Page 264 - Fundamentals of Enhanced Oil and Gas Recovery

252 Alireza Keshavarz et al.

In spherical crushed core samples, the relationship between the sorption time con-
stant, t 0 , and diffusion coefficient, D, is presented in Eq. (8.24) [63]:
r p 2
D 5 (8.24)
t 0
In this equation, r p represents the mean radius of coal particles, and the term D=r p 2
is referred to as diffusivity with the dimension of 1/time.

Example 8.3: Sorption time.
Keshavarz et al. conducted sensitivity analyses on diffusion coefficient measure on
18 Australian coal samples [64]. The sample No. 8 had the diffusivity measure of
0.098 and 0.53 hour 21 for CH 4 and CO 2 , respectively. The sample also had the β
value of 0.53 and 0.5 for methane and CO 2 . The required time for this sample to
release 90% of the adsorbed gas for each of the gases is calculated using Eq. (8.23).
For CH 4 ,

0:53

0:9 5 1 2 exp 2 0:098t 90% Þ -t 90% 5 49 hour
ð
For CO 2 ,
0:5

0:9 5 1 2 exp 2 0:53t 90% Þ -t 90% 5 10 hour
ð
The results of this example show that the gas diffusion happens much quicker for
CO 2 compared to methane.

8.4.2.4 Upscaling From Laboratory to Reservoir Scale
As discussed above, pseudo steady state diffusion model, Eq. (8.18), could closely
describe the gas flow from matrix system to cleats during desorption and from cleats
to matrix system within adsorption process in CBM reservoirs, as observed on
Fig. 8.4 [60,61]. However, there is a difference between the time constant, t 0 , related
to laboratory experiments to that of reservoir scale. Kazemi model suggests that the
matrix fracture interface area per unit bulk volume, σ, in naturally fractured reser-
voirs is defined as [65 67]
!
1 1 1
σ 5 4 1 1 (8.25)
a 2 a 2 a 2
x y z
where a i represents the fracture spacing in the i direction.
Therefore, in reservoir scale, the adsorption/desorption time, τ, would be
1
τ 5 (8.26)
Dσ