Joint estimation of porosity and saturation using stochastic rock-physics modeling

Sediment porosity and saturation affect bulk modulus, shear modulus, and density. Consequently, estimating hydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem: Uncertainty in porosity will lead to errors in saturation prediction, and vice versa. Porosity and saturation can be jointly estimated using stochastic rock-physics modeling and formal Bayesian estimation methodology. Knowledge of shear impedance reduces the uncertainty in porosity and thus also reduces uncertainty in saturation estimation. This study investigates joint estimation of porosity and saturation by using rock-physics, stochastic modeling, and Bayesian estimation theory to derive saturation and porosity maps of expected pay sands. In the field example, the uncertainty in porosity, quantified by the standard deviation (STD) associated with the posterior probability density function (pdf), derived from inversion of seismic data is much less than the uncertainty in the derived saturation. For a typical case, the STD associated with saturation is similar to 24% while porosity STD is about 1.34 porosity units given seismic-derived inversion attributes with reasonable accuracy. Comparison of these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15% of the prior uncertainty while saturation uncertainty was only reduced to 92% of the prior uncertainty. Although these results may vary from one location to another, the methodology is general and can be applied to other locations.