Using a pseudo-steady-state flow equation and 4D seismic traveltime shifts for estimation of pressure and saturation changes

Abstract

Pressure and saturation changes cause a change in seismic P-wave velocity resulting in a shift in 4D traveltime. A discrimination between both effects is important to enhance reservoir management decisions. We explored the possibility of linking the fields of reservoir engineering and 4D seismic. A simple inversion scheme based on a reservoir engineering flow equation for pore pressure predictions combined with the Hertz-Mindlin and Gassmann rock-physics models to discriminate pressure and saturation effects from 4D time shifts was presented. To account for no-flow reservoir boundaries, the pseudo-steady-state flow equation giving the pressure distribution was extended with a superpositioning method. During the inversion, three parameters were determined by a nonlinear, least-squares fitting method: the thickness of the hydrocarbon column, the pressure at the well position, and its decay rate away from the well. We successfully tested our approach on a synthetic and a field data case, where the [Formula: see text] injection well at the Snøhvit field, Norway, served as a good example to demonstrate our method. We observed a good correlation between simulation and inversion in our synthetic study. Our theory was limited to homogeneous reservoir conditions and produces spatially low frequent outputs. To apply the model in complex fields, such as at Snøhvit, we introduced a spatially varying Mindlin-exponent over the field and used the theory as an heuristic model assuming that a variation of the Mindlin-exponent takes a change in pressure sensitivity into account. This assumption provided the possibility to indirectly include heterogeneities in grain sorting and porosity variation and improved the model significantly. We see the advantage of our method in its fast and direct implementation to study first-order effects of pressure and saturation behavior on time-lapse seismic data using a simple inversion algorithm instead of computationally intensive simulations.