Abstract

SAVIOLI, G. B.  and  FERNANDEZ-BERDAGUER, E. M.. The estimation of oil water displacement functions. Lat. Am. appl. res. [online]. 2007, vol.37, n.3, pp.187-194. ISSN 0327-0793.

We introduce an algorithm to solve an inverse problem for a non-linear hyperbolic partial differential equation. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The direct model is non-linear: the sought for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the election of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The parameter is inferred from measurements of saturation at different spatial points as a function of time. The estimation procedure is carried out linearizing the solution of the direct model with respect to the parameter and then computing the least-squares solution in functional spaces. The sensitivity equations are derived. We test the algorithm with several numerical experiments.

Keywords : Parameter Estimation; Non-Linear Equation; Conservation Law; Two-Phase Flow.

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