A Two-Region Averaging Model For Solid-Liquid Flow In Horizontal Pipes

A theoretical analysis of a two-region solid-liquid flow system in horizontal pipes is presented, which considers a stationary bed of drill cuttings as a porous medium (-region) below of a two-phase dispersed flow (-region).The method of volume averaging was applied in this study to derive a rigorous mathematical model in which each variable is precisely defined. This model includes the volume-averaged transport equations for both the two-phase dispersed flow and the porous medium regions and terms from a macroscopic forces balance. The solution of the two-region model allowed evaluation of the behaviour of pressure gradient as a function of velocity, total volume fraction of cuttings and the relationship of the height of the stationary bed and pipe diameter. The solution is based on a backward finite difference explicit scheme. The simulated physical system is a pipe of 4.135 m in horizontal length and 0.0508 m in diameter. A one-dimensional, mesh-centred grid, consisting of 100 nodes, is used. The numerical results were compared with experimental data on slurry flows and a good agreement was found. Keywords: two-phase, cuttings transport, solid-liquid flow, drilling modelling, volume averaging.