Well control operations while drilling with an oil-base mud can suffer several unexpected phenomena. One of these is the dispersion (smearing) of the gas in solution whenever a gas kick is being circulated from the well. If the gas influx has gone into solution, it is very important to predict the movement of this gas-contaminated mud as it is circulated from the well. A computer model of non-Newtonian fluids flowing in an annulus of any eccentricity has been developed with which to accurately model this dispersion. The movement of the gas-contaminated mud is predicted as a consequence of the velocity profiles established as the displacement of the annulus progresses.