Pressure field in the reservoir and well, taking into account the dynamic level during the selection and subsequent shutdown

Abstract

An analytical solution of the non-stationary filtration problem is presented, taking into account the change in the dynamic level of the fluid in the well during extraction with a variable flow rate, which made it possible to construct calculation formulas for the pressure field in the well when operating at a constant pump performance and subsequent shutdown. The problem contains the equation of piezoconductivity for non-stationary plane-radial filtration in a formation surrounded by an impermeable bottom and tire. It also includes an integro-differential condition connecting the pressure fields in the well and the reservoir, the condition of equality of pressures at the outlet from the reservoir to the well, the absence of disturbances at the initial time and in remote sections of the reservoir. When constructing an exact analytical solution of the problem in dimensionless variables, the Laplace — Carson integral transformation with respect to time was used. The originals of the solution are also obtained analytically and contain the Bessel functions of the zeroth and first orders. The general analytical solution for the pressure during extraction with a constant flow rate and subsequent shutdown is written using the Heaviside function. Based on the solution found, computational experiments were performed in which the reservoir parameters of the oil-saturated reservoir are varied, and pump stops are performed at various stages of well operation: relaxation, transitional and stabilization. It has been established that the main influence on the dynamics of the pressure field is exerted by the permeability of the reservoir. Reducing the displacement capacity of the reservoir by an order of magnitude leads to an increase in the amplitude of the pressure perturbation by 25-35%. However, the influence of this parameter does not exceed the contribution of permeability. The contribution of the reservoir porosity is less than 6% of the peak pressure values in the stabilization mode. The viscosity of the sampled fluid has a significant impact on the pressure field recorded in the well.