Macrokinetics of Matrix Gas Release and its Influence on Coalbed Methane Flow and Production
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AbstractIn coalbeds and shales, gas transport and storage are important for accurate prediction of production rates and for the consideration of subsurface greenhouse gas sequestration. They involve coupled fluid phenomena in porous medium including viscous flow, diffusive transport and adsorption. Standard approach to describe gas-matrix interactions is deterministic and neglects the effects of local spatial heterogeneities in porosity and material content of the matrix. In this work, adopting weak-noise and mean-field approximations and using a statistical approach in spectral domain, matrix heterogeneity effects are investigated in the presence of non-equilibrium adsorption with random partition coefficient. It is found that the local heterogeneities can generate non-trivial transport and kinetics effects which retard gas release from the matrix and influence the ultimate gas recovery adversely. Macro-transport shows 1/ [1 + NPe / (1+ NPe)] dependence on the Pclet number, and persists at the diffusive ultra-low permeability limit. Macro-kinetics is directly related to Thiele modulus by the following expression: NTh / (1+2 NPe). It leads to trapping of gas in the adsorbed phase during its release from the matrix and to an adsorption threshold during the gas uptake by the matrix. Both effects are proportional to the initially available adsorbed gas amount and become more pronounced with the increasing variance of the porosity field. Consequently, a new upscaled deterministic gas mass balance is proposed for practical purposes. Numerical results are presented showing free and adsorbed gas distributions and fractional gas sorption curves for unipore coal matrix exhibiting Gaussian porosity distribution. The work is a unique approach for our further understanding of the coalbeds and gas shales, and it is important for the development of sound numerical gas production and sequestration models.
