Particle size effects on optimal sizing and lifetime of pipelines transporting multi-sized solid-liquid mixtures

A life-cycle cost analysis model is developed in this study, to examine the effects of particle size distribution of the solid particles to be transported on the optimal sizing and lifetime of the pipelines used for transportation of solid-liquid mixtures. The method determines the lifetime of the pipe corresponding to the least annual total cost per unit length of the pipe. The optimum diameter is obtained so that the total cost per unit pipe length per unit volume of the transported mixture throughout this lifetime is minimum. The total cost includes manufacturing and repair cost of pipe, cost of pumping power as well as the cost of power required for the crushing of particles from an initial size distribution to a desirable particle size distribution. The repair cost of pipe and cost of pumping power increase as the pipe becomes older due to more frequent pipe breaks and due to the pipe wear that makes wall roughness, and thereby pressure drop, greater. These costs together with the cost of power for crushing must be considered for through life costing of pipelines. Since the transportation of solid-liquid mixtures is maintained by several pumping stations in long pipelines, the spacing between two successive pumping stations must also be determined. The study shows interdependence of parameters such as the lifetime, the optimum diameter, the corresponding spacing for a given pumping power and the particle size distribution of solid particles transported in the pipeline. Furthermore, the method also provides the interrelation between the total length of pipeline when crushing is economical and the different particle size distributions.