Geoscience Reference

In-Depth Information

Gravity dominated

Reality ?

Viscous dominated

Capillary dominated

Fig. 4.13
The fluid forces triangle with sketches to illustrate how a water-flood would behave for a layered rock

(
yellow
¼
high permeability layers)

gradient term, while the gravity/capillary ratio is

the buoyancy term against the capillary pressure

gradient.

z represent the physical length

scales - essentially the size of the model in the x

and z directions. There are several different

forms of derivation of these ratios depending on

the physical assumptions and the mathematical

approach, but the form given above should allow

the practitioner to gain an appreciation of the

factors involved. It is important that a consistent

set of units are used to ensure the ratios remain

dimensionless.

For example, a calculation to determine when

capillary/heterogeneity interactions are impor-

tant can be made by studying the ratio of capil-

lary to viscous forces. Figure
4.14
shows a

reference well pair assuming 1 km well spacing

and a 150 psi pressure drawdown at the produc-

ing well. We are interested in the balance of

forces and a rock unit within the reservoir,

represented by alternating permeability layers

with a spacing of

ʔ

x and

ʔ

150psi

x

1 km

D

Fig. 4.14
Sketch of pressure drawdown between an

injection and production well pair for water-flooding an

oil reservoir

ratio for different layer contrasts and heterogene-

ity length-scales (Ringrose et al.
1996
).

If the layering in a reservoir occurs at the

>

10 m scale then viscous forces tend to dominate

(or the Viscous/Capillary ratio must be very low

for capillary forces to be significant at this scale).

However, if the layers are in the mm-to-cm range

then capillary forces are much more likely to be

important (or the Viscous/Capillary ratio must be

x. Figure
4.15
shows the

result of the analysis of the viscous/capillary

ʔ