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Gas and Liquid Injection Rates 197

be balanced by the UBD pressure differential to prevent further water
imbibition. If the underbalanced drilling pressure differential is less than
the critical capillary pressure, water imbibition will continue, and signifi-
cant formation damage is expected to occur (points D and E).
The existence of the critical capillary pressure can be proven on the
basis of capillary parachor. Figure 9.15 shows a plot of parameter group

S nw against S w ,where S nw and S w are nonwetting and wetting phase
2
P c
saturation, respectively, and P c is imbibition capillary pressure. The peak

value S nw 2 was defined by Guo and colleagues (2004) as capillary
P c
max
parachor. The significance of capillary parachor is that it corresponds to a
critical point where the nonwetting phase begins to lose its dominating
state of flow. The authors observed the following:
1. Permeability (in md) of porous media is directly proportional to the
-2
Hg-air capillary parachor (in Atm ) with a proportionality factor
of 0.054.
2. Permeability (in md) is proportional to the air-brine capillary parachor
-2
(in Atm ) squared, with a proportionality factor of 0.00007.
These observations imply that the capillary parachor is a parameter
reflecting the effective pore size distribution of a porous medium for

2500

2000

S nw /P c 2 (Atm −2 ) 1500

1000

500

0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
S (% bulk volume)
w
Figure 9.15 Plot of parameter S nw 2 versus S w for a sandstone sample in an air-brine
P c
system.