Study on 3D Permeability Modelling of Carbonate Reservoir Based

on Flow Unit Classification

Li Wei

1,*

, Changlin Shi

Lanqing Liu

and Caihong Yang

CNOOC EnerTech-Drilling & Production Co. Unconventional Oil & Gas Technology Research Institute;

CNOOC Energy Technology & Services Limited.

Email: weili4@cnooc.com.cn

Keywords: Carbonate reservoir, flow units, FZI method, permeability model

Abstract: RQI (Rock Quality Index) and FZI (Flow Zone Index) have proved to be effective methods of dividing the

flow unit in the carbonate reservoir of the R oil field. The method utilizes the porosity and permeability of

the core rock samples to divide the flow unit. The field consists of six flow units, and they represent

different flow characteristics. The FZI can be accurately predicted by establishing a mathematical model of

the log curves where core is not available, and the FZI/DRT (Discrete Rock Type) model of the whole

reservoir is established by geostatistics method. With the DRT model and the porosity model, the

permeability model can be estimated by using the characteristics of each flow unit with unique porosity-

permeability relationship. The results show that the permeability model established by this method does not

require a perm multiplier, the difficulty of curve fitting is greatly reduced and the work efficiency is

improved in the numerical simulations.

1 INTRODUCTION

As an important parameter of oilfield development,

rock permeability is generally converted into a

continuous permeability curves through the

petrophysical parameter model. Permeability is not

only related to porosity but also to pore shape and

pore size distribution. The porosity and permeability

of single-porosity sandstone reservoirs generally

show a simple function change. The established 3D

model of permeability can be converted from 3D

model of porosity. In carbonate reservoirs, however,

this simple functional relationship is hardly valid

due to the properties of carbonate rocks and the

properties that are easily changed. The pore-perm

relationship from the core test is very complicated,

often with small change in porosity, and the

permeability changes by several orders of magnitude

or even the same porosity value corresponds to

different magnitudes of permeability. This

phenomenon does exist in the actual production of

carbonate reservoirs in R oil field in Indonesia, and

the permeability cannot be matched with the actual

output. Therefore, R oilfield needs some method to

establish a permeability model that can truly reflect

the geological conditions of the oilfield and reduce

the uncertainty in development. Based on this, the

authors put forward the application of porosity and

permeability of rock samples, using flow unit index

method to divide flow units, establishing

corresponding permeability model in each flow unit,

and achieving the purpose of improving

permeability model evaluation accuracy.

2 THE BASIC THEORY OF

FLOW UNITS

The concept of flow units was first proposed by

Hearn (1984). He defined a reservoir zone with

vertical and horizontal continuum with similar

permeability, porosity and bedding features as flow

units (

Hearn et al., 1984). After the study by different

experts and scholars, the flow unit has more and

deeper understanding. W. J. Banks et al. Consider

flow units to be further subdivided according to

changes in the physical and petrophysical properties

that affect the fluid flow in the rock (

Ebanks, 1987).

D.C. Barr et al. (1992) consider flow units as a rock

block with similar water features in a given

rock(

Barr and Altunbay, 1992). Yinan Qiu et al.

consider that the flow unit is a naturally occurring

Wei, L., Shi, C., Liu, L. and Yang, C.

Study on 3D Permeability Modelling of Carbonate Reservoir Based on Flow Unit Classiﬁcation.

In Proceedings of the International Workshop on Environment and Geoscience (IWEG 2018), pages 547-551

ISBN: 978-989-758-342-1

547

fluid flow channel due to the heterogeneity of the

reservoir, the baffle and the by-pass conditions (

Qiu

and Wang, 1996). Longxin Mu believes that the flow

unit is a reservoir unit that is consistent with

percolation characteristic due to boundary

constraints, discontinuous thin barrier layers, various

sedimentary micro-interfaces, small faults, and

permeability differences within an oil sands body

(

Mu et al., 1996).

The authors through a large number of literature

research believe that D.C.Barr’s definition on the

definition of flow unit is Archie's early extension of

the definition of rock type (

Archie, 1952). Archie

believed that similar rock types were deposited

under similar geological conditions and underwent

similar diagenetic processes to form a type of rock

with unique pore structure and wettability. The

theoretical basis of the method adopted in this paper

is D.C. Barr's definition of flow units.

The flow units have the following features

(

Amaefule and Altunbay, 1993; Gunte et al., 1997; Guo et

al., 2005

) 1)Each flow cell has similar depositional

conditions and diagenetic reformation environment;

2)Under the proper classification conditions, each

flow unit has a unique porosity-permeability curve,

a capillary pressure curve (J-function), and a set of

relative permeability curves; 3)If properly applied,

the flow cell can accurately estimate the

permeability of non-coring section and generate a

reliable initial water saturation curve; 4)Through the

permeability model and oil saturation model build

by the facies control of flow units ,the dynamic

characteristics and production status of the reservoir

can be truly simulated.

There are many ways to identify flow units

(

Varavur et al., 2005; Tan and Lian, 2013; Liu et al.,

2011

), pore throat structure parameter method, flow

zone index method (FZI/DRT), pore throat radius

method, comprehensive parameter method, outcrop

depositional interface analysis method, production

dynamic parameter method and cluster analysis

method. At present, the mainstream technology of

quantitative flow unit classification of carbonate

reservoirs is the flow zone index (FZI) method and

Winland'S R35 method. (

Wang et al., 2017; Chekani

and Kharrat 2009; Tillero, 2012; Shabaninejad and

Haghighi, 2011; Betancourt, 1997

)

3 FZI METHOD

FZI method include two petrophysical methods,

Rock Quality Index (RQI) and flow unit analysis.

The Rock Quality Index reflects the reservoir's

ability to store and seep. Flow unit indicators can be

inferred by the rock quality index, which reflects the

seepage abilities of different rock types under

current conditions, regardless of the rock deposition

in the formation. Porosity and permeability data

from core test were used to calculate the flow unit

according to the following formula (

Amaefule and

Altunbay, 1993

)

 = 0.0314





∅



(1)

In formula (1), K is permeability (md), ∅



effective porosity (%), RQI is rock quality index

(µm).

∅



=

∅



∅



 (2)

In formula (2), ∅



is a normalized porosity.

 =



∅



= 0.0314

∅



∅









∅



(3)

In equation (3), FZI is the flow zone index (µm).

FZI is a continuous variable, which is a

parameter that determines the pore structure by

combining structural and rock mineralogical and

pore throat features, and can accurately describe the

heterogeneous characteristics of the reservoir. We

can apply statistical rules to convert FZI to discrete

variables DRT,

 = 



2

(



)

+10.6



(4)

In equation (4), DRT is rock type. Equation (4) is

merely a simple tool to convert a continuous rock

type variable (FZI) into a discrete one (

Guo et al.,

2005

392 core samples from 7 wells in R oil field were

taken and flow units of the oilfield was calculated

according to the FZI method. Table 1 show the

results from one such well.

By calculating three parameters RQI, FZI and

DRT, the reservoir of R oil field can be classified

into 6 flow unit. This helps to build a relationship

chart of core porosity and permeability based on the

classification of FZI method (Figure 1).

Different colors represent different flow units,

and the relationship between core porosity and core

permeability becomes regular in each type of flow

unit, and each flow unit overlaps with each other to

a minimum. Fitting the functional relationship, the

porosity and permeability have a power function

relationship, the correlation is above 0.8 (Table 2).

IWEG 2018 - International Workshop on Environment and Geoscience

548

Table 1: FZI & DRT calculation results of well_01 in R

oil-field.

(feet)

Porosity

Permeability

(md)

RQI

(µm)

FZI

(µm)

DRT

3028 0.352 2.9 0.090 0.166 7

3013 0.248 1.4 0.075 0.226 8

3014 0.359 6.4 0.133 0.237 8

3021 0.347 5.7 0.127 0.239 8

3055 0.321 10 0.175 0.371 9

3012 0.304 16 0.228 0.522 9

3027 0.336 27 0.281 0.556 9

3047 0.306 31 0.316 0.717 10

3062 0.381 85 0.469 0.762 10

3052 0.321 57 0.418 0.885 10

3005 0.311 52 0.406 0.900 10

3037 0.346 94 0.518 0.978 11

3059 0.331 88 0.512 1.035 11

3046 0.286 81 0.528 1.319 11

Figure 1: The plot of permeability vs. porosity as

classified using FZI.

Table 2: The relationship of porosity and permeability in

DRT of R oil-field.

Flow Units Relationship formula Correlation

coefficient

DRT6 0.86

DRT7 0.921

DRT8 0.895

DRT9 0.941

DRT10 0.931

DRT11 0.812

Figure 2 is a photograph of six typical castings

thin sections, representing the rock mass of six

different flow units in the field. DRT11

development of holes, connected to each other to

form a fluid flow connectivity, so the permeability is

high. DRT10 development of large holes,

connectivity is better. The DRT6 is very dense, the

development of clay crystal micropores, porosity

and permeability are low, most of the fluid trapped

in the microporosity, it is difficult to form a good

seepage channel. DRT7-DRT9 followed by the

development of micro-mesoporous, mesoporous,

mesoporic-macroporous, structural features between

the DRT6-10.

(

)

DRT11

(

)

DRT10

(

)

DRT9

(

)

DRT8

(e) DRT7 (f) DRT6

Figure2: Typical thin section pictures of the six rock

types from the core wells.

The agreement between the two was very good

by comparing the experimental core permeability

with the permeability calculated by the FZI / DRT

method (Figure 3).

Figure 3: A comparison between core permeability and

calculated permeability based on FZI.

 =84.071 ∗ ∅

.

 =278.36 ∗ ∅

.

 =708.36 ∗ ∅

.

 =2443.9 ∗ ∅

.

 =9557 ∗ ∅

.

= 50.353 ∗ ∅

.

Study on 3D Permeability Modelling of Carbonate Reservoir Based on Flow Unit Classiﬁcation

549

Table 3: Coefficient statistics table.

a b c d e f g

ALL curve -0.16 0.37 0.17 1.17 0.95 -0.18 -0.88

NO DT curve -0.5 0.33 -0.05 1.07 0.79 0.22 0

NO SP curve -0.09 0 0.4 1.1 0.92 0.23 -1.41

NO RD curve 1.33 0.22 -0.33 0 0.38 -0.95 -1.44

4 PERMEABILITY MODEL

BASED ON FZI

4.1 Logging Calculation Method of FZI

Flow unit division is based on core data, and its

calculation method provides us with a more reliable

quantitative template, but the core data is limited

after all. How to apply it to a well or even the whole

field? Here we use the multiple linear regression

method to establish the relationship between log

data and FZI.

Several Well log curves that are sensitive to FZI

are selected. In this study, six log curves of

spontaneous potential(SP), natural gamma ray(GR),

resistivity(RD), neutron(NPHI), density(RHOB) and

acoustic(DT) were selected and normalized by using

the following formula:

 =

(

−

)

/( − )

(5)

In equation (5), Nx is the normalized value, X is

the logging curve value, Xmin is the minimum value

of the logging curve, and Xmax is the maximum

value of the logging curve.

Then use multivariate linear regression was used

to get the relationship between FZI and each curve,

the formula used being:

=+∗+∗+∗+∗

+∗+∗ (6)

where a=-0.16;b=0.37;c=0.17;d=1.17;e=0.95;f=-

0.18;g=-0.89

Since not all wells have these six well logs, the

regression equation is also considered with five

curves to calculate the FZI value, the results are

shown in Table 3

Using formula (6), the FZI curve for all non-

coring wells can be calculated.

4.2 Calculation of Permeability Model

The FZI curve is scaled up and the FZI model is

built by Sequential Gaussian Simulation conditioned

to the porosity model (Figure 4). The FZI model is

an interpolation model with continuous variables. In

order to characterize different flow units more

clearly, the FZI model is transformed into the DRT

model (Figure 5) using formula (4). The DRT model

is a discrete volume. The data type is similar to

sedimentary facies or lithofacies. According to the

characteristics of the flow cell, under the proper

classification conditions, each flow cell has a unique

pore-perm curve. Therefore, under the constraint of

the flow cell (under DRT model control),

permeability value for each DRT can be calculated

to get the permeability model (Figure 6).

The permeability model established in this way

can more accurately reflect the geological conditions

of the reservoir. In the numerical simulation, it can

reduce the inconsistent dynamic characteristics and

static characteristics and improve the working

efficiency of the numerical simulation. The RQI /

FZI method facilitates the study of permeability of

carbonate reservoirs.

ure 4: FZI modellin

ure 5: DRT modellin

IWEG 2018 - International Workshop on Environment and Geoscience

550

Figure 6: Permeability modelling.

5 CONCLUSIONS

The FZI / DRT method was used to study the flow

units of carbonate reservoir in R oil field. According

to the experimental results of core porosity and

permeability, the reservoir was divided into six

different flow units by empirical formula.

As each flow unit has a distinct structure and

percolation characteristics, the flow unit can be used

as a property to build the 3D model and the

permeability model can be built under the flow unit

constraints. This method can be used to accurately

describe the spatial characteristics of permeability in

a carbonate reservoir.

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Study on 3D Permeability Modelling of Carbonate Reservoir Based on Flow Unit Classiﬁcation

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