www.elsevier.com/locate/petrol

Journal of Petroleum Science and E

Reservoir properties determination using fuzzy logic and neural

networks from well data in offshore Korea

Jong-Se Lim *

Division of Ocean Development Engineering, Korea Maritime University, Busan, 606-791, Republic of Korea

Accepted 20 May 2005

Abstract

Petroleum reservoir characterization is a process for quantitatively describing various reservoir properties in spatial variability

using all the available field data. Porosity and permeability are the two fundamental reservoir properties which relate to the amount

of fluid contained in a reservoir and its ability to flow. These properties have a significant impact on petroleum fields operations

and reservoir management. In un-cored intervals and well of heterogeneous formation, porosity and permeability estimation from

conventional well logs has a difficult and complex problem to solve by statistical methods. This paper suggests an intelligent

technique using fuzzy logic and neural network to determine reservoir properties from well logs. Fuzzy curve analysis based on

fuzzy logic is used for selecting the best related well logs with core porosity and permeability data. Neural network is used as a

nonlinear regression method to develop transformation between the selected well logs and core measurements. The technique is

demonstrated with an application to the well data in offshore Korea. The results show that the technique can make more accurate

and reliable reservoir properties estimation compared with conventional computing methods. This intelligent technique can be

utilized as a powerful tool for reservoir properties estimation from well logs in oil and natural gas development projects.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Reservoir properties; Porosity; Permeability; Fuzzy logic; Neural networks

1. Introduction

Reservoir characterization is a process of describing

various reservoir characteristics using all the available

data to provide reliable reservoir models for accurate

reservoir performance prediction. Reservoir character-

ization plays a crucial role in modern reservoir man-

agement. The reservoir characteristics include pore and

grin size distributions, permeability, porosity, facies

distribution, and depositional environment. The types

of data needed for describing the characteristics are core

0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.petrol.2005.05.005

* Fax: +82 51 404 3986.

E-mail address: jslim@mail.hhu.ac.kr.

data, well logs, well tests, production data and seismic

survey. Especially well log data can provide valuable

but indirect information about mineralogy, texture, sed-

imentary structures and fluid content of a reservoir.

Generally, well logs appear to be continuous informa-

tion with intensive vertical resolutions.

Reservoir porosity and permeability are the two

fundamental rock properties which relate to the amount

of fluid contained in a reservoir and its ability to flow

when subjected to applied pressure gradients. These

properties have a significant impact on petroleum fields

operations and reservoir management. In un-cored

intervals and well, the reservoir description and cha-

racterization methods utilizing well logs represent a

significant technical as well as economic advantage

ngineering 49 (2005) 182–192

Fig. 1. Conventional cross plot of data sets (a) A random data set

(0–1), and (b) A random data set plus a square root trend.

Fig. 2. Fuzzy curves generated from data sets (a) A random data set

(0–1), and (b) A random data set plus a square root trend.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192 183

because well logs can provide a continuous record over

the entire well where coring is impossible.

However, porosity and permeability estimation from

conventional well logs in heterogeneous formation has

a difficult and complex problem to solve by conven-

tional statistical methods. This paper suggests an intel-

ligent technique for reservoir characterization using

fuzzy logic and neural network to determine reservoir

properties from well logs. Simple cross-plotting each

input against the output may give an indication of the

quality of linear or multiple linear regression models

that could be formed. For more complicated relation-

ships found in many oil field problems, such simple

tools often do not provide adequate solutions. Fuzzy

ranking algorithm can be used to select inputs best

suited for predicting the desired output. Fuzzy curve

analysis based on fuzzy logics is used for selecting the

best related input (well logs) with output (core porosity

and permeability).

Parametric methods like statistical regression require

the assumption and satisfaction of multi-normal behav-

ior and linearity. Therefore, neural network as a non-

linear and non-parametric tool is becoming increasingly

popular in well log analysis. Neural network is a com-

puter model that attempts to mimic simple biological

learning processes and simulate specific functions of

human nervous system. Neural network can be used as

a nonlinear regression method to develop transforma-

tion between the selected well logs and core analysis

data.

2. Fuzzy curve analysis

A global prioritizing technique called fuzzy ranking

is used to select well logs to correlate with core mea-

surements. Fuzzy ranking is a tool to select variables

that are globally related. It also can be used to select

neural network inputs by filtering the noise in the

dataset. The significant inputs to the neural network

are identified using fuzzy curves that can identify rela-

tionships between an available parameter and variables

in noisy data sets (Weiss et al., 2001).

Consider a data pair (x, y) where x is the event and y

is the reactions. The problem is to predict y when x

changes slightly, in a neighborhood close to x. The

fuzzy membership function of (x, y) gives a local

prediction of y according to the information from

only (x, y). The fuzzification of the data is done with

Gaussian function. Fuzzy membership function is de-

fined as Eq. (1).

Fi xð Þ ¼ exp � xi � x

b

� �2� �d yi ð1Þ

Where b defines the shape of the fuzzy membership

curves and is about 10% of data set range. A fuzzy curve

function is used to rank noisy data. The fuzzy curve

function gives a global prediction y because it consists

Fig. 3. Schematic diagram of biological neuron.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192184

of the sum of the local predictions (fuzzy membership

functions). Fuzzy curve function is defined as Eq. (2).

FC xð Þ ¼

Xni¼1

Fi xð Þ

Xni¼1

Fi xð Þ=yi: ð2Þ

The two fuzzy curves resulting from defuzzification

of the fuzzified data in Fig. 1 are shown in Fig. 2 (Weiss

et al., 2001). As seen in Fig. 2, the random data set has

a no-slope dashed best-fit line while the random data set

plus the x0.5 trend has a best-fit line that has a range of

about 0.85. The range of fuzzy curves can be used to

Fig. 4. Block diagram of back propag

identify related variables in noisy data sets and rank the

input variables for further analysis. The selected well

logs then can serve as inputs to regression or neural

network to develop multivariate correlations with core

measurements.

3. Neural networks

Neural networks have been successfully used in a

variety of related petroleum engineering applications

such as reservoir characterization, optimal design of

stimulation treatments, and optimization of field opera-

tions (Mohaghegh, 2000; Tamhane et al., 2000).

The fundamental processing element of a neural

network is a neuron. Basically, a biological neuron

receives inputs from other sources, combines them in

some way, performs a generally nonlinear operation on

the result, and then outputs the result. A typical neuron

contains a cell body, dendrites, and an axon (Moha-

ghegh, 2000). Fig. 3 is a schematic diagram of a

biological neuron.

An artificial neural network is a computer model that

attempts to mimic simple biological learning processes

and simulate specific functions of natural neurons in

human nervous system. It learns from examples or

experiences, and is extremely useful in solving pattern

classification and mapping problem. The training or

learning phase is an essential starting point for use of

neural networks. This process requires training patterns

consisting of a number of input signals paired with target

signals. The inputs are presented to the network and the

corresponding outputs are calculated with the aim of

minimizing the model error, which is the total difference

between calculated outputs and target signals. The back

propagation algorithm utilizing the gradient descent

ation neural network algorithm.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192 185

method is the most commonly used method to reduce

model error. The training process creates a set of para-

meters that can be used for predicting property values in

situations where the actual output is unknown.

A typical back propagation neural network (BPNN)

contains three layers: input, hidden, and output layers.

Each layer is made of a number of processing elements

or neurons. Each neuron is connected to every neuron in

the preceding layer by a simple weighted link. Fig. 4

shows a schematic diagram of BPNN (Lim, 2003).

BPNN requires the use of training patterns, and involves

Fig. 5. Histogram and descriptive sta

a forward propagation step followed by a backward

propagation step. The forward propagation step sends

input signals through the neurons at each layer resulting

in an output value. BPNN uses the following mathemat-

ical function (Wong et al., 1997; Lim, 2003).

y ¼ f w0 þXn2j¼1

wjfj v0j þXn1i¼1

vijxi

!" #ð3Þ

Where y is the output variable, x is input variable, w and

v are the connection weights, n1 is the dimension of the

tistics for core measurements.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192186

input vector and n2 is the number of hidden neurons. The

backward propagation step calculates the error vector, E

by comparing the calculated outputs, y and the target

values, d. The gradient descent method is used to min-

imize the total error on patterns in the training set. In

gradient descent, connection weights are changed in

proportion to the negative of an error derivative with

respect to each weight.

Dwj ¼ � aBE

Bwj

¼ a � BE

Byf V NETð Þ

� �xj ¼ adyxj ð4Þ

Where a is a learning rate and d is an error signal. New

sets of connection weights are iteratively calculated

based on the error values until a minimum overall error

is obtained.

The connection weights are analyzed after training.

These weights relate to the average contributions of

each input log to the network (Wong et al., 1997):

Ci ¼

Xn2j¼1

jwijj

Xn1k¼1

Xn2j¼1

jwkjjð5Þ

Where Ci is the average contribution of input variable i,

wij is the connection weight from input neuron i to

hidden neuron j.

Fig. 6. Well log data of Well A,

This intelligent computing technique can help engi-

neers in solving problems which have not been solved

by traditional and conventional computing methods.

Neural networks do not require the specification of a

structural relationship between the inputs and outputs

unlike statistical regression analysis. Neural networks

are used as a nonlinear regression tool to develop

transformation between well logs and core analysis

data. Such a transformation can be used for estimating

porosity and permeability in un-cored intervals or wells.

Recent comparison studies have shown that BPNN

models may be more accurate than conventional meth-

ods and statistical regression for reservoir properties

estimation (Balan et al., 1995; Malki et al., 1996;

Soto et al., 1997).

4. Applications

The intelligent technique using fuzzy logic and

neural network is demonstrated with an application

to the well data of Well A, Block K in offshore

Korea. 13.25 m of core was recovered and 47 core

porosity and permeability values were measured in

this well. Fig. 5 shows the histogram and descriptive

statistics for core measurements. The following 8 con-

ventional well logs were considered for analysis: neu-

tron log (NPHI), sonic log (DT), gamma ray log

(GR), caliper log (CAL), laterolog deep (LLD), later-

olog shallow (LLS), density log (RHOB), and spon-

Block K in offshore Korea.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192 187

taneous potential log (SP). The well log data are

shown in Fig. 6.

The first step is to determine the strength of relation-

ships between the variables for selecting the best related

well logs with core porosity and permeability data. We

constructed the cross plots between well logs and core

measurements, but found weak correlation based on

correlation coefficients and visual observations (Figs.

7, 8). Next, fuzzy curve analysis based on fuzzy logic

was utilized to analysis correlations between the vari-

ables. Normalized data by the maximum–minimum

normalization equation were used for fuzzy curves

generation. Fig. 9 shows the fuzzy ranked porosity

and permeability curves for each well log. These

fuzzy curves could identify visual relationships be-

tween core measurements and well logs from noisy

data sets. Fuzzy curve analysis could help to select

Fig. 7. Scatter plots of core p

the best related well logs with core analysis data as

inputs for regressions and neural networks. The ranges

of fuzzy ranked curves were used as the ranking crite-

ria. The results of analyzing porosity and permeability

fuzzy curves are tabulated in Tables 1 and 2, respec-

tively. We selected six well logs (NPHI, CAL, LLD,

LLS, RHOB, and SP) for porosity estimation. NPHI,

DT, GR, LLD, RHOB, and SP were chosen for perme-

ability model.

For a comparative study, both multiple variable

regressions and neural networks were applied to the

selected well log data and the computed results were

compared with core measured porosity and perme-

ability. The neural networks were trained by a train-

ing set with six well logs and core analysis data.

Using the same data, we developed the porosity and

permeability models by multiple variable regressions.

orosity and well logs.

Fig. 8. Scatter plots of core permeability and well logs.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192188

The ability of a regression model to predict the

property extremes is enhanced through a weighting

scheme of the high and low values. But because of

this, the predictor can become unstable and also

statistically biased.

The contribution of each log for porosity model

is shown in Fig. 10. NPHI contributed the most to

the neural network, while LLD contributed the least

amount. Multiple regressions’ correlation coefficient

of porosity in Fig. 11 is 0.7640 while neural net-

work has a correlation coefficient of 0.9993. Fig. 12

presents the computed porosity and core porosity

versus depth. The regression model gives the best

results on the average while neural network provid-

ed more accurate results compared with multiple

regressions.

Fig. 13 shows the average contribution of each well

log data to neural network for permeability model. DT

was the most contributed log to the network. The

correlation coefficients for the permeability by regres-

sion and neural network models compared with mea-

sured core data were 0.5654 and 0.9998, respectively

(Fig. 14). Fig. 15 shows the estimated permeability and

core measured permeability versus depth. Multiple re-

gression under-estimates higher permeability values

while neural network shows better consistency in fol-

lowing the actual trend in permeability variation. It was

shown in these results that neural network performs

better than multiple regression method in estimating

reservoir porosity and permeability from well logs.

5. Conclusions

In this study, the intelligent technique is used to

estimate reservoir porosity and permeability from con-

ventional well logs. Fuzzy curve analysis based on

fuzzy logic can be used for selecting the best related

parameters with reservoir properties. Excellent correla-

Fig. 9. Fuzzy ranked porosity and permeability curves for well logs.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192 189

tion coefficients have been obtained for porosity and

permeability using neural network models.

The techniques using fuzzy logic and neural network

can make more accurate and reliable reservoir proper-

Table 1

Result of fuzzy curve analysis for core porosity

Well logs Range of fuzzy

ranked porosity

Rank

Neutron log (NPHI) 0.698 4

Sonic log (DT) 0.203 8

Gamma ray log (GR) 0.286 7

Caliper log (CAL) 0.840 1

Laterolog deep (LLD) 0.812 3

Laterolog shallow (LLS) 0.825 2

Density log (RHOB) 0.529 5

Spontaneous potential log (SP) 0.436 6

ties estimation compared with conventional methods.

This intelligent technique can be utilized a powerful

tool for reservoir properties determination from well

logs in petroleum industry.

Table 2

Result of fuzzy curve analysis for core permeability

Well logs Range of fuzzy

ranked permeability

Rank

Neutron log (NPHI) 0.371 4

Sonic log (DT) 0.523 1

Gamma ray log (GR) 0.441 3

Caliper log (CAL) 0.221 8

Laterolog deep (LLD) 0.350 6

Laterolog shallow (LLS) 0.285 7

Density log (RHOB) 0.491 2

Spontaneous potential log (SP) 0.352 5

Fig. 11. Cross plots of core porosity and estimated porosity (a) by multiple regressions and (b) by neural network.

Fig. 10. Average contribution of each input well log data to neural network for porosity model.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192190

References

Balan, B., Mohaghegh, S., Ameri, S., 1995. State-of-the-art in per-

meability determination from well log data: Part 1. A comparative

study, model development. Proc. SPE Eastern Regional Confer-

ence & Exhibition Morgantown, West Virginia, 17–21 Sep. SPE

30978.

Lim, Jong-Se, 2003. Reservoir permeability determination using arti-

ficial neural network. J. Korean Soc. Geosyst. Eng. 40, 232–238.

Malki, H.A, Baldwin, J.L., Kwari, M.A., 1996. Estimating perme-

ability by use of neural networks in thinly bedded shaly gas sands.

SPE Comput. Appl. 8, 58–62 (April).

Mohaghegh, S., 2000. Virtual-intelligence applications in petroleum

engineering: Part I. Artificial neural networks. J. Pet. Technol. 52,

64–73 (Sep).

Soto, B.R., Ardila, J.F., Ferneynes, H., Bejarano, A., 1997. Use of

neural networks to predict the permeability and porosity of zone

bCQ of the Cantagallo field in Colombia. Proc. SPE Petroleum

Computer Conference Dallas, TX, 8–11 June. SPE 38134.

Tamhane, D., Wong, P.M., Aminzadeh, F., Nikravesh, M., 2000. Soft

computing for intelligent reservoir characterization. Proc. SPE

Asia Pacific Conference on Integrated Modeling for Asset Man-

agement, Japan, 25–26 April. SPE 59397.

Weiss, W.W., Weiss, J.W., Weber, J., 2001. Data mining at a regula-

tory agency to forecast waterflood recovery. Proc. SPE Rocky

Mountain Petroleum Technology Conference, Keystone, Color-

ado, 21–23 May. SPE 71057.

Wong, P.M., Henderson, D.J., Brooks, L.J., 1997. Reservoir perme-

ability determination from well log data using artificial neural

networks: an example from the Ravva field, offshore India. Proc.

SPE Asia Pacific Oil and Gas Conference, Kuala Lumpur, Malay-

sia, 14–16 April. SPE 38034.

Fig. 12. Estimated reservoir porosity from well logs (a) by multiple regressions and (b) by neural network.

Fig. 13. Average contribution of each input well log data to neural network for permeability model.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192 191

Fig. 15. Estimated reservoir permeability from well logs (a) by multiple regressions and (b) by neural network.

Fig. 14. Cross plots of core permeability and estimated permeability (a) by multiple regressions and (b) by neural network.

J.-S. Lim / Journal of Petroleum Science and Engineering 49 (2005) 182–192192