Correlating Tertiary Oil Recovery in Water-Wet Systems
Authors: Dullien F.A.L. , MacDonald I.F. 
Published: December 2007

Microscopic displacement efficiency of oil recovery has been receiving increased attention. We propose a new correlating parameter for displacement efficiency, the "tertiary oil recovery number," N SAA, and compare it with the "capillary number," N ca, recommended recently by Melrose and Brandner.
From a physical perspective, both parameters are considered to be measures of the ratio of pressure to capillary forces in porous media. pressure to capillary forces in porous media. In expecting a correlation between displacement efficiency and either N SAA or N ca, it is assumed that externally applied pressure forces must overcome capillary forces to displace the oil. Therefore, the scope of these parameters is expected to be limited to tertiary oil recovery where the objective is to recover the residual oil, trapped as isolated ganglia by capillary forces, resulting from a conventional waterflood in which pressure and capillary forces cooperate to overcome viscous forces in displacing oil.
The tertiary oil recovery number is defined as
(pw/L) N =, .......................(1) SAA yow D
where Delta p w/L is the microscopic pressure gradient,
is the mean length of an oil ganglion, y ow is the oil-water interfacial tension, and D, the "structural difficulty index" proposed by Dullien et al., is a measure of the pore structure. Generally, we can use 1 1 D -------- - ---------,.............(2) De D where De and D are the mean pore-entry diameter and the median pore diameter, respectively. N SAA is equal to the ratio of the pressure drop in the flowing water between the two extremities of a typical trapped oil ganglion, (Delta p w/L), to the effective capillary pressure trapping the ganglion, y ow D. Therefore, N SAA is a measure of the relative magnitude of the pressure and capillary forces. According to Eq. 1, for fixed values of Delta p w/L y ow, called the Taber number, the tertiary oil recovery number varies for different porous media depending on the value of the ratio /D. N SAA is based on a physical picture similar to those given by Dullien et al. and by Melrose and Brandner.
Based on this picture of displacement, the critical condition in a given system for displacing any trapped oil is the equality of the pressure drop across those ganglia that are easiest to displace and the effective capillary pressure trapping these ganglia. That is,
p w 1 1 max = y ow --- - ---,........(3) L cr 1 De D min
where De and D are the pore-entry diameter and the pore diameter, respectively. Eq. 3 shows that the pore diameter, respectively. Eq. 3 shows that the larger the ganglion and the closer the size of the pore neck to the bulge size, the easier is the pore neck to the bulge size, the easier is the displacement. For the critical conditions specified above, the value of N SAA is
............................................(4)
Similarly, one can show that the smaller the ganglion and the smaller the ratio of neck diameter to pore diameter, the more difficult is the displacement. Accordingly, one can define a second, larger, structure-dependent critical value of the tertiary oil recovery number corresponding to complete oil recovery: ........(5)
P. 7