# Drilling Mud Filtrate and Solids Invasion and Mudcake Formation

Near wellbore mud filtrate and fines invasion during drilling operations and the resulting formation damage and filtercake formation are amongst the most important problems involving the petroleum reservoir exploitation. This chapter reviews the fundamental processes and their mathematical formulation necessary to develop models that can be used for assessment of the damaged zone, filtrate and fines concentrations, fluid saturations, and the filtercake thickness and permeability alteration during drilling. The effects of under and over balance drilling on near wellbore formation damage are discussed. The models for simulation of the single and two-phase flow situations in the formation with water or oil based drilling mud cases are described. External particle invasion prior to filtercake buildup and its effect on the formation damage by particle invasion and retention and filtercake formation are described. These models are demonstrated by various applications. The models presented here can be used for accurate estimation of the near wellbore fluid saturations and resistivity profiles, which are necessary for accurate welllog interpretation.

## Simplified Single Phase Mud Filtrate Invasion Model

Similar to Donaldson and Chernoglazov (1987), Civan and Engler (1994) assumed that the mud filtrate mixes with the reservoir fluid and the salt concentration varies. This model implicitly assumes a piston type immiscible displacement of oil similar to the formulations by Collins (1961) and Olarewaju (1990).

Thus, the fluid zone can be viewed in two parts: the water phase and oil phase zones behind and ahead of the displacement front, located at a distance, re(t). In this case, the front moves with time. The formulation is also applicable when the mud filtrate can mix with the reservoir fluid (i.e., of the same wetting type). The filtrate mixture is considered as a pseudo-component. The filtrate mass balance is given by:

The boundary conditions at the wellbore and the moving front are given, respectively, by:

in which the filtrate invasion rate is assumed to follow an empirically determined exponential decay law according to Donaldson and Chernoglazov (1987):

The dispersion coefficient is expressed as power-law function of the volume flux (Donaldson and Chernoglazov, 1987):

Next, three dimensionless groups are defined for computational convenience and scaling purposes. The dimensionless concentration is defined as:

The dimensionless time can be defined based on the dispersion or convection time scales, respectively, as (Civan, 1994):

Because the process is mainly convection dominated, we use Eq. 18-11. The porous media peclet number is expressed as:

where «0 and D0 are some characteristic values that are the maximum values of u and D, determined as following. Note that the filtration rate varies in a range of

where it can be shown by means of Eqs. 18-5, 6, and 11 that:

Therefore, Eqs. 18-1 through 4 can be transformed into a set of dimensionless equations, respectively, as:

Finally, substituting Eqs. 18-18 and 22 into Eqs. 18-23 through 26 and dropping the subscript "D" for dimensionless quantities, Eqs. 18-23 through 26, respectively, become:

In Eq. 18-27, the parameters a and (3 are given by:

Notice that Eq. 18-27 is linear, because a and (3 do not depend on the concentration, c.The exterior radius, re(t), of the invaded region can be determined from the following volumetric balance:

Civan and Engler (1994) considered the mixing of the mud filtrate with the resident fluid within a fixed, but sufficiently long, radial distance (re = constant] and obtained a numerical solution of the model using the Crank-Nicholson finite difference scheme as described in this article.

## References

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