Estimation of in-situ petrophysical properties from wireline formation tester and induction logging measurements: A joint inversion approach

We introduce a novel inversion algorithm for the in-situ petrophysical evaluation of hydrocarbon-bearing formations. The algorithm simultaneously honors a set of multi-physics data: (a) Pressure-transient, flowline fractional flow, and salt production rate measurements as a function of time acquired with a wireline-conveyed, dual-packer formation tester, and (b) borehole array induction measurements. Both time evolution and spatial distribution of fluid saturation and salt concentration in the near-borehole region are constrained by the physics of mud-filtrate invasion. The inverse problem consists of the simultaneous estimation of the near-borehole permeability and parametric saturation functions of relative permeability and capillary pressure. A two-dimensional axisymmetric petrophysical model is assumed for the near-borehole region. Both horizontal and vertical permeabilities are subject to inversion. Saturation functions of relative permeability and capillary pressure are parametrically represented using a modified Brooks–Corey model.We simulate the response of borehole logging instruments by reproducing the multi-phase, multi-component flow that takes place during mud-filtrate invasion and formation test. A fully implicit finite-difference black-oil reservoir simulator with brine tracking extension is used to simulate fluid-flow phenomena. Induction measurements are coupled to the physics of fluid flow using a rapid integro-differential algorithm. Inversion experiments consider both noise-free and noise-contaminated synthetic data. Joint inversion results provide a quantitative proof-of-concept for the simultaneous estimation of transversely anisotropic spatial distributions of permeability and saturation-dependent functions. The stability and reliability of the inversions are conditioned by the accuracy of the a priori information about the formation porosity and fluid PVT properties. We develop an alternative sequential inversion technique for cases where multi-physics measurements lack the degrees of freedom necessary to accurately estimate all the petrophysical model parameters. The first step involves estimation of horizontal and vertical permeabilities from late-time transient-pressure measurements. Subsequently, the entire set of measurements is jointly inverted to yield saturation-dependent functions.