Numerical Simulation of Mud Filtrate Invasion in Deviated Wells
Authors: Wu Jianghui , Torres-Verdin Carlos , Sepehrnoori Kamy , Delshad Mojdeh 
Published: December 2007

Abstract
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.

Introduction
Mud filtrate invasion takes places in permeable rock formations drilled with a well that is mechanically overbalanced by mud circulation. This phenomenon is of interest to numerous oilfield applications including drilling engineering, reservoir simulation, reservoir stimulation, and well log interpretation. Electrical, electromagnetic, sonic and nuclear measurements gathered by well logging tools are all influenced by the spatial distribution of fluids in the vicinity of the borehole resulting from the invasion of mud filtrate.
The phenomenon of mud filtrate invasion in permeable rock formations is responsible for both the development of a mud cake on the borehole wall (solids deposition), as well as for the displacement of existing in-situ fluids laterally away from the borehole1–3. Standard procedures used for the interpretation of well logging measurements conceive of the invasion of mud filtrate as a radial sequence of piston-like fluid saturation fronts. There have been a handful of approaches put forth to simulate numerically and in the laboratory the physics of mud filtrate invasion. Drilling variables such as mud density and chemistry, mud circulation pressure, and time of filtration may all significantly affect the spatial extent of mud-filtrate invasion. In-situ rock formation properties such as porosity, absolute permeability, relative permeability, pore pressure, shale chemistry, capillary pressure, and residual fluid saturations, also play a decisive role in controlling the dynamic formation of mud cake and in controlling the time evolution of the invasion process.