May 1, 2024 11:26:14 AM
Comparison of Compressible Flow Equations and FluidFlow - Part 2
In the previous article “Comparison of Compressible Flow Equations and FluidFlow Part 1”, the standard volumetric flow rate at a fixed pressure drop is calculated using commonly used compressible flow equations and compared with the FluidFlow result. Now, if the upstream pressure is fixed at a given flow rate, different downstream pressures will be predicted using FluidFlow and compressible flow equations. The comparison of flow equations vs. FluidFlow is discussed in Illustrative Example 1.
Illustrative Example 1:
Natural gas is flowing at a temperature of 85ºF through an 18-inch. STD steel pipe, operating at a flow rate of 100 MMSCFD in a 100-mile pipeline. Assume the natural gas is pure methane. With the upstream pressure fixed at 1500 psia, calculate the downstream pressure and pressure drop using FluidFlow. Compare the FluidFlow gas calculation result to the following commonly used steady-state compressible flow equations:
- Simplified Isothermal Equation (General Flow Equation)
- Weymouth Equation
- Panhandle A Equation
- Panhandle B Equation
- AGA Equation (fully turbulent flow)
- IGT Equation
Assume that the flow of natural gas is incompressible (constant density), isothermal, and follows the Darcy-Weisbach equation, calculate the downstream pressure and pressure drop.
Solution:
FluidFlow software and Microsoft Excel spreadsheet are used to calculate the downstream pressure and pressure drop across the pipeline. The table below shows the summary of the FluidFlow and Compressible Flow Equations results:
Software/Equation |
Upstream Pressure, P_{1}(psia) |
Downstream Pressure, P_{2}(psia) |
Pressure Drop, ∆P |
FluidFlow |
1500 |
1394 |
106 |
Isothermal Equation |
1500 |
1403 |
97 |
Weymouth Equation |
1500 |
1405 |
95 |
Panhandle A Equation |
1500 |
1424 |
76 |
Panhandle B Equation |
1500 |
1429 |
71 |
AGA Equation |
1500 |
1406 |
94 |
IGT Equation |
1500 |
1410 |
90 |
By examining the figure below, it is evident that the highest pressure drop is predicted by the FluidFlow and the lowest pressure drop is predicted by the Panhandle B equation. We, therefore, conclude that the most conservative method that predicts the highest pressure drop is the FluidFlow software and the least conservative is Panhandle B.
The calculated downstream pressure and pressure drop assuming the flow is incompressible (constant density), isothermal, and follows the Darcy-Weisbach equation is 1405 psia and 94.7 psi, respectively. In the figure below, it can be examined that the calculated downstream pressure and pressure drop are similar to the Weymouth equation results.
The 94.7-psi pressure drop (∆P) is 6.31% of the absolute inlet pressure which is 1500 psia. According to CRANE Flow of Fluids – Technical Paper No. 410, if the calculated pressure drop is less than 10%, the Darcy-Weisbach equation will give reasonable accuracy and the flow can be treated as incompressible (constant density).
In the next illustrative example, FluidFlow results are compared with the compressible flow equations from a different perspective.
Illustrative Example 2:
Natural gas is flowing at a temperature of 85ºF through a 30-inch. STD steel pipe, operating at different flow rates in a 100-mile pipeline. Assume the natural gas is pure methane. With the downstream pressure fixed at 800 psia, calculate the upstream pressure required for various flow rates, ranging from 100 to 600 MMSCFD using FluidFlow. Compare the FluidFlow gas calculation result to the following commonly used steady-state compressible flow equations:
- Simplified Isothermal Equation (General Flow Equation)
- Weymouth Equation
- Panhandle A Equation
- Panhandle B Equation
- AGA Equation (fully turbulent flow)
- IGT Equation
Assume that the flow of natural gas is incompressible (constant density), isothermal, and follows the Darcy-Weisbach equation, calculate the upstream pressure and pressure drop.
Solution:
FluidFlow software and Microsoft Excel spreadsheet are used to calculate the upstream pressure at various flow rates. The figure below shows the summary of the FluidFlow and Compressible Flow Equations results:
By examining the figure above, it is evident that the FluidFlow software predicts the highest upstream pressure at any flow rate, whereas the Panhandle A equation calculates the least pressure. We, therefore, conclude that the FluidFlow software result is the most conservative since it predicts the highest pressure drop and the least conservative compressible flow equation is Panhandle A.
The calculated upstream pressures, pressure drop, and ∆P/P_{1} percentage assuming the flow is incompressible (constant density), isothermal, and follows the Darcy-Weisbach equation are shown in the table and figure below:
Flow Rate (MMSCFD) |
Upstream Pressure, P_{1 }(psia) |
Downstream Pressure, P_{2 }(psia) |
Pressure Drop, ∆P (psi) |
∆P/P_{1}*100 |
100 |
813 |
800 |
13 |
1.56% |
200 |
849 |
800 |
49 |
5.80% |
300 |
910 |
800 |
110 |
12.06% |
400 |
994 |
800 |
194 |
19.51% |
500 |
1102 |
800 |
302 |
27.40% |
600 |
1234 |
800 |
434 |
35.15% |
For 100 to 200 MMSCFD flow rates, the calculated pressure drops are less than ~10% of the inlet absolute pressure. According to CRANE Flow of Fluids – Technical Paper No. 410, if the calculated pressure drop is less than ~10% of the inlet absolute pressure, the Darcy-Weisbach equation may be applied and reasonable accuracy may be obtained provided that the specific volume (or density) used in the equation is based upon either the upstream or downstream conditions, whichever is known.
For 300 to 600 MMSCFD flow rates, the calculated pressure drops are greater than ~10% but less than ~40% of the inlet absolute pressure. According to CRANE Flow of Fluids – Technical Paper No. 410, if the calculated pressure drop is greater than ~10% but less than ~40% of the inlet absolute pressure, the Darcy-Weisbach equation may be applied and reasonable accuracy may be obtained provided that the specific volume (or density) is based upon the average of the upstream and downstream conditions.
Results Comparison:
Let us compare the FluidFlow compressible pressure dop results vs. the incompressible flow pressure drop results:
Flow Rate (MMSCFD) |
Compressible Pressure Drop, ∆P (psi) |
IncompressiblePressure Drop, ∆P (psi) |
Percentage |
100 |
13 |
13 |
0% |
200 |
49 |
49 |
0% |
300 |
105 |
110 |
4.65% |
400 |
178 |
194 |
8.60% |
500 |
264 |
302 |
13.43% |
600 |
361 |
434 |
18.36% |
Commentary:
The FluidFlow compressible pressure drop results for 100 – 300 MMSCFD flow rates are comparable with incompressible flow pressure drop results. For 400 – 600 MMSCFD flow rates, the FluidFlow results have a large percentage difference compared with the incompressible flow results.
References:
Churchill, S.W., Friction factor equation spans all flow regimes, Chem. Eng. 84 (24) (1977) 91.
Coelho, P.M. and Pinho, C. (2207). Considerations About Equations for Steady State Flow in Natural Gas Pipelines. Journal of the Brazilian Society of Mechanical Sciences & Engineering, 29(3), 262-273.
Crane Co., Flow of fluids through valves, fittings, and pipe, Technical paper no. 410, 2011.
Hall, Stephen M.. (2018). Rules of Thumb for Chemical Engineers (6th Edition) - 4.11 Compressible Flow - Transmission Equations. (pp. 58-71). Elsevier. Retrieved from https://app.knovel.com/hotlink/pdf/id:kt011FN862/rules-thumb-chemical/compressible-flow-transmission
Menon, E.S. (2005). Gas Pipeline Hydraulics (1st ed.). CRC Press. https://doi.org/10.1201/9781420038224
Mohitpour, M., Golshan, H. and Murray, A., 2000, “Pipeline design & construction: A practical approach”, ASME Press.
Schroeder, D. W. 2001, “A tutorial on pipe flow equations”, Paper presented at the PSIG Annual Meeting, Salt Lake City, Utah, October 2001. Retrieved from http://onepetro.org/PSIGAM/proceedings-pdf/PSIG01/All-PSIG01/PSIG-0112/1893397/psig-0112.pdf/1