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.

Keywords

• nonlinear diffusion equation
• linear diffusion equation
• effective diffusion coefficient
• kinetics of CO₂ diffusion