Stress-Dependent Permeability and Porosity of Coal and Other Geologic Formations

Abstract

Summary Fundamental relationships have been derived for permeability, porosity, and density as a function of effective stress. The primary formation parameter is pore compressibility, and formulas are derived for both constant and variable pore compressibility. The grains are assumed to be incompressible. The Carman-Kozeny equation is assumed valid, and changes in tota porosity are proportional to changes in porosity effective stress. These relationships fit laboratory and field data. Eight laboratory core tests (four coal, one granite, two sandstone, and one clay are used to illustrate the applicability of the permeability and porosity theory. Additional clay and shale core samples yielded an excellent match with the theoretical density formula. In cases in which the correlation coefficient was applicable, it was above 0.95. A number of field permeability data points from the Piceance, San Juan, and Black Warrior basins were fitted to the theory. The correlation coefficient ranged from 0.85 to 0.92 in these cases. Mudstone porosity data from borehole lithologic logs also yielded excellent fits to the theoretical formulation. Of the 13 examples reviewed, only 2 (which were core tests) required a variable pore compressibility. Further improvements to the derived relationships will be required to include the effects of structurally enhanced permeability.