Investigation of Barree-Conway non-Darcy flow effects on coalbed methane production

Coalbed gas non-Darcy flow has been observed in high permeable fracture systems, and some mathematical and numerical models have been proposed to study the effects of non-Darcy flow using Forchheimer non-Darcy model. However, experimental results show that the assumption of a constant Forchheimer factor may cause some limitations in using Forchheimer model to describe non-Darcy flow in porous media. In order to investigate the effects of non-Darcy flow on coalbed methane production, this work presents a more general coalbed gas non-Darcy flow model according to Barree-Conway equation, which could describe the entire range of relationships between flow velocity and pressure gradient from low to high flow velocity. An expanded mixed finite element method is introduced to solve the coalbed gas non-Darcy flow model, in which the gas pressure and velocity can be approximated simultaneously. Error estimate results indicate that pressure and velocity could achieve first-order convergence rate. Non-Darcy simulation results indicate that the non-Darcy effect is significant in the zone near the wellbore, and with the distance from the wellbore increasing, the non-Darcy effect becomes weak gradually. From simulation results, we have also found that the non-Darcy effect is more significant at a lower bottom-hole pressure, and the gas production from non-Darcy flow is lower than the production from Darcy flow under the same permeable condition.