Page 220 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 201

Based on their experimental studies, Cernansky and Siroky (1985)
proposed an empirical permeability-porosity relationship as:

\-E
explGll- — -1 (10-92)
KJ e x p G - l L Jr I I -rf

where E and G are some empirical constants.

The Plugging-Nonplugging Parallel Pathways
Partial Differential Model

Gruesbeck and Collins (1982a) developed a partial differential model
based on the concept of parallel flow of a suspension of particles through
plugging and nonplugging pathways, as depicted in Figure 10-6. Relatively
smooth and large diameter flowpaths mainly involve surface deposition
and are considered nonplugging. Flowpaths that are highly tortuous and
having significant variations in diameter are considered plugging. In the
plugging pathways, retainment of particles occurs by jamming and block-
ing of pore throats when several particles approach narrow flow constric-
tions. Sticky and deformable deposits usually seal the flow constrictions
(Civan, 1994, 1996). Therefore, conductivity of a flow path may diminish
without filling the pore space completely. Thus, the fluid seeks alternative
flow paths until all the flow paths are eliminated. Then the permeability
diminish even though the porosity may be nonzero. Another important
issue is the criteria for jamming of pore throats. As demonstrated by
Gruesbeck and Collins (1982b) experimentally for perforations, the
probability of jamming of flow constrictions strongly depends on the
particle concentration of the flowing suspension and the flow constriction-
to-particle diameter ratio. Gruesbeck and Collins (1982a) assumed that
the liquid and particles have constant physical properties. The porous
media is incompressible, homogeneous and isotropic. There is hydraulic
communication through the interconnectivity of the plugging and non-
plugging pathways and therefore the pressure gradients and the particle
concentrations of the suspension flowing through the plugging and
nonplugging pathways are the same. The volume flux through the core
is constant and only the external particle invasion is considered. The flow
through porous media was assumed to obey the Darcy Law. In this
section, the Gruesbeck and Collins (1982) model is presented with the
modifications and improvements made by Civan (1995).
(J) PO and § npg denote the initial pore volume fractions of the plugging
and nonplugging pathways of the porous media (Civan, 1994, 1995).