CROSS FLOW IN THE WELL

Abstract

The article considers the problem of pressure fields in a system consisting of two perforated reservoirs penetrated by one well, providing a hydrodynamic connection between them. One-dimensional equations of piezoconductivity in radial geometry are used to describe the pressure fields in the reservoirs. The hydrodynamic connection between the layers through the well is given by an integro-differential equation obtained on the basis of mass balance and Darcy's law.It is assumed that there are no pressure disturbances at the initial moment of time and in the parts of the reservoirs remote from the well. At the boundaries between the well and the reservoirs for the time t>0, the conditions for equal pressures are set. Exact analytical solutions describing pressure fields in reservoirs and wells are constructed in the Laplace–Carson image space. Computational experiments for modeling pressure fields and flows were carried out using the Stehfestand den Iseger algorithms, which made it possible to eliminate the time-consuming procedure of transition to the original space. The joint use of these algorithms made it possible to increase the reliability and accuracy of the results of field calculations, since direct control based on analytical formulas in the originals is difficult. The purpose of computational experiments is to determine the conditions for the existence of interlayer cross flows and their temporal dynamics in the absence of production from the well. Calculations are made for the case when reservoir characteristics of reservoirs are the same. For definiteness, it is assumed that the reservoir, which occurs at a shallower depth, is high-pressure. It is shown that in the absence of production from the well, after some time, an equilibrium pressure that changes slightly with time is established in the wellbore, equal to the average hydrostatic pressure of the lower and upper reservoirs. At the same time, in the region of short times, the flow rate of each reservoir depends on the value of the initial hydrostatic pressure in the well, and in the region of long times, this pressure does not affect the dynamics of interlayer flows. It has been established that the total flow rate of reservoirs is equal to zero only for times longer than the relaxation time. It is noted that the pressure relaxation time in the well increases with a decrease in reservoir permeability.