ON THE EFFECT OF CAPILLARY FORCES ON PULSE DYNAMICS IN A POROUS MEDIUM

The study of elastic waves in porous media is of practical importance for the tasks of mineral prospecting, the use of porous screens for damping shock wave effects, studying the structure of the Earth's crust, etc. The elastic properties of a porous medium depend on the velocity of propagation of elastic waves, which, in turn, strongly depends on the degree of consolidation in the porous medium. The main acoustic feature of bulk sand (sand, glass balls, granular materials) media is the low speed of sound, about 100 m/s. Their compaction leads to a slight increase in velocity, and consolidation (sandstone, cementation with gas hydrate) leads to a multiple increase in the velocity of acoustic waves, about 2000-3000 m/s. In the process of hydraulic fracturing, water–gas exposure, treatment of porous formations with various acids to increase the bottom-hole zone of the formation, during the formation and decomposition of gas hydrates, the porous medium is saturated with a gas-liquid - bubble mixture. The morphology of the arrangement of bubbles and particles forming a porous skeleton can be different: the bubbles can be located in a liquid saturating the pores, cover several particles of the skeleton, or the liquid can be in the form of capillary water located in the form of a meniscus between two particles. To monitor the effectiveness of the above-described effects on porous media, acoustic sounding of porous media saturated with a gas-liquid mixture can be used. Therefore, the purpose of this work is to simulate the process of passing shock waves of small amplitude in sand saturated with liquid. The effect of the capillary coupling force on the dynamics of a shock wave pulse in a partially liquid–saturated porous medium is analyzed. A system of equations of mechanics of multiphase media is used for mathematical modeling, including the equation of conservation of mass for gas and solid phase, the equation of pulses and the equation of energy. The skeleton of a porous medium is assumed to be viscoelastic, the gas is calorically perfect; the forces of capillary adhesion between the grains of sand, the forces of viscous friction and the attached masses are taken into account. The control volume method is used for the numerical solution of the presented model.