This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.