On a Train That Fits 363 of 1,035 MMscfd, Nitrogen Room Is Worth Twice CO2 Room

On three synthetic fields feeding one LNG train, the largest feed that satisfies four inlet limits is 363 MMscfd of a planned 1,035, and the limit that costs the most of the missing gas is nitrogen. Each mol% of extra nitrogen allowance is worth 425.5 MMscfd at the margin and each mol% of CO2 allowance 50.3. Those two prices sit in units that cannot be compared directly, because one mol% is half of a 2 mol% nitrogen limit and an eighth of an 8 mol% CO2 limit. Put on the same footing, as the feed gained per 1% of relief, nitrogen is still worth 2.34% against CO2's 1.11%, about twice as much. The case is invented and the limits are placeholders; what carries over to a real train is the method, a linear programme whose duals price every line of an inlet specification in the currency a gas planner works in.

A blend check is a linear programme

The feed to an LNG train is a blend. Each well adds its rate and its gas analysis, and with ideal mixing at standard volume the blend concentration of a component is the rate-weighted mean over the wells. The acid gas removal, dehydration and mercury units were designed for an inlet envelope of so much CO2, H2S, nitrogen and mercury, and the usual check is whether the planned schedule stays inside it. The question a planner can act on is how much feed fits inside the envelope and what each limit does to that total. With rates q_i, concentrations c_ik and limits L_k:

$$\begin{aligned}\text{maximise}\quad & \sum_i q_i \\ \text{subject to}\quad & \sum_i q_i\,(c_{ik} - L_k) \le 0 \quad \text{for every limited component } k \\ & q_{i,\min} \le q_i \le q_{i,\max} \\ & \sum_i q_i \le Q_{\text{train}}\end{aligned}$$

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In words: take as much gas as the wells and the train allow, as long as the rate-weighted blend of every limited contaminant stays under its limit. A blend limit is a ratio, which is awkward to optimise, but multiplied through by the total feed it becomes the first constraint, which is linear in the rates. The dual of each limit row then gives the shadow price, the extra feed one more unit of limit would allow, exact for a small change. We solve it with HiGHS [1], the default solver behind SciPy's linprog, which returns the duals with the solution [2].

The method recovers an answer worked by hand. Take a 30 mol% CO2 well and a 5 mol% well, each able to give 100 MMscfd, against a 10 mol% limit. The clean well runs flat out and the dirty one runs until the blend reaches 10 mol%, at 25 MMscfd, for 125 in all. Loosening the limit by a small amount and differentiating by hand gives 6.25 MMscfd per mol%, and the dual returns 6.25.

Three invented fields

The case has three fields, each built to carry a different problem. Field A is a high-CO2 carbonate with five wells at 29 to 37 mol% CO2. Field B is a sour sandstone with mercury, five wells at 19 to 71 ppmv H2S and 40 to 104 µg/Nm3 of mercury. Field C is a lean clastic, four wells at 1.6 to 2.4 mol% CO2 but 4.1 to 5.8 mol% nitrogen. The data are synthetic and so is every result computed from them.

Field	Wells	Planned rate, MMscfd	CO2, mol%	N2, mol%	Hg, µg/Nm3
A, carbonate	5	445	33.4	1.0	21
B, sour sandstone	5	270	7.2	1.6	65
C, lean clastic	4	320	2.0	4.9	6

At planned rates the train would take 1,035 MMscfd at 16.83 mol% CO2 and 2.36 mol% nitrogen. We test that against four illustrative limits: 8 mol% CO2, 50 ppmv H2S, 2 mol% nitrogen and 50 µg/Nm3 of mercury. The blend is over on CO2 and nitrogen and inside on H2S and mercury, at 13 ppmv and 27.6 µg/Nm3.

Three limits bind at 363 MMscfd

The largest feed inside all four limits is 363 MMscfd, 35% of the plan. CO2 sits at exactly 8 mol%, nitrogen at 2 and mercury at 50, while H2S has slack at 29 ppmv.

The schedule that achieves it runs four of the five sour Field B wells at capacity and the fifth, B-04, at 36 of its 40 MMscfd. The sour gas is there because it dilutes two problems at once: at 5.6 to 9.0 mol% CO2 and 1.3 to 2.0 mol% nitrogen it pulls the carbonate's CO2 and the clastic's nitrogen towards their limits in the same stream. Seven wells sit at zero, including four of the five carbonate wells. The fifth, A-04, the carbonate's lowest in CO2, runs at 29 MMscfd, and one lean well, C-03, the clastic's lowest in nitrogen, runs at 68. Field B delivers 266 of its 270 MMscfd, Field A 29 of 445 and Field C 68 of 320. B-04 is the one sour well held below capacity, and at 104 µg/Nm3 it carries the most mercury of any well in the case.

Limit	Binds	Dual, MMscfd per unit	Feed per 1% of relief	Gain from a 10% looser limit, MMscfd
N2, 2 mol%	yes	425.5 per mol%	2.34%	52.3
CO2, 8 mol%	yes	50.3 per mol%	1.11%	30.2
Hg, 50 µg/Nm3	yes	5.8 per µg/Nm3	0.80%	3.8
H2S, 50 ppmv	no	0	0	0

The fourth column is the elasticity, the dual times the limit over the feed. It answers the question a licensor discussion turns on: if each clause were relaxed by the same proportion, which would return the most gas? Per mol%, nitrogen is worth 8.5 times as much feed as CO2. Per 1% of relief it is worth 2.1 times as much, and that ratio is the one to quote.

The last column is a reminder that a dual is a slope at one point. Solved again with the nitrogen limit at 2.2 mol%, the feed rises by 52.3 MMscfd, where the dual's straight line predicts 85.1. Mercury shows it more sharply: its dual promises 29 MMscfd for 5 more µg/Nm3, and the solve returns 3.8, because mercury stops binding almost at once. A whole extra mol% of nitrogen, from 2 to 3, lifts the feed from 363 to 681 MMscfd, a gain of 318 where the dual would say 426. The ranking survives every one of these checks; the magnitudes need the finite step.

Where nitrogen stops being the dearer limit

The ranking depends on where the envelope sits. Tighten CO2 to 6 mol% and the optimum falls to 280 MMscfd, mercury stops binding, and the duals become 149.1 MMscfd per mol% for CO2 and 388.8 for nitrogen. In elasticity CO2 is now the dearer limit, 3.19% against 2.78%. On this case the two cross at a CO2 limit of about 6.0 mol%, with nitrogen at 2. At every CO2 limit from there to 14 mol% nitrogen is the dearer of the two; below it, CO2 is. Loosen nitrogen instead and its limit stops binding altogether between 3.0 and 3.25 mol%, where the feed reaches 690 MMscfd with only CO2 holding it back.

So the finding is scoped to this case: at the default envelope, and across most of the plane around it, the nitrogen line costs the most gas. A train with different wells will have a different map, and the point of the method is that it draws that map from the train's own analyses.

CO2 ≤ 8.00 mol%N2 ≤ 2.00 mol%Mercury ≤ 50 µg/Nm3H2S ≤ 50 ppmv

try:the article's caseCO2 tightened to 6shut in A-03shut in B-03shut in all of Field B

shut in:A-01A-02A-03A-04A-05B-01B-02B-03B-04B-05C-01C-02C-03C-04

planned feed1,035 MMscfd

wells at capacity / part / off4 / 3 / 7

CO2 stripped at the optimum0.56 Mt/yrthe plan would strip 3.35

10% more room on N2+52.3 MMscfdthe dual's straight line says +85.1

Now. 363 of 1,035 MMscfd fits. N2 is the dearer limit: 1% more room is worth 2.34% more feed, against 1.11% for CO2.

The exhibit solves the programme live. It opens on the default envelope. Drag the point right, loosening CO2, and the feed climbs slowly while nitrogen keeps binding; drag it up and the feed climbs quickly as the lean Field C wells come on. Inside the amber outline CO2, rather than nitrogen, is the dearer limit: a strip along the edge of the infeasible corner, and a patch at high CO2 and low nitrogen limits. The hatched corner is where no blend of these wells meets both limits.

Shut-ins the optimiser has already made

Shut in the dirtiest carbonate well, A-03, at 37.2 mol% CO2. The planned feed drops by 80 MMscfd to 955, but the optimum does not move, because the optimiser had already put that well at zero. A shut-in decided in the control room can be worth nothing to the train.

Shut in a sour well and the answer reverses. Losing B-03 takes the optimum from 363 to 233 MMscfd, a loss of 130 for a well that plans at 65, because every MMscfd of it was diluting carbonate CO2 and clastic nitrogen at the same time. Shut in all of Field B and no feed fits at all. The carbonate and the lean gas cannot be blended into the envelope on their own: even the best pair, A-04 with C-03, needs at least 79% lean gas to bring CO2 down to 8 mol% and at most 36% to keep nitrogen under 2. The well that looks like the problem on an H2S and mercury report is the one holding the schedule together.

What the nitrogen line stands for

The 2 mol% nitrogen limit in this case is a placeholder, but the constraint behind it is physical. Commercial LNG specifications commonly hold nitrogen to about 1% or less so that the product can be stored with less concern about tank rollover, and a common way to get there is to flash the LNG at low pressure leaving the liquefier and burn the nitrogen-rich vapour as fuel in the gas turbines or for steam [3]. Without a dedicated nitrogen rejection unit, the nitrogen a train can take at its inlet is tied to how much of that flash gas its fuel system can absorb. Nitrogen also carries no heating value, so it pulls down the Wobbe number of the gas a terminal sends out. In Great Britain the lower Wobbe limit under the Gas Safety (Management) Regulations was cut from 47.20 to 46.50 MJ/m3 from 6 April 2025 [4].

At the optimum the treating units strip 1,530 t/d of CO2, about 0.56 Mt/yr, against the 9,180 t/d, or 3.35 Mt/yr, the plan would strip if the units could take it. Both are computed on the draft's 15 C basis, 23.645 L/mol. For a train whose CO2 goes to storage, the larger number is a design figure for gas that never reaches the inlet. Each schedule in the bench is kept with its inputs and a hash of its result, so the 363 can be rerun and checked [5].

Key takeaways

1. 1A blend limit is a ratio, but multiplied through by the total feed it is linear in the rates, so finding the largest feed inside an inlet specification is a linear programme, and its duals price each limit in MMscfd.
2. 2On the synthetic three-field case, 363 of 1,035 planned MMscfd fits four illustrative limits, with CO2, nitrogen and mercury binding together and H2S slack.
3. 3Per mol%, the 2 mol% nitrogen limit is worth 425.5 MMscfd and the 8 mol% CO2 limit 50.3. Per 1% of relief, the comparable measure, nitrogen is worth 2.34% more feed and CO2 1.11%.
4. 4Duals are slopes at one point: a 10% looser nitrogen limit returns 52.3 MMscfd where the dual predicts 85.1, so quote a finite step beside any dual.
5. 5With nitrogen at 2 mol%, nitrogen is the dearer limit at every CO2 limit above about 6 mol% on this case; tighten CO2 to 6 and CO2 becomes dearer, 3.19% against 2.78%.
6. 6The sour field is the diluent: shutting in the worst carbonate well changes nothing, shutting in sour well B-03 costs 130 MMscfd, and without Field B no blend of the other two meets both limits.

Limitations

The fields, wells and analyses are invented, and the four limits are the prototype's illustrative numbers, not any train's design basis. Every figure from the case is synthetic. The structure of the answer, which limits bind, which wells run and which limit is dearer, depends on the wells, so this case says nothing about any particular plant.

Mixing is ideal and at standard volume, each well's analysis is fixed, and there is no time in the model: no decline, no changing composition as a field depletes, no pressure, no gathering network and no hydraulics between the wells and the inlet. A real schedule also carries minimum rates, contracts and reservoir management rules that the bounds here leave out.

The duals are exact only for small changes, and the default envelope sits close to a corner where mercury starts and stops binding, so the finite steps in the table are the safer guide to what a relaxation is worth.

The model prices the inlet limits in feed gas and nothing else. The energy the amine unit spends on the CO2, and what a nitrogen rejection unit would cost against the gas it frees, are outside it. It is screening maths; a process simulation with the licensor's solvent and cold-box data would replace it for any real decision.

References

1. Q. Huangfu and J. A. J. Hall. Parallelizing the dual revised simplex method. Mathematical Programming Computation 10(1): 119 to 142, 2018: doi.org/10.1007/s12532-017-0130-5.
2. SciPy. scipy.optimize.linprog reference, for HiGHS as the default method and the marginals returned for each inequality row: docs.scipy.org.
3. Air Products and Chemicals. LNG production with nitrogen removal, US patent 11,674,749 B2, 13 June 2023, background section, for the specification of about 1% nitrogen or less with reference to tank rollover, flashing LNG to reject nitrogen and burning the nitrogen-rich vapour as fuel: patents.google.com.
4. The Gas Safety (Management) (Amendment) Regulations 2023, SI 2023/284, regulation 14(2)(a)(v), substituting 46.50 MJ/m3 for 47.20 MJ/m3 as the lower Wobbe limit, in force 6 April 2025: legislation.gov.uk.
5. EarthScan composition bench, synthetic throughout, the source of every figure from the three-field case; available on request.