Use of the cluster analysis and artificial neural network technology for log data interpretation Текст научной статьи по специальности «Медицинские технологии»

Journal of Siberian Federal University. Engineering & Technologies 4 (2011 4) 453-462

УДК 550.832

Use of the Cluster Analysis

and Artificial Neural Network Technology

for Log Data Interpretation

Anatoly V. Chashkov", Valery M. Kiselevb*

a OJSC Verkhnechonskneftegaz, 2955 B Baikalskaya St., Irkutsk, 664050 Russia b Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041 Russia 1

Received 5.08 .2011, received in re-vised form 12.08.2011, accepted 19.08.2011

Methods of the cluster analysis and artificial neural networks implemented in Schlumberger Techlog softwere modules were used for proceseing (end interpretation of data on 'wells from the Verkhnechonskoe Oil and Gas Condensate Field. It was demonstrated that clusterization of data allows for significant improiement in reliabilityand accuracy off lithotype determinations as well as porosity and permeability of rocks.

Keywords: ctuster anafydis, artificial neural networks, well logging, lithotypes, porosity, permeabilify.

Introduction

The following ¡assumptions shall be taken into account for justification and develop)ment of a technique foo well logging interpretation for reservoir delineation, assessment of saturation modf, and detevmination of reservoir properties. Firstly, fhf developed technique shall allow for t;li(; completeness, self-dsscriptivenessi and quality of a srindgid logging suit;«; conducted in the present fiald. Secondly, is ss essentiol to know the reservoit model, i.e. tine type of the reservoir, its pore geometry, maierial composition, lhe structure of skeletal and cemanting paets, variation eange of the main reservoir properties, etc. (Dobaynin et al., 2004; Latytdeva et ail., 1986). Sueh Peng roe obrained its a result of the lab core analysis. On the bashs of these data mam petrophysical re lttions and boundary values of the seservoit properties are established fVendelshtein et al., 1978; Dobrynin et al., 2004).

Permeability index Kperm is one of the most important reservoit properties in productive formations. It can be detemuned eithea based on a coae analysis made in labooatocy conditions, or as

0 result; of well tests. If such techniques fail ho cover rhe depth of the productive stratum (ov horizon), then log data are used to determian thg porostty tadex Kpor. Functional relation Kperm = f(Kpor) is revealed leased on tide available lab core analysis data.

d Corresrending author E-mail address: kvm@akadem.ru

1 © Siberian Fidetal University. All rights reserved

When a productive horizon has complex and inhomogeneous geology, it is reasonable to start from splitting log and core data into main typical classes and establish petrophysical relations for each individual class (Itenberg et al., 1984; Lider et al., 1986). This task can only be solved using the cluster analysis methods (Pospelov, 1988).

One of productive terrigenous horizons of the Verkhnechonskoe Field in East Siberia was reviewed as a target of research. This geological object has a complex structure due to severe salinization and anhydritization of productive strata and presence of tectonic dislocations which split the geological structure in a large number of blocks. Moreover, there is a high degree of variability in the thickness of productive strata and presence of extensive areas of reservoir substitution with impermeable rocks. All this lead to a number of problems related to determination of the in-place permeability by using traditional methods of log and core data interpretation. Such problems can be basically solved by using cluster analysis technique.

1. Preparation & Processing of Data

Preparation and preliminary processing of log data were carried out in Schlumberger Techlog software for core and log data processing. Log data from one of the productive horizons of the Verkhnechonskoe Field were processed pointwise. Processing included the following stages:

- uploading of log data;

- correlation of curves and 'joining' them in isolation intervals when necessary;

- entering the data stratigraphic arrangements, directional survey data, core analysis data, and well test results in the Techlog data base;

- setting up the processing flow for the parameters of the estimated target (entering of interpretation algorithms, petrophysical relations, criteria, etc.);

- lithological heterogeneity of the cross-section;

- removal of reference values for normalization of acoustic logging (AL), gamma-ray logging (GR), neutron gamma-ray logging (NGL), bulk density logging (DL) and potassium concentration (P);

- identification of thickness value based on logging data (general, effective, and effective and oil and gas saturated);

- determination of porosity and permeability based on logging data;

- comparison of acquired results with coring data.

The data on more than 100 wells that penetrated one of the productive horizons of the Verkhnechonskoe Field were used in our investigation.

2. Classification of Rocks through Cluster Analysis

Cluster analysis is the process of splitting certain sample objects into subsets called clusters in such a way that each cluster would consist of similar objects, whereas objects from different clusters would be considerably different. The task of making clusters pertains to statistic data processing (Pospelov, 1988; Jain Anil et al., 1996). Regardless of the object under study, application of cluster analysis implies the stages as follow (Kohonen, 1982):

- selection of samples for clusterization;

- determination of range of variables that will be used for evaluation of sample objects;

- calculation of values of certain similarity between the objects;

- splitting of tho sample to a certain number of clusters;

- verification of clusterization results.

A sample set of around 104 points in 5D space with coordinates associated with AL, GR, NGL, DL, and P was selected for study.

Requirements to input dfta for cluster analysis were confolidated in (Pospelov, r988; Parsaye, 1998). First, input daPa must be non-dimensional and have no runouts. It can be easily achieved through preliminary simplo processing of input data. Second, sats of input data must be uncofrelated and their distribution must comply with normal distribution law at least approximately. Checking if the data meet these requirements has to be dona in practice.

Cluster annlysis method is effective enough, since being an analytical method it has no subjective judgement associated with visual analysis of graphia objects (Pospelov, 199888; Parsaye, 19998; Jain Anil et al. , 19996»; Kohonen, 1982). Dozens of varioud dusterization algorithms have been proposed lately, but all of them produce almost identical results. Hence, there is no basis for favouring certain method (Herrick et al., 1998; Naeenr et al., 2010;Nashawi et al., 2010; Rezazadeh et al., 2010).

In the present study, c.asres of oocks were identified using rhe so-called «method of K-average» (Pospelov, 198888) whicf wns implemented in Ipsom module o. Tachlog srftware for core and log data processing. Algorithm al" fhis mstha d implies splitting of a set of elements in -vrec;t<tr spac e into a pre-defermined number K of clusters so that variability inside clusters can be minimized and distance between clusteas can be maximiaed.

An the firsf stage of algooiidm, earls element xi of a set is assigned random probability PiJ, which shows that this element belonrs to j cluster (j = 1,2, .K). At the second stage, centres of mass for each cluster are calculated, 1

i

where Q - factor that enhances scores of points foundnear the centres of mass. For our calculations we accepted Q = 1,2. Then, re-calculation of probability was conducted from equation

i

where Pnm probabiHty of the fact that element xn belongs to cluster number m,

rim = l|Xi - Ml. tim = IK - Ml .

If calculated probabilities do not coincide with the ptevious ones, they are used for identification of new centres of mass until this ioerative prf cest provides convergence.

This algorithm usfs the numbet of clusters as an input parametsr. In order to determine the optimum number of clnsters, it ir required to use the information which is prior to the input data. In our case input data were represented by vecters with coordinates that correspond to adjurted results of AL, GR, NGL, DL find P. Prior information was reptesented by teven lithotypes identified upon core Sests fot 4 weflr of the Vatkhnechonskoe Field with 100 % core recovery yn the interval of horizon under study. In 2009-e010, Specialiets ot Deoertment for Core and Formation Fluid Storage and Study of Tyumen Oil Research Institute conducted detailed settmentological cores studies wife tdentification of tocks that tave simitar petrophysicai parameters.

(fit OS 0.? M 9.f (j.J

03 a.l oj o

i

r

5 1 9 II 15

Number of cluste rs

Fig. 1 Error of lithotypes prediction depending on the number of clusters

.M.M.M."

1? 11 li

There were determined normalized errors of lithotype forecast based on log data for various numbers of clusters. The result is shown in Figure 1 that makes it obvious that when number of clusters exceeds 19, forecast error does not decrease significantly. Using less than 19 clusters may result in insufficient compartmentalization of a section for log data versus core data, cases when the number of clusters exceeds 19 are likely to account technical logging features rather than geological and geophysical properties of formation.

3. Result of Cluster Analysis and Application of Neural Network

In other wells of the Verkhnechonskoe Field that were drilled with core extraction but without sedimentological analysis, splitting rocks into clusters based on log data was conducted using Artificial Neural Network Unit. During the study neural network can identify complex relationships between input data and output data as well as can make synthesis. It means that in case of successful training, network can generate correct result on the basis of the data that were missing in the training sample as well as incomplete and/or noisy, partially corrupted data (Herrick et al., 1998; Naeeni et al., 2010; Nashawi et al., 2010; Rezazadeh et al., 2010).

For training and using Artificial Neural Network Unit for clusterization on the basis of logging data, there was used module «K.mod» of Techlog software. Core and log data from four wells that were studied in detail were taken as a training sample. Results of clusterization and core lithology are provided in Fig. 1.

After splitting the wells' sections into clusters based on log data, the data were aligned with available lab test core data, well sampling data, and with log data. All of that allowed assigning certain clusters to reservoir or non-reservoir and describing clusters in terms of argillite, salt, and gravelite content. Finally, 19 clusters formed seven groups associated with seven lithotypes (Table 2). Groups 1-5 fall into the category of reservoir, while Groups 6-7 are non-reservoir category.

4. Determination of a Porosity Index

The main logging method for determination of the terrigenous deposits porosity is the acoustic logging that was carried out almost in all drilled wells in the field. By the AL results the interval time is determined At, the function of which is the porosity index Kpor. Following the results of the AL data

Table 1. Description of lithological types of rock and corresponding to them geophysical characteristics by the result of the cluster analysis. AJal, AJgrl, AJp, AJngl, AJdl - normalized readings of acoustic log, gamma-ray log, potassium concentration, neutron gamma-ray log and bulk density log respectively.

Cluster number

10 11 12

13

14

15

16

17

18 19

AJa

i A

AJa

AJn

AJd

11*,..! i. i.

.1 I 1

iL ,,.i

i i,

X

1

A.

I 1 i. 1

i I 1, l i i 1 i L 1 I

J 4

X, k 1

i

ü

Jul I

I

J I.,..

ill

1 L

L

JL

III. „1

.1, [J

iIJ I i iLiikdhi i

L

JLk

Jl 111

Lithologe based on core

Completely saline coarsegrained sandstone

Saline coarse-grained sandstone

Moderately saline coarsegrained sandstone

Poorly saline coarse-grained sandstone

Mostly coarse-grained sandstone with good porosity &

permeability properties Coarse-grained sandstone with good porosity & permeability properties

Silty argillite

Mediom-grained sandstone with average porosity & permeability

properties Mediom-grained sandstone with good porosity & permeability properties Mediom-grained sandstone with good porosity & permeability properties

Siltstone

Siltstone to argillite, very fine

Fine-grained sandstone

Silty argillite, sandy in places

Argillite

Argillite with rare inclusions of gravel grains

Muddy gravelite

Gravelite reservoir

Saline gravelite

p

1

Table 2. (Cluster groups

S Group name Cluster number Core photo Mineral composition^ %

I Sandstones with good porosity & permeability properties 5, 6, 9, 10 quartz: 84; feldspar: 5; halite: 3; anhydrite: 2; calcite: 4; dolomite: 2; siderite: 0; clay: 0.

II Gravtlites (reservoir) 18 quartz: 71; feldsprr: 14; halite: 5; anhydrite: 3; calcite: 2; dolomite: 5; siderite: 0; clay: 0.

III Sandstones with average poro sity & permeability properties 8 quartz: 92; Oeldspar: 5; halrte: 0; anhydrite: 0; calciee: 2; dolomite: 1; sidarite: 0; clay: 0.

IV Sandstones "with poor porosity & permeability properties 13 quartz: 76; feldspar: 3; halite: 0; anhydrite: 2; calcite: 9; dolomite: 0; siderite: 1; clay: 9.

V Saline sandstones (reservoir) 3, 4 quartz: 74; feldsper: lh; halite: 3; anhydrite: 2; calcite: 3; dolomite: 5; siderite: 0; clay: 0.

VI Saline sandstones (nonreservoir) 1,2,19 quartz: 72; feldspar: id; halite: 11; anhydrite: 3; calcite: 1; dolomite: 3; sideoite: 0; clay : 0.

VII Argillites 7, 11, 12, 1^1, 1 5, 1(5, 11 quartz: 70; feldspar: 7; lialile: 0; anhydrite: 0; calciie: 2; dolomite: 1; siderite: ft; clay: 14.

processing, the acquired functional relations Kpor = f(At) for the reviewed cluster groups are presented in Table 3.

It is known that the open porosity values determined using the core samples, as well as the total porosity estimated by geophysical methods shall practically coincide for intergranular reservoirs (Vendelshtein et al., 1978; Latysheva et al., 1986). Fig. 2 gives the results of a comparison of porosity indexes determined by the acoustic logging data (KproAL) with the use of equations of Table 3, and by the results of measurements using the core (Kpro core) for wells of the Verkhnechonskoe field with more than 70 percent of core recovery. Correlation factor between the data of Kpro AL and Kpro core equals to 0.92.

Table 3. Determination of porosity index Kpro by the AL data for different reservoir groups

Group name Clusters number Dependence Kpro = f(At)

I. Sandstone:? with good porosity & permeability properties 5, 6, 9, 10 ^ 1320948 - 32264 • At + 311 • At2 - 1,3 • At3 + 0,002 • At4 por~ 1 +1261-At-9,8-At2+ 0,02-At3

II. Gravelites (reseovoir) 18

III. Sandstones with average porosity & permeability properties 8

IV. Sandstones with (oor porosity & permeability properties 13

V. Saline sandstonet (reservoir) 3, 4 55927 - 4341 • At + 101 • At2 - 0,7 • At3 + 0,001 • At4 k por 1 + 1124- At - 9,5- At2 + 0,02 • At3

25 20 15

I 10

10

15

Kpor AL, %

20

255

Fig. 2 Comparison of the porosity index measured using the core (Kpro core) with the porosity index determined by the AL (Kpro al)

5. Determination of a Permeability Index

The forecast of permeability as a function of porosity leads to considerable errors in its evaluation. This is explained by the fact that one value of porosity corresponds to the wide range of permeability change (up to 2 orders of magnitude) as the latter is controlled not only by the porosity, but above all by the perfection of the pore space structure (coarsening of grains of the skeleton, improvement of sorting and packing, increase of filtration channels radii, reduction of their tortuosity, etc.)

It is known that the splitting of relation Kperm = (Kpro) into individual lithological regressions leads to the considerable improvement of the permeability forecast Kperm. Therefore in our case for each of 5 selected lithotypes the individual regressions were established Kperm = (Kpro) that were used in future for forecasting the permeability as functions of porosity and reservoirs lithology (drawing

5

Table 4. Dependence of permeability index Kperm on porosity Kpro for different reservoir groups

Group name Clusters number Dependence Kperm = f(Kpro)

I. Sandstones with good porosity & permeability properties 5,6, e, 10 xz _ 11. K^'^ ^perm ^por

II. Gravelites (reservoir) C8 Kperm 0,25 • Kp0r

III. Sandstones with average porosity & permeability properties n it- _ 0 1^. K^'^ ^perm ivp0r

IV. Sandstones with poor porosity & permeability properties S3 IT- _ n nq , 1/2,07 ^perm f^por

V. Saline sandstones (reservoir)) 3,4 IT- _ 0 1? • ^perm f^por

loom

1000

100 -

10 -

0.1

aa a-aVT

10

15

20

25

30

Kpor, %

35

Fig. 3 Comparison ofporosity index and permeability index with splitting rocks into classes

3). Table 4 gives the obtained relations for various groups of reservoirs rocks. Fig. 3 demonstrates that permeabilities differing by 3 orders of magnitude correspond to the various lithotypes of the same porosity.

Conclusion

As a result of the conducted studies the following results were obtained:

- by means of the cluster analysis of materials of special core studies, five lithological classes of reservoirs were determined as well as the average values of petrophysical features corresponding to them;

- an algorithm of neural networks for identification of lithotypes on the basis of logging suite was adjusted; the expert evaluation and correction of adjustment results were conducted; the analysis of a reliability of lithological classes of rock prediction was done;

- the improved methodology for evaluation of the reservoir rock permeability as a function of their porosity and lithology was developed.

By virtue of the conducted target-oriented core analysis, we achieved a possibility to detect distinctive lithofacies categories visible not only in the space of porosity and permeability but as well characterized by the high degree of homogeneity in terms of their petrophysical features. The acquired lithological information may be successfully applied for populating geological models with data on porosity and permeability properties of the reservoir.

References

Vendelshtein, B.Yu. Geophysical Methods of Determination of Oil and Gas Reservoirs Parameters / B.Yu. Vendelshtein, R.A. Rezvanov - M.: Nedra. 1978. - 371 p. (In Russian)

Dobrynin, V.M. Petrophysics / V.M. Dobrynin, B.Yu. Vendelshtein, D.A. Kozhevnikov - M.: The Press of Russian State Oil and Gas University n.a. Gubkin. 2004. - 386 p. (In Russian)

Itenberg, S.S. Interpretation of the Complex Reservoirs Logging Results / S.S. Itenberg, G.A. Shnurman - M.: Nedra. 1984. - 256 p. (In Russian)

Latysheva, M.G. Reliability of Geophysical and Geological Information During Estimation of Oil and Gas Reserves / M.G. Latysheva, T.F. Dyakonova, V.P. Tsirulnikov. - M.: Nedra. 1986. - 121p. (In Russian)

Lider, M.R. Sedimentology. Processes and Products / M.R. Lider - M.: Mir. 1986.-439 p. (In Russian)

Pospelov, G.S. Artificial Intelligence: the Basis for the New Information Technology / G.S. Pospelov - M.: Nauka. 1988. (In Russian)

Herrick D.C. Facies prediction from core and log data using artificial neural network technology / D.C. Herrick, C.T. Kalkomey, L. Kapur, L.W. Lake // SPWLA 39th Annual Logging Symposium. -1998. - 11 p.

Jain Anil K. Leading to Artificial Neural Networks / K. Jain Anil, K.M. Mohiuddin, Mao Jianchang // Computer. - 1996. - V. 29. № 3. - P. 31-44.

Kohonen T. Self-organized formation oftopologically correct feature maps / T. Kohonen // Biological Cybernetics. - 1982. - № 43. - P. 59-69.

Naeeni M.N. Permeability Prediction of Un-cored Intervals Using New IMLR Method and Artificial Neural Networks: A Case Study of Bangestan Field, Iran / M.N. Naeeni, H. Zargari, R. Ashena, // SPE paper 140682-MS. Nigeria Annual International Conference and Exhibition, 31 July - 7 August 2010, Tinapa - Calabar, Nigeria.

Nashawi I.S. Permeability Prediction from Wireline Well Logs Using Fuzzy Logic and Discriminant Analysis / I.S. Nashawi, A. Malallah // SPE 133209-MS. - 2010. - 12 p.

Parsaye K. A Characterization of Data Mining Technologies and Processes / K. A. Parsaye // The Journal of Data Warehousing. - 1998. - № 1. - P. 41-63.

Rezazadeh M. Synergetic Use of Cluster Analysis and Artificial Intelligence Techniques to Improve Reservoir Upscaling / M. Rezazadeh, S.G. Choobary // SPE 130190-MS. - 2010. - 9 p.

Использование кластерного анализа и аппарата искусственных нейронных сетей при интерпретации данных геофизических исследований скважин

А.В. Чашкова*, В.М. Киселев6

а ОАО «Верхнечонскнефтегаз», Россия 664050, Иркутск, ул. Байкальская, 295б б Сибирский федеральный университет, Россия 660041, Красноярск, пр. Свободный, 79

Методы кластерного анализа и искусственных нейронных сетей, реализованные в модулях программного комплекса Techlog компании Schlumberger, использованы для обработки и интерпретации данных по скважинам одного из объектов Верхнечонского нефтегазового месторождения. Показано, что кластеризация данных позволяет заметно повысить надежность и достоверность определения литотипов, а также пористости и проницаемости пород.

Ключевые слова: кластерный анализ, искусственные нейронные сети, геофизические исследования скважин, литотипы, пористость, проницаемость.