Numerical simulation of multi-phase mud filtrate invasion and inversion of formation tester data
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Mud-filtrate invasion takes place in permeable rock formations drilled with an overbalanced borehole. This phenomenon is of interest to numerous oilfield applications including drilling, reservoir simulation, reservoir stimulation, and well-log analysis. Electrical, electromagnetic, sonic, and nuclear measurements acquired with well-logging instruments are all influenced by mudfiltrate invasion. This dissertation develops accurate and efficient algorithms for the numerical simulation of the phenomenon of mud filtrate invasion around an overbalanced borehole. Emphasis is placed on embedding geometry consistent with mud-cake buildup, multiple-bed rock formations, and deviated boreholes. Boundary and initial conditions for the simulation problem are enforced to replicate actual drilling environments, including the time-lapse process of mudcake buildup coupled to rock formation properties. Checks of numerical consistency and accuracy of the numerical simulation algorithm are performed against existing numerical and laboratory results. The simulation algorithms are used to perform an extensive sensitivity analysis to assess the influence of various drilling and petrophysical parameters on the phenomenon of mud-filtrate invasion. Results from this sensitivity analysis are used to construct parametric petrophysical models for the quantitative evaluation of wireline logs in terms of petrophysical parameters. Examples of such an assessment are presented for the petrophysical interpretation of electromagnetic induction logs. It is shown that the phenomenon of mud-filtrate invasion has a significant influence on electrical resistivity readings. In particular, simulation examples clearly show that the process of salt mixing between mud-filtrate and connate water is important to properly interpret induction logs in terms of in-situ fluid saturation. Numerical simulation of mud-filtrate invasion also provides the initial condition for the time evolution of fluid saturation behind casing and for the simulation of multi-phase wireline formation tester measurements. Examples are shown of the time-lapse behavior of the spatial distribution of fluid saturation behind casing once the process of mud-filtration comes to a halt. These examples are used to assess the sensitivity of behind-casing logging production measurements to fluid saturation, capillary pressure, and gravity segregation. A second component of the dissertation concerns the estimation of petrophysical properties from formation-tester measurements. Inversion algorithms are developed to approach such a problem. The algorithms account for the effect of mud-filtrate invasion and make use of a forward numerical model that correctly simulates the time-lapse behavior of 3D multi-phase fluid flow in the near wellbore region imposed by fluid pumpout. Fluid pumpout is simulated for the dual-probe configuration of Halliburton’s Reservoir Description Tool (RDT). Data for the inversion consist of (a) time series of pumpout flow rates, (b) time series of pressure acquired with the point pressure sensors, and (c) time series of fractional fluid flow rates acquired with the pumpout flowline of the RDT. The basic inversion algorithm estimates porosity, permeability, and permeability anisotropy for the cases of water- and oil-based muds invading oilbearing formations. An advanced inversion algorithm estimates relative permeability and capillary pressure curves under the assumption of a modified Brooks-Corey model. Inversion of wireline formation tester data is performed with two types of algorithms, one based on neural networks, and the other based on Bayesian inference that uses a Markov-chain Monte Carlo sampling method. In both cases, the inversion algorithm quantifies the uncertainty of the estimated parameters in the presence of noisy time-series measurements. Validation of the inversion algorithms is performed on both noisy synthetic and field data sets. Petrophysical parameters inverted from field data sets compare favorably to rock-core measurements and log-derived estimates of the same parameters. The numerical simulation and inversion algorithms developed in this dissertation embody a more efficient, reliable, and accurate methodology than used nowadays to assess rock formation properties from multi-phase formation tester measurements.