Mathematical modeling for prediction of the distribution and mixing of mud filtrates in the reservoir formation surrouuding a well being drilled and the filter cake build-up and its effect on the mud filtrate invasion into the formation, as well as the resulting formation damage effects is presented. The model can simulate the single and two-phase flow situations in the formation with water or oil based drilling mud cases. External particle invasion during the early period of filter cake initiation and its effect on the formation damage by particle migration and retention is considered. An application involving radial flow is given. This model is a useful tool for accurate interpretation of oil-mud-fluid system saturations and resistivity profiles which are essential for the development of efficient well-log interpretation.
Estimation of the extent of mud filtrate invasion and distribution within the near wellbore formation during drilling operations is essential for accurate well-log interpretation (Civan and Engler). This process is complicated by the formation of a mud filter cake and its effect on invasion by reducing the filtrate volume and the migration of fme particles info the porous formation. Simultaneously. the properties of the fluid phases in porous media, such as density and viscosity, vary as a result of mixing and interactions of reservoir fluids with the mud filtrate and fine particles.
In spite of many experimental studies of the invasion of mud filtrates in laborafory cores, there have been only a few reported attempts to mathematically model the problem. Clark and Barbat have developed a three-parameter empirical model for accurate correlation of dynamic fluid loss data. Jiao and Sharma proposed a simple model based on a power law relationship between the filtration rate and the shear stress at the cake surface. Donaldson and Chernoglazov have developed a single-phase leaky-piston model using experimentally derived dispersion coefficient and mud filtrate invasion rate. Civan and Engler have improved the Donaldson and Chernoglazov model and provided an accurate solution method for radial flow using the dimensionless form of the model for convenience in computation and scaling. Chase and Willis and Smiles and Kirby have presented compressible filter cakes without particle intrusion models. Corapcioglu and Abboud, and Abboud have developed models for compressible filter cakes allowing particle penetration. Liu and Civan have considered the effect of the filter cake and formation damage on mud filtrate and mud fines invasion in single and two-phase fluid systems.
In this study, an improved formulation of the multi-species and two-phase fluid transport in deforming porous media; derivation of compressible and incompressible cake models with and without particle invasion; and an application involving radial flow filtercake and mud filtrate invasion are presented.