# Modeling a Flow Meter with Compressible Flow

PIPE-FLO Professional has certain limitations concerning the use of compressible fluids in a piping network. The limits of the Darcy Weisbach equation pertaining to compressible fluids are covered on page 18 of the Method of Solution for PIPE-FLO and elsewhere in this knowledge base. Even when operating within the limits of the equation, the judicious use of fluid zone properties is required to achieve the best results. This same attention to detail is required when modeling flow meters with compressible fluids.

The following simple system is an excellent illustration of the sort of problems that can arise from the improper specification of compressible fluids.

The resistance in the pipelines (10" diameter, 0.00001ft length) is negligible, so the only pressure loss in the system is due to the flow meter. The meter is sized at 6.5" and the fluid zone in both pipelines is set to 90 psi steam at 450ºF.

A discrepancy emerges in the pressure drop for the system. The meter shows a non-recoverable pressure drop (NRPD)of 10.03 psi while the system shows a dP of (101.5 psi - 90 psi) 11.5 psi between the flow in and the outlet. Since dP = 0 in the pipelines, this indicates a problem in the calculations. The problem stems from the incorrect fluid zone pressure and resulting fluid properties.

Unlike PIPE-FLO Compressible, PIPE-FLO Professional and Flow of Fluids are not designed to iterate fluid properties along with the system conditions so if care is not taken in properly defining fluid properties significant error can be introduced. In this case the density of the fluid remains static and the incorrect value of 90 psi.

This data is from the system pictured above when the fluid pressure on the inlet side of the meter is varied from 50 to 150 psi and the resultant deviation of the system dP from the meter dP is calculated. The error grows rapidly as the fluid pressure deviates from the correct value.

The equations for the meter dP rely on the fluid properties, primarily density, which are assumed to be constant in PIPE-FLO Professional and Flow of Fluids. A user driven iterative approach will be required to find the best solution. Sensible guesses for the fluid pressure can be used to approach the correct value.  The pressure calculated at the flow demand can be used as a good starting point to find the correct fluid zone pressure, in this case 101.5 psi.

With the fluid pressure changed to 101.5 psi, the system yields better results with a 10 psi (100 psi - 90 psi) system dP and a 10.2 psi dP across the meter. This is much closer, but an additional iteration using the new pressure at the flow demand is warranted.

Changing the fluid zone pressure to 100 psi, the discrepancy is reduced to 0.02 psi which provides a suitable number, within display rounding, for the system inlet pressure.

This sort of iterative process is simple for small system such as this one, but may be more time consuming for larger systems. The knowledge base  article Analyzing Compressible Fluid Systems with PIPE-FLO Professional has an example of using xlink and excel to automate a similar iterative process. PIPE-FLO Compressible offers a truly rigorous compressible calculation and should be considered for more complex systems.

# Attachments:

Compresssible Flow Meter.pipe