In short: A liquids cracker is a joint production plant selling five or six products at once, so petrochemical margin optimisation that treats it as an ethylene business with by-products attached keeps producing surprises. Three different quantities get called margin in the same meeting and they answer different questions about the same plant. The feed decision is a co-product decision, because steam cracking yields are set by the feed and the furnace conditions, and gas and liquid feeds give very different slates. Solved as a linear program, the dual values matter more than the objective value for anyone making investment decisions, and they are usually the output that gets discarded.
The monthly margin review opens with the ethylene chain margin, which is down. The feedstock team points at naphtha, which is up. The commercial team points at ethylene, which is soft. Both are right and neither explains most of the movement, because a third of the cracker's revenue came from propylene, C4s and pyrolysis gasoline, and two of those moved more than either of the numbers on the slide.
A liquids cracker is a joint production plant selling five or six things at once. Any margin conversation that treats it as an ethylene business with some by-products attached will keep producing surprises in the direction of the products nobody is watching.
What margin means here depends on where you stand
Three different quantities get called margin in the same meeting, and they answer different questions.
The market spread, meaning a published product price minus a published feedstock price, is a screen number. It tells you what the industry looks like and it is not your plant. Your yields, your energy cost and your logistics are all different from whatever the spread assumes.
The cash margin of your own asset is feedstock plus variable conversion cost subtracted from the realised revenue of the entire product slate, per tonne of feed. This is the number that decides whether to run and at what rate.
The cost of ethylene by the co-product credit method takes the same figures and expresses them per tonne of ethylene after crediting every other product at its market value. This is the number that decides which feed to buy, and it is the one that behaves most counter-intuitively.
Getting the three straight is worth the ten minutes because they move in different directions. A rise in propylene raises the cash margin and lowers the cost of ethylene, and someone reading only the ethylene spread sees neither.
The feed decision is a co-product decision
Steam cracking yields are set by the feed and by the furnace conditions, and the difference between a gas feed and a liquid feed is enormous.
The yield ranges are published. Zimmermann and Walzl's ethylene article in Ullmann's Encyclopedia of Industrial Chemistry, in its 2009 revision, gives ethane cracking an ethylene yield around 80 percent by weight with very little else besides fuel gas, while full-range naphtha gives roughly 30 percent ethylene, a low to middling teens percentage of propylene, around 10 percent C4s and close to a fifth as pyrolysis gasoline.
That difference is the whole strategic question in the sector. An ethane cracker is an ethylene machine whose economics depend on two prices. A naphtha cracker is a chemical refinery whose economics depend on six, and whose competitive position swings with the aromatics and polypropylene chains as much as with polyethylene.
The operational consequence is that a naphtha cracker's feed decision cannot be made against an ethylene price. It has to be made against a valuation of the whole slate, which changes weekly and which almost nobody recomputes weekly.
Ethane and naphtha, worked to a cost of ethylene
Take one tonne of feed in each case and use round numbers you can replace with your own.
Naphtha at 650 per tonne, yielding 0.31 tonnes of ethylene, 0.14 propylene, 0.10 C4s, 0.20 pyrolysis gasoline, 0.04 fuel oil and 0.17 of methane and hydrogen taken as fuel gas.
Value the slate at ethylene 1,050, propylene 900, C4s 700, pyrolysis gasoline 750, fuel oil 400 and fuel gas at fuel parity of 350. Revenue is 325.50 plus 126 plus 70 plus 150 plus 16 plus 59.50, which is 747 per tonne of naphtha. Subtract the feed at 650 and a variable conversion cost of 60, and the cash margin is 37 per tonne of naphtha.
Now the cost of ethylene by credit. Total cost is 650 plus 60, which is 710. Co-product revenue is 747 minus the 325.50 of ethylene, which is 421.50. Net cost attributed to ethylene is 288.50, spread over 0.31 tonnes, giving 931 per tonne of ethylene.
Ethane at 250 per tonne, yielding 0.80 tonnes of ethylene, 0.02 propylene and about 0.15 fuel gas. Revenue is 840 plus 18 plus 52.50, which is 910.50. Conversion cost of 80 and feed of 250 gives a cash margin of 580 per tonne of ethane. Cost of ethylene is 330 minus 70 of co-product credit, over 0.80 tonnes, which is 325 per tonne.
The gap between 931 and 325 is the ethane advantage that has moved most of the sector's capital for two decades, and stating it as a cost of ethylene rather than as a margin makes it comparable across plants of different scale and configuration.
Now do the sensitivity, because that is where the useful information sits. Drop the propylene price by 200. The naphtha cracker's cost of ethylene rises by 0.14 times 200 divided by 0.31, which is 90 per tonne. Drop pyrolysis gasoline by 150 and the cost of ethylene rises by 0.20 times 150 over 0.31, which is 97.
So a 200 move in propylene is worth 90 per tonne on the ethylene cost, and a 150 move in an aromatics-linked stream is worth 97. Both are larger than the effect of a 25 per tonne move in naphtha itself, which works out at about 81. The feedstock price gets the attention because it is one number on one line, and the co-products carry more of the variance.
Severity is a lever between ethylene and propylene
Within a liquids cracker, coil outlet temperature and residence time set severity, and severity trades ethylene against propylene. Higher severity cracks harder, producing more ethylene, more fuel gas and less propylene. Lower severity does the opposite and raises the propylene to ethylene ratio.
That is a real operating lever with real value, and it is usually treated as an engineering setting rather than an economic decision. Shifting the propylene to ethylene ratio from 0.45 to 0.60 on a plant producing a million tonnes of ethylene moves roughly 150,000 tonnes of production between the two chains. At a 300 per tonne difference in net value between them, that is 45 million of annual margin sitting in a parameter that gets reviewed when the furnace engineers think about it.
Three qualifications keep this honest. Lower severity means more feed per tonne of ethylene, so the trade depends on the feedstock price too. Run length between decokes changes with severity, and a shorter cycle costs availability. And downstream units have hydraulic limits, so a large shift in the propylene to ethylene ratio can hit a splitter or a compressor before it hits the market.
Those qualifications are exactly what an optimisation model handles well and a rule of thumb does not, which is the argument for putting severity in the decision variables rather than in the assumptions.
The transfer price between the refinery and the cracker
Where a cracker sits alongside a refinery, the feedstock decision becomes an allocation decision, and the way the transfer price is set determines whether the two assets reach the group optimum.
Naphtha has two homes. It can go to the cracker or into the gasoline pool. Suppose it is worth 650 as cracker feed on the arithmetic above and 690 as a gasoline blendstock in a strong gasoline season. Priced at market, the refinery sends it to gasoline, and that is the right answer if the cracker's marginal value of naphtha is genuinely below 690.
The trap is in how the cracker's marginal value of naphtha gets estimated. The relevant figure is the value of the slate produced from an incremental tonne minus the incremental conversion cost, which on the numbers above is 747 minus 60, or 687, and the purchase price has nothing to do with it. Those two figures, 690 and 687, are close enough that the allocation is a real decision rather than an obvious one, and it flips several times a year with the gasoline crack.
Two structures fail here in opposite directions. A fixed transfer price set annually means one of the two assets is systematically making the wrong call for most of the year. Market-based transfer pricing with each asset optimising its own profit gets closer, and still misses whenever a constraint at one asset changes the other's marginal value, which is most of the time in an integrated site.
The clean answer is a single optimisation across both assets with one objective function, where internal streams are decision variables rather than priced transactions, and the transfer price used for management reporting is derived from the model's dual value rather than negotiated. Doing that requires the refinery scheduling layer covered in CC9 and the crude economics covered in N6 to feed the same model, which is a data problem before it is a modelling one.
The shadow prices are the output worth reading
When this is solved as a linear program, the objective value gets reported and the dual values get discarded, which is the wrong way round for anyone making investment decisions.
Every binding constraint in the model carries a shadow price, meaning the improvement in margin from relaxing that constraint by one unit. On a cracker complex the interesting ones are the furnace capacity, the cracked gas compressor, the C3 splitter, the propylene refrigeration, tankage for each product, and any logistics constraint on getting product out.
Read as a list ranked by shadow price times a plausible relaxation, those duals are a debottlenecking programme derived from economics rather than from engineering enthusiasm. A splitter with a shadow price of 40 per tonne and 60,000 tonnes of achievable expansion is worth 2.4 million a year, which sets the budget for the study.
Two cautions on reading them. A shadow price is valid locally, over the range where the same set of constraints stays binding, so a large relaxation needs re-solving rather than multiplying. And a constraint that binds in only three months of the year has a shadow price of zero in the annual average and a large one in those months, so duals should be read per period rather than pooled.
The limit
The whole calculation rests on yield vectors, and yield vectors from a licensor's design case describe a clean plant running on a specified feed. Real furnaces have fouled coils, real naphtha varies in paraffin content from cargo to cargo, and the yield you actually get can differ from the model by more than the margin you are optimising.
The correction is empirical. Reconcile the model's predicted yields against measured production for each feed type over several months, fit the residual, and use the corrected vectors. That work has to be repeated after every major maintenance event and whenever the feed slate changes materially, and it is the difference between a model people trust and one they override.
There is a second limit on the co-product pricing. Crediting propylene, C4s and pyrolysis gasoline at market assumes you can actually sell them at market, which depends on local demand and on whether a downstream derivative unit is running. A plant that has to place its C4 stream into a fuel outlet because the butadiene unit is down is realising a materially different value from the one in the model, and if that condition persists the whole feed ranking can invert.
And the numbers above are a snapshot. Feedstock and product prices move together with the oil complex, so a static comparison of ethane and naphtha at one set of prices tells you very little about the strategic position; what matters is the joint distribution, which is a different exercise and connects to the exposure work in N17.
Take last month's actual production by product, price the slate at realised values rather than at plan, and compute your cost of ethylene by the credit method for each feed you ran.