Influence of Considering the Sorption Effect in the Betti-Maxwell Reciprocal Theorem on Gas Transport Capacity in Unconventional Reservoirs

Abstract

Pore bulk modulus in continuum apparent permeability models was generally treated as an independent parameter or deduced from the Betti-Maxwell reciprocal theorem neglecting the sorption effect, which is not appropriate for the unconventional reservoirs with strong gas sorption. In this work, pore bulk modulus was firstly derived from the Betti-Maxwell theorem with the consideration of the gas sorption strain and was incorporated into the solid–fluid coupling apparent permeability model. Numerical simulation was then conducted under the uniaxial strain condition and the stress confined condition to investigate the gas transport characteristics. The results showed that when taking into account for the sorption effect in the Betti-Maxwell theorem, the pore bulk modulus dramatically decreased with the falling pore pressure during the gas transport process under two loading conditions. Moreover, gas transport ability under the stress confined condition was greatly degraded while it was hardly changed under the uniaxial strain condition. Both the pore bulk modulus and the stress distribution in the reservoirs were found responsible for the variation of gas flow capacity. Finally, the effects of the parameters associated with the pore bulk modulus were examined to further discuss the impact of involving the sorption effect in the Betti-Maxwell theorem.