Page 166 - Fundamentals of Enhanced Oil and Gas Recovery

154 Forough Ameli et al.

m s H s
z 5 2 h (5.81)
2
πr h MT s 2 T R Þ
ð
α t 2 t i Þ
ð
(5.82)
t Dz 5
2
ðz1hÞ=2
Removal of hot fluids in Boberg Lantz model:
_
Q 5 5:615q oh ρ C o 1 F WOR ρ C w ðT p 2 T R Þ (5.83)
o
w
p
Q p is the rate of energy removal (Btu/d), T p is the average T of heated region,

adjusted for removal of hot fluids ( F), F WOR is the water-to-oil ratio, energy
removed by hot fluid in (t 2 t i ):
t _
Q dλ
1 p
ð
δ 5 (5.84)
2 m s H s
t i
T p 2 T R
T Dp 5 5 T Dr T Dz 1 2 δÞ 2 δ (5.85)
ð
T s 2 T R
T p 5 T R 1 T s 2 T R Þ T Dr T Dz 1 2 δÞ 2 δ (5.86)

ð
ð
Gas water production in Boberg Lantz model is as follows:
_
Q 5 q oh H ogv 1 H wrv (5.87)
p

H ogv 5 5:615ρ C o 1 F GOR C g ðT p 2 T R Þ (5.88)
o
H wrv 5 5:615 F WOR ðH wT 2 H wr Þ 1 F wv λ s Š (5.89)
½
where H wrv is the enthalpy of produced water (Btu/bbl), H ogv is the enthalpy of pro-
duced oil and gas (Btu/stb), H wT is the enthalpy of saturated water at T (Btu/lbm),
F GOR is the GOR (scf/stb), F WOR is the WOR (bbl/stb), F WV is the for water
condensed from produced vapor (bbl/stb).
The amount of water condensed from vapor is determined by:

p wv
F wv 5 0:0001356ð Þ F GOR (5.90)
p w 2 p wr
where F wv is the WOR for water condensate from produced gas (bbl w@60 F/stb),
p wv is the vapor pressure of water at hTi, p w is the BHP, p wr is the vapor pressure of
water at T R , F GOR is the GOR (scf/stb).

p wv
F wv 5 0:0001356ð Þ F GOR (5.91)
p w 2 p wr