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 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 total 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 t points from the Piceance, San Juan, and Black Warrior basins were fitted t 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. Introduction Economical coalbed methane production depends on four important coal-seam characteristics-gas pressure, gas content, coal-seam thickness, and permeability. (Concerning gas pressure, note that most coal seams are initially water-saturated before production. if gas is present in solution, formation gas pressure is defined as the pressure that is in equilibrium with the measured gas content in pressure that is in equilibrium with the measured gas content in solution. If free gas is present, then the gas pressure is pressure of the gas phase. If gas is absent, gas pressure is determined by drawing the well down until gas first appears in solution. The bottomhole water pressure on the coal seam when gas first appears in the coal seam is equal to the formation gas pressure. In either case, the gas pressure so determined must be in equilibrium with the coal's desorption isotherm.) Without the necessary gas content or coal thickness, a project obviously cannot be viable. An extensive body of information exists for selecting a site with some degree of confidence based on gas contents and coal thickness. However, unexpected variations in coal gas content can occur. Information on coal permeability has been more difficult to obtain. For most coalbed methane wells, permeability tests either have not been conducted or, if they have, the results remain proprietary. Consequently, very few permeability values have been reported proprietary. Consequently, very few permeability values have been reported in the literature. In 1982, the Gas Research Inst. (GRI) began to pursue extensive permeability testing and data collecting to assess pursue extensive permeability testing and data collecting to assess the permeabilities of coalbed methane sites. A program was developed to acquire the necessary information from operators and from "wells of opportunity" using simple but effective slug-testing methods. Far more information was available in the form of specific capacity data, which relate well flow rate to drawdown; permeability can be estimated from these data by using available permeability can be estimated from these data by using available information or by assuming depths to water. In this manner more than 40 permeability data points were calculated for unstimulated wells in the San Juan, Piceance, and Black Warrior basins. While some scatter was evident, the data indicated that permeability decreased with depth. Some initial success was achieved by permeability decreased with depth. Some initial success was achieved by drawing empirical straight-line correlations between depth and permeability of log-log plots, and led to the search for a more permeability of log-log plots, and led to the search for a more fundamental theory to explain the data and correlations. In view of the advances in reservoir engineering research, it is surprising that stress-dependent permeability has not been more extensively studied. A natural gas reservoirs are found at ever greater depths, understanding stress-dependent permeability will become essential because, under large drawdown, reduced permeability can lower the production from a stress-sensitive reservoir. Work at the Inst. of Gas Technology (IGT) documented the strong stress dependence of core-sample permeability in laboratory experiments, and was the basis for establishing a theoretical relationship of permeability reduction as a function of increasing stress or depth. These and other laboratory studies have shown that coal permeability decreases by one to two orders of magnitude when permeability decreases by one to two orders of magnitude when effective stress is increased by 2,000 psi [ 13.8 MPa]. 9–11 Furthermore, stress-sensitive permeability and porosity have been observed in experimental studies on various reservoirs. As a result, a number of empirical permeability/stress relationships have been proposed. most of which show a strong decrease in permeability with proposed. most of which show a strong decrease in permeability with depth. Objectives These efforts laid the foundation for the theoretical relationship between stress-dependent permeability and porosity for coals. McKee et al. developed the first theoretical equations using matrix compressibility as a fundamental property. The theory of McKee et al. fits both laboratory and field data, and is of limited use because maximum closure stress, a function of matrix compressibility, is inherent and limits the depth to which the results apply. New theoretical equations are developed here for permeability and porosity in terms of pore compressibility. This formulation generally porosity in terms of pore compressibility. This formulation generally eliminates the need for variable compressibility in the range of interest, and therefore is simpler to use and not limited by maximum stress. The resultant formulas are shown to fit both laboratory and field data, but their practical significance is that they provide a simple, usable tool to establish favorable areas of permeability for gas production from coalbeds or other engineering applications where production from coalbeds or other engineering applications where permeability is a critical parameter. However, the theory and permeability is a critical parameter. However, the theory and correlations that use the effective stress gradient can only indirectly account for structurally enhanced or reduced permeability; hence, the role of the geologist is still paramount in selecting those geologic factors leading to the best production prospects. SPEFE P. 81