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Abstract
Laboratory measurements of relative permeability and capillary pressure are seldom performed on core samples retrieved from petroleum-production wells. Reservoir engineers rely on a limited number of small core samples to characterize many of the large-scale multiphase flow petrophysical properties affecting the production and recovery of hydrocarbon fields. The question also remains whether laboratory measurements are truly representative of in-situ rock properties. Non-linear regression methods were recently proposed to estimate saturation-dependent petrophysical properties from fractional flowrate measurements acquired with formation testers. However, such procedures are still unclear to many practicing analysts and to date have not been fully explored with both synthetic and field data. This paper develops and successfully tests a new method to estimate saturation-dependent rock properties on two field data sets.

Using in-house and commercial reservoir simulators, we model the processes of mud-filtrate invasion, acquisition of borehole resistivity measurements, and subsequent fluid withdrawal during sampling. In the examples considered, the formation tester consists of a dual-packer module acquiring pressure and fractional flow-rate measurements during the sampling operation. Based on the physics of water-base mud-filtrate invasion, borehole resistivity measurements and dualpacker measurements are first used to estimate both initial water saturation and permeability with initial estimates of capillary pressure and relative permeability. The latter are described with the Brooks-Corey model, which includes 6 independent unknown parameters. Subsequently, the measured pressure and fractional flow rates are used to estimate the 6 Brooks-Corey unknown parameters, thereby defining a new set of capillary pressure and relative permeability curves to refine the estimation of initial water saturation and permeability jointly from pressure and borehole resistivity measurements. This process repeats itself until borehole resistivity, pressure, and fractional flow-rate measurements are all honored within prescribed error bounds.

The estimation method satisfactorily reconstructs the relative permeability and capillary pressure curves with minimal apriori information. Whereas the relative permeability end-points of water and oil can be readily estimated in a couple of nonlinear iterations assuming that the remaining parameters are fixed, residual saturations add complexity to the inversion, especially for cases where the fractional flow rate exhibits a sharp decrease in contamination after oil breakthrough. We also investigate the use of Design of Experiment (DoE) tools to secure a reliable initial guess for nonlinear inversion and in understanding the separate contributions of the various measurements to specific inversion parameters. Such information is fundamental to designing a data-weighing scheme that selectively enhances the sensitivity of the measurements to unknown
parameters during progressive steps of nonlinear inversion.