Assessing the Impact of Different Types of Time-lapse Seismic Data on Permeability Estimation

We consider the impact of using time-lapse seismic data in addition to production data for permeability estimation in a porous medium with multi-phase fluid flows, such as a petroleum reservoir under water-assisted production. Since modeling seismic wave propagation in addition to modeling fluid flows in the reservoir is quite involved, it is assumed that the time-lapse seismic data have already been inverted into differences in elastic properties, or even fluid-saturation and pressure differences (pseudo-seismic data). Because an inversion process often leads to considerable error growth, we will consider pseudo-seismic data with large uncertainties. The impact of pseudo-seismic data is assessed through permeability estimation with and without such data, and through application of some uncertainty measures for the estimated parameters. A predictor-corrector technique is used for the parameter estimations. The predictor leads to a coarse-scale permeability estimate, using only dynamic data. The corrector downscales the predictor estimate into a more smoothly varying field, using also the prior model. A successful final corrector result will thus be consistent with the prior model and reconcile dynamic data. The predictor-corrector approach can reveal what parameter resolution that can be achieved in a stable manner with different data types, since it can be applied without an explicit regularization term in the objective function. In this work, the impact of pseudo-seismic data will be investigated based on both coarse-scale predictor solutions and fine-scale predictor-corrector solutions. The numerical examples clearly indicate that the permeability estimation problem is stabilized at a higher level of resolution when pseudo-seismic data are applied in addition to production data, even if the pseudo-seismic data have large associated uncertainties. Several types of pseudo-seismic data, like acoustic-impedance differences, fluid-saturation differences, and pressure differences, are tested, and the resulting estimates are compared.