Stress dependence of elastic and transport properties in tight gas sandstones

New experimental tests on a suite of tight gas sandstone samples show a strong dependence of both P- and S-wave velocities, V_p and V_s, on hydrostatic confining stress in the range from almost zero to 50 MPa. The Klinkenberg-corrected absolute gas permeability of these samples also exhibited a dramatic stress dependence. It decreased by one to two orders of magnitude as the stress increased. A new approach is used to consolidate the 18-sample dataset at each confining stress and arrive at the effective permeability and elastic moduli. For the former, we utilize a randomly generated permeability matrix with its elements drawn from the 18 datapoints. For the latter, we use the elastic bounds. As a result, we obtain permeability-stress, porosity-stress, and velocity-stress relations characteristic of the class of rock under examination. Theoretical simulations based on the inclusion-based differential effective medium theory mimic the experimental velocity-stress results. We also derive a permeability versus acoustic impedance and versus stress relation to be used for inferring permeability variations as a function of the measured impedance versus stress changes. This relation can serve to estimate the permeability from the elastic property variations during time-lapse monitoring, as well as during fracking of this rock.