Optimum single phase line size

Optimum single phase (liquid or vapor) line size is discussed in this section. It only applies to cases where Ime pressure drop has a cost to plant. For example, pump or compressor is used to overcome the line pressure drop. It is not applicable to eases where line pressure drop Is free, such as a pressure let down line. 

Theie are two types of cost associated with a Line. One is capital cost (total installation cost, (Cl, in S)), which includes materials and installation cost, which Is the cost before a plant is In operation. The other is operating cost (CO, in ), which is the total cost lequited to operate this line over its life time (N, in years). Total cost of a line (CT, in ) is the sum of its capital cost and its operating cost. The optimum line size is selected, so that the total cost is at minimum for the life time of this line. 

For a fiKcd flow tale and operating conditions (fluid physical properties) factors affecting Line capital cost are pipe material cost, complexity of piping (wtiieh affect installation cost), and factors affecting line operating cost are life time of the line, Utility (electricity) cost, pump or compieswr efficiency. For lines without pump or compressor, a faked pump or compressor efficiency of 100% should be used. 

The optimum Line size presented here is based on Yu s articles [14,15 with following changes  

Friction factor is calculated based on estimated optimum line size. 

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For optimum single phase line size, section IV see section IV. 

A size distribution of particles is always desired rather than a single size in a fluidized bed. The two-phase theory of fluidized-bed operation is suspect when a bed contains appreciable lines, and models based on uniform particles should be used with caution. The dense phase in such cases should really be regarded as consisting of two phases emulsion and clusters of lines (d < 40 pm). Indeed, the results of Yadav et al. (1994) on commercial propylene ammoxidation catalyst clearly show that the lines agglomerate. A critical level of lines (30%) was found in terms of bed expansion, aeratability, and cluster size at which fluid-bed behavior is optimum. They proposed a model that takes the two dense phase components (emulsion and cluster) into account. Adding lines widens the limits of operable gas velocities and minimizes the segregation of particles. 

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