Preface |
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v | |
About the Authors |
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ix | |
Acknowledgements |
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xi | |
Chapter 1 Introduction |
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1 | (18) |
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1.1 Geological uncertainty |
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2 | (1) |
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1.2 Reservoir modelling and heterogeneities |
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3 | (2) |
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1.3 Connectivity as the predominant feature of heterogeneous media |
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5 | (1) |
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1.4 Overlapping sandbodies models |
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6 | (2) |
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1.5 The percolation theory approach |
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8 | (3) |
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1.6 Variants of percolation |
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11 | (2) |
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13 | (2) |
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15 | (4) |
Chapter 2 Percolation theory-the basics |
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19 | (38) |
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2.1 Percolation on infinite lattices |
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20 | (3) |
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2.2 Percolation quantities and their properties |
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23 | (5) |
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2.2.1 Percolation probability |
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23 | (2) |
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25 | (1) |
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26 | (1) |
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27 | (1) |
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2.2.5 Effective permeability or conductivity |
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28 | (1) |
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2.3 Universality in percolation theory |
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28 | (1) |
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29 | (6) |
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2.5 Calculation of percolation parameters |
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35 | (7) |
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2.5.1 Analytical method for 1D percolation |
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36 | (3) |
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2.5.2 Monte Carlo simulations for 2D and 3D percolation models |
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39 | (3) |
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2.5.2.1 Percolation threshold |
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39 | (1) |
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2.5.2.2 Critical exponents |
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40 | (2) |
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2.6 Anisotropy and percolation |
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42 | (6) |
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2.6.1 Apparent threshold for anisotropic systems |
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44 | (1) |
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2.6.2 Finite-size scaling laws for anisotropic systems |
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45 | (3) |
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2.7 Percolation and fractals |
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48 | (3) |
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51 | (3) |
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54 | (3) |
Chapter 3 Continuum percolation for geological models |
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57 | (28) |
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3.1 Simple sandbody model |
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59 | (11) |
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3.1.1 Isotropic overlapping sandbody model in 2D |
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59 | (1) |
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3.1.2 Computational algorithm |
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60 | (5) |
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65 | (5) |
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3.2 Simple fracture network model |
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70 | (8) |
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3.2.1 Simple fracture network model in 2D |
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71 | (3) |
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3.2.2 Computational algorithm |
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74 | (1) |
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75 | (3) |
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78 | (1) |
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79 | (6) |
Chapter 4 The connectivity of overlapping sandbodies |
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85 | (58) |
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4.1 Effects of sandbody size variation |
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85 | (9) |
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4.2 Effects of anisotropy |
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94 | (5) |
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4.3 Effects of orientation disorder |
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99 | (5) |
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104 | (6) |
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105 | (1) |
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4.4.2 Spatial correlation |
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105 | (2) |
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107 | (3) |
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4.5 Analysis of connectivity in 3D |
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110 | (17) |
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4.5.1 Idealised overlapping sandbody model |
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110 | (5) |
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4.5.2 Anisotropy effects in 3D |
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115 | (5) |
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4.5.3 Sandbody size variation |
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120 | (1) |
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4.5.4 Effects of orientational disorder |
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121 | (3) |
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4.5.5 Other effects in 3D |
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124 | (3) |
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127 | (7) |
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4.6.1 Case study 1: A carbonate gas condensate reservoir |
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127 | (1) |
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4.6.2 Case study 2: An offshore oil reservoir |
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128 | (5) |
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4.6.3 Case study 3: A gas reservoir C |
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133 | (1) |
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134 | (3) |
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137 | (6) |
Chapter 5 Percolation and fracture systems |
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143 | (52) |
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5.1 Effects of fracture size variation |
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146 | (8) |
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5.2 Effects of fracture orientation variations |
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154 | (2) |
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5.3 Effects of anisotropy in the system |
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156 | (5) |
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5.4 Effects of spatial correlation on fracture connectivity |
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161 | (4) |
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5.5 Effective permeability of fracture systems |
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165 | (4) |
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169 | (14) |
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5.6.1 Idealised fracture network models |
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170 | (4) |
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5.6.2 More complex fracture models |
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174 | (7) |
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5.6.2.1 Anisotropy effects |
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175 | (3) |
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5.6.2.2 Fracture size variation |
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178 | (1) |
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179 | (1) |
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179 | (2) |
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5.6.3 Effective permeability |
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181 | (2) |
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183 | (2) |
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185 | (3) |
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188 | (7) |
Chapter 6 Backbone, dangling ends and effective permeability |
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195 | (32) |
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6.1 Backbones and dangling ends |
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195 | (9) |
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6.2 Effective (single-phase) permeability |
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204 | (11) |
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6.2.1 Anisotropic effects in 2D |
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211 | (2) |
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6.2.2 Effects of sandbody orientation disorder |
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213 | (1) |
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6.2.3 Effects of sandbody size distribution |
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213 | (2) |
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6.2.4 Effects of sandbody shape |
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215 | (1) |
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215 | (5) |
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6.3.1 Anisotropy effects in 3D |
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217 | (1) |
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6.3.2 Effects of sandbody orientation disorder |
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218 | (1) |
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6.3.3 Effects of sandbody size distribution |
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219 | (1) |
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220 | (2) |
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220 | (1) |
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221 | (1) |
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222 | (1) |
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223 | (4) |
Chapter 7 Beyond simple percolation |
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227 | (34) |
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7.1 Prediction of the percolation quantities in binary permeability media |
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228 | (15) |
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7.1.1 The connected sand fraction |
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229 | (3) |
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7.1.2 The backbone fraction |
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232 | (3) |
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7.1.3 The dangling-ends fraction |
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235 | (2) |
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7.1.4 The effective permeability |
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237 | (6) |
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7.2 Estimation of effective permeability in heterogeneous media |
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243 | (14) |
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7.2.1 Methods based on the connectivity in the medium |
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244 | (13) |
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257 | (1) |
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258 | (3) |
Chapter 8 Dynamic reservoir prediction using percolation |
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261 | (32) |
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8.1 Breakthrough-time prediction |
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262 | (15) |
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8.1.1 Scaling for the average breakthrough time |
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263 | (3) |
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8.1.2 Probability distribution for the breakthrough time |
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266 | (5) |
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271 | (6) |
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272 | (1) |
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272 | (1) |
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273 | (2) |
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275 | (2) |
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8.2 Post-breakthrough behaviour |
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277 | (12) |
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8.2.1 Scaling for the average post-breakthrough production decay |
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277 | (4) |
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8.2.2 Probability distribution for the production decay |
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281 | (1) |
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8.2.3 Uncertainty in post-breakthrough oil production decline |
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282 | (4) |
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286 | (15) |
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286 | (1) |
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287 | (2) |
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289 | (1) |
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289 | (4) |
Chapter 9 Percolation and pore-scale applications |
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293 | (66) |
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9.1 Modelling pore-scale fluid displacements |
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295 | (3) |
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298 | (3) |
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9.3 Invasion-percolation-type displacement |
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301 | (15) |
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304 | (3) |
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9.3.2 Invasion percolation in the presence of gravity |
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307 | (5) |
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9.3.3 Invasion percolation in the presence of viscous force |
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312 | (3) |
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9.3.4 Invasion percolation in the presence of both gravity and viscous forces |
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315 | (1) |
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9.4 Percolation and porous medium characterisation |
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316 | (22) |
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9.4.1 Scaling functions for relative permeability and capillary pressure |
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317 | (2) |
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9.4.2 Percolation and residual-phase saturation |
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319 | (7) |
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9.4.3 Percolation and network models |
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326 | (7) |
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9.4.3.1 Capillary bundle model |
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326 | (3) |
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329 | (4) |
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9.4.4 Percolation and pore-structure characterisation |
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333 | (5) |
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9.5 Diffusion and dispersion |
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338 | (7) |
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340 | (2) |
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342 | (3) |
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345 | (1) |
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346 | (13) |
Index |
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359 | |