1. 72nd
EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
Permeability Estimation Using Hydraulic Flow Units
Mehri M., MSc Petroleum-Exploration Engineering, University of Tehran
Memarian H., Professor of Geo-Engineering, University of Tehran
Summary
Permeability is a key factor for reservoir characterization and reservoir modeling, various methods
exist for estimation of this critical parameter, most of them concentrate on petrophysical properties
and ignore geological and flow characters. This paper focuses on the theory and application of method
based on the concept of hydraulic flow units with the aim of a better zonation and understanding of
hydrocarbon reservoirs. First, flow zone indicator and reservoir quality index have been determined
from core measurements. Then using graphical and clustering methods, the number of HFU
(hydraulic flow units) was obtained and corresponding permeabilities were estimated. For uncored
wells or drilled intervals, a backpropagation neural network was used to predict FZI and HFU. By
determining FZI, it's possible to estimate permeability. Comparing of this method with traditional
ones shows the privilege of this zoning for a better understanding of reservoir properties.
Key words: Permeability, Reservoir Characterization, Hydraulic Flow Units, Flow Zone Indicator, Neural
Network.

2. 72nd
EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
Introduction
Since permeability is a critical parameter in reservoir characterization, this study focuses on
permeability estimation, using the concept of hydraulic flow units.
Permeability data can be obtained from well tests, cores or well logs. Among them using well logs is
the cheapest estimation method.
Due to the wide range of depositional environments and diagenetic processes in development of
carbonate reservoirs, their characterizations have always been a challenging procedure.
Most existing procedures for reservoir zonation concentrate on petrophysical characters, and ignore
other parameters, such as geological properties, that control reservoir characters.
In this paper we have calculated flow zone indicator and reservoir quality index from cores, using
concept of hydraulic flow units. Using graphical and clustering methods, we have also estimated the
number of hydraulic flow units which control the studied reservoir flow properties.
Method and/or Theory
Concept of HU: A Hydraulic Unit is defined as the volume of the total reservoir rock within which
geological and petrophysical properties, which affect fluid flow, are internally consistent. Hydraulic
units are related to geological facies but not necessarily coincide with facies boundaries; therefore,
they may not be vertically continuous. They are controlled by pore geometry, which is a function of
mineralogy and texture.
Amafule et.al (1993) presented a method, using modified Kozeny-Carmen equation and the concept
of mean hydraulic radius ( mhr ). By invoking the concept of mhr , Kozeny-Carmen considered the
reservoir rock is composed of a bundle of capillary tubes. They applied Poisseuilles’s and Darcy’s
Laws to get a relationship between porosity and permeability. The generalized form of Kozeny-
Carmen relationship is given by Eq.1:
( ) 







−
= 222
3
1
1 gvse
e
SF
k
τϕ
ϕ
(1)
Where sF is the shape factor. The term 2
τsF is called Kozeny constant which can vary from 5 to 100
in real rock reservoirs. Various investigators try to calculate the exact value of this constant, which is
not an easy task. So Kozeny-Carmen divided the both sides of Eq.1 by porosity eϕ and took the
square root of both sides, the result is:
( ) 







−
=
gvse
e
e SF
k
τϕ
ϕ
ϕ
1
1
(2)
Where k is in 2
mµ .
By changing the dimension of permeability to milidarcy, we have:
RQI ( mµ ) =Reservoir Quality Index = 0.0314
e
k
ϕ
(3)
zϕ is defined as the pore volume-to-grain volume ratio:






−
=
e
e
z
ϕ
ϕ
ϕ
1
(4)

3. 72nd
EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
FZI ( mµ ) =Flow Zone Indicator =
zgvs
RQI
SF ϕτ
=
1
(5)
Substituting these variables into Eq.2 and taking logarithm of both sides:
FZIRQI z logloglog += ϕ (6)
On a log-log plot of RQI versus zϕ , all samples with similar FZI values will lie on a straight line with
unit slope. Samples with different FZI values will lie on other parallel lines. The values of FZI for
each HFU can be obtained from the intercept of each line at 1=zϕ . Samples that lie on the same
straight lines have similar pore throat attributes and represent a hydraulic unit. Permeability can be
estimated in each HFU as follows:
( )
( )2
3
2
1
1014
e
e
FZIk
ϕ
ϕ
−
= (7)
Identifying the number of HFU: There are two approaches for determining the number of HFU,
graphical methods and clustering methods. Graphical methods are composed of histogram analysis
and probability plot, while different clustering methods, such as K-means, hierarchical, exist that can
work with various algorithms, such as Ward’s, nearest and furthest neighbour linkage and average
linkage.
Example
Data from a carbonate reservoir in southwest of Iran was used to test the procedure. We used most
methods for getting the optimum number of HFU in the studied reservoir. In figure 1, 4 HFU are
considered for the studied reservoir. In figure 2, there are 3 HFU based on probability plot of log FZI:
Figure 2: number of HFU based on probability plot
Figure 1: number of HFU based on histogram analysis

4. 72nd
EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
For this study K-means and hierarchical clustering were used. In figure 3, the average silhouette, that
is a good parameter for determining the correct number of clusters, for 6 HFU is 0.5026. If numbers
of clusters determine correctly, the average silhouette should be close to 1. So we used hierarchical
clustering to find out the optimum number of clusters, which is 6. Using different linkage algorithms
and computing various distance functions and determining cophenet parameter, that’s for comparing
all the methods used, the best value was 0.946, and belonged to average linkage and Euclidean
distance. In figure 4, dendrogram of log FZI is plotted, the best phenon line is where we have 6
clusters.
After obtaining the correct numbers of HFU, we estimated permeability for each HFU. Figure 5
shows the good correlation ( 803.02
=R ) exists between core and estimated HFU permeability. If we
compare this result with estimated permeability from porosity-log permeability regression line
(traditional method) shown in figure 6, it’s obvious permeability isn’t only the function of porosity,
and other factors, such as geological and flow properties, should be considered.
Figure 4: dendrogram of log FZI
Figure 5: core versus HFU permeability
for the studied reservoir
Figure 6: Traditional versus HFU permeability
for the studied reservoir
Figure 3: silhouette values for 6 HFU

5. 72nd
EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
A backpropagation 4 layers neural network composed of 7 and 5 neurons in layer 1 and 2, 1 neuron
for the last and output layer was used in this research. We used NPHI, RHOB, DT, LLD, SGR, CGR
well logs, which had the highest correlation with FZI, as input for the model. The correlation
coefficient between the output of the model and the target is 0.8176. Predicted FZI follows target FZI
very well (Figure 7).
Conclusions
1. Applying this method to the studied reservoir showed traditional method for permeability
estimation (porosity-log permeability regression) isn’t a precise method as it’s shown in figure
6, but reservoir zoning based on the concept of HFU, that considers geological and flow
properties, and permeability prediction in these zones showed high regression coefficient with
core permeabilities.
2. Combination of this method and a nonlinear method showed prediction of FZI and permeability
in uncored well is an accurate method.
References
1. Amaefule O., Altunbay M., Tiab D., Kersey G. and Keelan K., “Enhanced Reservoir Description: Using Core and
Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells”, SPE 26436,
1993.
2. Orodu O. D., Tang Z. and Fei Q., “Hydraulic (Flow) Unit Determination and Permeability Prediction: A Case Study
of Block Shen-95, Liaohe Oilfield, North-East China”, Journal of Applied Science, 2009.
3. Deghirmandjianan O., “Identification and Characterization of Hydraulic Flow Units in the San Juan Formation,
Orocual Field, Venezuela”, Submitted to the Office of Graduate Studies of Texas A&M University, 2001.
Figure 7: correlation between predicted and target FZI in the studied reservoir