Cosimulation as a perturbation method for calibrating porosity and permeability fields to dynamic data

The geological characterization of formations such as reservoirs or underground storage sites entails the description of the spatial distribution of porosity/permeability properties on the basis of the static and dynamic data collected. The integration of dynamic data can be expressed as an inverse problem: the purpose is to identify a set of porosity/permeability values which allows for reproducing the available data. This issue motivated the development of geostatistical-based parameterization techniques, which make it possible to vary the spatial distribution of porosity/permeability values within the geological model from a reduced number of parameters while preserving their spatial variabilities. This paper introduces first an algorithm for performing cosimulation, then a new method for continuously modifying realizations representing porosity or permeability fields. This one consists of simulating cross-correlated Gaussian random functions with identical means and covariances. The realizations resulting from the cosimulation process depend on the linear correlation coefficients between the random functions considered. Variations in these correlation coefficients induce variations in the realizations. Then, the proposed cosimulation perturbation method is incorporated into a history-matching process to calibrate porosity and permeability fields to dynamic data. The parameters to be adjusted are the various correlation coefficients. Last, an example is shown to stress the potential of the method.