Iterative geostatistical seismic inversion with rock-physics constraints for permeability prediction

Accurate prediction of the spatial distribution of subsurface permeability is a fundamental task in reservoir characterization and monitoring studies for hydrocarbon production and CO2 geologic storage. Predicting permeability over large areas is challenging, due to their high variability and spatial anisotropy. Common approaches for modeling permeability generally involve deterministic calculations from porosity using precali-brated rock-physics models (RPMs) or geostatistical cosimula-tion methods that reproduce observed experimental porosity -permeability relationships. Instead, we have predicted per-meability from seismic data using an iterative geostatistical seis-mic inversion method that combines the advantages of rock -physics and geostatistical modeling methods. First, we simulate facies through 1D vertical Markov chain simulations. Then,permeability, porosity, and acoustic impedance are sequentially generated and conditioned to the previously simulated facies model. An RPM is used to evaluate the misfit between the per-meability predictions obtained from geostatistical cosimulation at the well locations and well-log values computed from the acoustic impedance. The residuals of the misfit function are used as conditioning constraints in the stochastic update of the models in the subsequent iteration. The outcome of our methodology is a set of multiple geostatistical realizations of facies, permeability, porosity, and acoustic impedance condi-tioned to seismic data and constrained by an RPM. We first il-lustrate the method on a synthetic 1D example and compare it to a traditional geostatistical inversion approach. We then apply our inversion to a 3D real data set to assess the methodology performance with scarce conditioning data and in the presence of noise.