The role of capillary pressure curves in reservoir simulation studies.

Transcription

1 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

2 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.

3 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 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) Thickness of blocks [Upward] (ft)

4 Table 2 The values of saturation functions S wi K rw K ro S wi K rw K ro

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