Simulation and inversion of borehole electromagnetic measurements for the estimation of petrophysical properties in the presence of mud-filtrate invasion
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Acoustic, electromagnetic (EM), and nuclear open-hole measurements are affected by fluids saturating near-wellbore porous and permeable rock formations, including hydrocarbons, water, and mud filtrate. Fluid invasion effects can be quantified and advantageously used to estimate petrophysical properties of the invaded rock formations. This dissertation incorporates the physics of water-base mud- (WBM) and oil-base mud- (OBM) filtrate invasion to the simulation and inversion of borehole EM measurements. We assume vertical boreholes penetrating clastic hydrocarbon- or water-bearing formations subject to either WBM- or OBM-filtrate invasion. The simulation of EM measurements in the presence of mud-filtrate invasion considers three different approaches: (1) piston-like invasion profiles, where we solely consider invaded- (flushed) and virgin- (uncontaminated) zones, (2) two-phase immiscible displacement and salt mixing between the invading WBM filtrate and connate water, and (3) invasion of single or multi-component OBM-filtrate into a formation saturated with multiple hydrocarbon components wherein the individual components are first-contact miscible. The last two approaches honor the physics of mudcake growth as well as the petrophysical properties that govern the process of multi-phase, multi-component fluid-flow displacement and include the presence of irreducible, capillary-bound and movable water. Electromagnetic measurements are simulated from spatial distributions of electrical resistivity calculated from the simulations of mud-filtrate invasion using clean- or shaly-sand water-saturationresistivity models. Inversion of petrophysical properties is posed as the nonlinear minimization of quadratic objective functions that quantify the misfit between EM measurements and their simulations. In the case of WBM piston-like invasion profiles in water-bearing formations, combined inversion of array-induction resistivity and spontaneous potential (SP) measurements yields connate water electrical resistivity and Archie’s cementation exponent. Permeability is calculated from the inversion of array-induction resistivity measurements assuming immiscible fluid-flow displacement of WBM into hydrocarbonbearing formations. Accurate reconstructions of layer-by-layer permeability are primarily constrained by the availability of a-priori information about time of invasion, rate of mud-filtrate invasion, overbalance pressure, capillary pressure, and relative permeability. This dissertation also quantifies the influence of petrophysical and fluid properties on borehole resistivity measurements acquired in the presence of compositional mixing of OBM filtrate invading partially hydrocarbon-saturated rock formations. Numerical simulations of OBM-filtrate invasion are performed with an adaptive-implicit compositional formulation that allows one to quantify the effects of additional components of mud-filtrate and native fluids on EM measurements. Perturbations of petrophysical and fluid properties enable the quantification of rock wettability changes due to OBM-filtrate invasion and their effect on the simulated induction resistivity measurements. Finally, simulations of induction resistivity measurements in the presence of OBM are compared to the corresponding measurements in the presence of WBMfiltrate invasion. The latter analysis allows us to estimate a realistic flow rate of OBMfiltrate invasion that is responsible for the variation of induction resistivity measurements as a function of their radial length of response. The combined simulation of the physics of mud-filtrate invasion and EM measurements provides reliable estimates of true formation resistivity and hence of water saturation, thereby improving the assessment of in-place hydrocarbons reserves.