Page 68 - Percolation Models for Transport in Porous Media With

60 CHAPTER 4. MULTIPHASE FLUID FLOW

Q J;, I Ji
Figure 16: Typical form of the capillary pressure curve (Leverett's function)

the percolation threshold ~c. ~ - ~c ""' w- • In this case we obtain the following
1
estimate for a(rk), a(rk) ~ 10- 2 • Now we shall set a(rk) = 0 to make further
the computations easier. Taking account of this assumption, we can represent the
probability density function !I ( r) for capillaries, which defines the conductivity of
the ICD, in the following form

{4.4)

Using {2.1) and {4.4), we find the formula for the relative phase permeability

r~[< ] 11 !I ( r) dr { rc[rc ]II j ( r) dr }-1
kt(rk) = f [ fi(r)dr I(r) f [ f(r)dr ~ (4.5)

Here r~ is defined by the relationship
r,.
J j(r) dr = ~c· (4.6)

r~
It is interesting to obtain the correlation between the found expressions for the
relative phase permeabilities and the quantity S1 which characterizes saturation
of the medium with the wettable fluid.
Consider two limiting cases of S1 calculation. If we use model I, then we can
estimate S1 under the assumption that the number of pores filled with the wettable
fluid is proportional to the number of capillaries filled with it. If the sizes of the
pores do not differ significantly, then
r,.

St = j f(r)dr (4.7)
0