Laboratory study of the effective pressure law for permeability in Ta-Ba-Miao low-permeability sandstones

To obtain new knowledge on the effective pressure law for permeability,i.e.,P_(eff)= P_c-κP_p.and to see if there exist very small κ values and its variability,laboratory experiments with two modified factorial designs were performed to determine the effective pressure law for permeability of two samples from Ta-Ba-Miao low permeability sandstone formation.One modified factorial design for one sample included three cycles with different pore pressures.Each cycle was run through loading and unloading confining pressure (P_c) in constant-pore-pressure condition.Another design for the second sample contained four cycles under different confining pressures.Each cycle was run through raising and lowering pore pressure (P_p) in constant-confining-pressure condition.Permeability data were taken with the steady-state method.The response-surface method was used which supposed that nothing was known about the material behavior,and a model was built empirically by matching an approximate κ-P_c-P_p surface to the data.The coefficients describing the surface reflected the information about material behavior and were transformed into κ-P_c-P_p response surface.The κ-P_c-P_p surfaces showed that at intervals along the pressure path "local" values of the coefficient κ in the effective pressure law varied with pore and confining pressure and its range is from 0 to 1.02.The values of κ of two samples were significantly less than 1.0 and even approached zero at the high confining pressure and low pore pressure conditions.These experimental observations indicate that the variability of κ is not in agreement with present theories and other published laboratory work.The data suggest that κ values decrease with increasing confining pressure and are small at high confining pressure and low pore pressure.This is interpreted in terms of the changes in the geometry of the micro-cracks during closure and the elastic deformation of the rock particles after the closure of micro-cracks with increasing confining stress in the paper.