Page 101 - Introduction to Petroleum Engineering

86 MULTIPHASE FLOW
5.2 FLUID DISTRIBUTION AND CAPILLARY PRESSURE

Oil, gas, and water phases coexist in many hydrocarbon reservoirs. If these three phases
were in a bottle at rest on a table, they would segregate with the gas on top, the water
on bottom, and the oil between (provided that gas is least dense, water is most dense,
and oil density falls between the other two). The gas–oil boundary and the oil–water
boundary would be planar and well defined. In a reservoir, these same phases will seg-
regate, but not completely, and the boundaries between them will be very fuzzy. These
zones are known as transition zones. In an oil–water system, the transition zone sepa-
rates the water zone where only water flows from the oil zone where only oil flows.
Wells producing from transition zones typically produce two phases simultaneously.
Imagine that you and a pressure gauge could shrink to the scale of pores in a
reservoir that is saturated with oil and water. The less dense oil resides mostly in the
upper portion of the reservoir, and the more dense water is mostly in the lower
portion, but the segregation of these phases is not complete. If you were to measure
the pressure in immediately adjacent phases of oil and water, you will find a difference
that is termed the oil–water capillary pressure, p :
cow
p cow = p − p w (5.4)
o
As explained in the previous section, this difference results from the curvature of the
interface between the phases. If you were to climb to a higher elevation in the reser-
voir, the pressure in the water phase would decrease at approximately 0.45 psi/ft. The
pressure in the oil would decrease at a lower rate, perhaps 0.35 psi/ft, because the oil
density is lower than the water density. Consequently, the capillary pressure increases
at a rate of 0.10 psi/ft as you climb upward and decreases at the same rate as you
climb downward in the reservoir. In your up‐and‐down exploration, you will likely
find an elevation for which the capillary pressure is zero. Above that elevation, p is
cow
positive; below that elevation, it is negative. In Figure 5.2a, the linear relationship
between measured capillary pressure and elevation is shown. Figure 5.2b shows a
trend for water saturation that you might have seen in your exploration of the
reservoir. Clearly, the boundary between the oil and water is blurred.
Combining the observed capillary pressure and water saturation for each elevation
in Figure 5.2 will yield Figure 5.3. Such relationships are routinely measured for
rock samples taken from oil and gas reservoirs. The details of such measurements are
found elsewhere. After the relationship between capillary pressure and water satura-
tion has been measured, the distribution of fluids in a formation can be estimated.
The relationship between capillary pressure and fluid saturation depends on the
direction of change of saturation. Consider a rock sample that is initially saturated
with water. If oil is injected into the sample at increasing saturations, the “primary
drainage” trend in Figure 5.4 might be obtained. If water is next injected into the
sample, the “secondary imbibition” trend might be obtained. And finally, if oil is again
injected, one might obtain a trend like the “secondary drainage” trend in Figure 5.4.
The variation of the capillary pressure relationship with direction of saturation change
is termed hysteresis. Historically, drainage referred to decreasing saturation of the
wetting phase, and imbibition referred to increasing saturation of the wetting phase.