Mathematical model of drilling mud filtration in a porous medium taking into account dynamic changes in parameters

Purpose. The aim of the study is to develop a mathematical model of drilling mud filtration in a cellular medium, taking into account dynamic changes in its parameters and interaction with rocks. Methods. Analytical and numerical modeling methods were used to study filtration processes, including a system of differential equations, a modified Darcy's law, the continuity equation, and viscosity dependence on pressure. The numerical solution was implemented using the finite difference method, which effectively describes the dynamic filtration processes. The effects of time, temperature, and solid phase concentration on changes in the permeability of the porous medium were considered. Model verification was performed by comparing the obtained results with experimental data. Results. The proposed model accounts for nonlinear effects associated with changes in viscosity, permeability, and pressure gradient under real drilling conditions. An analysis was conducted on the impact of temperature, mechanical, and chemical clogging on the filtration process. The formation of a filter cake on the wellbore walls and its impact on drilling mud circulation losses were investigated. A numerical analysis of scenarios involving changes in drilling mud characteristics and their influence on drilling stability was carried out. Scientific novelty. A mathematical model of drilling mud filtration has been developed, incorporating nonlinear and non-stationary effects not previously considered in classical approaches. The model introduces permeability dependence on time and solid phase concentration, allowing for more accurate predictions of filter cake formation. For the first time, the interrelation between filtration rate and changes in the porous medium structure due to clogging has been examined. Practical significance. The proposed model can be used to optimize the parameters of the drilling fluid, which will reduce the risks of complications during drilling, such as circulation losses and leachate penetration into the productive layer. The obtained results can be applied in the design of drilling flushing systems and improvement of filtration control methods in the oil and gas industry.