I investigate the estimation of relative permeability curves through core flooding experiments. This estimation problem is formulated as a nonlinear least squares problem governed by a coupled system of partial differential equations (PDEs) modeling the flow of water and oil through the porous medium. This complex PDE-constrained least squares problem is solved using a Gauss-Newton method. The sensitivity information required for this method is needed to derive statistical bounds for the parameter estimation error based on the Fisher Information Matrix.
The introduction of statistical confidence intervals for maximum likelihood estimators allows practitioners to quantify uncertainty due to noise in measurements for parameter estimation problems. In future steps, this approach can be extended to compute optimal experimental designs to further improve the quality of the computed parameters. This research has immediate applications to many pertinent problems in the oil and gas community including reservoir simulation, experiment design of core flooding, and history matching.
