IEEE Signal Processing - March 2018 - 122

preprocessing operations for artifact removal. Examples of typical artifacts in CT scans include noise, streaks, and beam-hardening effects. Next, a segmentation algorithm is used to divide
the acquired data into pores and grains representing the various
mineral compounds in the rock. A segmentation result using
the K-means algorithm is shown in Figure 1. Finally, numerical simulation algorithms are employed to compute the desired
physical properties. An outline of the major steps in a typical
DRP framework is shown in Figure 2. In this article, we present
an overview of the recent developments in DRP with the goal of
connecting the signal and image processing communities with
this research field.

K-Means

0
200
400
600
800
1,000
1,200
1,400

Rock properties of interest

1,600
0

500

1,000

1,500

Figure 1. A μCT image slice of an andesite rock sample segmented using

the K-means algorithm. The pores are white, minerals gray, and matrix
(i.e., the ground mass of the rock) light brown. (Figure used with permission from [7].)

CT
Scanning

Artifact
Removal

Segmentation

Computation
of Physical
Properties

The ability of reservoirs to store hydrocarbons relies on several
physical rock properties. We briefly describe some properties
that are of interest to DRP and reservoir engineers. For a more
detailed review, see [8].

Porosity and permeability
Pores are void spaces between rock grain material. Oil, gas,
and water reserves are found within these pores. The size,
shape, and textural properties of rock grains determine the
nature of rock pores. The porosity of a rock is a measure of the
ratio of rock volume occupied by pores. It is mathematically
described as

Figure 2. A typical workflow for a DRP algorithm.

Core analysis laboratories have traditionally provided physical rock properties through experiments conducted on core
plugs. However, laboratory-based methods developed to estimate
physical rock properties have a high turnover time. DRP represents a time- and cost-effective alternative for determining rock
properties. Furthermore, the theoretical models used in conventional rock physics models are often oversimplified and do not
provide details on the internal mechanisms affecting estimated
properties. For example, experiments used to study fluid flows
in porous media simply measure the amount of fluid that went in
and what came out.
The most important factor governing the physical behavior
of a real rock sample is the rock micro-structure, i.e., the distribution of the grains and pores. An understanding of pore-scale
physics can provide valuable insights on our understanding and
estimation of the physical properties of rocks. DRP provides
high-resolution CT images of rock pore and mineral geometries
from which various physical properties can be estimated. The use
of high-resolution images and the efficient numerical simulation
techniques in DRP offer a deeper understanding of the relationship between pore geometry and physical properties [4]. Previous
results have confirmed that digitally computed porosity, absolute
permeability, electrical properties, and relative permeability values are acceptable and can fall within the measurements of traditional laboratory experiments [5], [6].
The typical workflow of DRP algorithms starts with threedimensional (3-D) rock-image volume acquisition followed by
122

Volume of pore space in the rock
.
Total rock volume

(1)

Permeability is a measure of a medium's ability to transmit
fluids through its pore spaces under the influence of pressure differences. Even though rocks with higher porosity values can be
expected to have higher permeability, the relationship between
these variables is more complex. The connectedness of pores and
the shape of pore channels formed are key factors that can influence permeability values significantly.
Absolute permeability is computed using Darcy's law. Assuming a laminar linear flow of fluid through a porous medium of
length L and a pressure gradient ^2p 2L h, Darcy's law can be
described as
y = -c

k mc 2p m,
2L

(2)

where y is fluid velocity, k is rock permeability in the medium,
and h is fluid viscosity. Permeability, k, is measured in darcies
(D). In reservoir studies, permeability is often measured in millidarcy (mD). Because of the heterogeneity of oil reservoirs, rock
properties may vary significantly across different directions. Permeability estimates are often provided with a directional reference, e.g., k x, k y, and k z.
Porosity is often easier to measure than permeability. Good
estimates for porosity values can be found using well-logging
tools such as gamma rays or sonic tools. Permeability-porosity
trends are often used to predict permeability values from available porosity measurements.

IEEE Signal Processing Magazine

March 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018