J. Hydrol. Hydromech., 67, 2019, 4, 372–383
DOI: 10.2478/johh-2019-0009

Computational and experimental pore-scale studies of a carbonate rock sample
William Godoy1*, Elizabeth M. Pontedeiro1, 2, Fernanda Hoerlle1, Amir Raoof2,
Martinus Th. van Genuchten2, 3, José Santiago1, Paulo Couto1
1

Civil Engineering Program – PEC/COPPE – LRAP, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands.
3
Center for Environmental Studies, CEA, São Paulo University, UNESP, Rio Claro, SP, Brazil.
*
Corresponding author. E-mail: wmgodoy@petroleo.ufrj.br
2

Abstract: Carbonate rocks host several large water and hydrocarbon reservoirs worldwide, some of them highly heterogeneous involving complex pore systems. Pre-salt reservoirs in the Santos Basin off the south-east coast of Brazil, are an
example of such rocks, with much attention focused on proper characterization of their petrophysical and multiphaseflow properties. Since it is very difficult to obtain rock samples (coquinas) from these very deep reservoirs, analogues
from north-eastern Brazil are often used because of very similar geological age and petrophysical properties. We used acoquina plug from an outcrop in a quarry in northeast Brazil to perform a comprehensive set of analyses. They included
Scanning Electron Microscopy (SEM), Energy-Dispersive X-ray Spectroscopy (EDS), X-ray Diffraction (XRD), andmicro-computed tomography (μCT) image acquisition using a series of pixel sizes, as well as direct permeability/porosity measurements. Some of the experimental data were collected from the plug itself, and some from a small
sample of the rock slab, including thin sections. Results included the carbonate rock composition and the pore system at
different scales, thus allowing us to reconstruct and model the porosity and absolute permeability of the coquina using
3D digital imaging and numerical simulations with pore network models (PNMs). The experimental and numerical data
provided critical information about the well-connected pore network of the coquina, thereby facilitating improved predictions of fluid flow through the sample, with as ultimate objective to improve hydrocarbon recovery procedures.
Keywords: Pore network modeling; Carbonate rock; Coquina; Absolute permeability; μCT.
INTRODUCTION
Carbonate rocks host about 50% of worldwide hydrocarbon
reserves (Vik et al., 2013). In Brazil, the pre-salt carbonate
reservoirs accounted for 50% of total national oil production in2018 (ANP, 2018). Although the annual production from thepre-salt reservoirs is increasing constantly, there are several
challenges regarding their geological and petrophysical characterization (Corbett et al., 2017; Luna et al., 2016), as well as
quantifying multiphase flow in their pore systems (Corbett etal., 2016). This because of the extremely heterogeneous natureof many carbonate rocks. One challenge of the pre-salt reservoirs is the difficulty to obtain samples for purposes of geological, sedimentological and petrophysical characterization. An
alternative is to use analogue samples that are geologicallysimilar to the pre-salt reservoir rocks (Corbett et al., 2016). For
this many have used carbonate rocks samples from an outcrop
in the northeast region of Brazil (Azambuja Filho et al., 1998),
mostly to study their porosity and permeability properties.
These samples, called coquinas (Tavares et al., 2015), containlarge amounts of shells and as such exhibit considerable heterogeneity and anisotropy.
In order to study the petrophysical properties of carbonate
rocks, with special focus on their pore networks, nondestructive visualization techniques such as X-ray computed
microtomography, μCT (Blunt, 2001; Bultreys et al., 2015;
Cnudde and Boone, 2013; Dal Ferro et al., 2013; Wildenschildand Sheppard, 2013) and scanning electron microscopy, SEM(de Boever et al., 2015; Fäy-Gomord et al., 2017; Hemes et al.,2015), have been widely used. Energy-dispersive X-ray spectroscopy (EDS) is also used often for qualitative (Goldstein etal., 2003) and even quantitative (Newbury and Ritchie, 2013)
analyses of the composition of different rocks and soils. Although destructive, energy-dispersive X-ray diffraction (XRD)

techniques are similarly important for qualitative/quantitative
analyses (Hillier, 1994).
In our work we used μCT as an excellent non-invasive
method for characterizing and quantifying rock structures andstudying dynamic pore-scale processes. Digital reconstructionsof image stacks are then used to represent the internal structureof a coquina sample, thereby providing connections between
the different pores (i.e., pore bodies and throats) in a pore network, leading to a quantitative understanding of fluid behavior
in the sample. An extremely important step after acquiring μCT
images is the processing of generated data. This processing step
can be done using one or more filters (e.g., anisotropic diffusion and/or non-local means filters) to correct and enhance thequality of the images. Non-local means filters (Buades et al.,2005) are especially popular when working with images ofheterogeneous carbonate rocks (e.g., Shah et al., 2015).
Subsequent to treatment of the images using one or more filters, a segmentation step is needed to isolate the pore systemfrom the rock matrix, thus allowing their digital reconstruction.
Segmentation can be done using different algorithms (automated methods) or by direct analysis using optical microscopy or
SEM (manual procedures), thus allowing one to separate between the pore spaces and the solid rock matrix (Al-Raoush andWillson, 2005; Wildenschild et al., 2002). The use of thin sections impregnated with blue epoxy resin helps to more accurately identify pore spaces, especially for detecting the intraparticle porosity of coquina samples. Although the use of visualsegmentation methods requires some experience, they often
improve the selection of regions where meso- and macro-poresare dominant, among other applications. The use of SEM as an
auxiliary tool also guarantees the possibility of visualizing, withhigh resolution, regions that may become indistinct in μCT
images generated with larger pixel sizes (Blunt et al., 2013;
Bultreys et al., 2016). Several automated methods for segmen-

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Computational and experimental pore-scale studies of a carbonate rock sample

tation are now available for different types of images (Andrӓ etal., 2013; Iassonov et al., 2009; Sezgin and Sankur, 2004).
After segmentation and subsequent skeletonization to define
the pore structure in terms of pore bodies and pore throats, various approaches can be used for modeling the absolute permeability and related pore-scale transport processes. These include
methods for solving the Navier–Stokes equations (or simplifications thereof), including Lattice Boltzmann methods (Jafari etal., 2011; Ramstad et al., 2010), traditional mesh-based computational fluid dynamics approaches (e.g., finite difference, finite
volume and finite element methods) as described by Thijssen(2007) among others, as wll as pore network modeling (PNM)
and related techniques (Blunt et al., 2013; Bultreys et al., 2015;
Joekar-Niasar and Hassanizadeh, 2012; Raoof et al., 2013).
Several alternative approaches are available to estimate theabsolute permeability from pore space characteristics, such as
effective-medium approximations, EMAs (Doyen, 1988; Ghanbarian et al., 2018) and critical path analyses, CPAs (Ghanbarian et al., 2016; Katz and Thompson, 1986) techniques. The
main difference between EMA and CPA techniques refers to
the pore-throat size distribution: EMA approaches are better
suited for media having relatively narrow pore-throat size distributions, while CPA techniques are best used for more heterogeneous media having broader pore-throat distributions (e.g.,
Ghanbarian et al., 2018).
Specific objectives of this study were to generate and study
the pore-scale network of a real coquina plug using experimental and digital data, and to perform numerical fluid flow
simulations based on porous networks based on 3D X-ray microtomography images obtained using different pixel sizes.
Experimental data obtained for the plug and rock slab (takenfrom the same plug) using different techniques (permeameter/porosimeter, SEM-EDS and XRD measurements) wereanalyzed to improve identification of the pore system and thecomposition of the rock material. Our main objective was toconstruct the pore structure of a real coquina sample that serves
as a geologically analogue of a Brazilian pre-salt reservoir rock,using experimental data, geological information, 3D modeling,
and numerical simulation to identify and understand the main
parameters that influence reconstruction of the pore system,
which will allow us to simulate fluid flow and transport within
the medium with good correlation with real data.
MATERIALS AND METHODSIn this section we provide a geologic description of the area
where the carbonate rock sample for our study was taken, as

well as its characterization regarding the pore system and mineralogical composition. Based on this information, we provide
details about the digital reconstruction of its pore system and abrief description of the pore-scale network modeling approach
used to estimate absolute permeability values.
Carbonate rock sample description and preparation
The carbonate rock sample selected for our study was takenfrom an outcrop of the Morro do Chaves Formation in the Sergipe-Alagoas Basin in north-east Brazil. The coquina samples
from this site are close analogues in terms of porosity and permeability of coquinas taken from the pre-salt hydrocarbon
reservoirs off the coast of south-east Brazil, such as the presence of well-connected meso- and macro-pores ranging fromfew micrometers up to several millimeters. The SergipeAlagoas Basin is located in the Brazilian states of Sergipe andAlagoas, and with a small portion in the state of Pernambuco
Brazil (Fig. 1). Although the basins of Sergipe and Alagoas
exhibit important differences in terms of their structure andstratigraphy (Thompson et al., 2015), it is possible to define theSergipe-Alagoas Basin as a single entity (Campos Neto et al.,2007). The basin is known in that its outcrops include all sections of the Brazilian continental margin, with a total estimatedarea of over 44,000 km². According to Campos Neto et al.
(2007), the evolution of this basin is related to the separation of
the Gondwana continent, with its subsidence occurring in the
Rifte phase. At this stage the first tectonic pulse occurred,
which commenced a sedimentary sequence during which theMorro do Chaves Formation was generated.
The Morro do Chaves Formation is defined by Azambuja
Filho et al. (1998) as a carbonate succession that is interspersedwith siliciclastic rocks of the Coqueiro Seco and Rio Pitanga
formations. Located in the municipality of São Miguel dos
Campos, in the state of Alagoas, the Morro do Chaves Formation currently corresponds to a quarry (mine) called MinaSão Sebastião (Fig 1). The coquinas were formed by bivalves
and non-marine ostracodes with varying percentages of terrigenous deposits. As detailed by Tavares et al. (2015), shells
have different sizes and degrees of fragmentation, with facies insome cases containing bivalves in living or articulated positions. They noted that coquinas from Morro do Chaves havecalcite as the main mineralogical component, while containing
mostly mollusc shells. The rock matrix is composed of clay,
siliciclastic sand (mainly quartz), as well as some lithoclasts of
igneous, sedimentary and metamorphic rocks. According
Tavares et al. (2015), six lithofacies can be identified in theFig. 1. Location of the Sergipe-Alagoas Basin, in the northeast region of Brazil, identifying the constituent sub-basins and the location of
the quarry called Mina São Sebastião (in the city of São Miguel dos Campos), where the Morro do Chaves Formation is located.

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William Godoy, Elizabeth M. Pontedeiro, Fernanda Hoerlle, Amir Raoof, Martinus Th. van Genuchten, José Santiago, Paulo Couto

Morro do Chaves Formation, using both taphonomic (for shellfragmentation) and compositional (for the presence of micriteand siliciclastic sand) criteria.
A well-studied layer (Corbett et al., 2016; Luna et al., 2016)
in the Morro do Chaves Formation (Fig. 2a), called Bed 2B(Fig. 2b) was selected. Corbett et al. (2016) pointed out that it ispossible to use cross-stratification as evidence that the coquinas
in this layer were deposited lakewards or lagoonwards as accreting bioclastic bars. A plug from that layer (Fig. 2b), designated as plug 1-34A (Fig. 2c), was selected for our study. The
plug was prepared, flattened (top and bottom), cleaned withmethanol and toluene, and placed in an oven at 60°C for 24hours. The cleaning and drying processes were the same as
adopted by Corbett et al. (2017), without needing a humiditycontrolled drying environment since the carbonate sample did
not contain gypsum or solid hydrocarbon-like gilsonite or pyrobitumen. After preparation and cleaning, the plug was approximately 35 mm in diameter and 35 mm in length. Porosityand absolute permeability measurements were performed in thelaboratory using a Wheaterford DV-4000® gas porosimeter/permeater, while the porosity was measured using Helium(He) gas and the absolute permeability using Nitrogen gas (N2).
The equipment had a reliable range between 0.001 mD and
40,000 mD for absolute permeability measurements. We alsomeasured the pore volume, grain density, mass, length and theactual diameter.
A 30-μm thick thin section having dimensions of 70 mm ×
45 mm (Fig. 2d) was prepared, as well as a rock slab (Fig. 2e),from the cuts (top and bottom) of plug 1-34A after flattening of
the surface of the sample. During preparation of the rock slab, aregion of 10 mm × 10 mm and 5 mm thickness (red region in
Fig. 2e) was selected, cut, and then used to obtain various data.
We used SEM to characterize the surface and to visualize thechosen pore spaces, and EDS for qualitative analysis and identification of the main elements composing the surface. SEM was
performed in a Hitachi TM3030® Plus low vacuum atmosphereand an acceleration voltage of 1.5 kV, and EDS using a Bruker
XFlash® MIN SVE detector. The same region (shown in red inFig. 2e) was used to acquire μCT images using smaller pixel
sizes (of 6.77 and 9.97μm).
The remaining material after preparing the rock slab was
powdered and taken for analysis using XRD techniques. Pulverization was carried out in an agate grinding mill followed by
micronization in a McCrone mill. The powdered material
weighted around 2.0 grams. XRD analyses were performed in a
Bruker D8® Advanced diffractometer using the following test
conditions: Cu tube, 40 kV nominal voltage and 40 mA current,
Soller slit 2.5°, primary slit 0.6 mm, secondary slit 5mm,
LINXEYE® linear detector with opening of 189 channels, Ni of
0.02mm, step size of 0.02 and speed of 1.1° / min. Qualitativemineralogical analyses were done with Jade 9 software (withPDF-2 database). Quantitative analyses were carried out using
the Rietveld Method within the TOPAS software.
X-ray computed microtomography
We used a Bruker X-ray computed microtomography Skyscan® model 1173 with a sealed X-ray source, tungsten target
and a flat panel detector. The X-ray tube with tungsten filaments (Hamammatsu, model L9181) operates effectively between 40 and 130 kV voltages with a maximum current of 200
μA, reaching a maximum power of 8 W and a maximum focal
size of 5 μm (Machado et al., 2016). The detection system(Hamammatsu model C7942SK-05) consisted of a flat-panel
sensor, operated with a maximum pixel array of 2240 x 2240,
and with its recording carried out by an array of photodiodes
forming electrical and digital signals.
Because of the large size of the plug, the size of the obtained
pixel was approximately 9.97 μm. This value is the maximum
supported by the equipment given the dimensions of the entire
plug to perform the acquisition and reconstruction at feasible
times (approximately 360 min for acquisition and 420 min forreconstruction of the 9.97 μm pixel size μCT images involving
a stack of images with 3,749 slices). For our study we obtained
several μCT images with pixel sizes of 9.97 μm, 18.17 μm, and24.95 μm. The rock slab X-ray microtomography provided

Fig. 2. (a) Image of the Morro do Chaves Formation in the Mina São Sebastião quarry of the city of São Miguel dos Campos; (b) identification of a layer (called Bed 2B) highlighted by the red arrow, from which the sample (named 1-34A) was taken; (c) image of the plug showing some vugular porosity in the sample; (d) thin section obtained from the cut of one end of the sample during flattening; and (e) rock slab
prepared from the thin section, with the red square showing the region that was analyzed using SEM-EDS, XRD, and μCT with higher
resolution.

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Computational and experimental pore-scale studies of a carbonate rock sample

images with 6.77 μm pixel size, close to the maximum limit
supported by the equipment, and 9.97 μm pixel size images.
The selection of 9.97 μm was deliberate since this value represents the smallest pixel size when using the whole plug. The
acquisition parameters for the plug and the rock slab, with thedifferent pixel sizes, are listed in Table 1.
After the data acquisition step, it was necessary to use a specific software from the equipment manufacturer, capable ofconverting information from the detector (based on an analysisof the attenuation suffered by a beam of incident radiationpassing through, in this case, a carbonate rock) into data that isinterpreted as digital images that can be loaded and interpretedby other software. We used for this purpose the Bruker
NRecon® (v.1.6.9.4) and InstaRecon® (v 1.3.9.2) softwares,
which allowed us to correct and treat the main image artefacts
generated during acquisition, such as beam hardening and thepresence of ring artefacts (Table 1). We further used a workstation with 2 Intel® Xeon® E5-2640 v3 processors, 256 Gb
RAM, and a NVIDIA® Quadro® M4000 (8 GB RAM) GPU forμCT image acquisition and reconstruction.
Digital reconstruction, image post-processing andsegmentation
A first step after μCT image acquisition is the application of
specific filters to reduce noise from the images and to sharpen
them. We used the Avizo® 9.5 software to pass the non-local
means filter (Fig. 3b) and to reconstruct the 3D model of therock, as well as to segment the image, by means of the Interactive Thresholding function (Fig. 3c) after definition of thethreshold value.
We next used an algorithm to detect the grey-level value that
corresponds to the threshold value based on the selected Kittler
and Illingworth (1986) segmentation method. The selectedvalue was supported by analyses of SEM images and the greylevel histogram obtained from the μCT images. Verification of
the pore systems impregnated with blue epoxy resin on the thinsection was performed using a Zeiss Imager M2m® optical
microscope with an increase of 2.5 times. Scanning was doneby capturing images in mosaics, which were automaticallyjoined by the microscope itself, resulting in a panoramic imageof the entire thin section. Finally, we followed the methodologyof Kaczmarczyk et al. (2011) for analysis of the grey value
histograms using the Fytik® 0.9.8 software (Wojdyr, 2010) togenerate Gaussian curves that represented the population of thepore system and the rock matrix itself. This to verify and evaluate the results by Kittler and Illingworth (1986) based on visual
methods. The procedure was repeated for each image stackgenerated with different pixel sizes. The overlapping pixels
were considered as part of the pore system. Imaging, 3D reconstruction, modeling and numerical simulations were carried out
using a workstation with 2 Intel® Xeon® E5-2640 v4 processors, 512 Gb RAM, and a NVIDIA® Quadro® P6000 (24 GBRAM) GPU.
Pore network modelingAfter reconstruction of the 3D pore system, based on selection of the appropriate threshold value, the connected networks
were analyzed to simulate fluid flow using an in-house code
based in part on previous work by Raoof et al. (2013). We
selected networks based on the size of the clusters (voxel
count), since the numerical simulations were carried out assuming connectivity between the top and bottom of the sample (thez-axis), being the direction of the experiments with this plug.
We kept the same procedure for the rock slab models (reconstructed from different pixel size μCT images). The Avizo® 9.5
software was used to separate the larger networks and to generate topology information for subsequent reconstruction of the
PNM. The pore domains were generated based on topology
information provided by the software.
Pore bodies of the pore network were identified as the largest elements present in the network, with spherical geometry,
while pore throats were identified and calculated based on

Table 1. μCT acquisition and reconstruction parameters.
Image pixel size(μm)
6.77 (rock slab)
9.97 (rock slab)
9.97 (plug)
18.17 (plug)24.95 (plug)

Source voltage
(kV)
70
70
130
130
130

Current
(μA)
114
114
61
61
61

Smoothingfactor5
6
5
3
7

Ring artefact correction
factor561
55Filter: Al / Cu
(mm/mm)0.5 / 0.5
0.5 / 0.5
0.5 / 0.5
0.5 / 0.5
0.5 / 0.5

Fig. 3. Main steps related to treatment of (a) an original μCT image using (b) a non-local filter, and (c) interactive thresholding for segmentation purposes from Avizo® 9.5.

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William Godoy, Elizabeth M. Pontedeiro, Fernanda Hoerlle, Amir Raoof, Martinus Th. van Genuchten, José Santiago, Paulo Couto

being smaller spherical elements, depending upon their size andtopology, as discussed by Fouard et al. (2006). The length ofthe pore throats was defined by the distance between two connected pore bodies, while their radii were calculated as a function of the mean radii of the spherical elements along the path
between the two pore bodies. We calculated the radii of thepore throats using three different averaging methods: harmonic,
geometric, and arithmetic. Absolute permeabilities were calculated using the generated pore structure, while saturated fluid
flow within the network domain was simulated using a PNM
algorithm.
Since extensive reviews of PNM techniques can be found in
the literature (de Vries et al., 2017; Raoof and Hassanizadeh,
2010, 2012; Raoof et al., 2010, 2013), we present here only themain equations. The approach assumes laminar flow within the
porous media, using Poiseuille’s formula to obtain the volumetric flow rate within each pore:

qij =

(1)

where qij is the discharge through the pore throat between porebodies i and j; pi and pj are pressures of the two adjacent porebodies; rij is the pore throat radius; lij is the throat length, and µ
is the fluid dynamic viscosity.
Considering incompressible flow, the volume balance foreach pore body i requires:
Ni

π

j

Ni

pi − p j

j

lij

=0

(2)

where Ni is the pore coordination number of pore i. Applying
this equation to each pore body results in a linear system of
equations with a sparse, symmetric and positive-definite coefficient matrix, which is to be solved for the pore body pressures.
Next, considering the sample as a representative elementaryvolume (REV), the average pore water velocity, v , can becalculated as (Raoof et al., 2013):v=

Qtot LVfk=μ Qtot L
AΔ P=

μ vV f(4)

AΔP

where μ is the fluid dynamic viscosity, ΔP is the pressure difference between the inlet and outlet pores, and A is the crosssectional area of the pore network.
For our study we imposed a pressure differential of 5.0 ×
10–3 Pa between the upper and lower boundaries of the PNM
along the z-axis. This small differential was adopted to guarantee laminar flow (low Reynolds number), an important assumption to solve Eqs. (1) to (4).
RESULTS AND DISCUSSION

π 4 pi − p j
rij
8μ
lij

qij = 8μ rij4

can be calculated at the inlet or outlet of the pore network as thesum of all fluxes. Finally, the intrinsic permeability, k , of thesample can be determined using Darcy’s law using the resultsfrom (3):(3)

where Qtot is the total discharge rate through the pore network,
L is the length of the pore network, and Vf is the total volume of
the fluid phase within the pore network. The total discharge rate

Before presenting results of the various pore network calculations for the entire coquina plug, we first summarize datafrom the experimental tests, as well as results from the rockslab pore network numerical simulations.
Experimental data

The first results for the plug were obtained using the DV4000® equipment, after the cutting, flattening and cleaning
procedures. The measured values were used for comparison
with estimates obtained digitally and numerically for the porosity and absolute permeability, respectively. Table 2 presents
the main experimental results for plug 1-34A. The data are
indicative of groundwater reservoirs, which generally have arelatively high porosity (15–20%) and an intermediate permeability (150–650 mD), with relatively good connectivity between
the various pores.
After this step we analyzed images of the thin section for the
purpose of characterizing and identifying the coquina poresystem. Fig. 4 shows images obtained with optical microscopy.
The images show that the rock is formed by fragments of robustshells (Fig 4b), with the bioclast fragments varying in size from
1 to 8 mm. The bioclasts are oriented moderately, with little
fragmentation and only slight abrasion. A very few (about 2%)
siliciclastic grains were observed, sub-rounded, spherical andwith an average size of 0.5 mm.

Fig. 4. Scanned images obtained with optical microscopy showing (a) blue epoxy resin filling the pores of the thin section, (b) highlighted
in red the contours of bivalve shells, and (c) highlighted in yellow the size of the bivalve shells.

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Computational and experimental pore-scale studies of a carbonate rock sample

Several dissolution phases generated the current porosity ofthe selected sample. The types of porosity present are intraparticle, interparticle, vugular and intercrystalline, with a predominance of interparticle and vugular porosities, and lower
intraparticle porosities. The measured porosity and absolutepermeability indicate good connectivity between the meso- andmacro-pores. This information is important not only to aid in
the segmentation step, but also to predict the absolute permeability through numerical simulations. The results suggest thatfluid will flow preferably through pore spaces that can be reconstructed digitally, disregarding sub-resolution porosity that
is identified using high-resolution images from very small
sample volumes. Rabbani et al. (2017) recently estimated theabsolute permeability from an analysis of thin sections, but
their approach could not predict the behavior of carbonate rocksamples having absolute permeabilities above 200 mD. For thisreason we did not predict the permeability of our coquina basedon an analysis of thin sections since the permeability was morethan 600 mD.
SEM was used next to analyze the surface of the selected cutof the rock slab (red region in Fig. 2e) in order to evaluate thecharacteristics and dimensions of different pore structures. We
selected a central area of the cut, which constituted the innerpart of a bivalve shell. The images in Fig. 5 show a gradualzoom of this region, with increases of 50, 150, 300, 800, 1200
and 2000 times the original size. Fig. 5a shows the presence ofseveral large pores in the order of a few millimeters, externallyto the center of the bivalve, while the largest zoom shows pores
larger than 30 μm (Fig. 5f). These observations suggest that
optical microscope analyses of the thin section were consistentsince they showed the same patterns: predominance of interparticle and vugular porosities in different regions. These results
are important to understand the main aspects related to the poresize distribution and the connectivity of these pore systems.
Several regions were particularly challenging for analyzing
the pore system and the rock composition. We selected a southern region from the cut rock slab to perform an EDS analysis.
The analysis helped us to evaluate dubious regions, which
could be interpreted visually as pores or as material with alower attenuation coefficient in the μCT images, as well as
providing a qualitative indication of the elements presented in
the sample. Fig. 6a shows three well-identified regions (repre-

sented by the letters A, B and C above the arrows, in theimage). The yellow arrow (A) indicates a pore that is a few mm
wide, while the red arrow (B) points to a well-defined pore (inthe center) surrounded by a region that is more poorly defined.
That region has a grey-level quite similar to that of the area inblue (C), which clearly does not correspond to a pore. The EDS
allowed us to identify the latter region (C) as being composedof siliciclastic material (Fig. 6d), which was already identified
in the thin section.
Fig. 6b provides a qualitative analysis using different colors
indicating the main components of the sample: a blue area inthe center and a predominantly pink region throughout theremaining area. A more refined analysis revealed the presenceof calcium (Fig. 6c), silicon (Fig. 6d), oxygen (Fig. 6e) andcarbon (Fig. 6f). Results suggest that the studied rock is composed mainly of calcium, oxygen and carbon (most likely CaCO3), indicating that the coquina was probably formed by calcite as previously shown by Tavares et al. (2015) from evaluations of coquinas from the same Morro do Chaves formation.
In order to confirm the results above, an XRD-based qualitative and quantitative mineralogical analysis of the rock slab was
performed using the Jade 9 software (with the PDF-2 database),
and also with the Rietveld Method of the TOPAS software,
respectively. The composition was defined as 99.8% calcite(CaCO3), thus corroborating the EDS results. Another important result of the XRD analysis was that the grey-level regions associated with the siliciclastic materials were not significant in size, and not representative, thus reducing uncertainties
in the automated segmentation procedure. These evaluations areimportant to verify possible grey level regions where the poresystem may be interpreted erroneously during segmentation.
Coquina rock slab modeling

Based on insight from the experimental data, we proceededwith modeling the selected rock slab region. The μCT imagesof the thin section showed the presence of clear vugular porosity, as well as some intraparticle porosity. Fig. 7a shows theselected region (red square) that was used for the SEM, EDS
and μCT images using two different pixel sizes, whose 3D
reconstruction can be observed in Fig. 7b. The 3D reconstructions of the pore systems from the 6.77 μm (Fig. 7c) and

Fig. 5. SEM images obtained with an increase of (a) 50; (b) 150; (c) 300; (d) 800; (e) 1200, and (f) 2000 times the selected region of therock slab. Fig. 5a shows the presence of two large pores of a few millimeter each (A and B).

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William Godoy, Elizabeth M. Pontedeiro, Fernanda Hoerlle, Amir Raoof, Martinus Th. van Genuchten, José Santiago, Paulo Couto

Fig. 6. (a) EDS image of the analyzed area, identifying three well-defined regions (A, a well-defined pore, B, a pore-centered region withdark grey level around it, and C, a dark grey level region similar to B but with no obvious pore boundary), (b) visual evaluation (colors) of
the different components of the sample; (c) abundant presence of calcium, (d) presence of silicon in a small region (white dots), (e) oxygen,and (f) carbon distributed around the sample.

9.97 μm (Fig. 7d) pixel size μCT images showed that the vug
was part of the largest pore system within the rock slab, andclose to a region whose contours delimited a bivalve shell. Thisregion showed very little porosity, regardless of the pixel sizeused for μCT imaging. Digital porosities obtained with the twodifferent pixel sizes are shown in Table 3.
Next, we performed PNM simulations for laminar fluid flowin two digitally reconstructed rock slabs, to obtain the absolutepermeability. As shown in Table 3, estimated values were muchhigher than the measured value of 639 mD data for the entire
plug (Table 2). The higher calculated values were to be expected because of the very small rock slab volume used in theμCT analysis. The volume presumably was much smaller thanthe minimum representative elementary volume (REV) needed
for scale-independent permeability measurements (or calculations in this case). By comparison, the rock slab was large
enough for the porosity calculations and measurements. We
hence emphasize here that the PNM-based permeability estimates we obtained for the modeled rock slabs do not have an
immediate direct relationship with the permeability measured
using the entire coquina plug. To properly compare the measured absolute permeability of the plug, the PNM model should
be applied to the entire plug.
We selected the largest pore systems from each reconstructed model, which are visualized in Fig. 7e (from the 6.77 μm

pixel size μCT images) and Fig. 7f (from the 9.97 μm pixel sizeμCT images). The number of voxel-based clusters in Fig. 6e
was higher than that found when we analyzed Fig. 7f, indicating that small clusters (represented by different colors) are only
generated from higher-resolution images. Figs. 7g and 7h show
the PNMs of the regions discussed previously. A first direct
observation refers to the amount of pore bodies and pore throats
generated for the construction of the PNMs. For construction of
the model imaged with 9.97 μm pixel size, we generated amuch smaller number of points (Figs. 8a and 8b), although the
topology of the system was maintained.
Some important conclusions can be drawn from the PNM
simulations based on different pixel size μCT images. Most
important, the results for porosity and absolute permeability
were larger for the reconstructed model using higher resolution
μCT images (6.77 μm), thus suggesting that some pore bodies
and pore throats were not included in the lower resolution μCT
images (9.97 μm), which must have influenced the numericalestimates. Differences between the absolute permeability values
varied between 11.8% and 22.2%, considering the different
averages for pore-throat construction in each model. The porethroat radii based on harmonic means of the spherical elementsthat composed them were physically coherent, since they accounted for regions of constriction prior to modeling the porethroats using the PNM.

Table 2. Experimental results from plug 1-34A.
Sample
1-34A

Pore Volume
(cc)
5.74

Porosity He (%)

Permeability N2 (mD)

16.30

639.08Grain Density(g/cc)
2.69

Diameter (cm)Length (cm)Mass (g)

3.60

3.53

79.3

Table 3. Porosity (ϕ) and absolute permeability (kabs) estimated from the reconstructed coquina rock slab obtained with two different pixel
sizes.
PNM – μCT Pixel size images (μm)
6.77
9.97
Difference (%)

ϕ (%)
8.43
7.72
8.4

Harmonic
2,568
2,137
16.8

kabs (mD)
Geometric
2,755
2,422
12.1

Arithmetic
2,984
2,746
8.0

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Computational and experimental pore-scale studies of a carbonate rock sample

Fig. 7. (a) Image of the selected area for μCT, indicating with a red arrow the presence of vugular porosity; (b) 3D volume reconstructionof the region using 6.77 μm pixel size μCT images, with the red arrow highlighting the same vug as in Fig.6a; (c) 3D segmentation andreconstruction of the pore region of the sample, with the right upper extremity being the assimilated vug and a central region with lower
porosity showing well-defined bivalve contours from the 6.77 μm pixel size μCT images; (d) same from the 9.97 μm images (e) selectionof the largest pores from the 6.77 μm μCT images; (f) same from the 9.97 μm images; (g) PNM generated with the largest pores from the
6.77 μm pixel size μCT images; and (h) same from the 9.97 μm images.

Fig. 8. Pore size frequency distributions (equivalent diameters) of the digital pore system of the rock slab obtained using (a) 6.77 μm and(b) from 9.97 μm μCT images. Notice a much larger number of spherical elements in the reconstructed model using the higher resolution.

An analysis of the region with the greatest pressure differential, which was responsible for most of the fluid flow, is shownin Fig. 9. The plots visualize the length of the pore throats andthe radii of the pore bodies for the slab reconstructed PNM
using 6.77 μm (Fig. 9a) and 9.97 μm (Fig. 9b) pixel size μCT
images as obtained with the Paraview® software (Ayachit,2015). A larger number of pore bodies and pore throats areapparent when using higher resolution μCT images, whichleads to higher absolute permeability values. The images in Fig.
8 were generated from the models whose pore throats were
calculated using harmonic means of their constituent sphericalelements. The smaller pore throat diameters for both models
can be seen in Fig. 9c and Fig. 9d, as well as the pressure (ranging from 0 to 5.0x10–3 Pa) in each pore body of this region. The
simulation results indicate that fluid in this rock slab flows
preferably through the mesopores and macropores.

Coquina plug modelingAfter analysis of the rock slab, we similarly performed ananalysis of the coquina plug in its entirety. Our objective was toestimate its petrophysical properties as well as to study PNM
performance for a heterogeneous and complex pore system
involving a large number of mesopores and macropores. We
selected for this purpose the μCT images generated using threedifferent pixel sizes of 9.97, 18.17, and 24.95 μm, thus testing
the effects of resolution on the calculated parameters. Table 4
presents results of the 3D modeling scenarios and the experimental data of the selected petrophysical properties. Regarding
porosity, the pore network reconstructed with higher resolution
μCT images clearly presented better results when comparing
the digital estimates to the measured data in Table 1. The sameis true for the absolute permeability estimates using PNM.

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William Godoy, Elizabeth M. Pontedeiro, Fernanda Hoerlle, Amir Raoof, Martinus Th. van Genuchten, José Santiago, Paulo Couto

Fig. 9. PNMs of the reconstructed slab (a) from the 6.77 μm pixel size μCT images, and (b) from the 9.97 μm images, showing the distributions of pore radii and pore lengths. PNMs of the regions with greater pressure differentials between pore bodies following numerical simulation of fluid flow, as well as of the diameters of the pore throats in these regions, using (c) 6.77 μm pixel size μCT images and (d) 9.97
μm images. The length and pressure units are m and Pa, respectively.
Table 4. Porosity (ϕ) and absolute permeability (kabs) of the reconstructed coquina plug using PNM.
PNM – μCT
Pixel size
images (μm)
9.97
18.17
24.95
Experimental

ϕ (%)
12.4
11.3
10.0
16.3

kabs (mD)Harmonic

Geometric

Arithmetic

548.3
480.5
464.9

953.9

1,236.9
1,419.0
1,283.9

911.5
848.4
639.1

Another important point refers to the average used to calculate
the pore throats, based on the spherical elements that do not
represent pore bodies on the models. Harmonic averaging gave
the best results compared to the measured data, presenting apercentual difference of 14.2%, 24.8%, and 27.3% for the PNM
based results using μCT images with 9.97μm, 18.17μm, and24.95 μm pixel size, respectively. We note here that the comparison between the PNM and the measured data for the entire
plug does not require some REV verification since the experimental results were measured also on the entire plug.
Fig. 10 shows frequency distributions of the generated porethroats and pore bodies. The results indicate that the total number of pore bodies and pore throats for the model using higher
resolution μCT images is more than 60 times larger than obtained with the lower resolution μCT images. This impressive
increase relates to the capacity to recreate pore bodies and porethroats that are not detectable from lower resolution μCT images, as can be seen in Fig. 10d, 10e, and 10f, which presents therange of pore throat radii (in m) for the models based on μCT
images with 9.97 μm, 18.17 μm, and 24.95 μm, respectively.

We next present PNM results for plug I-34A obtained with
the intermediate resolution (18.17 μm pixel size μCT images)
and assuming the harmonic averages of the pore throats as shownin Fig. 11. The input and output boundaries were implemented
based on the selection of 2% of the plug length, which leads to awell-defined layer for fluid entrance. As expected, some overlap
occurred of the distributions of the pore bodies and pore throats,
but with the largest pore throats being linked to the largest porebodies, thus indicating good results regarding the PNM generation methodology. A selected few pore throats were several mm
wide, which created regions for considerable fluid flow between
the two linked pore bodies. However, the majority of pore throatsremained within the μm range. The larger pore throats were
important to preserve connections between vugs, thus creating
preferential paths for fluid flow.
We also compared PNM results (all using harmonic averages of the pore throat radii) obtained with the different resolutions. Fig. 12 shows the final generated pore network and thecalculated pressure fields. Results indicated that part of thewell-connected network could not be generated using lower
resolution μCT images. Still, in terms of fluid flow, the PNM
captured important connections between mesopores andmacropores since the calculated absolute permeabilities values(as shown in Table 4) were close to the measured value. The
three PNM simulations showed specific regions with higher
pressure drops, which were preferably accessed by fluid during
the flow experiment. Fig. 12 further shows that the number ofpore bodies and pore throats increases immensely as the μCT
images resolution increased.
Another important result relates to the possibility to conduct
numerical experiments using relatively large sample volumes.

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Computational and experimental pore-scale studies of a carbonate rock sample

Fig. 10. Pore size frequency distributions (equivalent diameters) of the digital pore system of the plug obtained using (a) 9.97 μm, (b) 18.17
μm, and (c) 24.95 μm μCT images; and the range of pore throat radii (scale in m) found with the models generated using (d) 9.97 μm, (e)18.17 μm, and (f) 24.95 μm μCT images.

Fig. 11. PNM results for plug 1-34A based on 18.17 μm μCT images presenting: (a) input (white region) and output (red region) boundaries
for the fluid flow numerical simulations, and ranges of (b) pore body radii, (c) pore throat radii, and (d) pore throat lengths (scales are in m).

We showed that this is feasible despite the computational
demand. The use of relatively large plugs avoids non-representative results, especially for the absolute permeability inview of the required REV. This characteristic is crucial when
upscaling results from plugs to cores and beyond.

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William Godoy, Elizabeth M. Pontedeiro, Fernanda Hoerlle, Amir Raoof, Martinus Th. van Genuchten, José Santiago, Paulo Couto

Fig. 12. (a) Image of plug 1-34A, and PNM results of the pressure field based on (b) 24.95 μm, (c) 18.17 μm, and (d) 9.97 μm pixel sizeμCT images (pressure scales are in Pa).

CONCLUSIONSThis study investigated experimentally and numerically several aspects of a coquina carbonate rock sample, a very close
analogue to important pre-salt hydrocarbon reservoir rocks ofSantos Basin (Brazil). A series of analyses were carried out ona thin section using optical microscopy, on a rock slab takenfrom a plug using SEM, EDS, XRD and μCT, and on a larger
plug using both μCT images and direct measurements. These
analyses together with 3D imaging was used to examine therock matrix composition and to verify and digitally reconstruct
the pore systems, which provided much insight about the matrix
and macropore fluid flow processes in the naturally very heterogeneous rock sample. Using PNM numerical simulations, we
could estimate the absolute permeability of the rock slab andthe entire plug, which presented a properly REV relative to themeasured value. The experimental results were important tostablish significant correlations for the entire plug, mostly toobtain reliable information about the pore structure required in
the modeling step. In our study we could detect bivalve andostracode shells within the coquina sample and identify mesopores and macropores providing the main pathways for fluid
flow inside the almost pure calcite rock sample. Digital reconstruction of the pore system, along with detailed experimental
analyses, allowed us to construct and use the PNM models withconfidence. The models were also used to verify the main aspects related to fluid flow modeling: (i) rock slab models provided less accurate permeability values compared to the entire
plug due to their volumes below the REV; (ii) pore throat radii
calculated with harmonic averages gave the best results for theabsolute permeability; and (iii) higher μCT resolution images
provided the best result for the permeability according to theexperimental data for the entire plug. In order to generate more
realistic pore systems for the coquinas, we intend to use additional experimental techniques like nuclear magnetic resonanceto verify prevailing pore distributions, and to further improve
the segmentation procedures for additional PNM studies, especially for multiphase flow conditions.

Acknowledgements. This research was carried out in association
with ongoing R&D projects registered as ANP 19027-2,“Desenvolvimento de infraestrutura para pesquisa edesenvolvimento em recuperação avançada de óleo – EOR no
Brasil” (UFRJ/Shell Brasil/ANP) for setting-up an advanced
EOR Lab facility for R&D in Brazil, and ANP 20163-2,“Análise experimental da recuperação de petróleo para as rochas
carbonáticas do pré-sal brasileiro através da injeção alternada deCO2 e água”, both sponsored by Shell Brasil under the ANP
R&D levy as “Compromisso de Investimentos com Pesquisa e
Desenvolvimento”. This study was financed in part by the
Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorBrasil (CAPES) - Finance Code 001. We acknowledge Professor
Ricardo Tadeu, Olga Oliveira and Alessandra Machado from
LIN/UFRJ for using their µCT equipment and their technicalsupport with image acquisitions. We also acknowledge Professor Leonardo Borghi and the LAGESED/UFRJ team for geological discussions, Adão Gonçalves from LIAP/UFRJ for the
SEM-EDS analysis, Petrobras Research Center (CENPES) for
the XRD analyses, and the LRAP/UFRJ team for sample preparation and petrophysical measurements.
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Received 13 March 2019
Accepted 16 April 2019383
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