Evaluation of the non-Darcy effect in coalbed methane production

• A coupled model is developed to study non-Darcy flow in coal.
• Variable β factor as function of permeability is coupled.
• Constant β factors may significantly under or over estimate production rate.
• Evolution of non-Darcy factor becomes tortuous with variable β factor applied.
• Increasing coal cleat compressibility intensifies the tortuous behavior.

The non-Darcy factor, an indicator for the non-Darcy effect, is dependent on the properties of porous media and pore fluid including permeability, viscosity, density, flow velocity and a coefficient named as β factor. Experimental results show that the β factor can be expressed as a power law of permeability. For conventional gas reservoirs, this β factor can be assumed as a constant as the permeability change is negligible. However, the constant β factor may not be suitable for coal seams with remarkable permeability change and a variable β factor as a function of coal permeability should be an alternative. Moreover, the coal permeability change is complex due to the competing effects of coal cleat compression and sorption induced coal shrinkage/swelling. Few studies have been done previously to incorporate the variable β factor as a function of coal permeability in reservoir simulations. In the present work, both the coal permeability change and the variable β factor are coupled in a dual porosity model to study the non-Darcy flow behavior in coal seams. The simulation results illustrate that the evolution of non-Darcy factor becomes tortuous by using a variable β factor, which differs from the monotonic behavior when constant β factors are applied. Furthermore, increasing the coal cleat compressibility and matrix shrinkage strain tends to intensify the tortuous behavior. The simulation results also indicate that using typical constant β factors, instead of the variable one, may significantly underestimate or overestimate the gas production rate for coalbed methane wells.