Page 202 - Reservoir Formation Damage

184 Reservoir Formation Damage

An evaluation and comparison of six selected models bearing direct
relevance to formation damage prediction for petroleum reservoirs are
carried out. The modeling approaches and assumptions are identified,
interpreted, and compared. These models are applicable for special cases
involving single-phase fluid systems in laboratory core tests.
Porous media is considered in two parts: (1) the flowing phase, denoted
by the subscript /, consists of a suspension of fine particles flowing
through and (2) the stationary phase, denoted by the subscript s, consists
of the porous matrix and the particles retrained.

The Thin Slice Algebraic Model

Model Formulation

Wojtanowicz et al. (1987, 1988) considered a thin slice of a porous
material and analyzed the various formation damage mechanisms assum-
ing one distinct mechanism dominates at a certain condition. Porous
medium is visualized as having tortuous pathways represented by N h tubes
of the same mean hydraulic equivalent diameter, D h, located between the
inlet and outlet ports of the core as depicted in Figure 10-1. The cross-
sectional area of the core is A and the length is L. The tortuosity factor
for the tubes is defined as the ratio of the actual tube length to the length
of the core.
-c = L h/L (10-1)

The cross-sectional area of the hydraulic tubes are approximated by

(10-2)

in which C l is an empirical shape factor that incorporates the effect of
deviation of the actual perimeter from a circular perimeter.
As a suspension of fine particles flows through the porous media, tubes
having narrow constrictions are plugged and put out of service. If the
number of nonplugged tubes at any given time is denoted by N np and the
plugged tubes by N p, then the total number of tubes is given by:

+N
N, = N p "n (10-3)
ly T
^ h
The area open for flow is given by
(10-4)