Page 341 - Enhanced Oil Recovery in Shale and Tight Reservoirs

314 Enhanced Oil Recovery in Shale and Tight Reservoirs

which is for the matrix. The parameters for the capillary desaturation curves
used in the base model for the fracture at (N C ) C are reported in Table 11.2,
and the parameters for the fracture at (N C ) max are the same as those for the
matrix in Table 11.3. The same values of T p in Table 11.3 are used for the
matrix and the fracture.
The model is symmetric along the Y direction. To cut the simulation
running time, the model is cut into two halves along the Y direction.
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Furthermore, 1 of matrix in the X direction (1/3 of model in the X
direction) and one fracture (half model in the Y direction) are included in
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the model. The final model sizes become 1 1.5 1 . The grids are
00
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11 6 3. The injection rate is changed to one-sixth of that of the exper-
3
iment, that is, 0.00033 ft /day. Based on this smaller model, the
permeability and porosity in the base model are replaced by shale properties
2
which are 300 nD (w3 10 19 m ) and 0.1 for the permeability and
porosity, respectively.
In general, a surfactant may change wettability and reduce IFT. Since the
surfactant is injected with the alkali, the model assumes the surfactant
reduces IFT and the alkali changes wettability. The degree of wettability
alteration is controlled by interpolation scaling factor parameters u kr to
represent the changes in relative permeability and u pc to represent the
changes in capillary pressure:
k r ¼ u kr k ww þð1 u kr Þk mw (11.1)
r r
p C ¼ u pc p ww þð1 u pc Þp mw (11.2)
C C
where the superscript ww and mw denote water-wet and initially mixed-wet
conditions. The capillary pressure p C is a scaled with IFT, porosity, and
permeability as follows:

r ffiffiffi ww ! E pc
jj
ww 4 s 0 S j S jr
p Cjj 0 ¼ C pc ow 1 P 3 j0; j ¼ 1; 2; 3 (11.3)
jj j¼1 jr
k s 0 1 S
p ffiffiffiffiffiffiffiffi
where C pc f=k takes also into account the effect of permeability and
porosity using the Leverett-J function (1941), f is the porosity and k is the
permeability, s is the interfacial tension, S is the saturation at the water-wet
condition, the subscripts j; j0 denote phases with j being the wetting phase,
and S jr denotes the residual saturation of phase j. Phases 1, 2, and 3 represent
water phase, oil phase, and microemulsion phase, respectively. The capillary
pressure endpoints in Table 11.2 are C pc here. Assume the same C pc