Page 154 - Primer on Enhanced Oil Recovery

144 Primer on Enhanced Oil Recovery

Figure 12.2 Rheology of dilatant and pseudoplastic fluids (τ shear stress).

stable water-oil bank and reduce speed of infected fluid flow in high permeability
channels.
Indeed, assuming that the flow of a polymer solution in a porous medium obeys
a power law, the flow rate can be determined by the following formula:

1 21
n dP
dP
v 52 B 0
dx dx
(12.3)

1 1 31 1 1 11 1 1 11 1
n 2 n 2 n 2 2 n 2 n
B 0 5 η 2 m k
3n 1 1
For the Newtonian liquid (for the case when viscosity does not depend on shear
rate, e.g. no viscosity dependence on the flow speed) n 5 1, for a dilatant liquid
n . 1, for the shear-thinning liquid n , 1.
Let us consider a simplified flow diagram of the polymer composition in a lay-
ered heterogeneous reservoir. Let the filtration of the polymer composition occur in
two parallel layers with permeability k 1 and k 2 (with other conditions being the
same), and k 1 .. k 2 and corresponds to a power law. Then, according to the
above equation, the ration for the flow volumes

11 12n

Q 1 v 1 k 1 2n
5 5 (12.4)
Q 2 v 2 k 2
It is immediately obvious that for a dilatant liquid the flow will be much less
affected by the permeability variations.