A new physical model for the pressure sensitivity of unconsolidated sands

Abstract

Knowledge of the pressure dependencies of rock properties in unconsolidated sands is important for accurate time-lapse feasibility studies, pore pressure prediction, and reservoir characterization. A key problem that arises in determining such pressure dependencies is an accurate model at low effective stress. We propose a double exponential model to describe the pressure sensitivity of the bulk modulus (K) or shear modulus (G) for unconsolidated sands. The physical basis for our model relies on observed porosity-depth trends in unconsolidated sands, and the concept of critical porosity. Our new model matches laboratory measurements on unsaturated sand samples that have a range of grain size distributions and compositions. Grain size distribution data is first used to estimate critical porosity, which is then used as a zero effective pressure constraint in the data fitting process. We show that our new model more accurately predicts pressure sensitivity near zero-effective pressure compared to current methods, and is thus more accurate for situations in which core measurements at low effective stresses are not available.