Mathematical Models for Oil Production Optimization in Fuzzy Environments: Well Stock Forecasting and Regulation

Abstract

The relevance of this study is the importance of investigating mathematical models and systems to optimize oil production in forecasting and regulating well stock in fuzzy environments. The purpose was to assess the practical application of Markov chain models and fuzzy set theory to optimize oil production. This study specifically analyzed operating and idle well stocks in Kazakhstan's Kenkiyak oil field using a Markov chain system of equations. Fuzzy set theory was then applied to model linguistic relationships between oil production parameters like depth and porosity. The Markov model successfully predicted linear asymptotes of well stock over time and assessed impacts of changing repair crew productivity. The fuzzy approach effectively modeled the dependence of production efficiency on depth and reservoir rock porosity. Results showed a 15% improvement in forecasting accuracy and a 10% increase in production efficiency. This demonstrates the value of mathematical models in optimizing realworld oil production processes and their ability to enhance management system performance. The models provide oil field designers with tools to better regulate well stock and staff operations.