Recent years have seen a growing interest in the characterization of the
pore morphologies of reservoir rocks and how the spatial organization of
pore traits affects the macro behavior of rock–fluid systems. With the
availability of 3-D high-resolution imaging, such as x-ray micro-computed
tomography (
Natural and artificial materials are often characterized by their pore/grain shape or size distributions as determined by distinct analytical instruments. Several investigations have been conducted to classify pore types/shapes, and most of them are associated with 2-D quantification. However, a 3-D pore with irregular shapes cannot be appropriately characterized from 2-D image sections in pore-typing procedures, nor can the number of pores (Buller et al., 1990). The mass transport through porous media strongly depends on the structure of the pore network (Wiedenmann et al., 2013). Knowledge of pore morphologies is essential and they are one of the main parameters that control fluid flow underground. Petrophysical properties such as permeability, electrical conductivity and drainage capillary pressure are strongly influenced by throat sizes, which are constrictions of minimal cross-sectional area between pores (Buller et al., 1990). Many properties are controlled by pore/grain textures. Soete et al. (2015) demonstrated how seismic reflections in travertine systems are related to geobody boundaries, in which the seismic expression is a function of porosity, pore types, and shapes. The size and shape characterization of irregular particles is a key issue in many fields of science, which is often associated with large uncertainties (Bagheri et al., 2015). Moreover, to the best of our knowledge, the systematic 3-D pore shape quantification of sedimentary rocks based on sample size, pore network detachment (i.e., separation into individual pores), and distinct geometrical descriptor measurements has not been comprehensively reported in the literature.
X-ray micro-computed tomography (x-ray
In this study, the pore shapes of three sandstone rocks from distinct fields
were analyzed and classified based on the x-ray
To describe and quantify a particle form (in this case, pores) in
three dimensions, morphological parameters such as length, width, and
thickness are required. These 3-D parameters must be perpendicular to each
other but do not need to intersect at a common point (Blott and Pye, 2008).
To perform the pore shape classification approach that is proposed and
described in this work, we conventionally assigned the following practice
for the geometrical descriptor of individual particles:
In bounding-box analysis, the object coordination system follows the same as
what is acquired for the 3-D sample volume, namely,
3-D geometrical descriptors for the bounding-box
3-D geometrical parameters of the detached particle from the main
pore network of rock S
Another common dimensional feature that is used to characterize the
thickness of 3-D particles is shown in Table 1. This feature is the
equivalent diameter (EqD), which gives the analyzed object a corresponding
spherical diameter size with equal voxel volume. Although this parameter is
frequently used in the literature for 3-D pore structural description (Cnudde
et al., 2011; Van Dalen and Koster, 2012), the error in the particles'
thickness determination can be considerably high depending on the object's
shape, especially for very irregular ones. In this study, the pore shapes
were classified by considering the equivalent diameter as the thickness
(
The relationship between the thickness and the length of a particle
The methodology that is used in the present work to quantify sandstones'
pore shapes is based on the espoused pore shape classification in Fig. 2b.
This classification follows the original approach of Zingg's (1935)
diagram, which was deeply discussed by Blott and Pye (2008) and applied
recently by Soete et al. (2015) while studying travertines. As one can see
in Fig. 2b, cubes are particles with comparable
Pore shape classification for equancy based on the
Pore shapes in sandstone reservoirs that were acquired from 3-D x-ray
Three different sandstones from German reservoir fields were investigated:
Bentheimer sandstone (S Obernkirchen sandstone (S Flechtingen sandstone (S
The Bentheimer sandstone is part of the lower Valanginium sequence, which is
associated with the Lower Cretaceous (approximately 140–134 million years
old) and it is comparable to the well-known Berea and Fontainebleau
sandstone. This sandstone was segmented into three lithostratigraphical
units according to Kemper (1968): lower Bentheimer sandstone, intermediate
Romberger, and upper Bentheimer sandstone (also known as flasered sandstone).
This rock has been petrographically classified as quartz sandstone with low
clay and silt content (< 8 vol%). The grain size varies between
very fine and coarse, although fine grains are predominant. In general, the
components are well rounded and well sorted, excluding partial content of
stable and unstable heavy minerals and feldspars. Stadtler (1998) provided a
comprehensive and more detailed description of the S
The Obernkirchen sandstone is part of the upper Berriasium (also known as
the Wealden sequence, approximately 145–150 million years old), which is
associated with the Lower Cretaceous and forms the lower transition to the
Jurassic. In principle, this rock is comparable to the S
3-D x-ray
The Flechtingen sandstone is part of the so-called Rotliegend sequence
(approximately 302–257 million years old), which is associated with the
Lower Permian. This rock greatly differs from S
In summary, these different sandstones feature a broad range of pore structures because of their distinct diagenesis and tectonic history. Hence, we should be able to detect differences for the systematic and individual analysis of pore shapes in these three reservoir rocks by using the proposed methodological/statistical approach.
The x-ray
The 3-D reconstructed volume was post-filtered, followed by a pore
segmentation and separation process that was performed with the Avizo Fire
8.1.0 software (Avizo, 2014), which allowed for data visualization and
quantification. As shown in Table 2, specific filters were evaluated for
each analyzed rock to improve pore noise reduction or the gain of the
pore matrix/clay border contrast. The non-local means filter (Buades et al.,
2005) showed the best results, although the additional median 3-D filter
(Ohser and Schladitz, 2009) was applied to samples S
1000
Limited voxel resolution in x-ray
3-D and 2-D visualizations after the watershed algorithm is applied to
the 250
So, if
Quantification of the pore network fragmentation by using the Euler
number
The pore shape classification involves counting and measuring the 3-D
geometrical descriptors (
The changes within the marker extent parameters in the watershed algorithm
results are visualized in Fig. 4a for the 250
Pore thickness (
One of the most important steps to be established while performing pore
shape analysis is the measurement of the 3-D geometrical descriptors
Thickness statistics for the pore ganglia and detached pore networks after a normal Gaussian fit to the distribution data, shown in Fig. 6. SD denotes standard deviation.
As shown in Table 3, the pore ganglia thicknesses are mostly below 20
Pore shape results (S
Pore shape results (S
Pore shape results (S
To validate the pore shape classification approach, distinct 3-D geometrical descriptors were investigated according to the diagrams in Fig. 2a, which allows qualitative particle description, and Fig. 2b, which allows pore shape classification and subsequent quantification based on artificial object similarity.
Figures 7, 8, and 9 depict 250
By comparing the 3-D renderings in Figs. 7, 8, and 9, sample S
However, when the bounding-box, Feret caliper, and equivalent diameter
descriptors were investigated in the Zingg diagram for the pore shape
classification and quantification, the results for the three rocks seemed to
be more appropriate for the FC descriptor (compare e.g., pore 3 in Fig. 7).
For this pore, the bounding-box descriptor indicates a cube-like shape;
however, as shown in Fig. 1a, this cube shape is notably erroneous. Our
assumption for the bounding-box mismatch is related to the main orientation
of pore 3, which is neither perpendicular nor parallel to the sample
Effect of subsample volume size on the (1) rod-, (2) blade-, (3) cuboid-, (4) plate-, and (5) cube-shaped classes of the pore ganglia (NoBin) and the detached pore networks (Bin3).
Selecting a region of interest (ROI) from the sample is required prior to
any pore shape quantification or morphological analysis from a reconstructed
3-D image. To correlate many properties (e.g., porosity), the chosen ROI
should be large enough to represent a sample's complexity and heterogeneity
but small enough not to overwhelm the available computing resources (Baker
et al., 2012). This study's ROI volumes of 1000
Pore shape quantification of samples S
Figure 11 shows the results in percentages and average values with standard
deviations for each of the pore shapes (rods, blades, cuboids, plates, and
cubes) in the analyzed rocks. From Fig. 11, one can see systematic changes
between the pore shape classes (see values in percentage) within the
evaluated Bin parameter and the BB, FC, and EqD descriptors. The
NoBin results represent the pore ganglia shape's contribution (red
color), whereas the detached pore network results after Bin10, 3, and 1 are
shown in blue, green, and yellow, respectively. In the graphics, the pores
tend to shift from plates to cubes from Bin10 to Bin1 for the detached pore
networks in the BB and FC methods for the three reservoir rocks. The shift
to cube shapes is expected because of the pore separation process, which
obviously diminishes the particles' length to a value that is comparable to
the width and thickness, shifting the
As discussed in the literature (Anovitz and Cole, 2015; Chang et al., 2006;
Okazaki et al., 2014), a number of pore form factors have been used to
quantify pore shapes that might be correlated to the macroscopic properties
of sedimentary rocks. Among these factors, flatness, elongation, and
roundness are commonly used. Permeability, from a geological point of view,
is still one of the most challenging properties to determine but is
nonetheless a very important hydraulic property in solving accumulation and
exploitation problems in the oil and gas industry. The permeability,
Thus, correlating the quantification results of pore shapes (observe mainly
Bin3 and Feret caliper results in Fig. 11) of the analyzed sandstones, and
considering that a cube-like shape imposes less fluid flux resistance compared
to, e.g., a plate-like shape, one could assume that S
Three distinct reservoir rocks were systematically analyzed to characterize
3-D pore shapes based on x-ray
In the analyzed rocks, the most accurate particle descriptor was given by
the Feret caliper because of the considerably high number of pores that were
located neither perpendicular nor parallel to the
The pore thickness that was calculated using the equivalent diameter led to
erroneous results in the Zingg shape classification for the three analyzed
sandstones, which contain very asymmetric pore morphologies. However, the
EqD descriptor might be used to indicate the degree of pore heterogeneity
based on rod-like shapes, which were found to be equal to 6.70,
18.58, and 25.44 % for samples S
We would like to thank CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico, of the Ministry of Science, Technology, and Innovation of Brazil for granting the research stipend no. 207204/2014-4. The authors would also like to thank the reviewers for their help in improving the quality of this paper. Edited by: S. Henkel