Page 212 - Percolation Models for Transport in Porous Media With

210 CHAPTER 12. ACOUSTIC WAVES AND PERMEABILITY

Although the heat conductivity of water and the surrounding rock are of the
same order("' 1 watt per meter-Kelvin), we shall neglect the heat transfer from
the fluid to the solid skeleton in the zero approximation. In this case we obtain
the condition
E1 =E2

Using this condition and relationships (12.19) - (12.21), we obtain
(V'p)2 1 r3
D.T=-----
8p. PJCT ht
For a simple harmonic wave (12.18) we have
2
1
2
2 3
D.T = 7r r p~(2J.LPJCr.A ht)- sin [27r(vot- x/.A)] (12.22)
After averaging (12.22) over the wave period
1/vo
< D.T >= v0 j D.Tdt

0
we obtain an expression for the temperature increase in a capillary with radius r
after a period of T 11 of action of a simple harmonic wave source with frequency Vo
and intensity Ib:
(12.23)
where Qp is the coefficient of transmission showing the extent to which the ultra-
sonic wave is reduced as it passes from the source through the liquid filling the
well and through the partition of the well into the rock.
The obtained relationship (12.23) shows that the considered thermal slide
mechanism permits to qualitatively explain and quantitatively estimate the con-
sequences of acoustic action upon a saturated porous medium. If the process does
not cause phase transitions in the liquid phase, then the formula (12.23) shows
how the temperature and the pressure increases in the fluid depend on the ratio of
the parameters of the fluid and the medium and on the operating conditions. The
effect of phase transitions (here, the gas release) can be estimated, at least qualita-
tively, by taking into account the relations p.(r'), cr(r'), Cm(r'), where r' is the
parameter that characterizes gas release, e.g., volumetric or mass concentration of
gas bubbles in the liquid.

12.5 Gas Colmatation During Acoustic Action

on Porous Media

As in the case of electric action (see chapter 11), gas colmatation of a fluid-
containing rock, as the fluid gets heated due to the dissipation of acoustic energy,