UNSTEADY PRESSURE FIELD IN A POROUS BED WITH A WEAKLY COMPRESSIBLE FRAMEWORK IN NONLINEAR RADIAL FILTRATION OF FLUID IN IT

Consideration has been given to a nonlinear problem of a fi ltration pressure fi eld in a porous bed operated in a specifi ed depression regime with a one-dimensional radial fl ow of a compressible medium in it. Solutions have been obtained of a problem for the zeroth and the fi rst expansion coeffi cients of a nonlinear fi ltration pressure fi eld, which represent the main and the fi rst asymptotic approximations describing high-amplitude pressure fi elds in oil and gas beds with a weakly compressible framework. The development of the asymptotic method as applied to the problem under consideration has led to the creation of a new method of constructing analytical expressions for expansion coeffi cients, which coincides with the method of succession of steady states in solving the problem for the leading approximation. Based on a computational experiment, it has been shown that the pressure fi eld in a porous bed with a weakly compressible framework is most accurately described using the method of succession of steady states, according to which pressure disturbances in the bed are absent at short times. It has been established that with increase in the distance from the well axis the disturbance delay time increases, and the velocity of the buildup of perturbations, caused by the operation of the well in a constant depression mode, decreases.
Consideration has been given to a nonlinear problem of a fi ltration pressure fi eld in a porous bed operated in a specifi ed depression regime with a one-dimensional radial fl ow of a compressible medium in it. Solutions have been obtained of a problem for the zeroth and the fi rst expansion coeffi cients of a nonlinear fi ltration pressure fi eld, which represent the main and the fi rst asymptotic approximations describing high-amplitude pressure fi elds in oil and gas beds with a weakly compressible framework. The development of the asymptotic method as applied to the problem under consideration has led to the creation of a new method of constructing analytical expressions for expansion coeffi cients, which coincides with the method of succession of steady states in solving the problem for the leading approximation. Based on a computational experiment, it has been shown that the pressure fi eld in a porous bed with a weakly compressible framework is most accurately described using the method of succession of steady states, according to which pressure disturbances in the bed are absent at short times. It has been established that with increase in the distance from the well axis the disturbance delay time increases, and the velocity of the buildup of perturbations, caused by the operation of the well in a constant depression mode, decreases.
Author:  A. I. Filippov, M. A. Zelenova, O. V. Akhmetova
Keywords:  fi ltration, nonlinearity, asymptotic method, steady state, quasi-stationary state, piezoconductivity equation.
Page:  895-905