Page 283 - Fundamentals of Gas Shale Reservoirs

CANISTER DESORPTION TEST 263

Valve 1 P c Valve 2

V d

V p

V r

FIGURE 11.17 Schematic model of the canister desorption apparatus. The upper and lower faces of the drill core sample (volume V and
p
radius R ) are sealed to allow for a radial flow. The cumulative volume of desorbed gas (V ) is chronologically recorded for the permeability
d
a
estimation.

The theoretical basis of the canister desorption data anal- drill core is negligible, the analytical solution of Equation
ysis is similar to the analyses of pulse‐decay and crushed 11.60 in terms F is given as,
R
sample tests. Assuming that the length of the drill core L is
sufficiently larger than its diameter (L > 2R ), the material 1 2 / 2
a
balance equation is described in cylindrical coordinates as, F D 14 2 e n Kt R a , (11.64)
n 1 n
m k 1 m
r 2 , (11.60) where n is the nth root of the Bessel equation, J (ξ ) = 0, R is
0
a
n
t c [ (1 ) K r ] 2 r the drill core radius, and K is the apparent transport
a
g
coefficient,
where m = m(p) is the pseudo‐pressure potential, defined in
Equation 11.27. Equation 11.60 is subject to two boundary K k . (11.65)
conditions and one initial condition, c g (1 ) K a
m
BC-1: 0, r , 0 (11.61) 11.10.1 Permeability Estimation with Early Time
r
Cumulative Desorbed Gas Data
BC-2: m m , r R , (11.62)
e a Equation 11.64 is approximated for the early time
(τ = Kt/R < 0.0002) as,
2
IC : m m 0 , 0 r R a , t , 0 (11.63) a
4 K
where m is the initial gas pseudo pressure in the drill core, F D t. (11.66)
0
and m is the pseudo pressure at the ambient pressure and R a
e
reservoir temperature conditions.
We define the cumulative desorbed gas mass fraction F Equation 11.66 implies the early‐time cumulative
D
as the ratio of the cumulative gas desorbed from the drill desorbed gas fraction plotted against the square root of time
core to the ultimate cumulative desorbed gas. Assuming a would yield a straight line,
one‐dimensional radial flow in an infinitely long cylinder,
such that the boundary effects on the top and bottom of the F D s 1 t. (11.67)