A two-phase (oil-water) relative permeability correlation for mixed-wet reservoir rock is developed and validated in this paper, including bounding drainage and imbibition processes and scanning [sms1] hysteresis loops, allintegrated with the corresponding changes in capillary pressure.
The Corey-Burdine type relative permeability correlation is widely used in theindustry. It was originally developed for water-wet reservoirs from aBrooks-Corey power-law capillary pressure correlation in combination with abundle-of-tubes model of the pore network.
We have adjusted the Brooks-Corey capillary pressure correlation to be validfor mixed-wet rock and now present the ensuing Corey-Burdine relative permeability correlation for mixed-wet reservoirs.
The functional form of the relative permeability correlation is symmetric with respect to fluid-dependent properties since neither fluid is privileged in amixed-wet environment. It reverts to the standard Corey-Burdine correlation for the completely water- or oil-wet case. A water-wet behavior is displayed at low water saturations and an oil-wet behavior at low oil saturations, in accordance with experiments. The correlation provides an inverted S-shape oil relative permeability curve with an inflection point, and closed hysteresis scanning loops, as observed.
The correlation is validated by comparison with measured relative permeability curves and simultaneously measured capillary pressure and relative permeability curves from the literature.
The correlations and hysteresis logic are easily programmed, and we suggest that the Killough hysteresis model, employed in many numerical reservoir simulators, should be updated with the new scheme.
In an earlier paper, we presented a capillary pressure correlation for mixed-wet reservoirs and suggested to extend the Corey-Burdine relative permeability relationships from water-wet to mixed-wet conditions. In the present paper, we develop this idea further and include hysteresis logic, integrated with the capillary pressure hysteresis loops.
The main design constraints of the relative permeability correlation are
the functional form is symmetric with respect to the two fluids oil andwater. That is, the functional form is invariant to interchange of index o with index w.
the hysteres is loops are closed,
the hysteres is loops of the capillary pressure and the relative permeabilities form a consistent set,
imbibition oil relative permeability curves have the characteristic inverted‘S’ shape.
The validity of the relative permeability correlation and the integrated hysteres is schemes are verified by detailed, published relative permeability measurements and by simultaneously measured hysteretic relative permeability and capillary pressure curves.
The integrated hysteres is scheme is easily programmable and could replace the Killough-scheme which presently is the most common in use in numerical reservoir simulators.
There is now wide acceptance of the view that most reservoirs are at wettability conditions other than water-wet, and network-models incorporatethis fact. However, to incorporate mixed-wet rock properties into a numerical reservoir simulator, validated correlations are required.