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HYDRODYNAMICS AND ACOUSTICS
2021 ◊ Volume 2 (92) ◊ Issue 1 ◊ p. 41-67
V. L. Polyakov*
* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine
Calculation of a well in compressible fractured porous medium
Gidrodin. akust. 2021, 2(1):41-67
TEXT LANGUAGE: Russian
ABSTRACT
Fractured rocks formed in tectonic processes often contain a useful fluid in their matrix. The system of cracks that serves for its transport ensures the productive operation of wells. High pressures in deep reservoirs cause the expansion of cracks which, with intensive fluid pumping, can not only shrink but even close. As a result, the permeability of the rock decreases sharply, and the flow rate in the drain drops. Therefore, mathematical modeling of the action of a single well in a compressible fractured-porous medium is of considerable interest. It is advisable to perform it by introducing two conditional continuums based on the system of fractures and the matrix of the reservoir being exploited. The rate of intercontinuum fluid exchange is assumed to be proportional to the difference between the heads in them. So, the description of the relationship between the permeability of the first continuum and the pressure in it is of great importance. The article considers three different ways of formalizing this connection. A nonlinear mathematical problem is formulated for pumping an incompressible fluid from a compressible fractured-porous medium with a constant discharge. Its solution is obtained for two stages of the filtration process. The first of them is characterized by the fact that the perturbation introduced into the filtration regime of the productive formation propagates at a finite speed. After the perturbation zone covers the entire filtration area, the second stage begins when the pressure uniformly decreases in the reservoir. Several examples illustrate the methodology for calculating the filtration characteristics. The patterns of pressure decrease inside the reservoir and at the bottom hole are established. The developed method allows for reliably determining the space-time changes in the filtration regime characteristics, assessing their consequences in advance, and making rational engineering decisions.
KEY WORDS
fractured medium, permeability, pressure, well, compressibility, engineering calculations, underground flow