Economic Pipe Diameter

Background: As stated on page 497 of the 4th edition of Peters & Timmerhaus, “Piping is a major item in the cost of chemical process plants. These costs in a fluid-process plant can run as high as 80 percent of the purchased equipment cost or 20 percent of the fixed-capital investment.” The diameter of the pipe strongly influences the present value of the plant, through both the annual cost of electric power and the installation cost of the piping system (pipe, pumps, valves, etc.). As one increases the pipe diameter, the cost of the pipe increases but the pressure drop decreases, so that less power is required to pump (liquid) or compress (gas). The net result is that there is a minimum cost as manifested in the net present value (which is negative if one considers the piping system in isolation of the rest of the plant). The diameter corresponding to this minimum cost is known as the economic pipe diameter. Several methods have been developed to provide quick estimates of the economic pipe diameter without going through detailed economic calculations. These are given below. Before deciding on a diameter, it’s probably a good idea to compare the predictions of the methods.

Perry’s 5th edition: The nomograph below was created using cost data from the early 1960's. Since only relative cost data are important, the economic diameter should not change significantly over time. To use, draw a straight line between the flow rate (in gallons per minute for liquids or cubic feet per minute for gases) to the density (top for liquids, bottom for gases). Where this line crosses the middle scale gives the economic diameter of Schedule 40 steel pipe. Smaller diameters should be used for more expensive piping, larger diameters for more expensive pumps or compressors.

Peters & Timmerhaus 5th edition (Max S. Peters, Klaus D. Timmerhaus and Ronald E. West, “Plant Design and Economics for Chemical Engineers,” McGraw-Hill, NY, 2003) p 501: For turbulent flow in steel pipes with an inside diameter ≥ 1 inch (2.54 cm):

13.045.0vopt,i m363.0D ρ≈ &

where Di,opt is the optimal inside diameter (m), vm& is the volumetric flow rate in m3/s and ρ is the fluid density in kg/m3. Note that this and the following equations are not dimensionally consistent, so you must convert all parameters to the specified units. For viscous flow in steel pipes with an inside diameter ≥ 1 inch:

13.040.0vopt,i m133.0D µ≈ &

where µ is the fluid viscosity in Pa⋅s.

On page 502, P,T&W give an updated nomograph similar to that above, for both viscous (laminar) and turbulent flow.

Perry’s 7th edition: On page 6-14 it states “For low-viscosity liquids in schedule 40 steel pipe, economic optimum velocity is typically in range of 1.8 to 2.4 m/s (5.9 to 7.9 ft/s). For gases with density ranging from 0.2 to 20 kg/m3 (0.013 to 1.25 lbm/ft3), the economic optimum velocity is about 40 m/s to 9 m/s (131 to30 ft/s). Charts and rough guidelines for economic optimum size do not apply to multiphase flows.”

Towler & Sinnott (Gavin Towler and Ray Sinnott, “Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design,” Butterworth-Heinemann/Elsevier, Burlington, MA, 2008) p 269: For turbulent flow in A106 carbon-steel pipe: 25 to 200 mm, di,opt = 0.664 G0.51ρ-0.36 250 to 600 mm, di,opt = 0.534 G0.43ρ-0.30 For turbulent flow in 304 stainless-steel pipe: 25 to 200 mm, di,opt = 0.550 G0.49ρ-0.35 250 to 600 mm, di,opt = 0.465 G0.43ρ-0.31 where di,opt is the optimum diameter in m, G is the flowrate in kg/s, and ρ is the fluid’s density in kg/m3.

Example of detailed optimization: http://web.ontrackengineering.com/downloads/pipetrackasme.pdf