Page 111 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 93

factor will be introduced. Following this, a reformulation of the governing
Eqs. (3.23, 3.26, and 3.31) alongside the appropriate initial and boundary
conditions for the problem of fines migration under high velocity will be
given. The exact solution for this problem for 1D linear flow will be pre-
sented in Section 3.3.2 which will be used to analyze laboratory data in
Section 3.3.3.

3.3.1 Formulation of mathematical model
The primary assumptions of the model follow from those presented in
Section 3.2. These being the additivity of particle concentrations,
sufficiently small strained concentration to provide a constant filtration
coefficient, neglecting permeability decline due to attached particles, and
steady-state, incompressible, laminar flow.
In the formulation of the mass balance equation for fine particles, the
advective flux of suspended particles is proportional to their velocity U s .
This parameter is typically set to the value of the fluid velocity as the sus-
pended particles experience advective flux due to the transport of the
bulk fluid through the porous media (Khilar and Fogler, 1983, 1998;
Sharma and Yortsos, 1987). Long stabilization times in experimental stud-
ies of fines migration (Oliveira et al., 2014; Yang et al., 2016) suggest that
the particle velocity is significantly smaller than that of the carrier fluid.
Rolling of particles along the pore surface as well as limited accessibility
to small pores provide physical justification for the distinction between
the two velocities. As both of these effects will reduce the particle veloc-
ity, it is typically assumed that the particle velocity is strictly smaller than
the fluid velocity.
Following the decoupling of particle and fluid velocities, their ratio is
introduced as a dimensionless parameter:

U s
α 5 : (3.32)
U
This parameter will be referred to as the drift delay factor α, and
assumed to be constant for all particles during any period of injection.
Although the fluid velocity is known under test conditions, the particle
velocity is unknown; hence, the drift delay factor will be an unknown
parameter of the model.
The system of equations governing fines migration can now be pre-
sented. Firstly, the mass balance equation for suspended, strained, and