Bulk density and bulk modulus of adsorbed coalbed methane

The bulk density and bulk modulus of adsorbed coalbed methane are required to calculate the undrained bulk and shear moduli as well as the fluid-saturated density of the coal reservoir. We derived the formula for the bulk modulus and bulk density of adsorbed methane using the Langmuir equation for isothermal adsorption. The bulk density of adsorbed methane is positively correlated with the gas pressure and Langmuir volume, but it is negatively correlated with the Langmuir pressure and adsorbed methane saturation. The bulk density of adsorbed methane is greater than that of free-state methane for the same gas pressure. The bulk modulus of adsorbed methane is positively correlated with the gas pressure and negatively correlated with the Langmuir pressure; it is much larger than that of free methane, but it is still much smaller than that of water within the normal gas pressure range. Coal samples from the study area demonstrate that the water saturation is less than 95%. Considering adsorbed methane as a pseudosolid, calculations yield a very small difference in the bulk modulus of coal under room-dry conditions. Considering adsorbed methane as a gas, calculations based on spatially uniform or patchy saturation indicate that multiphase fluid saturation produces a very small difference in the elastic parameters and wave velocity of the fluid-saturated coal from the dual-phase fluid (water and free methane).