Page 205 - Advances In Productive, Safe, and Responsible Coal Mining

184 Advances in Productive, Safe, and Responsible Coal Mining

properties: desorption from coal surfaces, diffusion through the coal matrix, and flow
through the coal seam fracture system. The two more common methods used in
modeling the rate of CMM emissions are Fick’s and Darcy’s laws.
In order to perform a mathematical analysis using Fick’s method, the coal seam is
assumed to be composed of small spheres, at the surface of which diffusion occurs.
Fick’s law describes diffusion from spheres along the concentration gradient as:

2
∂C ∂ C 2∂C
¼ D + (10.1)
∂t ∂r 2 r∂r
3
3
where C is CMM concentration in coal in ft /ft , t is time in second, D is coefficient of
2
diffusion in ft /s, and r is radial coordinate in ft. Solving this equation for various ini-
tial and boundary conditions results in different solutions that can be used to model
CMM emissions.
In Fick’s law, the size of the hypothetical sphere where diffusion takes place is
important since it determines the degree of fragmentation of the coal seam. In addi-
tion, combining the radius of the sphere (a) with the coefficient of diffusion (D) results
2
in a new diffusion parameter D/a that determines both the rate at which a coal seam
will diffuse methane and the fraction of seam gas content that can be drained in a
given time.
On the other hand, Darcy’s dynamic flow equation describes gas transport through
the fracture system in coal where the driving force is the pressure gradient. In fact,
Darcy’s law holds that the flow rate of CMM through a porous medium is proportional
to the potential or pressure gradient, which is simplified for low pressures in homo-
geneous medium, linear case, and laminar flow as:

2 2
∂ P μϕ ∂P 2
¼ + (10.2)
∂x 2 kP ∂t
where P is gas pressure in atm, x is distance into coal seam from face in ft, μ is absolute
viscosity of methane in lb mass/ft s, ϕ is pseudoporosity, k is permeability of coal in
millidarcies, and t is time in second.
According to these equations, it is apparent that the net rate of CMM emission
under normal conditions is a function of reservoir pressure, permeability, coal gas
content, porosity, and diffusivity.

10.2.4 Methane’s importance in industry
Methane offers a unique opportunity for the coal industry to proactively address the
climate change issue and simultaneously increase available energy supply. The rela-
tive abundance of methane on Earth makes it an attractive fuel, though capturing and
storing it poses challenges due to its gaseous state under normal conditions for tem-
perature and pressure. Capturing CMM has the potential to be a cost-effective method
to reduce GHGs, increase energy security, provide coal mines with economic and
environmental benefits, recuperate ventilation air quality, and improve miners’ safety.