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Mathematical modeling of methane flow in a borehole coal mining system

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Abstract

Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.

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Abbreviations

a :

sorption capacity parameter

A :

area, m2

b :

slip parameter, Pa

c :

compressibility parameter, Pa-1

d :

methane density, kg m-3

D :

diffusion-dispersion parameter, m2s-1

g :

gravitational acceleration, m2 s-1

G :

sorbed methane volume, nm3 m-3

H :

height, m

k :

permeability, m2

m, n :

sorption parameters

M :

molecular weight, kg kmol-1

p :

pressure, Pa

q :

flow rate between systems, kg m-3 s-1

r :

radius, m

R :

universal gas constant, Pa m3 mol-1 K-1

S :

specific area, m-1

t :

time, s

T :

temperature

v :

Darcy velocity, m s-1

V :

volume, m3

z :

methane compressibility

φ :

porosity

μ :

viscosity, Pa s-1

div:

divergence operator

grad:

gradient operator

a :

macro

ae :

macro-mezo

c :

sorption

e :

mezo

ei :

mezo-micro

i :

micro

K :

Klinkenberg

max:

maximum

n :

normal

o :

reference

r :

relative

R :

rock

s :

total

.t :

time

,t :

ordinary differential operator with respect to time

t :

partial differential operator with respect to time

a :

average

g :

free methane

G :

sorbed methane

References

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Authors and Affiliations

  1. Computer Center, Technical University for Heavy Industry, H-3515, Miskolc, Miskolc-Egyetemváros, Hungary

    László Balla

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  1. László Balla
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Balla, L. Mathematical modeling of methane flow in a borehole coal mining system. Transp Porous Med 4, 199–212 (1989). https://doi.org/10.1007/BF00134997

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  • DOI: https://doi.org/10.1007/BF00134997

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