Nonlinear and Linear Equation of Gas Diffusion in Coal—Theory and Applications

Abstract

The authors derived the analytical solution to diffusion equations. The solution requires linearization of diffusion equations, as well as developing the obtained expression into a series. In particular, the result of the first procedure is highly deviated from the exact solution. The authors conducted a sorption experiment and then, in relation to the registered kinetics of the diffusion of CO2 inside hard coal grains, approximated the linear solution and the numerical nonlinear solution by means of the least squares method. As confirmed by the lower value of the sum of deviation squares, it can be clearly demonstrated that the nonlinear equation represents the actual measurement more accurately.

Influence of Grain Size and Gas Pressure on Diffusion Kinetics and CH4 Sorption Isotherm on Coal

“…in the kinetic description of the methane (cH 4 ) sorption/desorption process model on coal, the diffusion stage is presumed to be the predominant factor [44,45]. the parameter that quantifies diffusion kinetics is the effective diffusion coefficient.…”

Biogeochemical Controls on Methane Generation: A Review on Indian Coal Resources

“…Further, in an attempt to derive the gas diffusion equations in coal, Gawor et al [48] introduced the term "accumulation kinetics" to understand the temporal kinetics of the gas molecule transportation in sorption processes. They suggested that the amount of gas sorption and, consequently, the gas transport in coal depends on the pore size distribution.…”

Fractal-Time-Dependent Fick Diffusion Model of Coal Particles Based on Desorption–Diffusion Experiments

“…Coalbed methane (also known as gas) is an unconventional natural gas mainly composed of CH 4 (containing a small amount of CO 2 and N 2 ) formed during the coalification of the parent coal material and stored in a coal seam. − Studies generally recognize that the following two gas flow modes control gas migration in coal: one is through the diffusion in coal matrix pores ,, and the other is the seepage through cleats and fracture systems in the coal body. − The first process is driven by the concentration difference and follows Fick’s law, − and the second is driven by the pressure difference and follows Darcy’s law. ,, During gas drainage, CH 4 molecules first desorb from the pore surface, then diffuse through the pore system in the matrix driven by the gas concentration difference, and finally flow in the cleat system caused by the gas pressure difference, where diffusion plays an important role. ,− Diffusion refers to the phenomenon in which gas molecules migrate from a high- to low-concentration region until they are distributed uniformly. It is considered the first step of gas migration in coal (desorption is deemed to be finished instantaneously, approximately 10 –10 –10 –5 s). ,, The diffusion coefficient is a key parameter to characterize the diffusivity of methane, which is also required to evaluate gas diffusivity in coalbed methane exploitation, gas control, CO 2 displacement, or storage. − Therefore, it is imperative to understand the calculation model for obtaining the diffusion coefficient.…”

“…7−9 The first process is driven by the concentration difference and follows Fick's law, 10−12 and the second is driven by the pressure difference and follows Darcy's law. 9,13,14 During gas drainage, CH 4 molecules first desorb from the pore surface, then diffuse through the pore system in the matrix driven by the gas concentration difference, and finally flow in the cleat system caused by the gas pressure difference, where diffusion plays an important role. 12,15−17 Diffusion refers to the phenomenon in which gas molecules migrate from a high-to low-concentration region until they are distributed uniformly.…”