Optimum pipe diameter

In a chemical plant the capital investment in process piping is in the range of 25-40% of the total plant investment, and the power consumption for pumping, which depends on the line size, is a substantial fraction of the total cost of utilities. Accordingly, economic optimization of pipe size is a necessary aspect of plant design. As the diameter of a line increases, its cost goes up but is accompanied by decreases in consumption of utihties and costs of pumps and drivers because of reduced friction. Somewhere there is an optimum balance between operating cost and annual capital cost. 

For small capacities and short hues, near optimum line sizes may be obtained on the basis of typical velocities or pressure drops such as those of Table 6.2. When large capacities are involved and lines are long and expensive materials of construction are needed, the selection of line diameters may need to be subjected to complete economic analysis. StiU another kind of factor may need to be taken into account with highly viscous materials the possibility that heating the fluid may pay off by reducing the viscosity and consequently the power requirement. 

Adequate information must be available for installed costs of piping and pumping equipment. Although suppliers quotations are desirable, pubhshed correlations may be adequate. Some data and references to other pubhshed sources are given in Chapter 20. A simphfication in locating the optimum usually is permissible by ignoring the costs of pumps and drivers since they are essentially insensitive to pipe diameter near the optimum value. This fact is clear in Example 6.8 for instance and in the examples worked out by Happel and Jordan (Chemical Process Economics, Dekker, New York, 1975). 

Two shortcut mles have been derived by Peters and Timmerhaus (1980 hsted in Chapter 1 References) for optimum diameters of steel pipes of 1-in. size or greater, for turbulent and laminar flow  

D is in inches, Q in cuft/sec, p in Ib/cuft, and p in cP. The factors involved in the derivation are power cost = 0.055/kWh, friction loss due to fittings is 35% that of the straight length, annual fixed charges are 20% of installation cost, pump efficiency is 50%, and cost of 1-in. IPS schedule 40 pipe is 0.45/ft. Formulas that take additional factors into account also are developed in that book. 

Two shortcut rules have been derived by Peters et al. [Plant Design and Economics for Chemical Engineers, McGraw-Hill, New York, 2003, p. 403], for laminar (eq. 6.33) and turbulent flow conditions (eq. 6.32)  

Economic Optimum Pipe Size for Pumping Hot OU with a 

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Operating line, humidifying towers 778 Optimum pipe diameter, example 371 — water velocity, heat exchanger 505 Orifice meter 244,246, 248... 

This will be possible for only a few practical design problems. The technique is illustrated in Example 1.1, and in the derivation of the formula for optimum pipe diameter in Chapter 5. The determination of the economic reflux ratio for a distillation column, which is discussed in Volume 2, Chapter 11, is an example of the use of a graphical procedure to find the optimum value. 

Equations for the optimum pipe diameter with laminar flow can be developed by using a suitable equation for pressure drop in the equation for pumping costs. 

Estimate the optimum pipe diameter for a water flow rate of 10 kg/s, at 20°C. Carbon steel pipe will be used. Density of water 1000 kg/m3. 

Capps, R. W. (1995) Chem. Eng. NY, 102 (July) 102. Select the optimum pipe diameter. 

The sensitivity to the particular property how much will a small error in the property affect the design calculation. For example, it was shown in Chapter 4 that the estimation of the optimum pipe diameter is insensitive to viscosity. The sensitivity of a design method to errors in physical properties, and other data, can be checked by repeating the calculation using slightly altered values. 

Suppose you want to design a hydrocarbon piping system in a plant between two points with no change in elevation and want to select the optimum pipe diameter that minimizes the combination of pipe capital costs and pump operating costs. Prepare a model that can be used to carry out the optimization. Identify the independent and dependent variables that affect the optimum operating conditions. Assume the fluid properties (/i, p) are known and constant, and the value of the pipe length (L) and mass flowrate (m) are specified. In your analysis use the following process variables pipe diameter (D), fluid velocity (v), pressure drop (A/ ), friction factor (/). 

The relation between cost per unit length C of a pipeline installation and its diameter d is given by C = a + bd where a and b are independent of pipe size. Annual charges are a fraction of the capital cost. Obtain an expression for the optimum pipe diameter on a minimum cost basis for a fluid of density p and viscosity p flowing at a mass rate of G. Assume that the fluid is in turbulent flow and that the Blasius equation is applicable, that is the friction factor is proportional to the Reynolds number to the power of minus one quarter. Indicate clearly how the optimum diameter depends on flowrate and fluid properties. 

The design engineer must specify the diameter of pipe that will be used in a given piping system, and economic factors must be considered in determining the optimum pipe diameter. Theoretically, the optimum pipe diameter is the... 

Turbulent flow NRe >2100 Connect values of /> and by straight line to obtain optimum pipe diameter... 

Economic Pipe Diameter, Turbulent Flow The economic optimum pipe diameter may be computed so that the last increment of investment reduces the operating cost enough to produce the required minimum return on investment. For long cross-country... 

For any given flow, the optimum pipe diameter, dopt. will be related to optimum pressure gradient by modifying Eq, (2) so... 

Problem 9.7 Optimum Pipe Diameter vs Flow Rate... 

Note that the optimum diameter for stainless steel is smaller than for carbon steel, as would be expected given the higher materials cost of the pipe. Note also that equations 5.14 and 5.15 predict optimum pipe diameters that are roughly double those given by the rule of thumb at the start of this section. This most likely reflects a change in the relative values of capital and energy since the period when the rule of thumb was deduced. 

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