICH DECLINE CURVES ANALYSIS (43)
3.1 SOLUTION FOR A WELL IN A BOUNDED CIRCLE RESERVOIR:CONSTANT PRESSURE PRODUCTION (43)
3.2 DEVELOPMENT OF FETKOVICH TYPE CURVES (45)
3.2.1 Fetkovich dimensionless variables (45)
3.2.2 Fetkovich dimensionless decline rate and decline cumulative production curves (46)
3.2.3 Fetkovich-Arps dimensionless decline rate and decline cumulative production curves (48)
3.2.4 Fetkovich-Arps dimensionless decline rate integral curves (49)
3.2.5 Fetkovich-Arps dimensionless decline rate integral derivative curves (52)
3.3 DECLINE CURVES ANALYSIS USING FETKOVICH STYLE TYPE CURVES (53)
3.3.1 Type curves matching of Fetkovich-Arps (53)
3.3.2 Type curves matching of Fetkovich-Arps (Normalized Data) (55)
3.3.3 Ambiguity of Fetkovich-Arps decline curves analysis (57)
3.4 EXAMPLE OF FETKOVICH-ARPS DECLINE CURVES ANALYSIS (58)
4 BLASINGAME DECLINE CURVES ANALYSIS (62)
4.1 SOLUTION FOR A WELL IN A BOUNDED CIRCLE RESERVOIR:CONSTANT RATE PRODUCTION (62)
4.2 DEVELOPMENT OF BLASINGAME TYPE CURVES (66)
4.2.1 Material balance time-oil well (66)
4.2.2 Material balance time- gas well (67)
4.2.3 Material balance time curves (69)
4.2.4 Normalized dimensionless decline rate curves (70)
4.2.5 Normalized dimensionless decline rate integral curves (71)
4.2.6 Normalized dimensionless decline rate integral derivative curves (72)
4.2.7 Blasingame type curves (73)
4.3 DECLINE CURVES ANALYSIS USING BLASINGAME STYLE TYPE CURVES (74)
4.3.1 Type Curves Matching Procedure- Oil Well (74)
4.3.2 Type Curves Matching Procedure- Gas Well (75)
4.4 EXAMPLE OF BLASINGAME DECLINE CURVES ANALYSIS (77)
5 AGARWAL-GARDNER DECLINE CURVES ANALYSIS (83)
5.1 DEVELOPMENT OF AGARWAL-GARDNER TYPE CURVES (83)
5.1.1 Agarwal-Gardner dimensionless variables (83)
5.1.2 Agarwal-Gardner dimensionless decline rate curves (84)
5.1.3 Agarwal-Gardner dimensionless decline inverse pressure derivative curves (84)
5.1.4 Agarwal-Gardner dimensionless decline inverse pressure integral derivative curves (85)
5.1.5 Agarwal-Gardner type curves (86)
5.2 DECLINE CURVES ANALYSIS USING AGARWAL-GARDNER STYLE TYPE CURVES (87)
5.2.1 Type Curves Matching Procedure- Oil Well (87)
5.2.2 Type Curves Matching Procedure- Gas Well (88)
5.3 EXAMPLE OF AGARWAL-GARDNER DECLINE CURVES ANALYSIS (90)
6 NORMALIZED PRESSURE INTEGRAL (NPI) DECLINE CURVES ANALYSIS (95)
6.1 DEVELOPMENT OF NPI TYPE CURVES (95)
6.1.1 Dimensionless variables (95)
6.1.2 Dimensionless decline pressure curves (95)
6.1.3 Dimensionless decline pressure integral curves (96)
6.1.4 Dimensionless decline pressure integral derivative curves (96)
6.1.5 NPI type curves (97)
6.2 DECLINE CURVES ANALYSIS USING NPI STYLE TYPE CURVES (98)
6.2.1 Type curves matching procedure- oil well (98)
6.2.2 Type curves matching procedure- gas well (99)
6.3 EXAMPLE OF NPI DECLINE CURVES ANALYSIS (100)
7 TRANSIENT DECLINE CURVES ANALYSIS (105)
7.1 DEVELOPMENT OF TRANSIENT TYPE CURVES (105)
7.1.1 Solution for a well in a bounded circle reservoir:constant rate production (105)
7.1.2 Dimensionless decline rate curves (105)
7.1.3 Dimensionless decline inverse pressure integral curves (105)
7.1.4 Dimensionless decline inverse pressure integral derivative curves (106)
7.1.5 Transient type curves (107)
7.2 DECLINE CURVES ANALYSIS USING TRANSIENT STYLE TYPE CURVES (107)
7.2.1 Type curves matching procedure- oil well (107)
7.2.2 Type curves matching procedure- gas well (109)
7.3 EXAMPLE OF TRANSIENT DECLINE CURVES ANALYSIS (110)
8 DECLINE CURVES ANALYSIS OF LONG LINEAR FLOW (114)
8.1 SOLUTION FOR A FRACTURED WELL IN A BOUNDED RECTANGULAR RESERVOIR (114)
8.1.1 Solution for a fractured well in a bounded rectangular reservoir:constant rate production (114)
8.1.2 Development of Wattenbarger type curves (115)
8.1.3 Wattenbarger style type curves matching procedure- oil well (115)
8.1.4 Wattenbarger style type curves matching procedure- gas well (117)
8.1.5 Example of Wattenbarger (118)
8.2 SOLUTION FOR A FRACTURED WELL IN A BOUNDED RECTANGULAR DOUBLE POROSITY RESERVOIR (122)
8.2.1 Physical model (122)
8.2.2 Linear PSS mathematical model (122)
8.2.3 Linear transient mathematical model (123)
8.2.4 Laplace space solutions (124)
8.2.5 Results and discussion (125)
8.3 SOLUTION FOR A FRACTURED WELL IN A BOUNDED CIRCLE RESERVOIR (125)
8.3.1 Development of type curves (125)
8.3.2 Type curves matching procedure (126)
8.3.3 Example (128)
9 DYNAMICS(FLOWING) MATERIAL BALANCE (134)
9.1 MATTAR METHOD (134)
9.1.1 Flowing material balance(constant rate) (134)
9.1.2 Dynamics material balance(variable rate) and example (341)
9.2 AGARWAL-GARDNER METHOD (136)
9.2.1 Oil well (136)
9.2.2 Gas well (136)
10 METHODOLOGY AND EXAMPLES OF ADVANCED DECLINE ANALYSIS (138)
10.1 METHODOLOGY AND EXAMPLES OF ADVANCED DECLINE ANALYSIS (138)
10.1.1 Data preparation (138)
10.1.2 Data diagnosis (138)
10.1.3 Model diagnosis (139)
10.1.4 Methodology (139)
10.2 EXAMPLE OF GAS WELL (140)
10.2.1 Data preparation (140)
10.2.2 Decline curves analysis (141)
10.3 EXAMPLE OF OIL WELL (142)
10.3.1 Data preparation (142)
10.3.2 Decline curves analysis (142)
10.4 EXAMPLE OF OIL FIELD (144)
10.4.1 Adaptability of classic method to evaluate OOIP(OGIP) (144)
10.4.2 Integrating production analysis and welltest analysi to evaluate OOIP(OGIP) (146)
11 DECLINE CURVES ANALYSIS FOR COMPLEX RESERVOIR (152)
11.1 DECLINE CURVES ANALYSIS FOR COMPOSITE RESERVOIR (152)
11.1.1 Solution for a well in a bounded composite reservoir:constant rate production (152)
11.1.2 Development of Blasingame type curves (155)
11.1.3 Results and discussion (155)
11.2 DECLINE CURVES ANALYSIS FOR TWO LAYER RESERVOIR (157)
11.2.1 Solution for a well in a bounded two layer commingled reservoir:constant rate production (157)
11.2.2 Development of Blasingame type curves (158)
11.2.3 Results and discussion (159)
11.2.4 Solution for a well in a bounded two layer crossflow reservoir:constant rate production (159)
11.3 DECLINE CURVES ANALYSIS FOR TWO POROSITY RESERVOIR (161)
11.3.1 Solution for a well in a bounded two porosity reservoir:constant rate production (161)
11.3.2 Development of Blasingame type curves (163)
11.3.3 Results and discussion (163)
11.4 BLASINGAME DECLINE CURVES ANALYSIS FOR TRIPLE POROSITY RESERVOIR (165)
11.4.1 Physical model (165)
11.4.2 Solution and type curves of triple porosity reservoir (166)
11.4.3 Solution and type curves of triple porosity nest reservoir (168)
11.4.4 Solution and type curves of triple porosity double permeability reservoir (170)
11.4.5 Solution and type curves of triple porosity continuum reservoir (173)
11.5 A NOTE ON THE DEVELOPMENT OF TYPE CURVES (175)
11.5.1 Incorrect Blasingame type curves (176)
11.5.2 Results interpretation (178)
11.5.3 Development of Blasingame type curves for complex reservoir (178)
APPENDIX (180)
APPENDIX 1 NOMENCLATURE (180)
APPENDIX 2 MAJOR EQUATIONS (188)
APPENDIX 3 SOURCE PROGRAM AND INTERFACE OF BLASINGAME METHOD (193)
APPENDIX 4 SOURCE PROGRAM AND INTERFACE OF NORMORIZED PSEUDOPRESSURE (2111)
APPENDIX 5 APPROXIMATE SOLUTION FOR BOUNDARY DOMINATED FLOW PERIOD OF COMPOSITE RESERVOIR (219)
APPENDIX 6 APPROXIMATE SOLUTION FOR BOUNDARY DOMINATED FLOW PERIOD OF TWO LAYER COMMINGLED RESERVOIR (222)
REFERENCE (224)
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