Optimal design of a multi-stage capsule handling multi-phase pipeline

Based on the least-cost principle, a methodology has been developed for the determination of the optimal size and optimal spacing between two successive pumping stations of an inclined up or down spherical capsule pipeline. The analysis indicates that the optimum diameter increases with increase in throughput as well as specific gravity of the capsule, whereas the optimum spacing has a trend opposite to that of optimum diameter. The capsule velocity is found to decrease with increase in capsule specific gravity and is always within the prescribed practical limits. As one would expect, the friction factor increases with increase in specific gravity of the capsule; however, in each case it decreases with increase in Reynolds number. The procedure can be applied to obtain the optimal size of the fluid pipeline by simply dropping the cost of the capsule term from the total cost. The procedure outlined is of a versatile nature and can be used for the design of the cylindrical capsule pipeline as well.