Page 380 - Petrophysics 2E

348 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

of water (wetting phase) in the capillary tube, W, which is acting
downward, is equal to:

W = mchyw (5.59)
2
The buoyant force (weight) of the displaced fluid (oil) is upward and
equal to:

2
B = m, hy, (5.60)

The vertical component of interfacial tension force (Fz), acting upward,
is equal to:

FZ = 2mc ow, cos €Iwo (5.61)

Equating the forces and solving for h:

(5.62)

Welge and Bruce showed that Equation 5.62 can be used to calculate
the water and oil saturations at any height above the free liquid surface
if the capillary pressure versus saturation data are available [30, 311.
They applied this to the calculation of vertical water-oil-gas saturation
distribution as a function of height for hydrocarbon reservoirs:

0,102 P, 2.3 Pc
h(m) = and h(ft) = (5.63)
Pw - Po Pw - Po
where:
h is the height of capillary rise in m (ft);
pw and po are the densities of water and oil, respectively, in g/cm3
(lb/ft3); and capillary pressure P, is in kPa (psi).
Using the capillary pressure curve for oil displacing water from an
initial water saturation of loo%, the oil saturation in the reservoir can be
calculated at any height above the free water level, FWL, which occurs
at zero capillary pressure, as shown in Figures 5.16 and 5.22.
The free water level is difficult to locate in a reservoir, but the oil-water
contact, OWC, is apparent in well logs. Knowing the threshold pressure,
Pct, from a capillary pressure curve obtained from reservoir cores and oil,
the Iocation of the free water level can be determined and the vertical
saturations profile can then be calculated as a function of height above