Page 111 - Reservoir Formation Damage
P. 111
94 Reservoir Formation Damage
Power-Law Flow-Units Equation
Civan (1996, 2000) expressed the mean-pore diameter as a three-
parameter power-law function of the pore volume to solid volume ratio:
= Yi (5-71)
in which a, P and y are empirical parameters, and usually a = 1. P and
y depend on the pore connectivity and can be correlated as a function of
the coordination number, Z, respectively, by:
1
1
p- /p- . 0 =l-exp(-CZ + D) (5-72)
= i - exp(-AZ + fl) (5-73)
The interconnectivity parameter can also be approximated by a power law
function of porosity as (Civan, 1996):
y = cty n (5-74)
in which c and n are empirical parameters, y is zero when the pores are
blocked by deposition. Civan (2000) verified the validity of Eqs. 5-71
through 74 using the data by Rajani (1988), Verlaan et al. (1999), and
Bhat and Kovscek (1999).
Effect of Dissolution/Precipitation on
Porosity and Permeability
Civan (2000) expressed the precipitation/dissolution rate by:
d£
= *, (F-1)«|> 0-£)" (5-75)
dt
subject to the initial condition
(5-76)
where, t is time, k } is a rate constant, (|) 0 is the initial porosity, e is
the volume fraction of deposits in porous media, F is the solution
