Page 160 - Fundamentals of Enhanced Oil and Gas Recovery

148 Forough Ameli et al.

5.2.2.3 CSS Aziz and Gontijo Model
Aziz and Gontijo developed a model for vertical radial flows in the well. In this
model, gravity and potential were introduced as the driving force. The steam zone
was considered conical. To derive this model, the following assumptions were made:
1. There should be considered an initial saturation for water and oil phases.
2. By injection of the steam, a conical volume is formed.
3. The heat transfer is ignored in the phase of steam injection and the reservoir mean
temperature is equal to steam temperature.
4. Oil is moved below a thick layer at oil steam interface.
5. The heat transfer mechanism from steam to oil zone is conduction.
6. The flow regime is pseudosteady state.
7. By oil production, the steam occupation zone is increased.
8. A combination of pressure drop and gravity leads to flow through the reservoir.
9. The mean temperature of the heated zone is determinative for the steam pressure
and consequently pressure draws down.
Using the above assumptions, heat transfer equation is as follows:

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k o ϕΔS o αΔ[
q o 5 1:87R x (5.35)
m o v avg lnR x =R w 2 0:5
where

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
R x 5 h t 1 R h 2 (5.36)
ΔS o 5 S oi 2 S ors (5.37)
P s 2 P wf
Δ[5 ΔHgsin θðÞ 1 (5.38)
ρ
o
h t
sin θðÞ 5 (5.39)
R x
(5.40)
Δh 5 h t 2 h st
θ represents the interface and reservoir base angle. The pressure is determined
using the following equation:

4:4543
T s
P s 5 (5.41)
115:95
The thickness of the steam zone is calculated using Van Lookeren [33] equation as
follows:

h st 5 0:5h t A RD (5.42)