A dual-porosity model for coal bed reservoirs

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A dual-porosity model for coal bed reservoirs S. Nikoosokhana , M. Vandammea , P. Danglaa a Lab.

Navier (Ecole des Ponts ParisTech, LCPC, CNRS), Universit´ e Paris-Est, 77420 Champs-sur-Marne, France.

Key words: CO2 sequestration, Coal bed reservoirs, Adsorption, Surface effects, Dual-porosity

1. Introduction In parallel with the international debate on climate change, CO2 sequestration in deep unminable coal seams has attracted attention as a method for reducing the output of greenhouse gases in the atmosphere [1]. Coal is a naturally fractured dual-porosity reservoir [2] which accommodates a large amount of methane (CH4 ) during the coalification process. This methane is then produced and used for energy production. As is the case for enhanced oil recovery (EOR), such primary production can in principle be enhanced by injecting CO2 in the coal seam. This process, schematized in figure 1a, is called Enhanced Coal Bed Methane (ECBM) recovery [3]. a)

b)

Figure 1: (a) Schematic of an ECBM operation: CO2 is captured from a power plant and is injected into the coal seam while CH4 is produced. Injection and production wells can in general be more than one; and (b) Injectivity decline of CO2 over time, Allison unit in the San Juan basin (adapted from [5]).

During the injection process, CO2 gets preferentially adsorbed at the surface of the coal micropores. This adsorption, by modifying the surface energy of the pores, makes the coal swell [4]. In confined conditions, such swelling leads to the closure of the coal reservoir cleats (small natural fractures) system, which impedes further injection of CO2 (see the early stages in figure 1b). After this initial decrease the injectivity increases back (see the late stages in figure 1b), a phenomenon known as the ’permeability rebound’ and attributed to a reopening of the cleats due to an increase over time of the fluid pressure in the cleat system. Our aim in this paper is to provide a realistic reservoir model that is able to predict such permeability variations. Following the comprehensive study and description of the CO2 -induced swelling of the coal material in [4], this paper introduces a dual-porosity model for coal bed reservoirs. 2. Constitutive equations of the dual-porosity coal bed reservoir model The model here developed is based on a two-scale porosity: coal bed reservoirs are considered to exhibit both macropores and micropores (see figure 2). We assume that macropores (the cleats) are responsible for the transport properties and that adsorption occurs at the surface of the micropores only. We also assume that the fluid (CO2 ) pressures in macropores and micropores are equal (the transfer of fluid between macropores and micropores is considered to be much faster than the injection process).

Figure 2: Two-scale porosity model used for a coal bed reservoir. The transport properties are governed by the macroporosity (cleats), while swelling is due to adsorption in the microporosity.

Based on a thermodynamic approach, we derive the following non-linear elastic isotropic constitutive equations for a saturated dual-porosity coal bed reservoir that govern the change dϕM of macroporosity and dϕm of microporosity: dσ dϕM dϕm

= K(σ 0 )d − b(σ 0 )dp − (1 − bM (σ 0 ))dpaM + bm (σ 0 )dpam dp dpaM dpaM − dpam = bM (σ 0 )d + − − NM (σ 0 ) NM (σ 0 ) G(σ 0 ) a a dpm dp − dpa dp − − m 0 M = bm (σ 0 )d + 0 0 Nm (σ ) Nm (σ ) G(σ )

(1) (2) (3)

where K and b are the tangent poroelastic properties of the reservoir; bM and NM those associated to the macroporous system; bm and Nm those associated to the microporous system. They are effective stress dependent (σ 0 = σ +p) and involve the knowledge of compression modulus at the macro, meso and micro scales. paM and pam are pore pressures induced by adsorption effects in macropores and micropores, respectively [4]. 3. Reservoir simulations We use the constitutive equations here derived in order to simulate an injection of CO2 into a coal bed reservoir. The equations are implemented into Bil, a finite element/volume-based modeling environment whose structure enables to easily implement new models [6]. Gmsh, a finite element mesh generator, is used for pre- and post-processing. Unidimensional simulations are performed and the effect of several parameters on the injectivity is studied: boundary conditions, compressibility of the coal matrix, adsorption isotherm,... We show that the model here developed is able to capture the permeability rebound. The model, coupled with the numerical simulations, illustrates how the CO2 injectivity is controlled by the competition between the pressure-induced opening of the cleats (which tends to increase the injectivity) and the adsorptioninduced swelling (which tends to close the cleat system and thus to decrease the injectivity). References [1] Gale, J., Freund, P., Coal bed methane enhancement with CO2 sequestration worldwide potential, Environmental Geosciences, 8(3), 210 − 217 (2001) [2] Seidle J.P., Jeansonne M.W., Erickson D.J., Application of matchstick geometry to stress dependent permeability in coals, Proceedings of the SPE rocky mountain regional meeting Casper, Wyoming, Paper SPE 24361, (15 − 21 May 1992) [3] White C.M., Smith, D.H., et al., Sequestration of carbon dioxide in coal with enhanced coalbed methane recovery - a review, Energy Fuels ,19(3), 659 − 724, (2005) [4] Vandamme, M., Brochard, L., Lecampion, B., Coussy, O., Adsorption and strain: The CO2 -induced swelling of coal, Journal of the Mechanics and Physics of Solids, 58(10), 1489 − 1505,(2010) [5] Reeves, S.R., The coal-seq project: key results from field, laboratory and modeling studies. In: Wilson, M., Rubin, E.S., Weith, D.W., Gilboy, C.F., Morris, T., Thambimuthu, K., Gale, J. (Eds.), Seventh International Conference on Greenhouse Gas Control Technologies, Vancouver, BC, Canada (2004) [6] http://perso.lcpc.fr/dangla.patrick/bil