Bayesian inversion of DC electrical measurements with uncertainties for reservoir monitoring

This paper describes a method to infer the geometry of the saturation front (the boundary of the region swept by water) around a water injection well in an oil reservoir. Information on how injected water displaces oil in different layers is essential to best design a sweep of the reservoir. We use a Bayesian inference approach, which combines DC electrical measurements from an electrode array in the injection well with background information on the thicknesses and resistivities of each reservoir layer. The solution is the posterior probability density function of the saturation front location. We estimate its characteristics by a combination of nonlinear optimization and Monte Carlo sampling. Using synthetic data, we show how to jointly invert measurements acquired at different times after the beginning of injection and how the uncertainty in the inferred location of the saturation front depends on uncertainties in the background information available and on the amount of noise in the data.