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Reservoir Properties of Coal Seams 239
The two processes work in series, and the one with a lower rate will control the net
flow. Thus, in a shallow reservoir with high permeability and a low diffusion coeffi-
cient, the diffusivity determines the flow rate. In a deeper coal of high rank, the diffu-
sivity is one or two orders of magnitude higher, and the permeability is lower. Hence,
permeability determines the flow rate. It is, therefore, important to analyze the diffu-
sion of gas from coal. It also determines how much methane can be ultimately drained
from a coal seam.
14.3.1 The Diffusion Process
When a gas composed of molecule A (methane) comes in contact with gas composed
of molecule B (air), the contact will cause diffusion of A into B and B into A. The pro-
cess tends to produce a mixture of a uniform composition. Many enhanced methane
production techniques from coal use a gas driver, such as carbon dioxide (CO 2 ) or he-
lium (He), to increase production. Gas-to-gas diffusion is an important part of the study
to predict the diffusion process. Similarly, when gas is passed through a porous me-
dium wet with liquid (oil), the rate of attaining equilibrium between the gas and liquid
phases depends on the diffusion process.
Fig. 14.8 shows a simple diffusion process. Container A has CO 2 at 100% concen-
tration. Container B has 99% methane with 1% carbon dioxide. If the two vessels are
connected by a conduit 1 1 cm and 1 cm long, CO 2 will try to go into container B
and likewise methane will try to go into container A.
Assuming the containers are large in relation to the diffusion rate, the process is
expressed mathematically as
dc dc
¼ DA (14.15)
dt dx
where c ¼ number of molecules diffusing; t ¼ time; D ¼ diffusivity coefficient;
A ¼ area; dc/dx ¼ concentration gradient.
14.3.2 Determination of Sorption Time
The rate of gas diffusion from coal matrix to bore spaces in coal is, of course, deter-
mined by the diffusivity coefficient, D. Because it is not certain what the coal “mole-
2
1
cule” diameter, a, is, the diffusivity is often expressed as D/a that has a unit of sec .
Figure 14.8 Diffusion process for gases.