Page 154 - Fundamentals of Enhanced Oil and Gas Recovery

142 Forough Ameli et al.

Position of
interface Oil flow
T = T in dQ
s
steam
chamber ξ
T = T R in
Normal original
velocity chamber
U Heat
conduction
y
θ

x
Figure 5.1 Representing Darcy law in SAGD process. SAGD, steam-assisted gravity drainage.

plays an important role in recovery of Alberta’s oil sand deposits. For shallow bitumen
reservoirs, strip-mining technique is mainly applied. However, for the large deep
deposits that surround the shallow ones, application of SAGD method is more suit-
able. This technology is expected to be the primer for oil recovery from Canadian oil
sands [18]. On the other hand, application of surface mining techniques consumes
more than 20 times water quantity in comparison to other common techniques.
Darcy flow for oil (per unit thickness) in SAGD process is formulated as the
following equation (Fig. 5.1):

Kdξ 3 1Þ ρ 2 ρ gsinθ
ð
g
o
dq 5 dξ (5.1)
μ
o
where dq is the incremental oil flow rate, K is the permeability, dξ is the incremental
oil thickness, θ is the interface inclination.
SAGD-Darcy flow of mobilize oil is formulated as follows:
Kgsinθ
dq 5 dξ ðheated reservoirÞ (5.2)
ν o
Kgsinθ
dq r 5 dξ ðcold reservoirÞ (5.3)
ν r
If the only mechanisms of heat transfer beyond the interface (ξ-direction) is
conduction, then

T ξðÞ 2 T R ð 2Uξ=αÞ
5 e (5.4)
T s 2 T R