Mathematical Modeling of Steam Injection in Vertical Wells - Selected Topics of Computational and Experimental Fluid Mechanics - page 330

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the mass balance equation (Eq. 1 ). Also, water and steam densities at k 1 2,

ˁ g k + 1 / 2 = ˁ g k .
6. In-situ volume fraction, f g , is calculated using correlations for downward two
phase flow for different flow patterns.
7. v sg is recalculated using the momentum balance equation (Eq. 2 ), and the fluid
properties are reevaluated.
8. Heat loss is calculated using Eq. ( 4 ).
9. v sg is calculated from the energy balance equation using an iterative Newton-
Raphson scheme. The v sg calculated is compared against the v sg assumed, and
if they are different, step 5 is repeated; otherwise, the pressure convergence at
current grid block is reviewed. If P sat calculated in step 7 is different than P sat
assumed, then step 2 is repeated; otherwise, steps 1-9 must be done for the next
grid block until all the grid blocks are visited.
10. Equation ( 6 ) is solved and the results are saved in a text file. If the simulation
time has been reached, the solution process will stop, otherwise; steps 1-9 must
be repeated for a next time step.

ˁ l k + 1 / 2 = ˁ l k and

are approximated as

4 Results and Discussions

In order to validate the computational code, predictions were compared against
numerical/field data reported in literature. Table 1 shows the field data parameters of
the Martha Big Pond well (Bahonar et al. 2009 ), which were used to get predictions.
Figure 2 shows a comparison of predictions (flow pattern, pressure, temperature,
steam quality, and heat loss) against numerical/field data. Pressure and temperature
profiles have good agreement and small differences (smaller than 2%) were gotten
for steam quality and heat loss. Figure 2 d shows that there is not a large steam
condensation, then: (1) the hydrostatic pressure drop is small and pressure diminishes
along the well (Fig. 2 a), (2) there is annular flow along the whole well.

Ta b l e 1 Field data parameters of Martha Big Pond well (Bahonar et al. 2009 )
r ti

0.2BTU/h ft ⓦ F

0.08850 ft k cem

r to 0.104167 ft ʵ to 0.9

r ins No insulation ʵ 0.9 ci

r ci 0.166667 ft W 4850 lbm/h

r co 0.187500 ft X 0.8

r wb 0.600000 ft P 250 psia

1BTU/hft ⓦ F 50 ⓦ F k e T wh

0.0286 ft 2 /h

ʱ e

Depth 1600 ft

0.0283 ⓦ F/ft g T Annulus pressure 14.7 psia