A method is presented for the volumetric estimation of subsurface fluid substitution based on the analysis of 4D seismic time shifts. Since time shifts cannot resolve for fluid saturation and layer thickness simultaneously without additional constraints, mass estimates are derived from the complete set of possible fluid saturations and layer thicknesses. The method considers velocity-saturation relationships that range from uniform fluid mixing to patchy fluid mixing. Based on a generalized velocity-saturation relationship that is parameterized by the degree of patchiness, explicit upper and lower fluid mass bounds are provided. We show that the inherent ambiguity between fluid saturation, fluid mixing, and layer thickness has a severe impact on the convergence of these mass bounds. That is, fluid substitution scenarios with patchy fluid mixing and roughly linear velocity-saturation relationships allow for more accurate fluid quantification than scenarios associated with uniform mixing. Application of the method to two 4D seismic monitor data sets from Sleipner results in CO2 mass bounds that are consistent with the true injected masses of CO2. Moreover, a linear relationship between progressively developing 4D time shifts and known injected CO2 mass is observed, suggesting that the evolving patterns of fluid saturation and fluid mixing in the CO2 plume have remained roughly constant with time.

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