Estimation of capillary pressure and relative permeability from formation-tester measurements using Design of Experiment and data-weighing inversion: Synthetic and field examples

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 flow-rate measurements acquired with formation testers. However, such procedures are still unclear to many practicing analysts and to date have not been fully explored with either synthetic or field data. aper presents the development and field test of a new method to estimate saturation-dependent rock properties. The two data sets considered in our examples use in-house and commercial reservoir simulators to model the processes of mud-filtrate invasion, acquisition of borehole resistivity measurements, and subsequent fluid withdrawal during formation tester sampling. Capillary pressure and relative permeability are described using the Brooks–Corey model comprised of 6 independent unknown parameters. The iterative procedure repeats itself until measurements are all honored within prescribed error bounds. As a result, the estimation method satisfactorily reconstructs the relative permeability and capillary pressure curves with minimal a-priori information. Whereas relative permeability end-points of water and oil can be readily estimated in a couple of non-linear iterations (assuming that the remaining parameters are fixed), residual and irreducible saturations add complexity to the inversion. We also investigate the use of Design of Experiment (DoE) tools to secure a reliable initial guess for nonlinear inversion and to understand the separate contributions of the various measurements to specific inversion parameters. Such information is fundamental in the design of a data-weighing scheme that selectively enhances the sensitivity of the measurements to unknown parameters during progressive steps of nonlinear inversion.