CLEANING THE BOTTOMHOLE FORM ZONE USING ACOUSTIC WAVES

Abstract

The problem of acoustic heating of a porous medium is considered. When constructing a mathematical model, classical laws and equations were used. The law of conservation of the mass of a liquid is written for the case of the absence of sources of mass. The equation of motion is written for the case of non-stationary fluid filtration.This equation takes into account the effect of the volume friction force. The system of equations is closed using the equation of state of a liquid in a porous medium. For the boundary x equal to zero, the condition for the presence of a source of harmonic pressure waves is written, i.e. the pressure at this boundary varies according to the cosine law. Three cases are considered for the right boundary: a) the porous medium is semi-infinite, i.e. its length is much greater than the characteristic depthof penetration of acoustic waves; b) the porous medium has a finite width equal to l and the boundary at is imper- meable x l ; c) the porous medium has a finite width equal to l and the boundary at is highly permeable x l . The solution of the system of equations is sought in the form of traveling waves. Analytical solutions for pressure and filtration rate are obtained. The complex wave number is found. The volumetric heat source in a porous medium was obtained taking into account the volumetric friction force in the relative motion of the phases (liquid relative to the skeleton). It is believed that dissipation of the energy of the acoustic field occurs due to friction. The power of the dissipated energy of the acoustic field per unit volume of the porous medium is equal to the power of the bulk friction force, i.e. the product of the friction force and the true velocity of the fluid. To solve the temperature problem, the heat conduction equation with a volumetric heat source is written. When calculating the temperature of a porous medium, the average heat influx per unit volume of the porous medium over the oscillation period is used. Analytical formulas are obtained for calculating the average value of the power of the acoustic pressure forces over the oscillation period for all boundary conditions considered in the work. A numerical study of the resulting system of equations is carried out. The dependences of the acoustic field power on the circular frequency are constructed for the values of the parameters of the acoustic field, liquid, and porous medium. It is shown that as the permeability of the porous medium decreases by an order of magnitude, the power of the acoustic field also decreases by an order of magnitude. The research results can be used to determine the optimal methods and modes of impact on the bottomhole zone by the acoustic field.