## Change of bulk and shear moduli of dry sandstone with effective pressure and temperature

### John Jianlin Zhang, Laurence R. Bentley

The bulk and shear moduli of dry sandstone increase with effective pressure and decrease with temperature and the rate of change varies with effective pressure and temperature. In order to calculate the effect of effective pressure, a rock physics model based on pore aspect ratio spectra (KT model) is adopted in computation of elastic moduli and velocities. The pore aspect ratio spectra for a set of water-saturated sandstone samples are first assumed to be proportional to that of the standard sample, and are then adjusted to fit velocity measurements. Dry bulk and shear moduli at different pressures are calculated with the optimized pore aspect ratio spectra by setting the bulk moduli of contained fluid equal zero. It is found that the exponential relationship exists between the rate of change of elastic moduli and effective pressure as follows:

dKd/dP = 0.746exp(-0.0773P)

dd/dP = 0.372exp(-0.0791P)

The effective pressure is between 5-40 MPa and the temperature at 22 degrees C in laboratory. The temperature effect, which is due to pore volume change, is manifested as a more or less linear trend, and is modeled, based on experimental data, as straight lines:

dKd/dT = -0.0155

dd/dT = -0.0065

The temperature ranges from 10 to 200 degrees C and the effective pressure is from 25 to 500 MPa in laboratory.