Prediction of Sulfate Scale Depositions in Oilfield Operations Using Arithmetic of LR Fuzzy Numbers

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.