Sampling hydrocarbon fluids from a reservoir during an early phase of formation testing (typically during interruptions in drilling) represent an important step in formation evaluation targeting the characterization of composition and pressure/volume/temperature (PVT) properties of petroleum reserves required for their efficient development. A sampling job is usually accomplished with a tool, the formation tester, which can be conveyed downhole on a wireline cable, drill-pipe, or tubing. This tool has a probe and a pump allowing for the production of reservoir fluid from a small spot of a borehole wall covered by filtercake or mudcake deposited during drilling. The filtercake is built by the invasion of mud filtrate into the formation under pressure overbalance created by the mud column inside the wellbore. For this reason, after drilling, each wellbore is surrounded by a cylindrical zone saturated with mud filtrate and, prior to obtaining a sample of virgin formation fluid, cleanup production must be initiated to overcome the consequences of invasion. A 3D model of flow and contamination transport during cleanup production is considered in this article. The model assumes a piston-like displacement and no filtrate leakage through mudcake. This model leads to a multiscale problem of flow and transport in porous media with geometrical and hydrodynamic singularities. A full sensitivity analysis of its solutions has been carried out versus the initial depth of filtrate invasion and the viscosity contrast between the formation fluid and invaded mud filtrate. The numerical modeling has revealed two phases of cleanup production. During the early phase, the contamination of produced fluid is predominantly affected by a circumferential contamination transport. During the later phase, the evolution of contamination is controlled mainly by mud-filtrate displacement vertically. In the absence of viscosity contrast, both phases of cleanup can be described by exponential laws for the contamination versus the produced volume with exponents matching the empirical correlation (−5/12) and the far-field pseudospherical flow pattern (−2/3) for the early and late phases A. Skibin Schlumberger Moscow Research, 5A Ogorodnaya Sloboda Per,