Computer Modeling and Simulation of Coalbed Methane Reservoir

Abstract

Abstract The development of a three-dimensional coalbed-methane (CBM) numerical reservoir simulator is presented for modeling flow mechanism of coalbed methane gas reservoir and predicting its production performance. This model is a diphase (gas-water) mathematical model of applying dual grid system, and three processes, i.e. desorption, diffusion and percolation flow, undergone by coalbed methane from the coal matrix surface into wellbore are considered in the simulator. On the basis of the real gas law, Darcy's law and continuity equation, a mathematical model was established and numerically solved by use of differential discrete method; the coefficient term and production term in the equation were explicitly dealt with; and the implicit format treatment and solution were adopted to acquire the parameters and the amount of mass exchange of the coal matrix-cleat system. In addition, the program source code was written; through analyzing and contrasting examples, the simulator proved efficient and reliable in modeling the behavior of coalbed methane reservoir. The new model we have developed also permits to precisely describe the phenomena occurring within the coal cleats and micropores, and to be better understanding the production mechanisms of coalbed reservoir. Introduction Coal seams are categorized as unconventional gas reservoirs together with tight gas sands, Devonian shales, geopressured aquifers and hydrate. Coal differs from most normal porous gas reservoirs in pore structure, coal "rock properties" (porosity, permeability, and gas-water relative permeability), reservoir characteristics and fluid transport mechanism, which making the mathematical description of gas flow in coal seams a relatively complex problem and analytical solution to the coalbed gas transport problem being also challenging. However, much work has done in measuring coal-rock properties, analyzing production performance and modeling fluid flow in coal seams. At present, three type of the mathematical models of describing the coalbed gas transport were developed in order to increase the understanding in coalbed methane well production behavoir, i.e. empirical model, equilibrium adsorption model and non-equilibrium adsorption model. Empirical models being based on the simple mathematical descriptions of the physical phenomena observed, are mainly used for predicting methane release. Gas transport in the micropores of coal is generally modeled with equilibrium sorption and non-equilibrium sorption formulations. Non-equilibrium sorption models are further classified as unsteady state and pseudo-steady state models. Gas absorption/ desorption in equilibrium adsorption model is assumed to be strictly pressure dependent, while Gas absorption/ desorption in non-equilibrium adsorption model is assumed to be a function of pressure and time. The amount of absorbed gas in equilibrium sorption formulation is controlled by Langmuir's theory. Non-equilibrium models of desorption/diffusion processes in the micropores obey Fick's laws of diffusion. Many technical papers have been reported on coalbed methane modeling for decades. In earlier times, Several models based on empirical models described the single-phase release of methane gas from underground mine working1–2. Price et al. developed a two-phase, equilibrium sorption simulator with the capable of considering heterogeneous and anisotropic seam properties and non-stationary mine workings, handling PVT properties as a function of pressure and incorporating irregular external boundaries3. Some researchers proposed quasisteady-state models4–6. It is generally accepted that the sorption rate in theses models is proportional to the difference between the gas concentration in the external matrix surface and the average concentration within the matrix. In contrast Price et al.'s model, The extra capabilities of these models include stress-dependent porosity and permeability, horizontal-wellbores drilling from a vertical shaft or from the peripheries of the reservoir, and "dual-mechanism" gas slippage. Earlier true unsteady-state sorption models developed by Smith and Williams7, and Ancell and Lambert8 relate the sorption rate to the concentration gradient at external surface of the coal micro-pore. In true unsteady-state sorption models, this concentration gradient is considered as a nonlinear function of the micro-pore radius. These models provided the most realistic description of the diffusion controlled desorption process requiring no apriori assumption regarding the kinetics of the desorption process. Nevertheless, it is difficult to estimate micro-pore radius for field-scale simulation.