| Popis: |
Many crude oils contain dissolved waxes that can cause significant problems, such as blockage of pipeline, because of the precipitation and deposition of wax particles during the production and transportation of the oil. The waxy oils are transported through very long pipelines from warm natural reservoirs to cooler conditions in the surrounding of the pipe. An important phenomenon occurring during the under-cooling of the pipeline is the formation of solid matter inside the pipe. The wax deposition is one of the most serious problems, potentially restricting flow and plugging the pipe. Wax deposits begin to form when the temperature is below the wax appearance temperature. We model a particle's growth in the oil pipe once the temperature falls below the wax appearance temperature. We determine the temperature distribution in the oil, formulate and solve a self-similar problem of wax particle growth from a single point. A corresponding initial boundary value problem is studied numerically by a time-stepping numerical algorithm. The numerical algorithm is used to compute the non-linear solution of an initial value problem of diffusion and transport of wax towards the particle. The numerical solution is compared with and validated against the self-similar solution derived for specific conditions. Then the boundary value problem is formulated for the general case. A coupled diffusion/flow problem of a single wax particle is formulated. An asymptotic analysis is used to describe the motion and growth of the wax particle. At the leading order, we consider a spherical wax particle and assume the velocity of the particle to be close to the local velocity of the flow. The flow relative to the wax particle is negligible in the leading order problem. In the first-order correction problem, the wax particle is treated as spherical initially, and the correction to the particle shape is caused by a small difference between the wax particle speed and the speed of the local flow. We draw conclusions and recommendation for further work at the end of this thesis. |
