Flare network hydraulic modelling — from isometrics to backpressure

Introduction

The flare network sizing exercise answers the question what flows into the flare system, and when? — every contingency, every common-cause event, every simultaneous load. It does not answer whether the piping can actually carry that flow. That is the job of the flare network hydraulic model: a pressure-drop simulation of every tailpipe, sub-header, header, knock-out drum, seal, and tip, run case by case against the scenarios the contingency study produced.

The model is where the arithmetic of API 521 meets the as-built isometrics. It is also the deliverable most often inherited, patched and re-run on brownfield projects — every new PSV tied into an existing header changes the backpressure on every valve already connected to it.

This post covers how a flare network model is built, which pressure-drop method to use, what each scenario is checked for, and the two checks that frequently get left out: cold temperatures and acoustic-induced vibration. It sits between the relief and flare systems overview and the flare radiation and siting analysis that takes the model's tip conditions as its input.

What the model has to answer

For every scenario, the model returns a set of numbers per segment and per relief source. The acceptance criteria are what the whole study is organised around:

A network that passes the backpressure check but fails on temperature or AIV is not a working design. All eight are evaluated in the same scenario runs.

Building the model

Topology from the isometrics

The network is a tree: relief sources at the leaves, the flare tip at the root. Each segment needs:

• Pipe ID and wall thickness from the line list, not the nominal size. A 6" Sch 80 line has an internal diameter about 5% smaller than Sch 40, and pressure drop scales roughly with D⁻⁵.
• Length and elevation from the isometrics. Elevation matters little for gas but a lot for liquid-bearing headers draining back to the KO drum.
• Fittings: elbows, reducers, tees, valves. Modern tools apply resistance coefficients per fitting rather than a blanket equivalent length. Tees deserve care. The loss through a branch tee depends on the flow split, and a header tee carrying two converging flows is one of the largest single losses in the network.
• Roughness: 0.046 mm for new carbon steel is the textbook value. Aged flare headers with scale and corrosion product can be several times rougher. A sensitivity run is cheap.

A model built from line-designation tables rather than isometrics is a screening model. It is fine for concept work. It is not fine for a revalidation that will be used to justify keeping a conventional PSV in service.

Sources and boundary conditions

Each relief source is defined by its relieving pressure (set plus allowable overpressure), relieving temperature, composition, and flow. The downstream boundary is atmospheric pressure at the tip exit, plus the vendor's tip pressure drop at that flow. The model then solves upstream from the tip, accumulating losses back to every source.

Rated or required flow?

This is the most argued-over input in the model, and it is not one number for the whole network.

• Tailpipe and the segment immediately downstream of a single spring-loaded PSV: use rated capacity, the flow the installed orifice actually passes at relieving conditions. A spring-loaded valve does not modulate; once open, it passes its rated flow regardless of what the contingency required. API 520 Part II bases the built-up backpressure check on rated flow for this reason.
• Modulating pilot-operated valves: required flow is generally acceptable, since the valve opens only as far as the upset demands.
• Main headers in multi-source global scenarios: practice varies. Some operators sum rated capacities. Others use required flows with a margin, on the argument that not every valve in a power-failure case opens fully at the same instant. Whichever basis is used, write it in the design basis and apply it consistently. A revalidation that switches basis between revisions makes the backpressure history meaningless.

Pressure-drop methods

Commercial flare network tools (Aspen Flare System Analyzer, the successor to Flarenet, is the common one) offer several calculation methods. The choice has a measurable effect on the answer.

Isothermal compressible flow

The classic flare equation. It assumes constant temperature along the segment and integrates the momentum balance:

P1² − P2² = G² · (RT/M) · [ f·L/D + 2·ln(P1/P2) ]

where G is the mass flux, f the Darcy friction factor, and the logarithmic term the acceleration loss. Isothermal flow gives a slightly higher pressure drop than adiabatic flow for the same conditions, so it errs on the conservative side for backpressure. It is the method of choice for screening and hand checks.

Adiabatic compressible flow

More physically correct for insulated or short, high-velocity segments, where the gas cools as it accelerates. It matters most near sonic velocity and in tailpipes downstream of large pressure drops.

Two-phase methods

When the relief carries liquid (a liquid-full vessel case, a two-phase blowdown, condensing heavy ends in a cold header), gas-only correlations under-predict pressure drop badly. Beggs-Brill, Lockhart-Martinelli or a homogeneous model is applied per segment. Two-phase segments also need a slug and momentum check, since the force of a slug at a header elbow is a structural load case, not a hydraulic one.

Static or total pressure

Near sonic velocity, the difference between static and total (stagnation) pressure becomes significant. Backpressure on a PSV is a static-pressure quantity. Some tools report total pressure at the nodes by default. Check which one the result table shows before comparing it against the 10% limit.

Running the scenarios

The scenario list comes straight from the contingency study, and it always has two families:

1. Global scenarios: general power failure, cooling water failure, instrument air failure, each fire zone. Every source that lifts in that event flows at once. These govern the main header, the KO drum and the tip.
2. Single-source scenarios: each PSV relieving alone at its rated flow. These govern the tailpipe and sub-header for that valve, and they are the cases that confirm the 3% inlet loss and built-up backpressure for that valve in isolation.

A third family is easy to miss: blowdown scenarios. Depressurisation valves opening on fire or ESD, often together with PSVs in the same fire zone. Blowdown peaks early and decays, so the peak flow (not the average over 15 minutes) is what loads the network. The emergency depressurisation post covers how that peak is calculated.

For each scenario the model reports, per source, the backpressure and the ratio to the allowable. The useful output is a single table of every PSV against every scenario, with the governing case flagged. That table is what a reviewer actually reads.

Low temperature: the check that fails quietly

Gas expanding across a PSV or blowdown orifice cools by the Joule-Thomson effect. For a high-pressure blowdown of a light gas, discharge temperatures of −40 °C to −80 °C are not unusual. They get colder still late in the blowdown, as the vessel contents themselves cool.

Carbon steel without impact testing is typically rated down to about −29 °C. Below the MDMT, a pipe that would hold pressure comfortably can fail by brittle fracture under the same load.

The model must therefore carry temperature along every segment, not just pressure:

• Use adiabatic flash at each source to set the discharge temperature.
• Track heat exchange with ambient along long uninsulated headers. A header at −50 °C at the BDV outlet may warm to −20 °C 100 m downstream, which decides where the low-temperature carbon steel (LTCS) or stainless section can end.
• Check the mixing temperature where a cold blowdown joins a header carrying warm relief, and the reverse case where the cold stream flows alone.

The output is a temperature map that sets the material break points on the piping specification. On brownfield work, it is often the check that reveals an existing carbon steel header sitting downstream of a new high-pressure blowdown.

Acoustic-induced vibration

High-pressure-drop sources (PSVs, BDVs, control valves venting to flare) generate intense broadband noise inside the pipe. The noise excites the pipe wall at high frequency. Fatigue cracks then form at the stress concentrations: small-bore branch connections, weldolets, and support attachments, usually within metres of the source.

The screening approach in common use is the Energy Institute Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework:

1. Calculate the sound power level (PWL) at each source from mass flow, pressure ratio, temperature and molecular weight.
2. Carry the PWL downstream, attenuating with distance, and evaluate it at each main-line discontinuity.
3. Compute a likelihood of failure (LOF) score from PWL, pipe diameter, wall thickness, and the type of branch fitting.
4. Where the LOF exceeds the threshold: increase wall thickness, change to a contoured fitting (sweepolet in place of weldolet), relocate the small-bore connection, or reduce the source pressure drop with a multi-stage orifice.

AIV is a dynamic-loading failure, not a hydraulic one, so it does not appear in the pressure-drop results unless the tool is asked for it. Large-diameter, thin-wall headers (the most economical hydraulic choice) are exactly the geometry most vulnerable to AIV. The cheapest fix is a wall-thickness change at the design stage. Every fix after commissioning is more expensive.

Worked example: a tailpipe that passes Mach but fails backpressure

Scenario: A conventional spring-loaded PSV, set at 15 barg, protects a gas separator. Rated capacity is 40,000 kg/h of gas, MW 20, at an outlet temperature of 40 °C. The tailpipe runs 25 m equivalent length (pipe plus fittings) into the main flare header. In the governing global scenario, the model shows the header at the tailpipe junction at 1.2 barg, the superimposed backpressure from every other source lifting at the same time.

6-inch Sch 40 tailpipe (ID 154 mm), isothermal method, roughness 0.046 mm:

Upstream pressure at PSV outlet:    3.8 barg
Mach at tailpipe exit:              0.87
Total backpressure / set pressure:  25%

The tailpipe fails on Mach (> 0.7) and the conventional valve fails on backpressure (> 10%).

8-inch Sch 40 tailpipe (ID 203 mm), same conditions:

Upstream pressure at PSV outlet:    1.9 barg
  of which built-up (tailpipe):     0.7 bar  (4.5% of set)
  of which superimposed (header):   1.2 bar  (8.0% of set)
Mach at tailpipe exit:              0.50
Total backpressure / set pressure:  12.6%

Mach is now fine, and the built-up backpressure alone is well within 10%. But the total backpressure is 12.6%. For a conventional valve, superimposed backpressure adds directly to the effective set pressure, and the operator's design basis caps total backpressure at 10%.

The options are:

• Change the PSV to balanced bellows. The bellows makes the set pressure largely insensitive to superimposed backpressure, and 12.6% sits well within its tolerance. This is usually the cheapest fix on a revalidation.
• Upsize the downstream header. This reduces the superimposed 1.2 barg for every valve on that header. It is the right answer if several valves are marginal, and an expensive one if only this valve is.
• Re-route to a lower-pressure sub-header, if one exists with capacity.

The point of the example: upsizing the tailpipe fixed the parameter the tailpipe controls (built-up backpressure and Mach) and left the one it does not control (superimposed backpressure from the header) unchanged. Reading the backpressure result without splitting it into built-up and superimposed leads straight to the wrong fix.

Validating the model

A flare model is easy to build wrong and hard to spot wrong, because nobody gets to measure the design relief case in the field. Before the results are used:

• Hand-check one branch with the isothermal equation above. If the hand calculation and the model disagree by more than 10–15% on the same segment, find out why before going further.
• Run isothermal and adiabatic side by side on the governing case. The difference should be small for long headers and larger for short, high-velocity tailpipes. A large difference on a long header points to an input error.
• Check the boundary condition: tip pressure drop at the scenario flow, molecular seal and water seal drop, KO drum drop. These are fixed losses that every source sees. Missing one shifts every backpressure in the network.
• Reconcile the source list against the PSV register and the cause-and-effect. A PSV in the register but not in the model is a valve whose backpressure has never been checked.
• Sensitivity on roughness and on the rated/required basis. If a valve passes only on the optimistic assumption, flag it as marginal rather than as a pass.

Common pitfalls

• Using nominal pipe size as the ID. Wall schedule changes the answer by 10–25% in pressure drop on small-bore tailpipes.
• Not splitting built-up from superimposed backpressure. The two have different limits for a conventional valve and different fixes.
• Running only the global scenarios. Single-source cases at rated flow govern most tailpipes and every inlet-loss check.
• Averaging the blowdown flow. The peak at the start of blowdown loads the header, not the 15-minute average.
• Pressure-only modelling. A header that passes every backpressure check can still be below its MDMT during blowdown.
• Treating AIV as a separate study that can wait. By the time it is run, the header wall thickness and branch fittings are already bought.
• Patching a brownfield model without re-running every scenario. A new tie-in changes the superimposed backpressure on every valve upstream of the tie-in point, not just the new one.

Conclusion

The flare network hydraulic model is the check that the relief system works as a system. The contingency study defines the loads. The model tests those loads against real pipe: real internal diameters, real fittings, and a tip with its own pressure drop. It returns, for every valve and every scenario, a backpressure, a velocity, a temperature and a vibration risk.

Done well, it produces a single table a reviewer can read in ten minutes: every PSV, every scenario, the governing case, and the margin. Done poorly, the conventional valve that was fine in 2010 has quietly gone to 13% backpressure after three brownfield tie-ins, and nobody re-ran the global case to notice.

The discipline is consistency. Use one design basis for flows, one method validated by hand, every scenario re-run after every change, and temperature and acoustic checks in the same model as pressure.