Economic pipe diameter of settling slurries

The notion of economic pipe size is extended to the case of settling slurries, which are commonly found in high tonnage, long distance pipelines of mineral ores. Water, energy and pipe infrastructure costs have been considered under the premise that the objective of this kind of infrastructure is to transport solids but not water. Unit costs for pipes have been expressed based on pipe weight or diameter. In the first case, both an assumption of a linear dependency of the pipe wall thickness with outside diameter and the special case of prescribed, outside diameter-independent pipe wall thickness, have been considered. On the other hand, a typical assumption of cost expressed as a potential function of the pipe diameter has been assumed to compare with the present model. A dimensionless formulation of the problem, including the requirement of turbulent flow transport above the deposit limit is proposed. Differently from previous analyses, made for homogeneous fluids, the present approach does not require a particular form of the friction factor. To this purpose it is shown, based on the general form of the dependency of the friction factor with the Reynolds number, that the friction factor that minimizes the operation and infrastructure cost is the maximum possible within the turbulent regime, i.e. that corresponding to the laminar-turbulent transition. Optimal conditions feature: (1) the solid concentration should be the largest possible provided safe transport is ensured, (2) the optimal pipe diameter is controlled either by costs and turbulent transition or by the deposit limit condition (not both of them simultaneously), where a dimensionless parameter has been derived to identify the relevant solution. Results with the present cost scheme have been extended to the case of homogeneous fluids.