Fuzzy Rule Base Model for Oil Wells Efficiency Estimation

Available online at www.sciencedirect.com

ScienceDirect Procedia Computer Science 102 (2016) 198 – 201

12th International Conference on Application of Fuzzy Systems and Soft Computing, ICAFS 2016, 29-30 August 2016, Vienna, Austria

Fuzzy rule base model for oil wells efficiency estimation Dj.I. Ramazanova*, A.J. Jabiyevab, V.X.Amirguliyevc b

a Baku Electric Distribution Grid, Bakikhanov str., 13, AZ 1065, Baku, Azerbaijan. Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan c CNCo.LTD Deputy, 9-th Akhmedli str., 28 Baku, Azerbaijan

Abstract In this paper a fuzzy expert system is used for determining amount of efficiency of the oil wells from energy consumption point of view. Knowledgebase is extracted from data by using Fuzzy C-means method based clustering. Knowledgebase is realized in environment Expert system shell ESPLAN. Experimental results have demonstrated efficiency of the proposed method and its advantages as compared to the existing classical methods. © The Authors. Published Elsevier B.V.access article under the CC BY-NC-ND license © 2016 2016 Published by Elsevier B.V.by This is an open (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility ofthe Organizing Committee of ICAFS 2016. Peer-review under responsibility of the Organizing Committee of ICAFS 2016

Keywords: Fuzzy expert system; fuzzy c-means clustering method; oil-water factor

1. Introduction In oil exploration, one challenging problem is estimation of efficiency of oil wells determined by set of criteria such as amount of mining oil, amount of water and energy consumption. In practice of oil exploration, working oil wells may be into two groups. In the first group, there are oil wells for which effectiveness obtained from mining oil is higher than energy consumption. In the second group, effectiveness getting from exploration is significantly lower than energy consumption. There is no problem with oil wells in the first group. But it is necessary to have economic investigation of oil wells included into the second group. The problem requires decision or to stop exploration ofthese oil wells or to involve additional capital for increasing of effectiveness of such type oil wells. It is obvious that this problem solving requires mathematical model of relationship between factors and affected efficiency of oil wells. Here difficulties arise related to high level of uncertainty in estimation of these factors.

* Corresponding author, Tel.: 012 4986539 E-mail address: [email protected]

1877-0509 © 2016 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICAFS 2016 doi:10.1016/j.procs.2016.09.389

Dj.I. Ramazanov et al. / Procedia Computer Science 102 (2016) 198 – 201

In this paper we investigate if-then rule based on the model described relationship between amount of mining oil, water amount and energy consumption as independent variables, and overall efficiency of oil wells taking into account fuzzy uncertainty of oil exploration environment. The paper is structured as follows. In Section II we give some preliminaries that will be used for modeling of oil wells efficiency. Section III includes statement of the problem, solving procedures and computer simulation. Section IV concludes. 2. Preliminaries Aliev’s Fuzzy Inference Method1,2. 1. 2. 3. 4. 5.

Advantages of the Aliev’s method is given below: It is intuitive. It has widespread acceptance. It is well suited to human input. Modeling under second-order uncertainty using the possibility-probability measure Computing with word The basic steps of the method are given below: 1. The truth degree of the rule is computed as:

rjk

Poss(vk / a jk ) ˜ cf k

Wj

min(rjk )

2. First the objects are evaluated, i.e. every w i object has appropriate linguistic value defined as (vi , cf i ) . where vi is linguistic value, c fk ]0,100] is confidence degree of the value vi . vk - linguistic value of the rule object, a jk -

current linguistic value (j is index of the rule, k is index of relation) value(for example , A_ir) 3. For each rule, calculate R j (min rjk ) * CF j / 100 , where CF is the confidence degree of the rule. j

4. The user or the creator of the rule defines the firing level ( S ), and R j t S is checked. If the condition holds true, then the consequent part of the rule is calculated. 5. The evaluated w i objects have Si value: wi , (vi1 , cf i1 ),....,..., (viSi , cf i Si ) Si is the number of the rules in fuzzy inference process 6. The average value is determined as follows: Si

n n ¦ vi ˜ cf i

vi

n 1 Si

¦ cf i

n

n 1

x x x x x x x x

Algorithm is realized by ESPLAN expert system shell. The shell of ESPLAN ensures : - creation of expert systems for various applications; - building module-oriented structures and segmentation of knowledge bases; - representation of fuzzy values; - compositional inference with possibility measures; - arithmetic operations with fuzzy numbers; - realization of simple question-ask dialogue by using special functions; - set of confidence degree for any rule (in per cent); - call of external programs;

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x - data interchange using file system. All above mentioned abilities are supported by ESPLAN knowledge representation language based on production rules. The inference engine of ESPLAN allows: x - forward-chaining width-first inference with truth degree calculation on the continuous scale [0,100]; x - set of a truth threshold during run-time in order to cut a rules with current truth degree less than the threshold; x - tracing inference to the screen; x - tracing inference to disk for further generation of the explanation; The shell of ESPLAN has own WORDSTAR compatible text editor. 3. Fuzzy c-means clustering method3 This algorithm works by assigning membership to each data point corresponding to each cluster center on the basisof distance between the cluster center and the data point. More the data is near to the cluster center more is its membership towards the particular cluster center. Clearly, summation of membership of each data point should be equal to one. After each iteration membership and cluster centers are updated according to the formula:

 ¦ (P ) x ,  ¦ (P ) n

Pij

1 § dij · ¦¨ ¸ k 1 © d ik ¹

(2 lm 1)

, Q ij

c

i 1 n

m

ij

i

j 1,2,...c

(1)

m

ij

i 1

where, 'n' is the number of data points,'vj' represents the jthcluster center, 'm' is the fuzziness index m  [1, f) .'c' represents the number of cluster center.'μij' represents the member-ship of ithdata tojthcluster center.'dij' represents the Euclidean distance between ithdataand jthcluster center. Main objective of fuzzy c-means algorithm is to minimize: J (U , V )

n

c

i 1

j 1

¦ ¦ (P

ij

) m xi Q j

2

where, '||xi– vj||' is the Euclidean distance betweenithdata and jthcluster center. Let X = {x1, x2, x3..., xn} be the set of data points and V = {v1, v2,v3..., vc} be the set of centers. 1. Randomly select ‘c’ cluster centres. 2. Calculate the fuzzy membership 'μij' using above mentioned formula. 3. Compute the fuzzy centres‘vj’ using (1). 4. Repeat step 2) and 3) until the minimum'J' value is achieved or ||U(k+1)- U(k)||<ȕ. where,‘k’ is the iteration step. ‘ȕ’ is the termination criterion between [0, 1]. ‘U = (μij)n*c’ is the fuzzy membership matrix.‘J’ is the objective function. 4. Statement of the problem, its solving and computer simulation

As it is mentioned in Section 1, the problem of estimation of oil well efficiency requires mathematical model describing relationship between independent variables mining oil amount, water and energy consumption and dependent variable efficiency of exploring oil wells. As this problem is characterized by high level of uncertainty, for this purpose we use fuzzy rule based approach. Antecedent variables in the model are oil amount, water amount, energy consumption and consequent variable of overall efficiency. Fuzzy rules in the rule based model are obtained by using Fuzzy C-means clustering approach described in Preliminaries of this paper. Here cluster number is equal to 14, so we have 14 fuzzy rules in rule base. Implementation of the model is performed by using expert system empty shell ESPLAN briefly described in Preliminaries. The shell of ESPLAN is represented to a user like the multi-window interface .

Dj.I. Ramazanov et al. / Procedia Computer Science 102 (2016) 198 – 201

Using ESPLAN shell we have performed experimental investigations. Two fragments of these experiments are shown below. The first test is the following. Test 1. IF CRUDE OIL is more than 200 and water is more than 250 and electric energy is more than 4000 THEN efficiency=? Answer :Expert system shell ESPLAN isdefined efficiency; it is approximately 450 AZN Truth degree=31% The first test is the following. Test 2. IF CRUDE OIL is about 200 and water is about 400 and electric energy is about 4000 THEN efficiency=? Answer :Expert system shell ESPLAN is defined efficiency; it is approximately 474 AZN, Truth degree=37% 5. Conclusion

For estimation of efficiency of an oil wells exploration, fuzzy rules base model is suggested. For implementation of the suggested model, expert system ESPLAN is used. Experimental investigations show the validity and applicability of the suggested model and reasoning system. References 1. Aliev RA, Fazlollahi B, Aliev RR. Soft Computing and Its Applications in Business and Economics. Springer Verlag; 2004. 2. Aliev RA, Aliev RR. Soft Computing and Its Application. London, New Jersey: World Scientific; 2001. 3. Bezdek JC. Pattern Recognition with Fuzzy Objective Function Algorithms. USA: Kluwer Academic Publishers Norwell, MA, 1981. 4. https://sites.google.com/site/dataclustering algorithms/fuzzy-c-means-clustering-algorithm

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