Page 187 - Fundamentals of Enhanced Oil and Gas Recovery

175
Thermal Recovery Processes

3. The fluid and rock properties are uniform.
4. Consider no gravity segregation.
5. No heat is lost ahead of heated area.
The energy to heat unit volume of formation to temperature of T is formulated as
follows:

Q 5 M R ðT 2 T R Þ (5.112)

M R 5 1 2 φð Þρ C r 1 φ S o ρ C o 1 S w ρ C w 1 S g ρ C s (5.113)
r
o
s
w
where M R is the average heat capacity of reservoir (Btu/ft 3 F) or (kJ/m 3 C), C is
the mean specific heat capacity (Btu/lb F) or (kJ/kg C), S is the saturation, φ is the

3
3
effective porosity, ρ is the density (lb/ft ) or (kg/m ), r, o, w, s are the rock, oil, water,
and steam, respectively.
Heat balance over heated area is as follows:
_
_
Q 2 Q loss 5 dQ R 5M R T s 2 T R Þ hdA h (5.114)
ð
in
dt dt
where Q in is the rate of energy input by steam inj., Q loss is the rate of heat loss by
conduction to o/u, dQ R /dt is the rate of change of energy in reservoir, dA h /dt is the
rate of increase in heated area, M R is the heat capacity of reservoir, T R is the reservoir
T, T s is the steam T, t is the time, h is the reservoir thickness.
The input heat by steam injection is
CF 5 (350/24) lb/h when bbl/d (1 bbl 5 159 L)
_
ð
ð
Q 5 _m s C w T s 2 T R Þ 1 f s λ s Þ (5.115)
in
where Q in is the rate of energy in by steam inj. (Btu/h) or (kJ/s), m s is the (CWE)
stem inj. rate (lb/h) or (kg/s), f s is the steam quality (5wt fraction of saturated steam
as gas in the mix), λ s is the latent heat of vaporization of water at T s (Btu/lb) or (kJ/kg),

C w is the specific heat capacity of water (Btu/lb F) or (kJ/kg C).

5.2.11.2 Heat Loss to O/U
In this case, the lost heat to the boundaries is calculated using conduction heat mecha-
nism in a semiinfinite medium and T designated by a complimentary error function.
This case is represented in Fig. 5.13.
Temperature distribution for heat conduction in semiinfinite media is as follows:

z
T 2 T R
5 erfc p ffiffiffiffiffi (5.116)
T s 2 T R 2 αt