The role of capillary pressure curves in reservoir simulation studies ...

The role of capillary pressure curves in reservoir simulation studies.
M. salarieh, A. Doroudi, G.A. Sobhi and G.R. Bashiri Research Inistitute of petroleum Industry.
Key words:
Capillary pressure curve, Simulation, hysterises, Water coning, Well production.
ABSTRACT:
Capillary forces are one of effective parameters in Hydrocarbon Reservoirs which are notable
in the porous media. Capillary pressure is one of input data in reservoir simulation process
which should be considered in history matching procedures.
This paper is going to study the role of capillary pressure by using a black oil software named
“IMEX”. The data is about a given reservoir which is studied for, the curvature and capillary
pressures Hysterises is simulated and also water coning in well is a checking point for capillary
pressure effect.
Capillary Pressure ?
Capillary pressure is one of important parameter in porous media. This term is related to
capillary phenomena in capillary tube. The connected porous in a reservoir rock could be
considered as capillary tube with very low diameter. Because of different wettabillity in porous
surface with respect to two phases (i.e. water and oil) different forces are distributed on the
contact surface, if the surface is enough small, it causes a bending inside the one of phases. It
means that the pressure of two phases is not equal on the contact surface. In this case, the lower
pressure is related to the phase whose curvature of surface is towards to inside. The difference
is named capillary pressure which could be measured. as shown by P c and is. P O – P nP = P aw
The notion w & nw is wetting phase and Non-wetting phase respectively, this amount is always
a positive quantity and also is depended to different factor such as rock and fluid properties and
the structure of porous media. It is recommended that the petroleum engineers calculate for
water and oil as below:
P c = P O - P w
The notations o and w show the oil and water phases. Therefore it can sometimes be negative.
Capillary pressure curves
Fluid saturation is the difference of pressure between two phase(P c ) which is shown the volume
fraction of porous media, increasing of saturation of wetting phase will cause the decreasing of
the saturation of Non-wetting phase. Hence, we have the reduction in P c.
The experimental studies show that capillary pressure at a given saturation depends on the
direction of saturation changes(increase or decrease). If the phase saturation in porous media
could displace, the non-wetting phase by a sufficient pressure of wetting phase, the drainage
performance is occurred and if the displacement of wetting phase by non-wetting is happened
the imbibition phenomena in porous media is occurred (normally it happens). The process is
called Imbibition in both of above cases, the capillary pressure depends on phases
saturation(figure 1) P c curves for different type of rocks and different properties (i.e. different

wettability) are not the same, shortly, the main role of capillary pressure is in the initial
distribution of fluids in reservoir. It can also affect on fluid flow.
In numerical reservoir simulation, capillary pressure is applied for input file and can be an
important parameter for history matching. The displacements on P c curve (i.e. displacement vs
Saturation) transfers the curve and the curvature can also be changed. However the
displacement of P c to a higher position shows the effective parameters on P c (like decreasing the
permeability, increasing the surface tension and wettability), the curvature in P c can be related
to the pore size distribution.
Capillary pressure Hysterises
As we mentioned, capillary pressure is depended to the saturation changes. This is called
capillary pressure hysterises. We can also observe this dependency in drainage and imbibition
curves, for example considering a water-wet rock, if we inject oil when it is completely
saturated, the capillary pressure curve is like D 0 in figure 1 and finally will get S wir . And if we
inject water at the end of drainage, the capillary pressure will be the curve I o and will reach to
the point S wor . Again, we inject oil, the drainage will be occurred but D 0 can not show the
capillary but D, do that. According to these process, different curves which called scanning
curves are achievement which is transferred from drainage to imbibition.
Similarly, we could have the same type of curves in transferring from imbibition to absorption,
hence, these are called the scanning curves between imbibition to drainage and drainage to
imbibition, like D 2 , I 1 , in figure 1.
The amount of drainage and imbibition capillary pressure which is used in Numerical
Simulations, is usually computed in the labs, but the number of laboratory tests are limited so
we have to apply the experimental estimates. [1,2].
Experiments
In this paper, a given reservoir with the specification in tables 1,2,3, and figure 4 was simulated
and run with IMEX. We estimated three cases, without P c , with P c , and high amount of P c .
Then, choosing an initial P c curve and changing the curvature in four stages the curve is
converted to an bias line and results were compared, finally the survey is continued with
capillary pressure hysterises and without it.
Conclusion
A - Effect of P c
In order to study the effect of P c in our given reservoir simulation in three cases (without P c , low P c
and high P c ) we studied the production behavior of productive wells, such as shown in figure 2, the
down curve is related to low P c and the upper curve is for high P c , the figure 5 & 6 show the
simulation output.
According to the curves, the wells have the best productive situation whenever the P c is zero and the
rate of oil was increasing versus time. In this case, the water coning is delayed or not happened, but
the condition differs if P c increase. These results could be considered in history matching. It is
illustrated in figure 3 that P c decreasing will be caused the curvature in P c curve at all four stages and
finally it will be converted to a straight line, the effect of curvature on production behavior is also
surveyed which is illustrated in figure 7 & 8. According to these curves, the low curvature in P c
graph will leads the production procedure toward to water coning.

B -Effect of capillary pressure hysterises
In order to study the effect of capillary pressure hysterisies, in our given reservoir, we did the
computation in two case with consider only the hysteris and with out it. Then compared the results.
As it is shown in figure 9 & 10, without hysteris the water coning will be more than the real
case(considering the hysterisis). This difference is occurred after a period of time and is about 5%.
This conclusion can not be considered as a general result, because our given reservoir was
completely uniform with a water-wet rock and did not confirm the killough states[1] who had said
that “the hysteris has no effect in water coning while the production rate is constant”. The research on
this claim will be continued and will be discussed in another paper.
Shortly, for a water wet reservoir with constant rate we can state that:
1 – water coning will be increased if the P c increases.
2 - water coning will be increased if the curvature of gravity drainage curve increases.
3 – Considering the capillary pressure hysteris in reservoir simulation will reduce the water
production.
We also surveyed the effect of P c in three above mentioned cases in any case the production is
considered.
Table 1- The description of fluied, reservoir and grid blocks
-------------------------------------------------------------------------
Oil density (lb/ft 3 ) 51.5
Water density (lb/ft 3 ) 62.4
Oil viscosity (cp) 0.34
Water viscosity (cp) 0.31
Porosity 0.207
External radius of formation (ft) 1300
Total thickness of formation (ft) 365
Depth of water and Oil contact (ft) 160
Reference pressure at water and Oil contact level (Psi) 2000
No. of production well block (from deep) 18
Horizontal permeability (md) 1000
Vertical permeability (md) 100
Radius at block boundaries (ft)
1300 1131.5 663.9 332 78.3 38.1 18.5 9 3.9 2.5
Thickness of blocks [Upward] (ft)
20 20 20 20 21.25 23.75 25 25 37.5 37.5 25 3.75 8.75 7.5 6.25 8.75 10 11.25 15 18.75

Table 2 – The values of saturation functions
-----------------------------------------------------------------------------------------------
S wi K rw K ro S wi K rw K ro
-------- -------- ------------ -------- -------- ------------
0.15 0.0 0.95 0.40 0.0305 0.2450
0.45 0.0392 0.1770 0.35 0.232 0.3325
0.50 0.0497 0.1200 0.25 0.0102 0.5876
0.30 0.8166 0.8862 0.55 0.0630 0.0722
0.60 0.0798 0.0374 0.20 0.004 0.75
0.65 0.10 0.0163 0.80 0.1870 0.0000
0.70 0.1244 0.0020 0.75 0.1525 0.0001