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E-raamat: Percolation Theory In Reservoir Engineering

(Imperial College London, Uk), (Sharif Univ Of Technology, Iran)
  • Formaat: 384 pages
  • Ilmumisaeg: 14-Sep-2018
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786345257
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  • Formaat: 384 pages
  • Ilmumisaeg: 14-Sep-2018
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786345257
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This book aims to develop the ideas from fundamentals of percolation theory to practical reservoir engineering applications. Through a focus on field scale applications of percolation concepts to reservoir engineering problems, it offers an approximation method to determine many important reservoir parameters, such as effective permeability and reservoir connectivity and the physical analysis of some reservoir engineering properties. Starring with the concept of percolation theory, it then develops into methods to simple geological systems like sand-bodies and fractures. The accuracy and efficiency of the percolation concept for these is explained and further extended to more complex realistic models.Percolation Theory in Reservoir Engineering primarily focuses on larger reservoir scale flow and demonstrates methods that can be used to estimate large scale properties and their uncertainty, crucial for major development and investment decisions in hydrocarbon recovery.
Preface v
About the Authors ix
Acknowledgements xi
Chapter 1 Introduction 1(18)
1.1 Geological uncertainty
2(1)
1.2 Reservoir modelling and heterogeneities
3(2)
1.3 Connectivity as the predominant feature of heterogeneous media
5(1)
1.4 Overlapping sandbodies models
6(2)
1.5 The percolation theory approach
8(3)
1.6 Variants of percolation
11(2)
1.7 Layout of the book
13(2)
References
15(4)
Chapter 2 Percolation theory-the basics 19(38)
2.1 Percolation on infinite lattices
20(3)
2.2 Percolation quantities and their properties
23(5)
2.2.1 Percolation probability
23(2)
2.2.2 Correlation length
25(1)
2.2.3 Cluster size
26(1)
2.2.4 Backbone fraction
27(1)
2.2.5 Effective permeability or conductivity
28(1)
2.3 Universality in percolation theory
28(1)
2.4 Finite-size effects
29(6)
2.5 Calculation of percolation parameters
35(7)
2.5.1 Analytical method for 1D percolation
36(3)
2.5.2 Monte Carlo simulations for 2D and 3D percolation models
39(3)
2.5.2.1 Percolation threshold
39(1)
2.5.2.2 Critical exponents
40(2)
2.6 Anisotropy and percolation
42(6)
2.6.1 Apparent threshold for anisotropic systems
44(1)
2.6.2 Finite-size scaling laws for anisotropic systems
45(3)
2.7 Percolation and fractals
48(3)
2.8 Problems
51(3)
References
54(3)
Chapter 3 Continuum percolation for geological models 57(28)
3.1 Simple sandbody model
59(11)
3.1.1 Isotropic overlapping sandbody model in 2D
59(1)
3.1.2 Computational algorithm
60(5)
3.1.3 Connectivity
65(5)
3.2 Simple fracture network model
70(8)
3.2.1 Simple fracture network model in 2D
71(3)
3.2.2 Computational algorithm
74(1)
3.2.3 Connectivity
75(3)
3.3 Problems
78(1)
References
79(6)
Chapter 4 The connectivity of overlapping sandbodies 85(58)
4.1 Effects of sandbody size variation
85(9)
4.2 Effects of anisotropy
94(5)
4.3 Effects of orientation disorder
99(5)
4.4 Other effects in 2D
104(6)
4.4.1 Sandbody shapes
105(1)
4.4.2 Spatial correlation
105(2)
4.4.3 Well patterns
107(3)
4.5 Analysis of connectivity in 3D
110(17)
4.5.1 Idealised overlapping sandbody model
110(5)
4.5.2 Anisotropy effects in 3D
115(5)
4.5.3 Sandbody size variation
120(1)
4.5.4 Effects of orientational disorder
121(3)
4.5.5 Other effects in 3D
124(3)
4.6 Case studies
127(7)
4.6.1 Case study 1: A carbonate gas condensate reservoir
127(1)
4.6.2 Case study 2: An offshore oil reservoir
128(5)
4.6.3 Case study 3: A gas reservoir C
133(1)
4.7 Problems
134(3)
References
137(6)
Chapter 5 Percolation and fracture systems 143(52)
5.1 Effects of fracture size variation
146(8)
5.2 Effects of fracture orientation variations
154(2)
5.3 Effects of anisotropy in the system
156(5)
5.4 Effects of spatial correlation on fracture connectivity
161(4)
5.5 Effective permeability of fracture systems
165(4)
5.6 Analysis in 3D
169(14)
5.6.1 Idealised fracture network models
170(4)
5.6.2 More complex fracture models
174(7)
5.6.2.1 Anisotropy effects
175(3)
5.6.2.2 Fracture size variation
178(1)
5.6.2.3 Fracture shape
179(1)
5.6.2.4 Well pattern
179(2)
5.6.3 Effective permeability
181(2)
5.7 Case studies
183(2)
5.8 Problems
185(3)
References
188(7)
Chapter 6 Backbone, dangling ends and effective permeability 195(32)
6.1 Backbones and dangling ends
195(9)
6.2 Effective (single-phase) permeability
204(11)
6.2.1 Anisotropic effects in 2D
211(2)
6.2.2 Effects of sandbody orientation disorder
213(1)
6.2.3 Effects of sandbody size distribution
213(2)
6.2.4 Effects of sandbody shape
215(1)
6.3 Extensions to 3D
215(5)
6.3.1 Anisotropy effects in 3D
217(1)
6.3.2 Effects of sandbody orientation disorder
218(1)
6.3.3 Effects of sandbody size distribution
219(1)
6.4 Case studies
220(2)
6.4.1 Case study 1
220(1)
6.4.2 Case study 2
221(1)
6.5 Problems
222(1)
References
223(4)
Chapter 7 Beyond simple percolation 227(34)
7.1 Prediction of the percolation quantities in binary permeability media
228(15)
7.1.1 The connected sand fraction
229(3)
7.1.2 The backbone fraction
232(3)
7.1.3 The dangling-ends fraction
235(2)
7.1.4 The effective permeability
237(6)
7.2 Estimation of effective permeability in heterogeneous media
243(14)
7.2.1 Methods based on the connectivity in the medium
244(13)
7.3 Problems
257(1)
References
258(3)
Chapter 8 Dynamic reservoir prediction using percolation 261(32)
8.1 Breakthrough-time prediction
262(15)
8.1.1 Scaling for the average breakthrough time
263(3)
8.1.2 Probability distribution for the breakthrough time
266(5)
8.1.3 Case studies
271(6)
8.1.3.1 Case study 1
272(1)
8.1.3.2 Case study 2
272(1)
8.1.3.3 Case study 3
273(2)
8.1.3.4 Case study 4
275(2)
8.2 Post-breakthrough behaviour
277(12)
8.2.1 Scaling for the average post-breakthrough production decay
277(4)
8.2.2 Probability distribution for the production decay
281(1)
8.2.3 Uncertainty in post-breakthrough oil production decline
282(4)
8.2.4 Case studies
286(15)
8.2.4.1 Case study 1
286(1)
8.2.4.2 Case study 2
287(2)
8.3 Problems
289(1)
References
289(4)
Chapter 9 Percolation and pore-scale applications 293(66)
9.1 Modelling pore-scale fluid displacements
295(3)
9.2 Invasion percolation
298(3)
9.3 Invasion-percolation-type displacement
301(15)
9.3.1 Trapping effects
304(3)
9.3.2 Invasion percolation in the presence of gravity
307(5)
9.3.3 Invasion percolation in the presence of viscous force
312(3)
9.3.4 Invasion percolation in the presence of both gravity and viscous forces
315(1)
9.4 Percolation and porous medium characterisation
316(22)
9.4.1 Scaling functions for relative permeability and capillary pressure
317(2)
9.4.2 Percolation and residual-phase saturation
319(7)
9.4.3 Percolation and network models
326(7)
9.4.3.1 Capillary bundle model
326(3)
9.4.3.2 Network models
329(4)
9.4.4 Percolation and pore-structure characterisation
333(5)
9.5 Diffusion and dispersion
338(7)
9.5.1 Diffusion
340(2)
9.5.2 Dispersion
342(3)
9.6 Problems
345(1)
References
346(13)
Index 359