Page 70 - Principles of Applied Reservoir Simulation 2E

Part I: Reservoir Engineering Primer 55

If the medium is horizontal, the condition for a system without gravity is
(1 ~ M)AP = 0 (6.47)
To see the effect of mobility ratio Mon finger growth for the gravity-free case,
we set g =• 0 in Eq, (6.45) to get
fife X 6 (1 -
W
(6.48)
dt <j>(l- S or - S-.J [ML
The finger grows exponentially if M> 1, decays exponentially if M< I, and does
not propagate if M = 1.

Exercises

Exercise 6.1 Show that Eq. (6.7) is a solution of Eq. (6.1).

Exercise 6.2 Use Eq. (6.45) to determine the rate of finger growth of a unit
mobility flood in a horizontal medium. Hint: Set M = 1 in Eq. (6.45) and
simplify.

Exercise 6.3 Use Eq. (6.48) to explain why the mobility ratio condition M< 1
is considered "favorable" for a displacement flood.