Accurate prediction of the spatial distribution of subsurface permeability is a fundamental task in reservoir characterization and monitoring studies for hydrocarbon production and CO2 geological storage. Predicting permeability over large areas is challenging, due to its high variability and spatial anisotropy. Common approaches for modelling permeability generally involve deterministic calculations from porosity using pre-calibrated rock physics models, or geostatistical co-simulation methods that reproduce observed experimental porosity-permeability relationships. Instead, we predict permeability from seismic data using an iterative geostatistical seismic inversion method that combines the advantages of rock physics and geostatistical modelling methods. First, we simulate facies through one-dimensional vertical Markov chain simulations. Then, permeability, porosity and acoustic impedance are sequentially generated conditioned to the previously simulated facies model. A rock physics model is used to evaluate the misfit between permeability predictions obtained from geostatistical co-simulation at the well locations and well-log values computed from 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 the proposed methodology is a set of multiple geostatistical realizations of facies, permeability, porosity and acoustic impedance, conditioned to seismic data and constrained by a rock physics model. We first illustrate the method on a synthetic one-dimensional example and compare it to a traditional geostatistical inversion approach. We then apply the proposed inversion to a three-dimensional real dataset to assess the methodology performance with scarce conditioning data and in the presence of noise.
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