IJE TRANSACTIONS B: Applications Vol. 19, No. 1 (December 2006) 99-106   

downloaded Downloaded: 107   viewed Viewed: 1812

M. Ranjbar*, R. Khatami and R. Younessi

Department of Mining Engineering, Shahid Bahonar University of Kerman
P.O Box 76175-133, Kerman, Iran
mranjbar@mail.uk.ac.ir - khatami@yradute.uk.ac.ir - younessi_min@yahoo.com

*Corresponding Author

( Received: November 16, 2005 – Accepted in Revised Form: April 05, 2006 )

Abstract    In this study fuzzy arithmetic is presented as a tool to tackle the prediction of the amount of barium, strontium and calcium sulfates scales in oilfield operations. Since the shape of fuzzy numbers’ membership functions is a spread representative of the whole possible values for a special model parameter, fuzzy numbers are able to consider the uncertainties in parameter determinations and thus give more real results than crisp values. Solubility product models and other required Equations for scale prediction contain uncertain parameters and therefore application of fuzzy numbers can be useful. LR fuzzy numbers and related primary arithmetical operations based on Zadeh's extension principle have been introduced and their use in predicting scale depositions has been investigated. Parameters such as solubility products, free sulfate concentration and scale mass have been determined as fuzzy numbers. As a case study, scale depositions of barium and strontium sulfate resulted from mixing two incompatible waters have been obtained and compared with none fuzzy approach. Fuzzy computations are able to predict the maximum scale mass with respect to existing information.


Keywords    Scale Prediction, Fuzzy Numbers, Sulfates, Uncertainty



1. Cowan, J. C. and Weintritt, D. J., “Water-formed scale deposits”, Gulf publishing company, Houston, Texas, (1976).

2. Yuan, M. D. and Todd, A. C., “Prediction of sulfate scaling tendency in oilfield operations”, SPE, (1991), Paper No. 18484, 63-72.

3. Kaufmann, A. and Gupta, M. M., “Introduction to fuzzy arithmetic”, Van Nostrand Reinhold, New York, (1991).

4. Zimmermann, H. J., “Fuzzy set theory and its applications”, Kluwer Academic Publisher, Dordrecht, 2nd Edition, (1991).

5. Zadeh, L. A., “Fuzzy sets”, Information and Control, Vol. 8, (1965), 338-353.

6. Dubios, D. and Prade, H., “Operations on fuzzy numbers”, International Journal of Systems and Science, Vol. 9, (1978), 613-626.

7. Vetter, O. J., Kandarpa, V. and Harouaka, A., “Prediction of scale problems due to injection of incompatible waters”, Journal of Petroleum Technology, (February, 1982), 273-284.

8. Oddo, J. E. and Tomson, M. B., “Why scale forms in oilfields and methods to predict it”, SPE, (1991), Paper No. 21710.

9. Atkinson, G., Raju, K. and Howell, R. D., “The thermodynamics of scale prediction”, SPE, (1991), Paper No. 210212, 20-22.

10. Atkinson, G. and Mecik, M., “The chemistry of scale prediction”, Journal of Petroleum Science and Engineering, Vol. 17, (1997), 113-121.

11. Tomson, M. B., Kan, A. T., Fu, G. and Al-Thubaiti, M., “Scale formation and prevention in the presence of hydrate inhibitors”, SPE, Vol. 11, No. 2, (2003), Paper No. 80255, 248-258.

12. Nguyen, H. T. and Walker, E. A., “A first course in fuzzy logic”, Chapman and Hall/CRC, 2nd Edition,(1999).


International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir