The early detection of the oil–water encroachment front is of prime interest during the water flooding of an oil reservoir to maximize the production of oil and to avoid the oil–water encroachment front to come too close to production wells. We propose a new 4-D inversion
approach based on the Gauss–Newton approach to invert cross-well resistance data. The goal of this study is to image the position of the oil–water encroachment front in a heterogeneous clayey sand reservoir. This approach is based on explicitly connecting the change of resistivity to the petrophysical properties controlling the position of the front (porosity and permeability) and to the saturation of the water phase through a petrophysical resistivity model accounting for bulk and surface conductivity contributions and saturation. The distributions of the permeability and porosity are also inverted using the time-lapse resistivity data in order to better reconstruct the position of the oil water encroachment front. In our synthetic test case, we get a better position of the front with the by-products of porosity and permeability inferences near the flow trajectory and close to the wells. The numerical simulations show that the position of the front is recovered well but the distribution of the recovered porosity and permeability is only fair. A comparison with a commercial code based on a classical Gauss–Newton approach with no information provided by the two-phase flow model fails to recover the position of the front. The new approach could be used for the time-lapse monitoring of various processes in both geothermal fields and oil and gas reservoirs using a combination of geophysical methods.
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