Transient and semi-steady-state solutions of the radial diffusivity equation are presented for the case of well tests on coalbed-methane reservoirs.
An inverse diffusion term, which characterizes coupled matrix-fracture gas. transport, is defined from a Langmuir desorption term and the inverse hydraulic diffusivity. The ratio of this total or coupled diffusivity to the hydraulic diffusivity is identified as the time delay of the bottom-hole flowing pressure response of the coalbed vis-a-vis that of a conventional gas reservoir during a constant-rate pressure drawdown test.
The modified transient and semi-steady-state equations for pressure drawdown as functions of time are completely analogous to those for conventional gas reservoirs when the inverse hydraulic diffusivity of the latter is replaced by the inverse coupled diffusivity of the coalbed.
A numerical simulator is employed to solve the open forms of both the conventional and coalbed radial diffusivity equations. The usual straight-line trends for the transient and semi-steady-state periods are manifest from simulation of both cases. These were parallel for the transient time period and divergent for the semi-steady-state period.
Values of permeability, net skin factor, area of drainage and shape factor are obtained directly from the pressure-versus-time plots of the two time periods.
The present analysis is limited to the extreme matrix-to-fracture transport rates, namely, instantaneous and zero. Actual pressure-response data, however, can be analyzed for any implicit transport rate.
The present work is limited to single-phase gas flow without wellbore storage and to a single net skin effect.