Type Curves for Dry CBM Reservoirs With Equilibrium Desorption
Authors: Gerami S. , Pooladi-Darvish M. , Morad K. , Mattar L. 
Published: March 2010

Abstract
The purpose of this work is to model the single-phase radial gas flow in coalbed methane including equilibrium sorption phenomena in the coal matrix and Darcy flow in the natural fracture network. Considering a control volume, the gas desorption rate as a function of time and space is incorporated into the radial continuity equation as a source term. Using a Langmuir-type sorption isotherm, the gas desorption rate is determined at any radius of the reservoir. Introducing the definition of pseudo-pressure and pseudo-time, the resulting continuity equation is converted into the linearized diffusivity equation by modification of total gas compressibility. It is shown how the traditional definition of the material balance pseudo-time is modified for dry CBM reservoirs. With the help of these transformations, the traditional (PTA and RTA) type curves can be employed for analysis of production data of dry CBM reservoirs. The model developed here is validated against Fekete's numerical CBM simulator over a wide range of reservoir parameters. In addition, one set of field data from Horseshoe Canyon coals of the Western Canadian Sedimentary Basin is analyzed using the solution procedure presented in this paper.

Introduction
Coalbed methane (CBM) is natural gas produced from coal seams. Coal is both the source rock and the reservoir for methane production. The world total CBM resource potential is evaluated at about 143.2 trillion cubic metres(1).
CBM reservoirs are naturally fractured reservoirs that are characterized by two distinct porosity systems including:micropores (matrix) with extremely low permeability andmacropores (natural fractures or cleats).
Due to the small pore diameter of less than 10 Å, the coal matrix has a large internal surface area of 100 to 300 m(2)/g(2, 3). As a result, substantial quantities of gas can be adsorbed on the surface of the coal grains. Micropores are impermeable to gas and inaccessible to water. However, the desorbed gas can be transported through the primary porosity system by diffusion. The macropores act as a sink to the micropores and provide permeability to fluid flow.
In porous media with larger pore size distributions, mass transfer is driven by pressure gradients, whereas in coal, mass transfer is driven by concentration gradients(4, 5). The diffusion through the micropores can be the result of three distinct mechanisms that may act individually or simultaneously(6):bulk diffusion, where molecule/molecule interactions dominate;Knudsen diffusion, where molecule/surface interactions dominate; andtwo-dimensional surface diffusion of the adsorbed gas layer.
The steady state diffusion coefficient of methane for most coals is on the order of 10−4 to 10−5 cm(2)/s(6). These experimentally determined diffusion coefficients represent averaged values including the contributions of the bulk, Knudsen and surface diffusion processes.
Diffusion effects can be quantified by determining a sorption time. The sorption time is equal to the time required to desorb 63.2% of the initial gas volume. It is determined from whole core canister desorption test. This time is related to fracture spacing and the diffusion coefficient(7).
Gas production from the CBM reservoirs is controlled by a four-step process that includes: