We develop a numerical algorithm intended to replicate the physics of mud-filtrate invasion in vertical, horizontal, and highly deviated overbalanced wells. This algorithm is adapted from a general three-dimensional multi-phase fluid-flow simulator otherwise widely used in large-scale reservoir applications. Checks of numerical consistency and accuracy are performed against equivalent geometries and against one commercial simulator. Special emphasis is placed on describing the influence of mud-cake buildup on the mud filtration process. We approach the latter problem by introducing an effective flow-rate function that describes the evolution in time of the rate of injection of mud filtrate into existing formations. Specific parametric representations of the equivalent flow-rate function are derived on the basis of previously published laboratory experiments of mud circulation.

An extensive sensitivity analysis is presented with the intention to quantify the influence of several geometrical and petrophysical parameters on the spatial distribution of mud-filtrate invasion away from the borehole wall. These parameters include relative permeability, capillary pressure, permeability anisotropy, dipping layers, degree of hydraulic communication between adjacent layers, and gravity segregation, among others. Our simulations shed new light to the character of invasion profiles in complex geometrical environments and taking place under realistic petrophysical conditions. We show that standard piston-like descriptions of mud-filtrate invasion, commonly used in well-log interpretation, can lead to rather inaccurate interpretations of wireline measurements. It is envisioned that our study will provide a sorely needed petrophysical and fluid-flow template that could be used to guide the integrated interpretation of several wireline measurements into a unique distribution of petrophysical parameters in the near-borehole region. We present an example of the use of such a template by calculating the sensitivity of electromagnetic induction measurements to three specific conditions of mud-filtrate invasion in a vertical well.

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