Multi-scale Image-Based Pore Space Characterisation and Pore Network Generation: Case Study of a North Sea Sandstone Reservoir

  • Gilbert ScottEmail author
  • Kejian Wu
  • Yingfang Zhou


In this paper, we examine the pore space geometry and topology of a North Sea sandstone reservoir rock based on multi-scale scanning electron microscopy. The reservoir was subjected to extensive diagenesis which has resulted in a complex pore space with a wide range in pore sizes. We quantify the pore size and pore coordination number distributions, and we find that the mean and standard deviation of the coordination number are power law functions of pore radius, where the scaling exponent varies from 0.3 to 0.5. We present a 2D stochastic algorithm to generate a pore network based on statistical information. The algorithm incorporates the concept of a weighted planar stochastic lattice which is a construction that naturally leads to scale-free character with power law behaviour. We validate the algorithm against SEM imaging by showing that it can reproduce the observed clustering and a realistic spatial distribution of pore space elements. We also try to explore the relationship between fluid flow properties of reservoir rock and 2D pore image features.


Porous media Pore network SEM imaging Multi-scale 

List of symbols


Proportionality factor in the relationship between \(Z_\mathrm{mean}(r)\) and \(r\)


Proportionality factor in the relationship between \(Z_\mathrm{stdev}(r)\) and \(r\)


Euclidean distance


Euclidean distance of pixel \(i\)


Exponent of \(\frac{r}{r_{1}}\) in the pore size probability distribution


Number of elements


Number of elements with radius greater than \(r\)


Total number of elements


Number of links


Number of links with radius greater than \(r\)


Total number of links


Radius of element


Radius of element \(i\)


Minimum element radius


Maximum element radius


Pore size distribution parameter, near the minimum radius


Pore size distribution parameter, near the maximum radius


Characteristic radius of largest pores which control permeability


Coordination number


Coordination number of element \(i\)


Mean coordination number


Standard deviation of the coordination number

\(\alpha \)

Scaling index in the pore size probability distribution

\(\beta \)

Scaling index in the relationship between \(Z_\mathrm{mean}(r)\) and \(r\)

\(\phi \)


\(\chi \)

Connectivity function



The authors would like to thank Anasuria Operating Company Ltd (AOC) for making available the rock samples for analysis. SEM imaging was performed at the University of Aberdeen Centre for Electron Microscopy, Analysis and Characterisation (ACEMAC). We would like to thank John Still for invaluable assistance in the SEM imaging work. We would like to acknowledge financial support from Royal Society through the International cost share programme with reference IE151092. The authors acknowledge the very helpful comments from three anonymous reviewers.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of EngineeringUniversity of AberdeenAberdeenUK

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