Abstract:
Lost circulation is frequent problem during the drilling of oil wells .That occurs when a considerable amount of pumped drilling fluid flows into the formation .This problem impairs safety ,efficient and economic viability process .for these reasons many previse study‟s were developed to understand problem and other to solve the problem in this work we applied mathematical model that takes into account rheological properties of the drilling fluid to estimate mud loss and maximum invasions radius in the fracture formation. To achieve the goals and ordinary differential equation we created but duo to complexity of equation it was resolved to diminution less equation and solve diminution less equation using 4 order Runge_ktta.the model incorporate three rheological models and allow analyzing fluid flow through fracture for constant width. Out puts of the models maximum volume and radius have been estimated sensitive analyses conducted to invested ,the effect of rheological properties ,and conceded that power law fluids are not suitable fluids in case of lost circulation
