Page 480 - Enhanced Oil Recovery in Shale and Tight Reservoirs

444 Enhanced Oil Recovery in Shale and Tight Reservoirs

Table 13.9 d c values for some geometries (Gray, 2016).
Geometry Dimensions d c

Infinite plane slab Width 2L 0.878
2
2
Rectangular box Sides 2L, 2r, 2m; 0.873 (1 þ L 2/12 þ L /m )
L < r, m
Cube Side 2L 2.52
Infinite cylinder Radius L 2.00
Equicylinder Height 2L, radius L 2.76
Sphere Radius L 3.32
Infinite square rod Side 2L 1.70

This method can be used to obtain activation energy when the critical
temperature and critical size are measured from the experimental work.
On the other hand, this method can also be used as a scaling law to predict
the critical ambient temperature for large-scale bodies from small laboratory
samples, where L is considered as the argument in the above equation. Or
the equation can be used to estimate the critical size L for a certain geometry
d c at a fixed critical ambient temperature T a;c . When doing so, parameters
such as reaction rate, activation energy, and heat of the reaction need to
be provided. They can be provided by TGA and DSC experiments. Specif-
ically, the TGA is used to obtain kinetic parameters for crude oil oxidation
reactions based on the Arrhenius method, and the DSC is used for estimating
the heat of reaction. The feasibility of this method is investigated below.
Consider an oil reservoir of the geometry of an infinite slab. The critical
dimensionless parameter, d c , is 0.878 according to Table 13.9. According to
Huang and Sheng (2017a), typical kinetic data for the activation energy E
vary from 20 to 70 kJ/mol (median 33 kJ/mol), and the typical values for
1 5 1 1
the frequency factor A from 0.1 s to 10 s (median 50,000 s )
for LTO. According to Zhang and Sheng (2017), the enthalpy values Q
for LTO are from 20 to 3635 kJ/mol. Earlier in Table 13.6, the enthalpy
values are 844 and 1210 J/g. If the molecular weight is 200 g/mole, the
enthalpy values are 168.8 and 242 kJ/mol, respectively. An average of
200 kJ/mol may be taken. The value of formation thermal conductivity l
used in Green and Willhite (1998) is about 2.6 J/(s$m$K). The oil density
3
of 850 kg/m is taken. The reservoir temperature T a is assumed to be
80 C. These average values or the base case values are listed in Table 13.10.

Using these values, the calculated critical reservoir thickness to lead to
spontaneous ignition is 0.00,073 m. This indicates that spontaneous ignition
is ready to achieve in the reservoir.