1. Multipoint Statistics to Generate Geologically Realistic Networks 1 Hiroshi Okabe supervised by Prof. Martin J Blunt Petroleum Engineering and Rock Mechanics Research Group Department of Earth Science and Engineering Imperial College London

2. Multipoint Statistics to Generate Geologically Realistic Networks 2 Contents Introduction Background / Motivation / Objectives Brief overview of current reconstruction method Our methodology: Multiple-point statistics model Preliminary results for sandstone Future work

3. Multipoint Statistics to Generate Geologically Realistic Networks 3 Introduction Background Flow modelling of Sandstone – successfully predicted A shortage of pore-scale network structures Carbonate – beyond the resolution of Micro-CT Necessary to find another approach in order to generate a pore space representation – a multiple-point statistical technique

4. Multipoint Statistics to Generate Geologically Realistic Networks 4 Introduction (cont.) Motivation -why carbonates? A significant amount of the world’s hydrocarbon reserves are located in carbonate formations. Particular interest to the petroleum industry. Objectives Develop a statistical methodology to generate geologically realistic networks as input for pore-scale modelling

5. Multipoint Statistics to Generate Geologically Realistic Networks 5 Brief overview of current reconstruction method Almost all the targets have been sandstones. Reconstruction approaches Stochastic reconstruction Gaussian field reconstruction Simulated annealing reconstruction Process based reconstruction - sedimentation, compaction and diagenesis model

6. Multipoint Statistics to Generate Geologically Realistic Networks 6 Results generated by published methods MicroCT Process-based Gaussian-field Simulated Annealing (Biswal B., Manwart C., Hilfer R., Bakke S. and Oren, P.-E., 1999)

7. Multipoint Statistics to Generate Geologically Realistic Networks 7 Percolation probabilities - a quantitative characterization of the connectivity (Biswal B.et al, 1999) Let K (r, L) denote a cube of sidelength L centered at the lattice vector r. Percolation probabilities are measured by changing L of a cube.

8. Multipoint Statistics to Generate Geologically Realistic Networks 8 Our methodology - Multiple-point statistics model Process-based method – more realistic but difficult for most carbonates Traditional two-point statistics – fail to reproduce the long-range connectivity Introduce multiple-point statistical technique to pore-scale modelling Start on sandstone before tackling carbonates

9. Multipoint Statistics to Generate Geologically Realistic Networks 9 Multiple-point statistics Use of training images At the field scale, typical for petroleum geostatistics, is the scarcity of hard data, then training data sets such as outcrops are borrowed. In pore-scale modelling, 2D thin- sections can provide multiple-point statistics that describe the relation between multiple spatial locations.

10. Multipoint Statistics to Generate Geologically Realistic Networks 10 Process of reconstruction Overview 1.pattern extraction 2.pattern recognition 3.pattern reproduction training image (2D thin-section) template or

11. Multipoint Statistics to Generate Geologically Realistic Networks 11 Pattern extraction u1u1 u2u2 u4u4 u3u3 u?u? ? Probability 75% matrix, 25% pore

12. Multipoint Statistics to Generate Geologically Realistic Networks 12 Expanded templates

13. Multipoint Statistics to Generate Geologically Realistic Networks 13 Pattern recognition & reproduction u2u2 u4u4 u1u1 u3u3 u?u? u? 1 2 3 If this pattern is missing in the training image, drop furthest away datum u? 1 2 1 2 1 2 1 2 1 1 1 2 Infer cpdf from training image reproduction

14. Multipoint Statistics to Generate Geologically Realistic Networks 14 Preliminary results for sandstone Fontainebleau SS (MicroCT) Realization

15. Multipoint Statistics to Generate Geologically Realistic Networks 15 Percolation probabilities of realizations

16. Multipoint Statistics to Generate Geologically Realistic Networks 16 Future work Need further study: noise, preserving porosity, suitable template Expand sample size Carbonates The statistical and direct imaging methods can be used interchangeably