Environmental Engineering Reference
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isothermal mathematical model that was resolved using the finite difference method
and a Godunov discretization scheme. The model solution was divided in three steps:
(1) the hydrodynamic modeling of two-phase flow through the well using a drift-flux
model proposed by Hasan et al. (
2007
), (2) the heat losses from the wall well toward
the formation using a global heat transfer coefficient, and (3) the heat diffusion in
the formation. The heat diffusion was modeled by the transient cylindrical 2D heat
equation. Their results showed good agreement against field data. On the other hand,
Mozaffari et al. (
2011
) solved numerically a mixture model for steam injection, fol-
lowing the same approach as Bahonar et al. (
2009
). Their predictions of pressure,
temperature and steam quality showed good agreement against field data.
Previous studies have shown that the drift-flux model coupled to a transient 2D
heat diffusion equation, allow to analyze the steam injection process in vertical wells.
The aim of this work is to study the behavior (pressure, temperature, steam quality,
and heat loss) of a vertical steam injection well using a drift-flux model.
2 Model Formulation
2.1 Physical Model
Figure
1
shows the physical model of a system formed by a steam injection vertical
well and a surrounding porous medium. The system is divided in three main parts:
(1) the well tubing, (2) insulation, annulus (filled with air), casing and cementing,
and (3) the porous medium, which is considered as a continuum media. The system
is fed with a water-steam mixture at constant pressure and steam quality.
2.2 Mathematical Model
To simulate the steam injection system showed in Fig.
1
, the semi-unsteady-state
model proposed by Bahonar et al. (
2009
) is used. Such model involves: (1) a steady-
state drift-flux model to simulate the hydrodynamic behavior of a steam-water down-
ward flow into the injection well, (2) an overall heat transfer coefficient to evaluate
the total heat loss from the well to the porous medium, and (3) a thermic model,
which consists of a 2D transient heat diffusion equation to evaluate the heat transfer
through the porous medium.
The hydrodynamic model consists of mass, momentum and energy conservation
equations as follows.
Mass balance equation
z
ˁ
g
v
sg
+
ˁ
l
v
sl
=
∂
∂
−
0
(1)
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