Drilling fluids consist of several components with different physical and structural form which can be assumed as complex fluids. Optimum performance of drilling process could be obtained through the dynamic fluid computation which requires a reliable mathematical model capable to predict transient and steady state rheological behavior of drilling fluid. Generalized Newtonian formulations are the most popular models for drilling fluids due to their simplicity in spite of their inabilities to predict transient and elastic behavior of such fluids. In this paper, we have developed a mathematical model to predict transient and steady state rheological behavior of the complex fluids on the scale between the microscopic and macroscopic which is named mesoscopic scale. Constitutive and governing equations are obtained using the generalized bracket formalism which is based on the thermodynamics of flowing systems in that Hamiltonian mechanics has been used to describe the transport phenomena of internal microstructures. The model is developed for the suspension of bentonite/polymer dispersion and compared with experimental rheological data of different types of drilling fluids under transient and steady state condition. Comparison of model prediction with published data in the literature shows that the model is able to predict rheological behavior of bentonite muds satisfactorily.

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