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

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multipoint statistics to generate geologically realistic networks

Multipoint Statistics to Generate Geologically Realistic Networks

Hiroshi Okabe

supervised by Prof. Martin J Blunt

Petroleum Engineering and Rock Mechanics Research Group

Department of Earth Science and Engineering

Imperial College London

Multipoint Statistics to Generate Geologically Realistic Networks

contents
Contents
  • Introduction
    • Background / Motivation / Objectives
  • Brief overview of current reconstruction method
  • Our methodology: Multiple-point statistics model
  • Preliminary results for sandstone
  • Future work

Multipoint Statistics to Generate Geologically Realistic Networks

introduction
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

Multipoint Statistics to Generate Geologically Realistic Networks

introduction cont
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 asinput for pore-scale modelling

Multipoint Statistics to Generate Geologically Realistic Networks

brief overview of current reconstruction method
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

Multipoint Statistics to Generate Geologically Realistic Networks

results generated by published methods
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)

Multipoint Statistics to Generate Geologically Realistic Networks

percolation probabilities a quantitative characterization of the connectivity
Percolation probabilities- a quantitative characterization of the connectivity

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.

(Biswal B.et al, 1999)

Multipoint Statistics to Generate Geologically Realistic Networks

our methodology multiple point statistics model
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

Multipoint Statistics to Generate Geologically Realistic Networks

multiple point statistics
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.

Multipoint Statistics to Generate Geologically Realistic Networks

process of reconstruction
Process of reconstruction
  • Overview
    • pattern extraction
    • pattern recognition
    • pattern reproduction

training image

(2D thin-section)

or

template

Multipoint Statistics to Generate Geologically Realistic Networks

pattern extraction
Pattern extraction

u4

u1

u2

u?

u3

?

Probability

75% matrix, 25% pore

Multipoint Statistics to Generate Geologically Realistic Networks

expanded templates
Expanded templates

Multipoint Statistics to Generate Geologically Realistic Networks

pattern recognition reproduction
Pattern recognition & reproduction

u1

u2

u4

u?

u3

1

1

u?

u?

1

2

u?

1

1

1

2

2

u?

u?

1

1

u?

2

2

u?

2

u?

3

Infer cpdf

from training image

reproduction

If this pattern is missing in the training image,

drop furthest away datum

Multipoint Statistics to Generate Geologically Realistic Networks

preliminary results for sandstone
Preliminary results for sandstone

Fontainebleau SS(MicroCT)

Realization

Multipoint Statistics to Generate Geologically Realistic Networks

percolation probabilities of realizations
Percolation probabilities of realizations

Multipoint Statistics to Generate Geologically Realistic Networks

future work
Future work
  • Need further study: noise, preserving porosity, suitable template
  • Expand sample size
  • Carbonates
    • The statistical and direct imaging methods can be used interchangeably

Multipoint Statistics to Generate Geologically Realistic Networks