128 (2024) 205363

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Gas Science and Engineering

journal homepage: www.journals.elsevier.com/gas-science-and-engineering

Upscaling relative permeability and capillary pressure from digital core

analysis in Otway formation: Considering the order and size effects of facies
Masoud Aslannezhad a, b, ** , Mohammad Sayyafzadeh c, d , David Tang e , Zhenjiang You a, b ,
Stefan Iglauer a, b , Alireza Keshavarz a, b, *
a
School of Engineering, Edith Cowan University, 6027, Joondalup, WA, Australia
b
Centre for Sustainable Energy and Resources, School of Engineering, Edith Cowan University, 6027, Joondalup, WA, Australia
c
School of Chemical Engineering, The University of Adelaide, Australia
d
CSIRO Energy, Australia
e
CO2CRC Ltd, Australia

A R T I C L E I N F O A B S T R A C T

Keywords: Digital Core Analysis (DCA) has emerged as a crucial instrument in reservoir characterization in recent times.
Digital core analysis With the advent of high-resolution micro-CT imaging, it is now possible to visualize the three-dimensional mi­
Upscaling crostructures of in-situ pores and flow patterns within rocks. DCA offers several notable benefits over traditional
Relative permeability
techniques, such as a higher density of measurements, faster processing times, and the preservation of rock
Capillary pressure
samples. It also demonstrates considerable flexibility with challenging core conditions and can derive numerous
parameters from each individual sample. The objective of this work is to utilise DCA data from Otway formation
to enhance reservoir characterisation and CO2 plume forecast. However, a critical challenge is that these data are
obtained at a micro-scale, necessitating an upscaling of DCA properties from the micro-scale to core scale, and
subsequently to the site and field scale, for compatibility with reservoir simulation and field studies. This study
proposes an implicit and iterative method to upscale DCA properties and explore the impact of facies order and
size on the upscaling process of relative permeability and capillary pressure. This method is implemented in an
open-source simulator known as the Matlab Reservoir Simulation Toolbox (MRST). The findings indicate that
relative permeability and capillary pressure outcomes from upscaling are influenced by order and portion of
facies. This highlights the importance of considering both the size and arrangement of facies during the upscaling
process, given their potential impact on fluid dynamics and the accuracy of reservoir simulation results.

1. Introduction depositional facies might exist, while at larger scales, sedimentary

structures such as planar bedding, cross bedding, and massive bedding
Sedimentary reservoirs are key storage sites for hydrocarbons can be found (Gao, 2011; Boon et al., 2022; Mishra et al., 2022). These
(Gabrielsen, 2015) and groundwater (MacDonald et al., 2012), and variations have diverse impacts on dynamic simulations (Dewever et al.,
serve as potential locations for geological carbon sequestration (Pires 2021; Proietti et al., 2023). For instance, certain depositional facies may
et al., 2011). Their significant role in these applications has propelled function as regional barriers to fluid flow (Leila et al., 2024), while
advancements in technologies for their analysis and static modelling. heterogeneity in sedimentary structures may lead to unexpected path­
The goal of these innovations is to enhance the outcomes of dynamic ways for fluid movement, thereby influencing effective permeability and
simulations, thus ensuring more accurate predictions and management local tortuosity (Gershenzon et al., 2017; Green and Ennis-King, 2010;
of these vital resources (Onoja et al., 2019; Hamza et al., 2021). Sedi­ Trevisan et al., 2017). This heterogeneity is particularly significant at
mentary reservoirs are marked by a natural variation in their rock the micro scales, especially in the context of geological carbon storage.
composition, or lithology. This heterogeneity can manifest itself at Some sedimentary structures contain thin layers, or laminae, which
different scales and in various ways. On a regional scale, differences in have lower porosity and permeability associated with higher capillary

* Corresponding author. School of Engineering, Edith Cowan University, 6027, Joondalup, WA, Australia.
** Corresponding author. School of Engineering, Edith Cowan University, 6027, Joondalup, WA, Australia.
E-mail addresses: m.aslannezhad@ec.edu.au (M. Aslannezhad), a.keshavarz@ecu.edu.au (A. Keshavarz).

https://doi.org/10.1016/j.jgsce.2024.205363
Received 22 January 2024; Received in revised form 29 March 2024; Accepted 29 May 2024
Available online 1 June 2024
2949-9089/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 1. The process of upscaling from pore-scale to field scale.

rock, particularly at the micro scale, fall below the resolution of these
logs. The resolution of traditional wireline logs typically ranges from
several centimetres to tens of centimetres (Mishra et al., 2020; De Jong
et al., 2020; Tian et al., 2019). For example, at the CO2CRC’s Otway
Research site, the vertical resolution of logs is 5 cm. While this resolution
is sufficient for identifying larger-scale geological features and varia­
tions in rock properties, it cannot capture the micro-scale heterogene­
ities present in sedimentary formations. As a result, these subtle
differences, crucial for understanding flow and fluid-rock reactions, are
lost when averaging properties at the log’s resolution (Doveton and
Prensky, 1992; Ruhovets et al., 1992). While certain algorithms have
been developed to extract more detailed information from the logs
(Sheng et al., 1987), they come with significant uncertainty and cannot
match the accuracy of observing sedimentary structures directly in core
samples. Second, current reservoir modelling software is not tailored to
accommodate the intricate details of such fine-scale grid resolutions.
The algorithms used for populating properties usually fail when
attempting to operate at these high resolutions (Mishra et al., 2020; Shin
et al., 2019).
Together, these limitations lead to a failure to include the critical
micro-scale heterogeneity in reservoir models. This omission can result
in inaccurate estimations of fluid flow and carbon dioxide (CO2) trap­
ping, especially in reservoirs where these small-scale variations are
particularly pronounced (Eigbe et al., 2023; Zhang et al., 2021; Ozotta
et al., 2022). Therefore, the integration of micro-scale properties
determined by digital core analysis (DCA) with reservoir modelling can
revolutionize the oil and gas industry, enabling more precise reservoir
characterization. However, a significant challenge lies in numerical
simulation that can be computationally expensive if it relies on
Fig. 2. a) Facies association and b) percentages of each facies type in the fine-scale parameters to simulate flow and transport problems directly.
simulation model. The same color code has been applied to facies association Consequently, the use of coarse-scale models is required to lessen
types in following figures. computational burden. This is where upscaling process comes into play,
which is described as the process of calculating high-level characteristics
entry pressures. As a result, these laminae act as barriers to flow, known derived from more detailed, smaller-scale attributes (Santos et al., 2022;
as baffles, boosting carbon storage through local capillary forces (Yu Eltom et al., 2023; Coimbra et al., 2022; Norouzi et al., 2022).
et al., 2017; Frykman et al., 2009; Shao et al., 2022). The term “upscaling” simply denotes the process of transitioning
Recognizing the significant impact of micro-scale heterogeneity on from a smaller scale to a larger one, Fig. 1. For instance, the process may
reservoir models is imperative. However, this fine-scale heterogeneity is commence at the minute pore scale (ranging from micrometers to mil­
frequently disregarded in regional geological models, and two primary limeters) and subsequently progress to the broader continuum scale.
technical reasons contribute to this oversight. First, traditional reservoir Similarly, upscaling may originate from laboratory experiments (typi­
modelling methods rely on wireline logs to populate grid cells (voxels) cally conducted in centimeters) to explore the larger field and regional
with rock properties. However, the detailed variations in sedimentary scales (measured in kilometers) (Hao et al., 2019; Chandra and Vishal,

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Table 1
Facies associations and sub-facies in Parasequence 1 in the lower Paaratte Formation at the CO2CRC Otway
site. ‘Res.’ and ‘Non-res.’ denote reservoir and non-reservoir facies, respectively.

2021). permeability, followed by two-phase upscaling of Kr. The upscaling

Broadly, upscaling techniques can be categorized into two types techniques utilized in this study, have been outlined in several publi­
based on the fluid phases present in the reservoir: single-phase and cations (Christie, 2001; Pickup et al., 2000; Sharmin et al., 2020).
multi-phase methods (Sanchez-Vila et al., 2006; Feng et al., 2022; Iraji Throughout this paper, an upscaled value, which could either be a scalar
et al., 2023; Zhou et al., 2020). Single-phase upscaling involves the or tensor, will be designated with a superscript asterisk ’*’. For instance,
calculation of large-scale characteristics like porosity, absolute perme­ K* signifies the upscaled version of the permeability field, K.
ability, and connate water, while multi-phase upscaling focuses on the
derivation of effective properties for multiple phases, including relative 2.1. Single-phase upscaling
permeability (Kr) and capillary pressure (PC). Comprehensive overviews
of upscaling methodologies have been documented in various studies The subject of scaling up based on single-phase flow has been thor­
(Farmer, 2002; Renard and De Marsily, 1997; Frippiat and Holeyman, oughly examined in various studies. In-depth reviews on this topic are
2008). available in Refs. (Farmer, 2002; Frippiat and Holeyman, 2008; Wen and
This paper addresses the challenge of integrating micro-scale het­ Gómez-Hernández, 1996). The upscaling of permeability relies on the
erogeneity into reservoir models by introducing a randomized upscaling selection of boundary conditions implemented. Examples of boundary
process. This process leverages a capillary-limit approach for upscaling conditions are: (a) linear boundary condition (Dirichlet condition); (b)
Kr and PC, provided by DCA. Unlike conventional methods, this inno­ constant boundary condition (Neumann condition); and (c) periodic
vative methodology considers the impact of facies order and size on boundary condition. Dirichlet boundary conditions set specific fluid
upscaled properties. By recognizing and incorporating these often- pressures or saturations at the edges of the domain, mirroring reservoir
overlooked details, the presented approach offers a more nuanced and conditions or interactions at these boundaries (Kumar et al., 2020;
accurate representation of the reservoir, which is essential for precise Mazlumi et al., 2021; Mazumder and Mazumder, 2016). Neumann
simulation and effective reservoir management. The numerical upscal­ boundary conditions define the flux of fluids across these edges, essen­
ing is performed utilizing the MATLAB Reservoir Simulation Toolbox tial for accurately depicting how fluids flow between different reservoir
(MRST), an open-source toolbox designed for efficient computational sections in responce to gradients (Mazumder and Mazumder, 2016;
analysis in reservoir engineering (Lie, 2019). Sakurai et al., 2019). Periodic boundary conditions are used to model
repetitive geological features or conditions, allowing properties to
2. Upscaling techniques and methodologies transfer from one boundary to its opposite side. This approach facilitates
the analysis of reservoir behavior on a larger scale while retaining focus
This study utilized the capillary limit method to upscale the Kr and on fine-scale details (Nguyen et al., 2012; Alpak, 2021; Matthai and
PC as determined by digital core analysis. The upscaling process Tran, 2023). With the assumption that constant boundary conditions are
employed involves a sequence of single-phase upscaling of the absolute used, the fine grid domain, used for upscaling to a singular coarse grid

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 3. The integrated display of logging outputs from CO2CRC Otway site. In the tracks from left to right are: 1) well-bore perforations; 2) facies associations; 3) clay
volume (VCL), water saturation; 4) formation density (RHOZ), porosity (PHIT), and 5) permeability (KINT). Also overlaid in tracks are core plug porosity and
permeability (circles).

Fig. 4. Distribution of a) porosity and b) permeability values obtained from individual core samples taken from wells CRC-2 and CRC-3 across different facies
(courtesy of CO2CRC).

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Table 2
Petrophysical properties for the samples obtained from micro-CT imaging.
Sub-facies Sub-facies code φtot (%) Kxx (mD) Kyy (mD) Kzz (mD) Fxx Fyy Fzz

MS F 27.04 1941 2134 1524 13.0 12.1 15.2

XBed MS D 27.46 2466 2796 2149 13.7 12.0 14.3
LMS E 25.67 1380 1608 597 27.0 23.6 48.8
Conglomerate I 25.39 2258 2440 40.1 17.8 17.1 436

iii) The average water saturation, S∗w , is calculated through pore

Table 3
volume averaging.
Characteristics of the micro-CT images from sub-facies F sample and the geo­
metric and petrophysical attributes of the extracted pore network. ∫
φ̂S w dV
S∗w = Ω∫ (7)
Image properties Values Network properties Values φdV
Ω
Size (voxel) 792, 764, Nodes 121723
1180
Voxel size (μm) 6.08 Links 261964
Total porosity 27.04 Average coordination 4.30
iv) The absolute permeability in the domain is equated to the water
(%) number
Open fraction (%) 25.29 Average aspect ratio 1.76 phase’s permeability K̂ w = krw ( ̂
S w )K. Then, a single-phase
Clay fraction (%) 3.56 Node radius (μm) 0.69–85.88 upscaling is performed in each direction d = {x, y, z} to acquire
Clay porosity (%) 49.15 Link radius (μm) 0.65–60.08 the upscaled effective phase permeabilities. Similarly, determine
̂ ∗,d .
the upscaled oil permeabilities K o
block, is denoted as Ω. For each direction, indicated as d = {x, y, z}, a v) Calculate the upscaled Kr using the provided equations,
pressure drop, ΔP, is imposed across the domain. Following the solution
( ∗) K
∗,d
of the pressure equation, ̃
rw Sw = ∗,d
K∗,d w
(8)
K
∇.(K∇P) = 0 (1)
( ∗) K
∗,d
̃
the flux field, denoted as νd , is ascertained. The average flux of the ro Sw = ∗,d
K∗,d o
(9)
domain is subsequently determined. K
∫
1 where K∗,d represents the upscaled absolute permeability in the d-di­
νd = νd .nd dA (2)
Ad ∂Ωd rection as specified by Eq. (4). The above procedure is iterated with
∫ varied P
̂ cow values to derive upscaled Kr for different S∗ values. Upon
w

Ad = dA (3) repeating this upscaling process in each direction, we generate an

∂Ωd upscaled Kr curve for all three dimensions.

where ∂Ωd signifies the boundary of Ω at the side with lower pressure in 2.3. Flow simulation method
the d-direction, while nd represents the vector normal to this boundary.
Consequently, the upscaled permeability in the direction d can be In the absence of assumptions related to the capillary limit, the
defined as follows. saturation distribution at steady state could be established by con­
Ld Ld
∫ ducting a two-phase flow simulation. By implementing a specific set of
K∗,d = νd = νd .nd dA (4) boundary conditions within the domain, the simulation continues until
Δp ΔpAd ∂Ωd
the change in saturation falls below a predetermined threshold. Clearly,
where Ld refers to the distance between the inflow and outflow bound­ this method is more computationally demanding than those based on the
aries. Once this upscaling process is sequentially applied to each direc­ capillary limit. However, it offers the advantage of not necessitating any
tion, the upscaled absolute permeability emerges as a diagonal tensor. assumptions about the predominating forces within the system. For each
direction d = {x, y, z}, execute the following stages (Lie, 2019; Begg
K∗ = diag(K∗,x , K∗,y , K∗,z ) (5) et al., 1989; Durlofsky, 1991):
For periodic boundary conditions, the upscaled permeability trans­
forms into a comprehensive upscaled permeability tensor due to the i) Choose a water saturation, ̂ S w , and initialize the domain with
inclusion of cross-flow (Lie, 2019). equal saturation across all cells.
ii) Use a pressure drop across the domain in the d-direction and
2.2. Capillary limit method conduct a two-phase simulation until the change in saturation is
less than a predefined threshold (a threshold for the fluxes could
The capillary limit method presumes that capillary forces have also be applied).
achieved equilibrium, and that they are predominant to the extent that iii) Calculate the average water saturation, S∗w , by using pore volume
viscous and gravitational forces can be disregarded. This assumption averaging as per Eq. (7).
might be true in regions of the reservoir where the flow rate is extremely iv) Conduct single-phase upscaling for the phase permeabilities
low. The procedure for this method is as follows (Lie, 2019): K S w )K
̃ w,d = krw ( ̂ (10)

i) A specific PC value is chosen, P

̂ cow ,
K
̃ o,d = kro ( ̂
S w )K (11)
ii) The PC curve is inverted to determine the saturation distribution,

S w = P−cow
̂ ( P cow )
1 ̂
(6) v) Determine the upscaled Kr using the following equations.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 5. Data of a) drainage relative permeability, b) drainage capillary pressure, c) imbibition relative permeability, and d) imbibition capillary pressure for sub-
facies D, E, and F within Proximal Mouthbar facies used for upscaling (courtesy of CO2CRC).

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 6. Possible sub-facies distribution with random order within Proximal Mouthbar facies.

Fig. 7. Effect of random facies order on the upscaled a) drainage relative permeability, b) drainage capillary pressure, c) imbibition relative permeability, and d)
imbibition capillary pressure. The sequence of letters in the legend reflects the stratigraphic ordering of sub-facies, each of equal length, within the Proximal
Mouthbar facies, indicating the vertical arrangement from bottom to top. For instance, ‘FED’ denotes the presence of three distinct sub-facies: sub-facies F at the
bottom, sub-facies E in the middle, and sub-facies D at the top.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

The facies associations within our static model are shown in Fig. 2.
Facies are categorized into two main groups: reservoir facies and non-
reservoir facies. The reservoir portion is characterized by two main
high-level facies associations, which are indicated by the colours brown
and yellow. The non-reservoir segment, on the other hand, consists of
three distinct facies associations represented by the colours green, red,
and grey.
The pie chart supplements this visual interpretation with numerical
data, quantifying the proportion of each facies within the static reservoir
model. The Proximal Mouthbar facies occupies the most significant
portion of the reservoir, comprising 45.82% of the total. The Distribu­
tary Channel is the second most abundant facies, making up 17.63% of
the reservoir. This is followed by the Distal Mouthbar facies with
13.23%. The Cement facies accounts for 11.76%, while the Delta facies,
albeit essential, constitutes the smallest proportion at 11.55%.
Table 1 provides a comprehensive representation of the facies and
associated groupings found within the first Parasequence of the lower
Paaratte formation at the CO2CRC Otway site. In the scope of this
article, we emphasize the upscaling process of Kr and PC. This upscaling
was performed from the sub-facies scale, extending to the log and model
scales for key reservoir rock types, specifically the Proximal Mouthbar
Fig. 8. Possible sub-facies distribution with random size/portion within prox­ (PM) and Distributary Channel (DC). The Proximal Mouthbar facies in
imal Mouthbar facie. To generate the figure an interval of 1 m was considered. our study is distinguished by three specific sub-facies, labelled as D, E,
and F. Each of these sub-facies is characterized by a unique set of
( ∗) K
̃ ∗,d
imbibition and drainage data, which are integral components of our
rw Sw = ∗,d
K∗,d w
(12) upscaling process. Sub-facies D, E, and F represent distinct geological
K
formations with individual characteristics. Note that these facies are
( ∗) K
̃ ∗,d present in Distributary Channel, Proximal Mouthbar, and Distal
ro Sw = ∗,d
K∗,d o
(13) Mouthbar facies associations to varying degrees.
K
Fig. 3 illustrates an integrated display of logging outputs obtained
These steps are subsequently reiterated with different values for the from the CO2CRC Otway site. The first track shows the well-bore per­
saturation, ̂
S w . Similar to the previous method, the outcome is a diagonal forations, followed by the second track which depicts the facies associ­
tensor depicting the upscaled Kr for each phase. ations. The facies in the Parasequence 1 (PS1) have a mean thickness of
In the context of two-phase flow, apart from the Kr, it is also 0.7–1.5 m. The third track provides measurements of clay volume (VCL)
necessary to upscale the PC. For this upscaling process, we employ and water saturation, while the fourth track includes data on formation
volume averaging as follows: density (RHOZ) and porosity (PHIT). The fifth track illustrates perme­
∫ ability (KINT). Additionally, core plug porosity and permeability mea­
( ∗) φPcow (Sw )dV
Pcow Sw = Ω ∫
∗
(14) surements are overlaid on the relevant tracks as circles, offering a direct
φdV
Ω comparison between log-derived and core-measured values.
All numerical upscaling, general computations, and graphical rep­ Fig. 4 shows the distribution of porosity and permeability for each
resentations in this paper have been accomplished using the Matlab facies association. The distribution plots reveal a bimodal pattern in
Reservoir Simulation Toolbox. This is an open-source platform designed both porosity and permeability for the Distal Mouthbar and Delta Front
to facilitate the efficient development of new computational method­ facies, while displaying a normal distribution for the distributary
ologies in reservoir engineering. channel facies. A slight bimodal trend is also observed in the Proximal
Mouthbar facies. The distributary channel facies exhibit the highest
values of porosity and permeability, in contrast to the delta front facies,
3. Sedimentology and available DCA data for Paaratte formation
which show the lowest. Based on the bimodal distributions, two pre­
dominant groups for porosity and permeability are identified: one group
On a regional scale, the lithology of the Paaratte Formation, a saline
with porosity exceeding 0.25 and permeability over 100 mD, and
aquifer at the CO2CRC’s Otway Research Facility site in Australia, is
another group with values below these thresholds. The data presented
known for its significant heterogeneity. It consists of a mixture of sands
are courtesy of CO2CRC Ltd., with a portion of these data accessible in
and gravels with varying permeability, interbedded with carbon-rich
Refs. (Mishra et al., 2019, 2020; Dance et al., 2019; Park et al., 2014).
mud layers. Additionally, this formation is marked by the presence of
To apply the DCA workflow, four samples from PS1 of the Paaratte
diagenetic carbonate cement layers with low average porosity and low
sandstone formation in the Otway Basin were used. These samples were
permeability, which act as seals with varying degrees of effectiveness
originally chosen to represent four main reservoir facies: massive or
(Mishra et al., 2020; Dance et al., 2019; Park et al., 2014, 2018). To
poorly stratified sandstone (MS), cross-bedded massive sandstone (XBed
achieve a high accuracy in field-scale models, it is crucial to have an
MS), laminated massive sandstone (LMS), and conglomerate sandstone.
ample number of measurements to effectively quantify the heteroge­
Table 2 provides a summary of calculated petrophysical properties for
neity in thin reservoir layers with a reasonable level of statistical con­
the samples, including total porosity, φtot, and tensor-based flow prop­
fidence. Furthermore, having a deep comprehension of sedimentary
erties, i.e., absolute permeability, K, and formation factor, F, in different
facies, their hierarchical sequences, and their associations is essential.
directions.
Consequently, reservoirs with high heterogeneity demand a more
The drainage and imbibition Kr and PC data obtained from DCA were
extensive characterization process (Michael et al., 2010).

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 9. Upscaled Kr and PC of drainage (up) and imbibition (down) processes with random sub-facies order within Proximal Mouthbar facies. The letters D, E, and F
represent the sub-facies, while the numbers preceding each sub-facies indicate their vertical lengths measured in centimeters.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

However, it should be noted that similar procedures were applied to the

Distributary Channel facies. The results of these procedures are pre­
sented in Appendix A for reference and comparison. Therefore, we
delved into the following strategies with an objective to achieve an ac­
curate depiction of the reservoir:

1. Examination of the impact of rock type/facies sequence variation on

Kr and PC upscaling: This strategy investigates how variations in the
order of rock types or facies affect the upscaled results for Kr and PC.
2. Analysis of facies proportion/size alterations on Kr and PC upscaling:
This approach assesses how changes in the proportion or size of
facies influence the upscaled Kr and PC.
3. Evaluation of the consequences of concurrent variation of facies
sequence and proportion on Kr and PC upscaling: This method
scrutinizes the effects of simultaneous changing of facies order and
proportion on the upscaling of Kr and PC.

The following section will conduct an in-depth analysis of these

strategies. This thorough investigation will provide vital insights into
the accurate representation of the reservoir, thereby advancing our
understanding of its behaviour and optimal management practices.
Fig. 10. Possible sub-facies distribution with random order and portion within
Proximal Mouthbar facies.
4. Results and discussion
provided by CO2CRC Ltd. Portions of these data are documented in
Ref. (Bagheri et al., 2021). These results were generated using pore In this section, the upscaling of Kr and PC from sub-facies to facies
network modelling for multiphase flow assuming quasi-static pore-scale associations is initially addressed, with the impact of the random
physics. Brine and CO2 fluids were used to obtain the two-phase relative sequence (Section 4.1.1), varying proportions (Section 4.1.2), and the
permeability curve, and the pore network model was constructed based combined effect of sequence and proportions of sub-facies (Section
on the difference between the dry and fully saturated micro-CT scans of 4.1.3) on the upscaling results. Subsequently, the process of upscaling
the samples. Dry and saturated micro-CT images of the samples were from facies associations to the simulation model is discussed (Section
analysed and transformed into a topological equivalent pore network 4.2). Lastly, a direct upscaling approach from sub-facies to the simula­
that is used as input to a two phase network model which simulates CO2 tion model is evaluated (Section 4.3). This upscaling methodology
injection (primary drainage) and subsequent brine injection (imbibi­ bridges the gap between fine-scale measurements and larger scale model
tion) under water-wet conditions (Ruspini et al., 2017). requirements, aiding in a more precise reservoir simulation and man­
Table 3 provides a detailed overview of the characteristics derived agement. Detailed procedures and results of this upscaling process are
from both dry and wet micro-CT images, each acquired with a voxel elaborated in the following subsections.
resolution of 6.08 μm and a total porosity of 0.27. This dataset served as
the basis for developing the pore network model. Table 3 also includes 4.1. Upscaling relative permeability and capillary pressure from sub-
information on the geometrical and petrophysical properties of the pore facies to facies association
network derived from these 3D micro-CT images. The sample is rela­
tively homogenous with low variance in pore and throat sizes. More­ 4.1.1. Upscaling with random order of sub-facies
over, it exhibits high connectivity with an average coordination number To assess the potential influence of rock type or sub-facies arrange­
of 4.3. The aspect ratio, indicating the ratio of pore body to throat size, is ment on the upscaling results, a method of randomized examination was
notably low at 1.76, which is less than typically seen in consolidated strategically adopted. This encompasses a detailed rearrangement of the
rocks (Ruspini et al., 2017). sub-facies order across various facies associations and the subsequent
The surface tension between CO2 and brine is measured at 38.2 dyn/ observation of changes in the upscaled parameters of Kr and PC. The
cm, with respective densities of 393 kg/m3 for CO2 and 1123 kg/m3 for core objective of this approach is to encapsulate any heterogeneity that
brine. All primary drainage simulations were conducted under strongly could arise due to variations in the organization of the sub-facies.
water-wet conditions, with receding contact angles randomly set be­ During the upscaling process, an interval of 1 m, equivalent to the
tween 0◦ and 10◦ . During these simulations, CO2 was injected at the inlet minimal grid size of the reservoir model along the z-direction, was
face of the fully saturated network, with brine exiting from the opposite considered. Within this scope, various possible facies arrangements were
side. Injection continued until CO2 saturation reached the pre­ examined. The permutation concept was utilized to compute the total
determined initial gas saturation, Sgi. Subsequently, the imbibition phase number of possible arrangements of the facies ‘D’, ‘E’, and ‘F’ within the
commenced with brine injection and stopped when CO2 was no longer interval, given their variable order and the potential absence of some
connected to the outlet faces. The drainage/imbibition Kr and PC ob­ facies. Fig. 6 exhibits the twelve possible combinations of the three sub-
tained for each sub-facies within the Proximal Mouthbar facies are facies within the interval of Proximal Mouthbar facies association. Each
shown in Fig. 5. state represents a unique permutation of sub-facies within the interval.
By utilizing the specific data sets pertaining to each sub-facies, we For each state graphically depicted in Fig. 6, the Kr and PC curves
aim to incorporate the detailed characteristics of these facies into our were upscaled from the sub-facies level to the facies association. This
larger reservoir model. For sake of brevity, this article details the procedure’s outcomes, for both drainage and imbibition processes, are
upscaling methods and results for the Proximal Mouthbar facies. illustrated in Fig. 7. The facies order’s variation can significantly impact

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 11. Upscaled Kr and PC of drainage (up) and imbibition (down) processes with random facies order and portion. In the legend, the initial three letters indicate
the sequence of sub-facies within the Proximal Mouthbar facies, illustrating their vertical ordering from the bottom upwards. The numbers preceding each sub-facies
specify their vertical extents in centimeters.

11
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Saad et al., 1995), affirming that the characteristics of facies within the
reservoir, specifically their heterogeneous and laminated structure, as
well as the small-scale heterogeneity and anisotropy, have a critical
impact on Kr and PC curves.
The benefits of using this approach are manifold. Firstly, it accounts
for the inherent geological variability, providing a more realistic rep­
resentation of the reservoir behaviour. Secondly, by including the order
variation of facies in the upscaling process, we increase the accuracy and
reliability of our predictions. Lastly, this method’s implementation can
be achieved with any standard simulator, allowing for its broad appli­
cability in the field of reservoir modelling and simulation.

4.1.2. Upscaling with random portion of sub-facies

To evaluate the influence of variations in the size or proportion of
sub-facies on the upscaled Kr and PC, we executed another randomized
study. In this section, we adjusted the proportions of sub-facies to
monitor the corresponding alterations in upscaled Kr and PC curves. The
aim here was to capture the impact of changes in facies geometry. Fig. 8
shows the potential distributions of sub-facies, featuring a range of sizes
Fig. 12. Extracted Sw data from PC curves at PC = 0.2 bar. The Sw index or proportions. The main advantages of this methodology are the
quantifies the number of capillary pressure curves from which water saturation increased understanding of how changes in sub-facies size or proportion
(Sw) values are derived. For instance, with Sw Index = 1, the corresponding Sw can impact the upscaled properties, and the broader view of potential
value of 0.155 is obtained from the first capillary pressure curve. reservoir behaviours.
For each state, the upscaled Kr and PC curves are shown in Fig. 9.
the upscaling results for both Kr and PC. This is an important finding, as Each curve in the figure provides a representation of the upscaled Kr and
neglecting the effect of facies order could potentially result in inaccur­ PC corresponding to the sub-facies D, E, and F. Within each state, the
acies in subsequent simulations. This discovery finds support in previous figure also visually depicts the relative lengths of these sub-facies in
research (Brigaud et al., 2014; Bakhshian et al., 2020; Han et al., 2010; centimeters. Notably, if, in a specific state, one of the sub-facies exhibits

Fig. 13. Final upscaled Kr and PC curves from D, E, and F sub-facies to Proximal Mouthbar facies scale for drainage (up) and imbibition (down) processes.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 14. Upscaled a) drainage relative permeability, b) drainage capillary pressure, c) imbibition relative permeability, and d) imbibition capillary pressure of
Proximal Mouthbar (PM) and Distributary Channel (DC) facies.

13
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

was conducted at a constant PC point, herein at PC = 0.2 bar, where

water saturation points were extracted from the entirety of the PC curves
as depicted in Fig. 11. The figure displays the quantity of upscaled Kr
and PC curves (y-axis), plotted against the respective water saturation at
PC = 0.2 bar for each curve (x-axis).
Three statistical parameters (P10, mean, and P90) were employed to
select three PC curves. These parameters are chosen because they
represent different levels of uncertainty in the Kr and PC curves. P10
(Percentile 10) represents the lower bound of uncertainty, which is the
10th percentile value of the data and reflects a scenario where Kr and PC
curves are relatively low. Mean (Average) shows the central or most
likely value within the dataset, which is often used as the base or most
probable case for modelling purposes. P90 (Percentile 90) signifies the
upper bound of uncertainty, which is the 90th percentile value of the
data and reflects a scenario where Kr and PC are relatively high. This
range is crucial for probabilistic reservoir simulations, where multiple
scenarios with different levels of optimism or pessimism are considered
(Amrollahinasab et al., 2023; Rezk et al., 2023). Fig. 12 shows the three
selected PC curves correspond to water saturation values equal to P10,
mean, and P90 at a predefined constant PC point (i.e., PC = 0.2 bar),
from a total of 12 upscaled PC curves.
Fig. 15. Possible facies distribution with random order and portion. This method aids in identifying the most suitable set of curves for our
simulations. It also emphasizes the significance of accurately deter­
mining the sequence and proportion of facies in the upscaling process of
a considerably greater length compared to the other two sub-facies, this Kr and PC for CO2 sequestration, as suggested by the range of water
signals the predominant influence of the larger sub-facies on shaping the saturation.
upscaled properties. This method revealed that, like variations in the Once the PC curves are identified, their corresponding Kr curves for
order of sub-facies, alterations in the proportions of sub-facies can both the drainage and imbibition processes are then selected. The ulti­
substantially impact the outcomes of upscaling for both Kr and PC, in mate Kr and PC curves, which are upscaled from sub-facies (D, E, and F)
agreement with the literature (Liao et al., 2023; Al-Kharusi and Blunt, to facies (PM) for both processes, are depicted in Fig. 13. These are
2008). To facilitate a more precise examination of the influence of shown for the pessimistic (P10), mean, and optimistic (P90) scenarios.
portion variation, we also included zoomed-in views of a selection of As illustrated in the figure, variations in both the arrangement and
curves. proportions of facies can exert a significant influence on multiphase
fluid flow. Neglecting these variations by simulating only a single,
4.1.3. Upscaling with random order and portion of facies uniform facies state would lead to results that deviate considerably from
In this section, we have examined the influence of variations in both reality. These findings are consistent with the literature (Boon et al.,
the sequence and proportion of facies on the results of the upscaling 2022; Wang et al., 2020; Kim et al., 2021; Pini et al., 2019). Therefore, to
process. This approach aids in creating a more realistic representation of ensure the accuracy of reservoir simulation studies, it becomes imper­
reservoir heterogeneity. The influence of heterogeneity on Kr and PC ative to consider all potential facies states and carefully select the most
differs based on the specific features of the heterogeneity within the suitable Kr and PC.
reservoir rock, leading to an increase in residual trapping. To ensure It is essential to note that these curves still require further upscaling,
accuracy in estimates of fluid flow and trapping during subsurface CO2 moving from the facies association level to the model scale, to be
injection, models should incorporate properties that account for the properly utilized in reservoir simulation. The process of this subsequent
effects of heterogeneity. Failing to do so may result in substantial errors upscaling will be discussed in the following section.
in simulation results (Reynolds et al., 2018; Burnside and Naylor, 2014;
Yoshida et al., 2016). In this study, we utilized 12 distinct random states,
4.2. Upscaling relative permeability and capillary pressure from facies
Fig. 10. Within each of these states, the upscaling of Kr and PC curves
association to simulation model
was undertaken.
Fig. 11 illustrates the upscaled curves for Kr and PC corresponding to
Following the successful upscaling of Kr and PC from sub-facies to
each state. Within each state, the figure provides the order and length of
facies association, the next step is to further upscale these critical pa­
the sub-facies within each state. This visualization clearly illustrates that
rameters to the reservoir model. The source data for this upscaling phase
a combination of order and proportion variation within the sub-facies
is illustrated in Fig. 14. As evidenced in the figure, the mean curves,
can have a pronounced effect on the upscaling outcomes. These find­
derived from the sub-facies upscaling, will serve as our base data for the
ings align with the existing literature (Chandra et al., 2015; Mikes et al.,
PM facies. It is worth mentioning that the identical upscaling procedures
2006; Abtahi and Torsaeter, 1998), highlighting the importance of
were applied to the DC facies. For brevity and clarity, we have provided
considering these variations when upscaling parameters for subsequent
the detailed upscaling procedures for DC facies in Appendix A.
use in reservoir simulation.
An in-depth reservoir analysis necessitates the consideration of
Due to the extensive number of curves originating from a multitude
various states of facies association. To this end, our methodology con­
of random combinations, it was necessary to devise a systematic method
siders the random sequence and proportion of the two key facies
for data extraction. A script was therefore developed with the purpose of
including PM and DC facies association. Fig. 15 represents the potential
singling out three principal types of PC curves. This selection process
variations in facies distribution, considering both the random sequence

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 16. Upscaled Kr and PC of drainage (up) and imbibition (down) processes from facies to simulation model scale with random facies order and portion. In the
legend, the first two letters indicate the sequence of facies associations, where P and D represent Proximal Mouthbar and Distributary Channel, respectively. The
numbers preceding each facies specify their vertical extents in centimeters.

15
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

randomly varied to illustrate the range of scenarios that could occur

within a reservoir. For the simulation process, a total of 200 random
states were utilized. However, to enhance the visual presentation and
focus on the most representative results, we have chosen 20 selected
states in this context.
The results of the upscaling for both drainage and imbibition pro­
cesses are shown in Fig. 16. The figure reveals the significant influence
that variations in both order and proportion within the facies association
can exert on the upscaling results. This confirms the crucial need to
account for these factors when performing the upscaling process inten­
ded for further reservoir simulations. Other research findings have
corroborated that the small-scale heterogeneity within rocks have a
pronounced impact on saturation dependent functions such as Kr and PC
(Wright et al., 2006; Clavaud et al., 2008; Holcomb and Olsson, 2003).
Furthermore, the alignment of stratified layers at the field scale in­
troduces anisotropy to the fluid flow characteristics by segmenting the
reservoir into compartments (Bakhshian et al., 2020).
Fig. 17. Extracted Sw data from PC curves at PC = 0.2 bar. The Sw index The water saturation values at PC = 0.2 bar is gleaned from all the PC
quantifies the number of capillary pressure curves from which water saturation curves, serving as a valuable input in the determination of pessimistic
(Sw) values are derived. For instance, with Sw Index = 1, the corresponding Sw (P10), mean, and optimistic (P90) scenarios (Fig. 17). This approach
value of 0.147 is obtained from the first capillary pressure curve.
ensures that even minute variations in PC are considered, resulting in
more accurate and reliable outcomes.
The final Kr and PC curves, which were upscaled from facies (PM,
and proportion of facies. The image captures the complexity and DC) to reservoir scale for both drainage and imbibition processes, have
randomness inherent in geological formations, providing a compre­ been established for three scenarios: pessimistic (P10), mean, and
hensive view of the multitude of possible configurations. The arrange­ optimistic (P90) (Fig. 18). The outcomes of this upscaling process serve
ment and share of each facies type, represented by distinct colours, are as immediate input for reservoir simulation purposes, thereby

Fig. 18. Final upscaled Kr and PC curves from facies to simulation model scale for drainage (up) and imbibition (down) processes.

16
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 19. Upscaled relative permeability and capillary pressure in different random states for drainage (up) and imbibition (down) processes using second method.

and proportion of all sub-facies within their respective facies, as well as

changing the order and portion of facies associations. Fig. 19 illustrates
all the potential upscaled curves for Kr and PC, corresponding to the
1458 random geological realizations. Due to the extensive quantity of
curves presented, the legend has been omitted from the figure to
maintain clarity and avoid clutter. The potential benefits of direct
upscaling from sub-facies to model scale include:

a) Improved accuracy: It is conceivable that the use of a larger number

of random states may broaden the model’s scope to encompass a
wider range of potential geological configurations, potentially
leading to more accurate predictions.
b) Comprehensive modelling: By randomizing both the sequence and
proportion of sub-facies and facies associations, the model gains the
ability to account for a variety of geological scenarios, thereby of­
fering a deeper understanding of the reservoir’s characteristics.
c) Efficient upscaling process: Despite the increased computational
time required, this methodology could potentially improve the effi­
ciency of the upscaling process. By considering a wider set of
geological possibilities, the method may reduce the margin of error
and deliver more accurate upscaled outputs.
d) Detailed visualization: As shown in Fig. 19, the methodology enables
Fig. 20. Extracted Sw data from PC curves at PC = 0.2 bar for the second the visualization of all potential upscaled Kr and PC curves for the
method. The Sw index quantifies the number of capillary pressure curves from
1458 randomly generated geological realizations, allowing for a
which water saturation values are derived.
thorough examination of the model’s outputs.

Fig. 20 depicts the probability distribution of upscaled Kr and PC.

streamlining the workflow and enhancing the efficiency of subsequent Highlighting the P10, mean, and P90 probability values offers a clear
analyses. statistical representation of the range of possible results, promoting a
more comprehensive and precise interpretation.
4.3. Direct upscaling of relative permeability and capillary pressure from It is important to note that choosing PC value is flexible and pri­
sub-facies to simulation model marily serves as a convenient point of extraction for water saturation
data. This choice enables a systematic extraction of the necessary in­
The second methodology, involving the direct upscaling of Kr and PC formation to determine the P10, mean, and P90 values. By representing
from sub-facies to model scale, offers a more detailed and comprehen­ the uncertainties inherent in reservoir simulation in a clear and under­
sive approach to geological modelling. Using a substantial number of standable manner, it allows for the implementation of more robust and
1458 random states, the method allows for randomizing the sequence

17
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. 21. Final upscaled Kr and PC curves of reservoir model for drainage (up) and imbibition (down) processes using the second method.

18
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

effective risk management strategies. The results of direct upscaling of In essence, our research provides valuable insights into upscaling
Kr and PC curves from sub-facies (D, E, and F) to the reservoir model techniques, presenting a fresh perspective on effectively upscaling
scale is illustrated in Fig. 21 for P10, mean, and P90 scenarios. This micro-scale data to field scale and integrating the order and portion of
method offers a broader perspective on potential reservoir behaviour facies for more precise and reliable reservoir simulation. These findings
under different conditions. These upscaled parameters represent the establish a groundwork for future studies and practical implementations
final data that can be directly input into simulation models, saving time aimed at enhancing the efficiency and accuracy of reservoir character­
and effort in additional data processing or adjustment. ization and modeling.
Although this methodology demands additional computational re­
sources, it may have the potential to improve upscaling and simulation CRediT authorship contribution statement
results by encompassing a broader range of real-world scenarios. The
potential for improving history matching and dynamic model quality Masoud Aslannezhad: Writing – review & editing, Writing – orig­
through this methodology will be evaluated in our forthcoming inal draft, Visualization, Software, Formal analysis. Mohammad
research. Sayyafzadeh: Writing – review & editing, Validation, Supervision,
Methodology, Formal analysis, Conceptualization. David Tang: Writing
5. Conclusion – review & editing, Supervision, Resources, Formal analysis. Zhenjiang
You: Writing – review & editing, Validation, Data curation. Stefan
This research highlights the significant impact of facies order and Iglauer: Writing – review & editing, Validation, Supervision, Formal
portion on upscaling relative permeability and capillary pressure, which analysis. Alireza Keshavarz: Writing – review & editing, Validation,
includes both drainage and imbibition processes. To account for these Supervision, Formal analysis, Data curation.
effects, we introduced a novel, randomized, and iterative method that
seamlessly integrates into existing simulators. Our algorithm, imple­ Declaration of competing interest
mented through the open-source Matlab Reservoir Simulation Toolbox
(MRST), demonstrated satisfactory performance, reinforcing its prac­ We hereby declare that the manuscript titled “Upscaling Relative
tical applicability. The implications of this research are manifold and Permeability and Capillary Pressure from Digital Core Analysis in Otway
can be outlined as follows: Formation: Considering the Order and Size Effects of Facies ", submitted
to Journal of Gas Science and Engineering is an original work and has
1. Enhanced accuracy and efficiency: The results demonstrated a pro­ not been submitted to any other journal for publication. We also confirm
nounced impact of facies order and portion on the upscaling of that all authors have read and approved the final version of the manu­
relative permeability and capillary pressure during both drainage script for submission.
and imbibition processes in reservoir modeling. Incorporating these
factors into simulations may enhance the accuracy and efficiency of Data availability
reservoir modeling.
2. Robust methodology: This research presents a robust and reliable Data will be made available on request.
methodology that accounts for a broader range of geological sce­
narios, thereby minimizing the margin of errors in the upscaling Acknowledgments
process. Despite the increased computational demands associated
with this approach, its potential to improve the predictive power of This research is part of a project (G1006454) supported by CO2CRC
our models cannot be understated. Ltd, in collaboration with Edith Cowan University in Australia, with the
3. Informed upscaling techniques: Through an exhaustive examination goal of enhancing comprehension of digital core analysis and how it
of various upscaling techniques, we conclude that randomizing the affects CO2 trapping methods. The authors wish to express their grati­
sequence and proportion of all sub-facies within their respective tude to CO2CRC Ltd. for allowing them to use data from the CO2CRC’s
facies, coupled with adjustments to the order and portion of facies Otway Research Facility and for supplying the funds for the project.
associations, despite being computationally more intensive, can have
the potential to improve the simulation results.

Nomenclature

F Formation factor, dimensionless

K Absolute permeability, mD
K* Upscaled absolute permeability, mD
Kr Relative permeability, dimensionless
Ld Distance between the inflow and outflow boundaries, cm
nd Normal vector to the boundary
PC Capillary pressure, bar
Sgi Initial gas saturation, dimensionless
S∗w Average water saturation, dimensionless

Greek letters
ΔP Pressure drop, bar
νd Flux field, m/s
Φtot Total porosity, dimensionless
Ω Grid domain
∂Ωd Boundary of grid domain

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Abbreviations
CO2CRC Cooperative Research Centre for Greenhouse Gas Technologies
DC Distributary Channel
DCA Digital Core Analysis
LMS Laminated massive sandstone
MRST Matlab Reservoir Simulation Toolbox
PM Proximal Mouthbar

Appendix A

A.1. Drainage/Imbibition relative permeability and capillary pressure obtained from DCA

Fig. A1. Data of a) drainage relative permeability, b) drainage capillary pressure, c) imbibition relative permeability, and d) imbibition capillary pressure for sub-
facies I, E, and D within Distributary Channel facies used for upscaling (courtesy of CO2CRC).

20
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

A.2. Upscaling relative permeability and capillary pressure from sub-facies to facies association

A.2.1. Upscaling with random order of sub-facies within Distributary Channel facies

Fig. A2. Possible sub-facies distribution with random order within Distributary Channel facies.

Fig. A3. Effect of random facies order on the upscaled a) drainage relative permeability, b) drainage capillary pressure, c) imbibition relative permeability, and d)
imbibition capillary pressure. The sequence of letters in the legend reflects the stratigraphic ordering of sub-facies, each of equal length, within the Distributary
Channel facies, indicating the vertical arrangement from bottom to top.

21
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

A.2.2. Randomized investigation of sub-facies portion

Fig. A4. Possible sub-facies distribution with random size/portion within the Distributary Channel facie. To generate the figure an interval of 1 m was considered.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. A5. Upscaled Kr and PC of drainage (up) and imbibition (down) processes with random sub-facies order within Distributary Channel facie. The letters I, E, and D
represent the sub-facies, while the numbers preceding each sub-facies indicate their vertical lengths measured in centimeters.

23
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

A.2.3. Random order and portion of facies

Fig. A6. Possible sub-facies distribution with random order and portion within Distributary Channel facies.

24
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. A7. Upscaled Kr and PC of drainage (up) and imbibition (down) processes with random facies order and portion. In the legend, the initial three letters indicate
the sequence of sub-facies within the Distributary Channel facies, illustrating their vertical ordering from the bottom upwards. The numbers preceding each sub-
facies specify their vertical extents in centimeters.

25
M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

Fig. A8. Extracted Sw data from PC curves at PC = 0.2 bar. The Sw index quantifies the number of capillary pressure curves from which water saturation (Sw) values
are derived.

Fig. A9. Final upscaled Kr and PC curves from I, E, and D sub-facies to Distributary Channel facies scale for drainage (up) and imbibition (down) processes.

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M. Aslannezhad et al. Gas Science and Engineering 128 (2024) 205363

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