Page 34 - Fundamentals of Enhanced Oil and Gas Recovery

22 Amirhossein Mohammadi Alamooti and Farzan Karimi Malekabadi

Figure 1.10 Difference in radius in oil drop in a tube surrounded with water.

2 q 1 r 2
P
B
A q
0
q 0
P 2 q 2 r 2
L
Figure 1.11 Pore doublet model.

The advancing contact angle is more than receding contact angle; therefore the
pressure at point A is more than the pressure at point B, and the direction of flow is
from A to B.
If the contact angle across the oil drop is the same and the radius of the capillary
tube is narrowed, the pressure required for mobilizing oil is determined as follows
(Fig. 1.10):

1 1
P B 2 P A 5 2σ ow cosθ 2
r A r B
The driving force required to push oil into the narrower part of the tube should
be increased until the oil drop comes out.
Another typical model for pore structure is the pore doublet model. This model is
more complicated, consisting of two connected parallel tubes. Fig. 1.11 shows the
schematic of this model.
Assumptions in this mode are water-wet connected tubes with different radiuses,
one of which is smaller than the other, and fluid flowing from point A to point B.
In the case of faster flow in one of the tubes and also inadequate driving force to
push oil from the tube with a slower flow rate, oil will be trapped.
The pressure difference between point A and point B can be written as:

P A 2 P B 5 P A 2P wi 1 P wi 2 P oi 1 P oi 2 P B