A TWO-REGION AVERAGING MODEL FOR SOLID-LIQUID FLOW WITH A MOVING BED IN HORIZONTAL PIPES
In this paper a methodology to obtain a two-region averaging model is presented. The model was applied to study a two-region two-phase flow system in horizontal pipes. The analysis considers a moving bed of drilling cuttings (γ -region) below of a two-phase dispersed flow (ω -region). To derive a rigorous mathematical model in which each variable is precisely defined, the method of volume averaging was applied. This model includes the volume-averaged transport equations for both regions and coupling terms obtained from a macroscopic forces balance. In order to solve the one-dimensional, time dependent, mathematical model, a backward finite difference explicit scheme with a point-distributed grid, consisting of 100x100 nodes, was applied. The simulated physical system is a pipe of 4.135 m long and 0.0508 m in diameter. The numerical simulation allows the prediction of the behavior of the pressure gradient of a flow with a moving bed as a function of velocity, total volume fraction of cuttings, cuttings density and the relation between the height of the moving bed and the pipe diameter. The numerical results agree with experimental data on slurry flows reported in literature. The maximum relative error between simulated results and experimental data was found to be 6.8%.
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