Effect of 3-D stress state on adsorption of CO2 by coal

Abstract

Though several models have been developed to describe unconfined swelling of coal exposed to adsorbing fluids such as CH4 or CO2 at elevated pressure, the role of stress supported by the solid framework (i.e. an effective stress in excess of the fluid pressure) has not hitherto been considered in thermodynamic descriptions of the adsorption process. In this paper, we develop a thermodynamic model, based on statistical mechanics theory, for the equilibrium concentration of CO2 adsorbed by stressed coal matrix material. For unconfined (zero effective stress) conditions, the model describes the change in adsorbed concentration as a combined effect of the changing chemical activity of the fluid and the changing availability of adsorption sites in the nanoporous solid matrix. For an ideal gas and an adsorbate under unconfined conditions, this model reduces to the widely applied Langmuir model. When the solid framework of the coal matrix material in subjected to a general stress state σij the adsorption energy of a single molecule is increased by a general stress–strain work term. The effect of this in the adsorption model is that the adsorbed concentration is reduced by several percent to several tens of percent for effective stress magnitudes similar to those expected in situ during (E)CBM production. This prediction was confirmed by a preliminary experiment, performed on a sample of Brzeszcze 364 high volatile bituminous coal at 15 MPa fluid pressure, a temperature of 40 °C, and an effective hydrostatic stress or confining pressure of 1–25 MPa. This showed that the equilibrated adsorption capacity at 1 MPa effective stress of 1.38 mmol·gcoal− 1 was reduced by almost 10% at 25 MPa effective stress. Combining our thermodynamic model with poroelasticity, a full constitutive equation is derived, which describes the competitive relation between adsorption-induced swelling strain and poroelastic compression, as a function of adsorbed concentration, fluid pressure and state of stress. Our equations offer a basis for full coupled modelling of the problem of injecting or producing a (single) fluid phase such as CO2 into or from a coal seam under in situ (E)CBM conditions. Moreover, the model provides a means to estimate the effect of “self-stressing” as a result of adsorption of CO2 by coal under confined in situ conditions. A first analysis of this effect for coal initially at 25 MPa effective stress, with CO2 injection at 15 MPa, showed an increase in effective stress to 35–105 MPa, which would lower CO2 uptake at equilibrium by a total amount of ~ 13–30% compared to conventional adsorption measurements made at 15 MPa CO2 pressure