Benchmark assessment of coal permeability models on the accuracy of permeability prediction

Abstract

When natural gas is extracted from coal seams, complex interactions of stress and sorptive chemistry have a strong influence on the properties of coal. These include influences on gas sorption and flow, coal deformation, porosity change and permeability modification. In this study, we define this chain of reactions as “coupled processes” implying that one physical process affects the initiation and progress of another. The individual process, in the absence of full consideration of cross couplings, forms the basis of the conventional coal seam gas reservoir engineering. Therefore, the inclusion of cross couplings is the key to rigorously formulate the unconventional coal seam gas reservoir engineering. Among those cross-couplings, the coal permeability model is the most important one. A variety of permeability models were developed to define how the coal permeability evolves during gas production. These models were derived normally under three common assumptions: (1) uniaxial strain; (2) constant overburden stress; and (3) local equilibrium. Under these assumptions, coal permeability can be defined as a function of gas pressure only. Our comprehensive review concluded that these models have so far failed to explain experimental results from conditions of the controlled stresses, and only partially succeeded in explaining in situ data. We identified the adoption of these three assumptions as the fundamental reason for failures. In this study, we relaxed the first two assumptions and derived a coal permeability model under variable stress conditions. Furthermore, we considered the effective stress transfer between matrix and fracture and transformed this stress transfer into the modification of fracture aperture. This relaxes the third common assumption, i.e., local equilibrium condition. We applied this approach to generate a series of permeability type curves under the full spectrum of boundary conditions spanning prescribed stresses through constrained displacement. We benchmarked the solutions generated by using the permeability models with three common assumptions against our “accurate” solutions by using permeability models without these assumptions for the full spectrum of boundary conditions, and concluded that these common assumptions could produce unacceptable errors.