How Do You Use the Expansion Factor to Properly Size Equipment for Compressible Gas Applications?

By Jeff Sines, Product Engineer, Engineered Software, Inc.

When sizing equipment for piping systems with compressible gas applications, it is important to account for all factors that influence the flow rate and pressure drop across the equipment. Under-sizing a pipeline, relief header, control valve, safety valve in compressible applications, or orifices can result in catastrophic failure that damages the equipment and piping system.  Disastrous failure due to under-sizing equipment can also jeopardize the safety of employees and the surrounding community, impact the reputation of the manufacturing plant, parent company, engineering consulting firms, and equipment manufacturers. Additionally, companies and staff are affected by expensive repairs and replacement costs, lost production, compensation for injuries or death, and potentially the loss of operating permits from regulatory agencies.

As compressible gas flows through each device in a piping system, head loss causes a drop in static pressure,  a decrease in density (expansion) and temperature, and an increase in velocity. Depending on the amount of expansion, the change in density, temperature, and velocity may be insignificant and can be neglected. If it is significant enough, it must be accounted for when designing a compressible gas system, sizing equipment, or evaluating plant operation. One way to determine the need to use compressible equations is by evaluating the Pressure Drop Ratio (x = dP/P1). For x < 0.2, the change in gas density is small, and the assumption of incompressible flow can be made. For x > 0.4, the density change is large and compressible flow should be assumed. 

The process of expansion adds resistance to flow that reduces the flow rate for a given overall pressure drop or results in a higher pressure drop for a given flow rate. The most common method to account for gas expansion is to determine an Expansion Factor to apply to the incompressible fluid flow equation for a particular device. Various equipment manufacturers approach the determination of the Expansion Factor differently. However, each method shows that it is a function of the pressure drop across the device, the fluid properties, and some measure of the device’s hydraulic performance. More complex solution methods can be used including adiabatic flow equations (Fanno Flow) and isothermal equations.

Gas Expansion in Pipelines, Valves, and Fittings

One form of the Darcy equation found in the Crane Technical Paper N. 410 for calculating the mass flow rate of incompressible fluid flow in a pipeline is given by Equation 1: