Page 205 - Percolation Models for Transport in Porous Media With

12.3 CAVITATION 203

of the surface layer u.: F-r = 211"ru •. Furthermore introduce the parameter

r 'T = o.sp1 < v > /3'- 1
2
where {3' = F-r / S' and S' = 211"r is the area of a unit surface of the capillary to
which the shear force F-r is applied. The parameter r -r characterizes the ratio of
the hydrodynamic head P! < v > 2 /2 to the critical shear stress {3' that can be
endured by the capillary surface without destruction. Obviously {3' = u., and
therefore finally
r-r = P! < v > u-; /2
2
1
Fulfillment of the condition
{12.7)
is the criterion for the destruction and entrainment of the surface layer from the
capillary surface by the flow.
Estimate the quantity r -r and verify the fulfillment of the condition {12.7).
Taking account of the velocity profile v( r 0 ) in a capillary, we obtain
r
< v >= ~ j 211"v(ro)ro dro = 8 1 r Vp
2
'/l"T ~
0
where "'Vp is the pressure gradient in the considered volume of the medium. Es-
timate "'Vp using the characteristic values for the parameters of acoustic action.
Wavelength ,\ is of the order 10- 1 m, and the amplitude of the pressure wave is
Po. ,..., 10 Pa; therefore, the characteristic value of "'Vp ,..., Po./,\ = 10 5 Pa/m. The
average value of the pore channel radius for a reservoir rock is of the order of 10- 5
m, as can be seen from {12.2) as well as (48). For our estimates, take the capillar-
ies that are thicker by one order, i.e., those with radii r ,..., 10- 4 m. In this case
2
2
< v >- 10- m/s, < v > - 10- m fs , and P! < v > /2 ,..., 1/2 · 10 Pa. Since
2
1
2
2
the shear strength of clay is no less than 10 3 Pa, while this value for mud is as a
rule no less than 10 - 10 2 Pa (84), it can be seen from the presented estimate that
the "shear stress mechanism" can work only for very large capillaries. However
in such capillaries, where maximal flow rates are realized, visible clay depositions
can hardly be found. Thus the given mechanism is unable to substantially change
both the radii of thick capillaries (since the layer of depositions on their surface is
minor) and the radii of thin capillaries, where the hydraulic head is too small.
12.3 Cavitation in Pore Channels under Acous-

tic Action

As an acoustic wave passes through a saturated porous medium, the effect of cavi-
tation may appear, if negative pressures exceeding the tensile strength of the fluid