Numerical Simulation of Filter Cake Formation on Borehole Walls Considering Effect of Non-Newtonian Drilling Fluid and Eccentricity

In overbalanced drilling operation, due to the pressure difference between the drilling fluid and formation mud filtration happens in which a layer of cake develops on the sides of a wellbore wall. In this research a numerical procedure was used for modeling and simulation of the cake growth in which at first, three-dimensional flow field of non-Newtonian drilling mud has been computed using finite difference scheme and using bipolar coordinate. Next, permeation flux of the filtrate is evaluated using the Darcy equation and the rate of cake growth has been calculated based on the probability of particle adhesion and using an explicit 4th order Runge-Kutta method. In the present paper, the effects of drill string rotation, eccentricity and particle radius on the cake thickness and permeate flux are studied. The results show filter cake thickness and filtrate flux remains invariable by increasing drill string rotation due to drilling fluid recirculation in the annulus. Increasing eccentricity not only changes the profile of filter cake thickness and filtrate flux but also increases the difference between its maxima and minima. Furthermore by decreasing particle size, the filter cake thickness increases and filtrate flux decreases.