Numerical investigation of filter cake formation during concentric/eccentric drilling

This paper deals with numerical study of filter cake formation and fluid loss on the borehole walls during an over-balanced drilling operation. Filter cake formation is a result of three interlinked phenomena; free flow of drilling fluid in the annulus, porous flow of filtrate through the formation and mud solids deposition on the well's wall. A numerical approach is developed for modeling and simulation of the cake growth, in which, initially, a three-dimensional non-Newtonian flow field of power law drilling mud is computed using finite difference method, and then, radial permeation of the filtrate and the rate of cake growth is accomplished by an explicit Runge-Kutta method. Extensive computer runs was carried out to investigate the effect of free flow parameters on the cake thickness profile and the simulation results indicated that, unexpectedly, increasing drill string rotation in a concentric case (within the conventional range of parameters for drilling operation) has almost no effects on cake thickness and permeate velocity. By increasing eccentricity, the effect of drill string rotation increases and a maximum and minimum cake thickness occurs in widening and narrowing gap, respectively. However, this impact can be neglected in high rotation rate. The effect of drill string and particle radius was studied as well.