Determination of the Effective Stress Law for Deformation in Coalbed Methane Reservoirs

Effective stress laws and their application are not new, but are often overlooked or applied inappropriately. The complexity of using a proper effective stress law increases when analyzing stress variation in coal as a result of gas production or mining. In this paper, an effective stress law is derived analytically for coalbed methane reservoirs, combining the concepts of matrix shrinkage/swelling and external stress by including the effect of sorbing gas pressure on the elastic response of the reservoir. The proposed law reduces to that of Terzaghi when the compressibility of bulk material is sufficiently greater than the compressibility of the solid grain, and without the strain associated with matrix shrinkage/swelling effect. Moreover, it is shown that the Biot coefficient (α) can have a value larger than unity for self-swelling/dilation materials, such as coal. The proposed stress–strain relationship was validated using experimental results. Overall, the effective stress law for deformation was extended for sorptive materials, providing a new and unique technique to analyze the elastic behavior of coal by reducing three variables, namely, external stress, pore pressure and matrix shrinkage/swelling along with the associated stress, down to one variable, “effective stress”.