Development and Validation of a Compositional Coalbed Simulator
Authors: Manik J. , Ertekin T. , Kohler T.E. 
Published: March 2010

Abstract
Development and validation of a three-dimensional, twophase, dual porosity, fully implicit, compositional coalbed simulator are presented. Multicomponent sorption equilibria using a thermodynamically consistent ideal adsorbed solution (IAS) theory is implemented to the simulator using a non-equilibrium sorption formulation. The sorption model accounts for the nonideality of the free gas phase, as partial fugacity of the gas component is calculated using the Peng-Robinson equation of state. Model predictions of multicomponent sorption of methane, nitrogen and carbon dioxide mixtures on the coal are found to be in good agreement with experimental measurements. The transport component of the compositional coalbed simulator is verified using an existing two-phase coalbed simulator.

Introduction
Enhanced coalbed methane recovery by means of injecting other gases into coalbed reservoirs is an attractive recovery technique. Reznik et al.(1) reported their experimental results of carbon dioxide injection in coal seams that can yield close to 100% methane recovery. Similar work performed by Puri and Yee(2) showed that almost all methane adsorbed to coal can be stripped by nitrogen. Modelling of carbon dioxide and nitrogen injection in enhanced coalbed methane recovery processes cannot be accurately achieved using conventional two-phase fluid flow formulations. The complex physico-chemical processes encountered require multicomponent gas sorption formulation to be coupled with compositional fluid flow formulation in coalbed reservoirs. Seidle and Arri(3) proposed a procedure to adapt conventional black oil reservoir models for coalbed methane simulation purposes. In their approach, adsorbed gas is modelled by gas dissolved in immobile oil where adsorption capacity in the physical coalbed is replaced by the solution gas-oil ratio in a black oil model. For a multicomponent gas system, they suggested to use Langmuir sorption constants and molar solution gas-oil ratio to calculate oil-gas equilibrium ratios (K-values). These K-values, together with the free gas concentration, are then used to calculate the adsorbed gas phase mole fraction and the adsorption capacity. Implementing this technique to conventional simulators with a K(p) approach, one can model compositional fluid flow in coalbed methane reservoirs without changing the original computer codes. This technique, however, requires alterations to the porosity, saturations, relative permeabilities and oil phase PVT properties data. Stevenson et al.(4) examined the validity of the thermodynamically consistent IAS and real adsorbed solution (RAS) theories in the prediction of multicomponent sorption at in-seam conditions. Later, Stevenson et al.(5) implemented this multicomponent sorption to their compositional, two-phase coalbed reservoir simulator and performed an economic evaluation and analysis of nitrogen injection for coalseam gas recovery. In these two works, information on the mathematical description of the compositional fluid flow formulation and an explanation on how to implement the sorption modelto the flow equation are not included.
The principal objective of this paper is to describe the development of mathematical and numerical models of the simultaneous flow of multicomponent gas and water in coalbed reservoirs. Formulations implement the thermodynamically consistent ideal adsorbed solution (IAS) theory, which can be used as a tool to study the potentials of enhanced coalbed methane recovery in field scale coalbed reservoir simulators.