Geoscience Reference
In-Depth Information
are assumed, implying perfect mixing or a fully-
miscible gas-oil system.
These functions describe the flows and
pressures for multi-phase flow. The third equa-
tion required to completely define a two-phase
flow system is the capillary pressure equation.
For the general case (any fluid pair):
distributions have a fairly flat function (as for
the 1,000 mD curve in Fig.
4.7
), while highly
variable pore size distributions have a gradually
rising function (as with the 50 mD curve in
Fig.
4.7
). The capillary entry pressure is a func-
tion of the largest accessible pore. Different P
c
curves are followed for drainage (oil invasion)
and imbibition (waterflood) processes.
We summarise our introduction by noting that
the complexities of multi-phase flow boil down
to a set of rules governing how two or more
phases interact in the porous medium. Figure
4.8
shows an example micro-model (an artificial
etched-glass pore space network) in which fluid
phase distributions can be visualised. Even for
this comparatively simple pore space, the num-
ber and nature of the fluid-fluid and fluid-solid
interfaces is bewildering. What determines
whether gas, oil or water will invade the next
available pore as the pressure in one phase
changes?
One response - the modelling approach - is
that good answers to this problem are found in
mathematical modelling of pore networks (e.g.
McDougall and Sorbie
1995
; Blunt
1997
; Øren
and Bakke
2003
; Behbahani and Blunt
2005
).
P
c
¼
P
non
wetting phase
P
wetting
phase
½
P
c
¼
fS
ðÞ
ð
4
:
10
Þ
Capillary pressure, P
c
, is a function of phase
saturation, and must be defined by a set of
functions. The capillary pressure curve is a sum-
mary of fluid-fluid interactions, and for any element
of rock gives the average phase pressures for all the
fluid-fluid contacts within the porous medium at a
given saturation. For an individual pore, P
c
can be
related to measurable geometries (curvatures) and
forces (interfacial tension), and defined theoreti-
cally - but for a real porous medium it is an average
property. Figure
4.7
shows some example
measured Pc curves, based on mercury intrusion
experiments (Neasham
1977
).
The slope of the P
c
curve is related to the pore
size
distribution. More
uniform pore-size
1000
Small pores
100
0.5mD
Medium pores
50mD
10
1000mD
Large pores
1
Non-wetting phase
invades largest
pores first
0.1
1
0
PV occupied
Fig. 4.7
Example capillary pressure functions: capillary drainage curves based on mercury intrusion experiments
measuring the non-wetting phase pressure required to invade a certain pore volume (PV)