Page 82 - Percolation Models for Transport in Porous Media With

74 CHAPTER 4. MULTIPHASE FLUID FLOW

region in fig. 20, b), with Tkt = O:Tk2 is
0, T ~ 0,
{
fo.(r) = /(T)/na, 0 < T < aTk2•
(1- K)/(T)/na, aTk2 ~ T ~ Tk2
rk! rk2
j
f
f},o. = J ( T) dr + ( 1 - K) J ( T) dr {4.33)
0 rk1
After substituting {4.33) into (2.1') we obtain the condition when the function
Teo.(Tk 2 ) can be found. This function plays in the analysis of the ICA formation
the same part as the function Teb(Tk2 ) does in the case of the ICB. Also, depending
on the correlation between the quantities Teo. and O:Tk2, two forms of the discussed
condition can be written

a~2 ~2
J j(T) dr + (1- K) J f(r) dr = ec, Teo. < O:Tk2 (4.34)
Tr.a
(1 - K) J Teo. ~ O:Tk2 ( 4.35)
rk2
j(r) dT = ec,

The case (4.34) is presented in fig.20, b, and the case (4.35), in fig.20, a. The
function Teo.(Tk2) varies between Te, when Tk2 = oo( -oo < Pk < 0), and 0 at some
minimal value Tk2 = Tc2o. determined from the following condition

O'Tc2a Tc2a
J f ( T) dT + ( 1 - K) J f ( T) dT = ee (4.36)
0 arc2a
When -oo < Pk < 0 Tk2 = Tkl = oo and ka(rk2) = 1. In the case described by
(4.34), the substitution of {4.33) into {2.1) gives the following

ko.(Tk2) = K0 ]a []a fo.(r) dr] ~o.(T')
1
0 r'
x ( ~~(r)dr+(l-K!l~(r)dr)

2 2
x ( 7k /(r) ~: + {1- K) 7 f(r) ~:) -:r',
~ a~2
Te2o. < Tk2 < 00, 0 < Pk < Pe2o.