Environmental Engineering Reference
In-Depth Information
where, S w is the water saturation, R w is the resistivity of water, R t is the
true resistivity of rock, and Φ is the porosity. From equation 5.118, the bulk
electrical conductivity of the reservoir rock can be found as:
S
R
2
1
Φ
*
w
(5.119)
s
=
.
t
2
w
Assuming a uniform current density in the reservoir, the radial distri-
bution of potential (voltage) is solved first. Then, the flux resulting from
potential (voltage) difference in cells is found using the TPFA scheme.
Finally, the total production due to applied electrical gradient at each time
step is added to the production due to the applied pressure gradient at that
specific time step and the computation is repeated.
Using the IMPES technique and implementing the TPFA scheme, the
numerical simulation of two-phase flow under applied pressure and elec-
tric gradients was accomplished on MATLAB. One layer of the model res-
ervoir from the SPE 10 model data (Christie and Blunt, 2001) was used
for a two-dimensional simulation of the flow under applied pressure and
electrical gradients (Ghazanfari, 2013). The model size is 60 x 220 x 1 cells
and the size of each scaled cell is 20 ft x 10 ft x 2 ft (figure 5.14). The fluids
are assumed to be immiscible and incompressible. The actual porosity and
permeability tensors of the selected layer from the SPE 10 model were used
for simulation. The tensor of EO permeability was assumed to be constant
as 1x10 -5 (cm 2 /V.sec) in the reservoir. The EO relative permeability coef-
ficients evaluated experimentally (see figures 5.5 and 5.6) were used as rep-
resentative functions of water saturation for the reservoir.
Gravity term and capillary effect were ignored in the simulation. The
reservoir was assumed to be initially filled with oil with S wc = 0.2 (con-
nate water saturation) and S or = 0.2 (residual oil saturation). The fluid vis-
cosities were assumed as m w = 1 cp and m 0 = 38 cp. Injection well was set
at the lower-left corner and production well at the upper-right corner and
no-flow conditions were imposed at the boundaries. Electric field (current
density:1 Amp/m 2 ) was assumed to be applied through electrodes inserted
inside the injection and production wells as shown in figure 5.14.
The saturation, production, and oil recovery profiles at three different
time steps are shown in figures 5.15 (a), (b), and (c) respectively. In these
figures, the left hand side graph shows the saturation profile, the middle
graph shows the changes in the production profile over time including
the fractional flow of water and oil, and the right hand side graph shows
the variation of oil recovery (%) with pore volumes of injected water. To
investigate the contribution of applied electric field to the oil recovery, two
 
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