A Comprehensive Study of Pressure Transient Analysis With Sorption Phenomena for Single-Phase Gas Flow in Coal Seams

Abstract

Abstract This paper identifies the need for the development of specialized solutions for pressure transient analysis in coal seams and, subsequently, provides a comprehensive solution package for these reservoirs. The proposed solutions are applicable to radial systems with finite wellbore radius and with either an infinite outer boundary, a constant pressure outer boundary or a closed outer boundary. At the inner boundary constant pressure or constant terminal rate cases can be specified. The single-phase flow formulation for coal bed methane includes non-equilibrium sorption phenomena in the coal matrix and laminar gas transport in the natural fracture network (clear system). The transport of methane in the coal matrix 1%. described by using spherical elements. The mathematical models which account for unsteady state and pseudosteady state matrix/tissure methane transfer are incorporated to the transport equationIn order to obtain a closed form solution in real time domain and avoid the pitfalls of numerical inversion approximate inversions of the solutions from the Laplacian space are also developed. These closed form solutions are found to be in good agreement with the numerically invened solutions. The effects of different models of matrix/tissure flow on the solution are also discussed. The validity of the proposed analytical solutions are checked against a numerical simulator and comparisons showing good agreements between the two are presented. The solution package describes forward solutions which have the potential to be used in an interpretation method for insitu characterization of coal seams and other gas reservoirs where adsorption and desorption phenomena are considered to be active. Introduction Coal seams are classified as unconventional gas reservoirs together with tight gas sands, Devonian shales and geopressured aquifers. Estimates of total recoverable gas from unconventional reservoirs range from 300 Tscf to 2600 Tscf, doubling the world's proven reserves if the optimistic estimate is correct. During the coalification process as much as 46 Mscf of gas can be liberated and some 20 to 500 scf of gas is retained by one ton of coal. Therefore, coal seams are reservoirs as well as source rocks for gas which is primarily composed of methane and which mostly needs little processing before its commercial distribution. Coal seam reservoirs have a dual porosity nature with macropores made by natural fracture network, and micropores which exist within the coal matrix. Natural fracture system consists of two fissure systems, namely, butt and face cleats. Butt cleats are less continuous and often terminate against the face cleat with a strike angle of 75 to 85 degrees. While the macropore space usually accounts for less then 2 percent of the bulk volume, as much as 85 percent of the coal's total porosity is due to the micropore structure. The pore diameter in the coal matrix ranges from 5 to 10 Angstrom units causing coal matrix to exhihit a large internal surface area. Due to the large internal surface areas of tight gas reservoirs. Devonian shales and coal seams a significant amount of gag is stored in the adsorbed state as well as free gas in the pore structure. Two different reservoir description techniques (single and double porosity approaches) and three models of sorption kinetic (unsteady state, pseudo-steady state and non-equilibrium) models are currently being used to describe the behavior of coal bed reservoirs in which sorption phenomena are significant. Reviews of more than 35 mathematical models related to unconventional gas resources are presented in References 8 and 9. The sorption kinetics models used in the literature are provided in detail in Reference 10.This paper provides solutions that employ non-equilibrium models of sorption/diffusion processes, for the reservoirs in which diffusion in the micropores obeys Fick's law of diffusion. The equilibrium isotherm which defines the amount of desorbed gas is obtained by using Langmuir's theory. Two nonequilibrium sorption models employed in the proposed solutions are based on unsteady state and pseudo-steady state formulations. Pseudo-statedy state sorption formulation is mathematically less Pseudo-statedy state sorption formulation is mathematically less rigorous than unsteady state formulation which requires more computational work and memory when implemented in the numerical models. Although long term forecasts of these two models do not differ significantly, Spencer et al. concluded that the early time predictions obtained using pseudo-steady state approach may not be accurate. P. 411