This thesis treats the laminar motion of two immiscible fluids in a pipe, where the original fluid occupying the pipe is much more viscous than the replacing fluid. Earlier works have shown that the less viscous fluid tends to form a core in the center of the pipe, while some of the more viscous fluid is left as a layer at the wall. It is expected that the thickness of the film of oil left in the pipe will be reduced as time goes by, but the asymptotic behavior of the drainage rate of this viscous film appears not to have been studied at all.
The main topic is the development of a one-dimensional hydraulic model able to describe the displacement process. We start by finding analytical results for a steady, fully developed flow, and then simulate the flow using FLUENT. A hydraulic model is developed, and stability of the equations is studied. We then solve the equations in the hydraulic model numerically, and try to validate the model by simulating flows with well established solutions, hereunder core annular flow. We also compare the results from the hydraulic model with results found using another model. Finally, we find results for how fast the layer of oil at the wall is washed out, and find an analytical approximation able to describe the drainage rate in some detail.