Hydraulic flow unit classification from core data: Case study of the Z gas reservoir, Poland
Journal of Mining and Earth Sciences Vol. 62, Issue 3 (2021) 29 - 36
29
Hydraulic flow unit classification from core data: case
study of the Z gas reservoir, Poland
Man Quang Ha 1,*, Anh Ngoc Le 2, Jadwiga Jarzyna 3
1 PetroVietnam Exploration Production Corporation - PVEP, Vietnam
2 Faculty of Oil and Gas, Hanoi University of Mining and Geology, Vietnam
3 AGH University of Science and Technology, Poland
ARTICLE INFO
ABSTRACT
Article history:
Permeability and porosity are essential parameters for estimating
hydrocarbon production from reservoir rocks. They are combined in an
additional factor, the FlowZone Index (FZI), which is the basis for defining
the hydraulic flow unit (HFU). Each HFU is a homogeneous section of a
reservoir rock with stable parameters that allow for media flow.
Hydraulic flow units are determined from the porosity and permeability
of core or well logs. The simple statistical methods are applied for HFU
classification and then improve permeability prediction. This paper also
shows how to quickly apply the global hydraulic elements (GHE) method
for HFU classification. The methodology is tested on the Miocene
formation of a deltaic facies from the Carpathian Foredeep in South-
Eastern Poland.
Received 09th Feb. 2021
Accepted 24th May 2021
Available online 30th June 2021
Keywords:
Flow Zone Index,
Global Hydraulic Elements,
Hydraulic Flow Unit,
Permeability prediction.
Copyright © 2021 Hanoi University of Mining and Geology. All rights reserved.
devices provide relatively good data, but it is still
difficult to parameterize factors such as tortuosity,
1. Introduction
Porosity and permeability are two properties
of reservoir rock that strongly influence the
movement of media in the rock’s pore space.
Formulas for permeability vs porosity defined by
Cozeny and Carman (1927, 1937) are the most
known equations used to describe water and
hydrocarbon ability to move throughout the pore
spaceof rock. Improved lab equipmentandlogging
specific surface, or the radius of pores in a rock
formation. To overcome these difficulties, the
parameters of Flow Zone Index (FZI) and then
Hydraulic Flow Unit (HFU) are defined as primary
parameters that implicitly describe the ability of
media to flow in the pore space of reservoir rock.
Our goal is to prepare petrophysical data for
modellingmediaflowintheporespaceofreservoir
rock. The rock formation represented by core
parameters and log data is divided into
homogeneous hydraulic flow units. Core data will
be used to calculate the Flow Zone Index (FZI) in
cored sections of the wells and then apply some
_____________________
*Corresponding author
E - mail: [email protected].vn
DOI: 10.46326/JMES.2021.62(3).04
30
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
statisticsmethodforHFUclassificationbasiconFZI
mean value. In this study, we also apply the Global
Hydraulic Element (GHE) method introduced by
(Corbett et al., 2003, 2004; Matyasik et al., 2007)
for a rapid and more straightforward approach to
plot the porosity and permeability data on the
predetermined GHE template.
Carpathian Foredeep, is multi-horizontal.
Sequences of thin shale laminas are sealing gas
horizons in thin sandstone strata and prevent the
movement of gas up to the top of sedimentary
systems. Porous sandstones of high permeability
belong to depositional elements of submarine fans,
sandstones of deltaic environments (largemouth
bars, distributor channels, and others), shallow
marine clastic deposits of estuaries, and sandy
barriers. In those horizons sandstones with gas are
difficult to recognize because of the low contrast of
parameters between sandstones and shales.
Deltaic sediments are well recognized in the
Carpathian Foredeep. Sandstone reservoirs
distribution in the Z gas field is of very good
reservoir parameters (Mysliwiec, 2006; Mysliwiec
et al., 2004).
2. Geological setting and data set
2.1. Geological setting
The majority of gas deposits recognized in the
Carpathian Foredeep basin occurred in the
Miocene strata. Most of them are small but
economically important. Generally, in all deposits,
good reservoir properties are observed. The Z gas
field was discovered in the early 60 of the 20th
century in the Northern part of the Carpathian
ForedeEquationThemaingashorizonsoccurredin
the upper part of the Sarmatian argillaceous -
arenaceous sequences at a depth interval between
390 and 545 m. Good reservoir parameters were
observed. The deeper productive horizons were
discovered on the basis of a new approach to the
seismic anomalies interpretation in the latest 90.
Now, the Z gas field is recognized in three parts:
Eastern, central, and western. Productive horizons
are discovered in the whole profiles of wells in the
Sarmatian deposits ( Figure 1).
2.2. Data set
Coredatafrom wells inthe Zgas fieldin theNE
Polish part of the Carpathian Foredeep were
available
(Figure
1).
Laboratory
core
measurements included effective porosity (Φe)
and absolute permeability (K), which were taken
from various depths in the selected wells. The
study dataset included 570 core samples from 11
wells, and the core interval ranges from 253 m to
1154 m. Only three samples were taken from
littoral facies at a depth between 253÷272 m, and
theotheronewas takenfromadeeperpartsection.
The Z gas reservoir, like many others in the
Figure 1. Location of the Z gas - field with the 11 wells location (after Mysliwiec, 2006; Mysliwiec et al., 2004).
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
31
All primary statistical analyses, i.e., Histogram of
porosity (Figure 2a), permeability (Figure 2b), FZI
(Figure 2c), and cross plot of permeability versus
porosity for 570 cores data (Figure 2d) were
performed on the full data set. Most of the samples
were obtained in deltaic sandy - muddy - shaly
deltaic facies
are internally consistent and predictably different
from the properties of other reservoir volumes. He
described the flow units as the following:
- A specific volume of a reservoir; it is
composed of one or more reservoir - quality
lithology and any none - reservoir - quality rock
types within that same volume, as well as the fluids
they contain,
- A correlative and mappable unit at the
interwell scale,
- A recognizable section on wireline logs,
- A unit is being in communication with other
flow units. However, flow units based on
lithostratigraphic characteristics are not always in
pressure communication (Figure 3).
3. Methodology
3.1. Hydraulic Flow Unit - HFU
The concept of hydraulic flow unit was
introduced by Ebanks et al. (1987, 1992), who
defined an HFU as a mappable portion of a
reservoir within which the geological and
petrophysical properties that affect the fluid flow
Figure. 2. Histogram of porosity (a), permeability (b), FZI (c), and cross plot of log permeability versus porosity
for 570 cores data (d).
32
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
e
1e
z
(2)
(3)
(4)
k
e
RQI 0.0314
1
FsSgv
RQI
z
FZI
3
Figure 3. Various parameters are used in defining
e
K 1014.24(FZI)2
(5)
geologic flow units; the flow units are defined based
on lithofacies, pore types, porosity, and permeability
cross - plots, capillary pressure measurements, and
gamma - ray log response (after Ebanks et al. 1992).
(1 e )2
On the basis of Equations (Equation 1÷4), we
assume that units of constant FZI have invariable
reservoir parameters that differ from the
surrounding neighbourhood. Proper division of
the data set into units of constant FZI forms the
basis for the HFU construction, resulting in the best
partial relationships of permeability vs porosity for
each HFU.
The structure, texture, and mineral
composition of rock formation strongly influence
the relationship between porosity and
permeability. Petrophysicists working for the oil
and gas industry and prospecting hydrogeology
and geothermal water reserves prospecting try to
find the best relationship between those two
reservoir parameters since the times of Kozeny
(1927) and Carman (1937). A breakthrough was
noted with an approach based on the FZI proposed
by Amaefule et al. (1993), which was then followed
by other authors (Prasad, 2000). FZI is a derivative
factor determined based on the generalized
Cozeny - Carman equation:
3.2. Global Hydraulic Elements - GHE
Corbett et al. (2003, 2004) proposed the rapid
and more straightforward approach to plot the
porosity and permeability data on the
predetermined global hydraulic elements (GHE)
template ( Figure4), which is constructed based on
eq. (5). A systematic series of a priori FZI values
were arbitrarily chosen to define 10 porosity -
permeability elements. Only ten were chosen to
split the wide range of porosity and permeability
parameter space into a manageable number of
GHEs (Table 1).
Data in the study projected on the Corbett and
Potter (2004) template shows the close
relationship between permeability and porosity in
each HFU = GHE. Thus, established equations are
used to calculate K from Φ and FZI. The
relationship between permeability from the core
dataandpermeabilitycalculatedfromthemeansof
FZIs in GHE is very close (Figure 4).
3
1-e
1
e
k
(1)
2
Fs
2S2
gv
where: K - the permeability; Φe - the effective
porosity; Fs - the shape factor; τ - the tortuosity of
pores; Sgv - the specific surface.
Amaefule et al. (1993) introduced two
auxiliary factors: Φz, the normalized porosity
(Equation 2), and RQI, the reservoir quality index
(Equation 3). This results in a new formula
(Equation 4), which is a definition of FZI.
The basis of HFU classification is to identify
groups of data that form the unit - slope straight
lines on a log - log plot of RQI versus z. The
permeability of a sample point is then calculated
from a pertinent HFU using the mean FZI value and
the corresponding sample porosity using the
following Equation (5).
4. Results and discussions
Probability function to select number of HFU
To confirm the division of the data set into the
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
33
Table 1. Global hydraulic elements (GHE) template parameters (Corbett et al. 2003).
GHE
FZI
GHE1
GHE2
GHE3 GHE4 GHE5 GHE6 GHE7 GHE8 GHE9 GHE10
0.0938 0.1875 0.375
0.75
1.5
3
6
12
24
48
10000000
1000000
100000
10000
1000
100
10
1
0.1
0.01
0.001
0
0.1
0.2
0.3
0.4
0.5
Porosity [dec.]
Figure 4. Global Hydraulic Element “basemap” template showing GHE1 to GHE10 (Corbett et al. 2003).
proper number of HFUs the probability function of
log(FZI) is calculated. A normal probability plot
illustrateshowthe localslopechanges according to
selected groups with a constant FZI. In Figure 5.a,
sixstraightlinesconnectingtheselectedsectionsof
the probabilityplotdetermined six uniforms HFUs.
the HFU for all core data. The curves represent the
porosity - permeability relationship based on
Equation 5 using the mean value of FZI for each
hydraulic unit.
Simple statistics of permeability, porosity, and
FZI show that the separate uniform groups are
unambiguously described by the mean value of FZI
(Table2). For thesesixdefined groups of data, each
with homogeneous HFU of constant reservoir
parameters, we calculated the equations relating
FZI to the permeability and porosity using core
data. Finally, the permeability that was calculated
based on Equation 5 with mean values of FZI for
each HFU was highly correlated to the core origin
permeability (Table 2 and Figure 8).
The core porosity and permeability data from
the Z gas field were projected on the appropriate
GHEtemplateconstructedforeach HFU(Figure9).
It was observed that the data will fit in the
prediction processing model. In each HFU/GHE
pair, the close relationship between permeability
and porosity was established, and those equations
were used to calculate K from Φ. Figure 10 shows a
comparison between permeability from the core
data and permeability calculated from the 7 GHEs
correspondings to 7 FZIs on Table 1.
Clustering the core data
Hierarchical cluster analysis is also applied to
agglomerate and differentiate the data (Davis,
1973). Elements belonging together in the group
are as similar as possible, and groups are as
different as possible from others. Based on Ward’s
algorithm,thedatasetoftheFZIandHFUisdivided
into 6 clusters. The three dashed lines show the
possiblecutoffs forthe proposeddivisions into 8, 6,
4, and 3 groups. We decided to use six groups (the
red line in Figure 5.b).
Because mean FZI values are not calculated
from the probability plots or Ward’s HFU
classification algorithm, a plot of z vs RQI for each
HFU was constructed (Figure 6). The unit slope
lines were drawn for each HFU through their data
clusters according to the mean value of FZI
calculated for each HFU at the intercept with z =
1.ThemeanFZIvalues werethenusedtoconstruct
the porosity - permeability relationship within
each HFU using Equation 5. Figure 7 shows the
porosity-permeability cross-plot combined with
The GHE results gave approximately the same
numberof GHEs as theHFU. Itwas thereforeuseful
to compare the previous conventional approach
34
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
Figure 5. a) Normal probability plot of log(FZI) with division into 6 homogeneous groups of HFU with
constant FZI; b) Dendogram of the FZI set into six groups, according to the Ward’s algorithm.
10
1
HFU6
0.1
HFU5
HFU4
HFU3
HFU2
HFU1
0.01
0.01
0.1
1
PhiZ
Figure 6. z vs. RQI cross-plot of all the hydraulic units. The mean FZI values for each hydraulic unit are
given by the intercept of the straight lines at z =1.
Table 2. Simple statistics of permeability (K), porosity (Ф), FZI, and the determination coefficients (R2) for
the permeability, calculated from the 6 FZI_mean and 6 HFU.
R2
(k_FZI_mean
K (mD)
PHI (%)
FZI
Nr. of data
in HU
HUs
min
0.02
0.17
mean
0.72
9.15
max
2.82
min
0.07
mean
0.16
0.21
max
0.233
0.251
min
mean
0.283
0.734
max
vs. k_core
)
HU1
HU2
28
58
0.095
0.466
0.400
0.971
0.728
24.33
0.078
0.888
HU3
HU4
HU5
89
117
214
64
9.78
50.75
144.72
445.77
1458.96
120.04
358.55
1461.7
3631.1
0.15
0.203
0.189
0.229
0.24
0.257
0.26
0.292
0.315
0.32
0.997
1.733
2.587
4.555
1.379
2.10
3.51
5.85
1.687
2.563
4.512
8.833
0.645
0.743
0.603
40.470
79.79
HU6
All
430.07
0.27
0.306
0.411
0.97
(Figure 7) with the GHE approach (Figure 9) to
show that GHEs are a useful concept, and the
number of arbitrary GHEs on the template is
probably appropriate. In the future, GHEs appear
to provide an easy, rapid way of classifying core
data.
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
35
10000
1000
100
10
HU1
HU2
HU3
HU4
HU5
HU6
1
0.1
0.01
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Figure 10. Dispersion plot and correlation line
between the core permeability (K_core) vs. the
permeability calculated (K_GHE) from the 7 GHEs.
PHI [fraction]
Figure 7. Dispersion plot of Ф_core vs. K_core, and
the six HFU defined in the area of core origin data.
Conclusions
10000
1000
The hydraulic flow unit technique has been
developed and applied to identify the reservoir
characteristics.Thistechniquehasawidevarietyof
practical field applications to both cored and
uncored intervals/wells. In the study, the Z gas
reservoirs were classified into 6 HFUs based on
570 core plugs data by applying conventional
cluster analysis techniques as probability plot and
Ward’s algorithm. The calculated permeability
using the 6 HFUs classification shows very good
results. The determination coefficient R2 between
the calculated permeability with the HFU method
and the actual permeability measured on core
plugs was 0.97, indicates a nearly perfect
correlation.
Applying the GHEmethod, the Z gas reservoirs
can be divided into 7 distinct GHEs. Estimated
permeability using the GHE method has a slightly
smaller correlation coefficient than using the HFU
method, 0.96 compared with 0.97. However, the
GHE method is very useful for a reservoir with
limited core plugs data and very quickly to divide
reservoirs into HFUs. In fact, using this method, we
can reduce the amount of core data taken from the
reservoir and still provide acceptably accurate
results.
y = 1.33x0.95
R2 = 0.97
100
10
HU1
HU2
1
HU3
HU4
0.1
HU5
HU6
0.01
0.01
0.1
1
10
100
1000
10000
K_core [mD]
Figure 8. Dispersion plot and correlation line
between the core origin permeability (K_core) vs.
the permeability calculated (K_pre) from the mean
values of FZI for HFU.
Nomenclature (selected quantities)
Ф: Porosity.
Figure 9. Displaying permeability vs. porosity core
data on the background of 10 GHE shows that the Z
gas reservoirs can divide to 7 GHE (range from
GHE1 to GHE7).
Фe: Effective porosity.
Фz: Normalized porosity.
K: Permeability.
: Tortuosity.
36
Man Quang Ha and et al./Journal of Mining and Earth Sciences 62(3), 29 - 36
Sgr: Specific surface area per unit grain.
geology: John Wiley & Sons, INC.
RQI: Reservoir Quality Index.
FZI: Flow Zone Index.
GHE: Global Hydraulic Element.
HFU: Hydraulic Flow Unit.
Ebanks W. J., (1987). Flow unit concept -
integrated approach for engineering projects.
Abstract presented June 8, during the
roundtable sessions at the 1987 American
Association of Petroleum Geologists Annual
Convention.
Author contributions
The first author, Man Ha Quang, built up
conception, data analysis and draft the article. The
second author, Anh Le Ngoc contributed to the
methodology and Jadwiga Jarzyna author give a
critical review for the final version to be submitted.
Ebanks, W. J. Jr., Scheiling, M. H., Atkinson, C. D.,
(1992).
Flow
units
for
reservoir
characterization. In: D. Morton - Thompson,
A.M. Woods (Eds.), Development Geology
Reference Manual, Amer. Assoc. Petrol. Geol.
Methods in Exploration Series No. 10. 282 - 284.
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8 trang
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