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polygon involves defining of a new permeability distribution
polygon with taking into account formation water-flushing
whereas velocity of filtration flow assumed as proportional to
permeability and incompleteness of oil displacement by water is
taken into account by residual-oil saturation. Transformed polygon
of distribution of permeability in the analytical form is written as
follows:
 z  z 1  n   
n    n    1 f   f    d  , (5.5)
1
  1   r o   b w   2   1 r o   b w   
where n 1(æ) - auxiliary function; z f - oil saturation at the front
water-oil displacement; ρ r o – residual oil saturation; ρ b w -
saturation of bound water; n(æ) - distribution density of
permeability, the nature of random variable distribution.
Auxiliary function n 1(æ) is principal in defining auxiliary
functions F 1(æ) and F 2(æ), using which gives to us ability to
estimate oil-extraction rate and water content in wellbore fluids.
The plot of auxiliary function n 1(æ) can be seen in Fig. 5.3.

Figure 5.3 - Auxiliary function n 1(æ)

Auxiliary functions F 1(æ) and F 2(æ) may be determined
as:

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