APPROXIMATE METHOD FOR DETERMINING THE COEFFICIENT OF PERMEABILITY OF THE LAYER

Akmoldina Anara, faculty of information technology, magistrate, 1st year

Baymankulov Abdykarim Tungutbaevich - doctor of sciences, Associate Professor of Software

Kostanay State University of A. Baitursynov, Kostanay

The general principle of non-stationary layers for study is that by changing the work of wells in the reservoir of artificially generated transients filtering and pressure is measured according to time in one or more wells. Based on data from the wells and flow rates of pressure change at certain points in the reservoir could receive information about the bed-permeability, permeability, about the location of the boundary layer, etc. [1]

Consider the one-dimensional axially symmetric motion (flat-radial) with elastic mode. Pressure distribution is defined as the solution to the heat equation in polar coordinates:

(1)

satisfying the initial condition

(2)

and the boundary conditions at .

Applications of particular importance is the task to which the borehole is constant flow. This is used in the most common ways of definition of parameters of the reservoir according to the observations of non-stationary flow to the wellbore. Suppose so

, (3)

where - the well's radius and .

Suppose that in the cylinder the pressure keeps a constant value equal

(4)

This condition is met if, for example, the region borders vast well of water permeable layer. Let the set pressure, depending on the time at the well. That is

(5)

In order to obtain homogeneous boundary conditions, we will introduce a new feature

(6)

then

(7)

On the other hand

и .

Substituting these values in (1) display

Here is the equation of heat conduction on functions :

(8)

where . If in the borehole constant flow, then

Under the new circumstances (5) written in the form

(9)

References

[1] G.I. Barenblatt, V.M. Entov, V.М. Ryzhyk. Theory of nonstationary filtration of liquid and gas. – Publisher Neira, 1992