The effects of pore geometry on adsorption equilibrium in shale formations and coal-beds: Lattice density functional theory study

• Lattice DFT model was extended to cylindrical and spherical geometries.
• Surface energy term of the model was modified.
• N2 adsorption on different pore sizes and geometries was evaluated.
• The model was verified on synthetic porous media.
• Pore geometry for shale and coal samples was determined using the proposed model.

Textural characterization is a critical step to assess and evaluate petrophysical properties of unconventional reservoirs, including shale-gas, coalbed and tight-gas systems. Gas adsorption, typically with N2 at 77 K or CO2 at 273 K, is the widely used method for such characterizations. To translate adsorption data into useful petrophysical quantities such as pore size, pore connectivity, and pore volume, one needs to exploit appropriate correlations to link molecular scale interactions and macro-scale phenomena. One important yet under-studied property of unconventional matrices is their true pore structure and its effects on fluid thermodynamics inside pore space. Herein, based on lattice density functional theory, we have developed a multilayer adsorption model with parameterized energy terms, to determine effects of pore shape and pore size (of shale and coal samples) on the thermodynamic state of reservoir fluid. The model is extended from its original slit pore geometry into cylindrical and spherical geometries to consider the effects of local pore curvature on adsorption energetics and uptakes mainly in mesopores (between 2 and 50 nm). In addition, the surface energy term is modified to consider the effect of the force field exerted by pore walls on both the adlayer and subsequent adsorbed layers. Modification of the energy term resulted in layer-by-layer, two-dimensional condensation followed by the final capillary condensation. The force field exerted by the pore walls together with local pore curvature shifted the condensation pressures toward lower relative pressures (P/P0). By applying the model to N2 porosimetry isotherms at 77 K for two reference samples, ordered mesoporous silica (SBA-15) and ordered mesoporous carbon (OMC), the model confirmed essentially cylindrical pore structure for both samples. The model was further applied to N2 at 77 K porosimetry isotherms of Woodford shale and Cameo coal samples, and identified the pore structures of the samples as dominated by cylindrical and slit pore geometries, respectively.