Assessing the pressure (in)dependence of cross-property relations

It is known that geological reservoir characterisation can be improved by the joint modelling and inversion of both electrical and elastic data, however the relationship between a rock’s electrical and elastic properties, which is intrinsic to these methods, is relatively uncertain. On top of this, estimating reservoir pressure from geophysical measurements is an essential part of the 3D and 4D monitoring of CO₂ injection and hydrocarbon production, and while electrical and elastic properties are affected by pressure, the effect of pressure on electrical-elastic relations is less obvious.

Here we use the Cross-Property Differential Effective Medium approximation to model public-domain electrical-elastic laboratory measurements made on brine-saturated clean and mixed sandstones cores at 6 effective pressures ranging from 8 MPa to 60 MPa. Although the approximation is able to realise a large proportion of the electrical-elastic space bounded by the Hashin-Shtrikman bounds using a range of permissible parameter values, we find the model parameter, equivalent pore aspect ratio, varies very little as a function of pressure when modelling the measured data. Interestingly, we see equivalent pore aspect ratio changes exponentially as a function of pressure with an R² value of over 0.99 when modelling clean sandstones, a trend which has been observed previously in single-property inclusion modelling. This small variance in the model parameter as a function of pressure corresponds to an observably small change in the samples’ electrical-elastic measurements with pressure.

We conclude the electrical-elastic properties of the examined clean and mixed brine-saturated sandstones are only weakly dependent on pressure and we demonstrate how a single, pressure-independent model parameter is able to model the electrical-elastic measurements of both the clean and mixed sandstones with reasonable accuracy over the full range of experimental pressures.