Page 90 - Reservoir Formation Damage
P. 90
Petrophysics-Flow Functions and Parameters 73
and
p,
~ fkr •, O, Oj, , (4-7)
: 7 = fluid 1 or 2
where / is a characteristic dimension of pores, such as the mean pore
diameter proportional to -Jk/fy , j and p 2, and |Aj and JI 2 denote the
p
densities and viscosities of the fluid phases 1 and 2, respectively, g is
the gravitational acceleration, p c is capillary pressure, a is interfacial
tension between the fluid phases 1 and 2, 0 is the contact angle, S is the
saturation of the fluid phase \,k rj denotes the relative permeability of
phase j, 7 = 1 for fluid 1 and 2 for fluid 2, and M represents all other
characteristics of porous media pertaining to the morphology of pores.
In lack of a better approach, frequently, the Leverett (1941) J-function
analogy is facilitated to estimate the capillary pressure for an oil/water
system during formation damage according to:
= J(S W)<5 cos (4-8)
Pc
where J(S W] is the empirical Leverett J-function, which is a dimension-
less function of the water saturation, S w. Marie (1981) points out that
using Equation 4-8 is not rigorously correct because grouping a and 6
as o cos 0 is only valid for cylindrical capillary tubes. Gupta and Civan
(1994) have shown that the porous media representative value of the cos 0
term depends on the wettability. The surface tension varies by temperature
and species concentration. A quick remedy to apply Equation 4-8 for a
nonuniformly-wet porous formation is to define a weighted average of
the various wetting fractions of pores as, extending the approach by
Cassie and Baxter (1944) and Paterson et al. (1998).
cos 0 = acos0
(4-9)
where 0. are the contact angles of the different wetting pore surfaces, a.
are the surface fractions of different wetting pores, defined by McDougall
and Sorbie (1995).
As a simplistic approach, assuming that the Leverett J-function remains
unchanged during formation alteration, Equation 4-8 can be applied at a
reference state and denoted by subscript "0" and at an instantaneous state
during formation damages to obtain:
