This work deals with the problem of estimating reservoir permeability and porosity distribution from multiple sources, including production data and well logging data. The work focuses on integrating long-term resistivity data into the parameter estimation problem, investigating its resolution power both in the depth direction and in area.

The resistivity logging tool considered in this project is a new tool proposed for permanent installation. The tool is installed in the cement around the well when the well is completed, and is capable of recording the long-term resistivity variation around the wellbore.

In this work, the Poisson equation with mixed boundary condition was used to model the infinite potential field around the resistivity logging tool. The behavior of the reservoir was modeled with a standard three-dimensional, two-phase, black-oil model. The resistivity response simulator was integrated into the flow simulator through Archie's law.

The Gauss-Newton algorithm was used to solve the inverse problem. This algorithm requires the calculation of the derivatives of the observation data with respect to the unknown parameters. These derivatives are called the sensitivity coefficients.

By running several simple inverse problems, it was concluded that the resistivity data has high resolution power in the depth direction and is capable of sensing the areal heterogeneity.

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