Link for citation: Nikitin V.I. Mathematical modeling of drilling fluid filter penetration into the bottom-hole of formation taking into account oil viscoplastic properties . Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 3, рр. 130-137. In Rus.

The relevance. The formulation of the problem of mathematical modeling of two-phase filtration in the approximations of the classical Darcy's law describes with insufficient accuracy the process of opening a productive formation containing oil exhibiting viscoplastic properties. Taking into account oil viscoplastic properties using a nonlinear filtration law will expand the scope of application of the methodology for calculating the saturation and depth of penetration of the drilling fluid filtrate into the formation for a larger amount of the fields in the Russian Federation. The practical significance of using mathematical modeling of the drilling-in process of a productive formation lies in the possibility of selecting the drilling fluid in order to preserve the porosity-reservoir properties of the reservoir rock and increase the further well production rate. The calculation of the penetration depth, among other things, makes it possible to assess the degree of decrease in the permeability of the reservoir during the initial opening. The main aim: development of a mathematical model of the drilling fluid filtrate interaction with viscoplastic oil in the pore space of the reservoir and its application to the selection of the drilling fluid of the reservoir rock. Methods. The mathematical formulation of the problem of drilling fluid filtrate penetration into a reservoir with viscoplastic oil is described by the theory of two-phase filtration. For the calculation, the modified Buckley–Leverett phase flow distribution function is used, in which the hyperbolic filtration law is applied to the displaced phase. Methods for measuring the input parameters of a mathematical model and their model analogs are described. A calculation criterion is used to select the drilling fluid. The calculation is performed using the Wolfram Language implemented in the Wolfram Mathematica package. Results. A mathematical model was developed for drilling fluid filtrate interaction with viscoplastic oil in the pore space of the formation. The computational technique of the numerical experiment was carried out to test the filtrates of five drilling fluids during their interaction with viscoplastic oil from the fields of the Samara region, Tatarstan and Bashkortostan. By applying the calculation criterion to the choice of drilling fluid, the choice of the most high-quality formulation for opening reservoirs with the presented reservoir fluid properties is substantiated.