Page 240 - Reservoir Formation Damage

220 Reservoir Formation Damage

Applications of the Ceriiansky and Siroky Model

The objectives of the experimental studies were threefold:

1. Determine an empirical relationship between permeability and
porosity in the form of Eq. 10-92.
2. Determine the values of the deposition and entrainment rate con-
stants, k p and k' e.
3. Study the effects of the length of porous media and the rate and con-
centration of the particle suspension injected into the porous media.

The pressure difference across the porous media and the particle
concentration of the effluent were measured as functions of time during
the injection of a suspension of finely ground limestone particles at a
given concentration and rate.
The porous material was prepared by using nonwoven felt of filaments
of polypropylene. The porous material samples of 4 cm diameter and 0.5,
1.0, 1.5, and 2.0 cm lengths were used. The particle suspension was
3
prepared using finely ground limestone of 2,825 kg/m density in water.
The porosity was determined by the weighting method. The discrete
times at which measurements are taken are denoted by the subscript
i = 2,3,...,N and the initial time is denoted by / = 1. The permeability
was determined by Darcy's equation by neglecting the effect of gravity
for short samples:

KI = wjiL/A/?,. : i = 2,3,..., TV (10-170)

The volume of particles deposited per unit volume of porous media was
calculated, by integrating Eq. 10-84 and applying the mean value theorem:

<te] = I f fk dx = K-^> (10-171)
dt) Ljdtdt L
L
o
from which

t
f
e = e +- fa -a }dt Ul (10-172)
C
° T \ V '" OUt)
O
where £ 0 =0 for an initially particle-free porous material. Eq. 10-172 is
evaluated numerically by applying the trapezoidal rule of integration as,
for a constant injection suspension particle concentration: