Two crude grades quoted at the same delivered price can differ by several dollars a barrel in netback, because they yield different product slates and load different units. The assay is the constraint set, since sulphur, density, metals content and the distillation curve decide which units can run the barrel and what comes off it. Blending rather than single grade selection is the real decision variable, and the useful output is a slate with the marginal value of each grade at current product prices. Netback economics leave out the plant's tolerance for change, so a slate that switches grades often carries transition, tankage and operator costs that can consume the modelled gain.
Crude selection looks like a procurement decision and behaves like an operating one. Two grades quoted at the same delivered price will produce different product slates, stress different units, and leave you with different amounts of material you did not want.
The gap between them is netback, meaning the value of the products you can make from a barrel minus the cost of making them, and it routinely differs by several dollars a barrel between grades that appear similarly priced. A procurement process optimising delivered cost is optimising the smaller of the two numbers.
What an assay actually constrains
A crude assay is a laboratory characterisation: density, sulphur content, the yield curve across boiling ranges, metals content, acidity, and the properties of each cut. It determines what the barrel can become before any economics enter.
Three properties do most of the work in a selection decision.
Density determines the broad split between light products and heavy residue. A light crude yields more naphtha and distillate directly. A heavy one yields more residue that has to be converted, which requires conversion capacity and consumes hydrogen or produces coke.
Sulphur determines hydrotreating load. Sour crude is cheaper for a reason, and the discount is only worth taking if you have the treating capacity and the hydrogen to use it. A refinery at its hydrotreater limit cannot capture the sour discount regardless of how attractive it looks.
Metals and acidity constrain which units can process the material at all, and carry maintenance consequences that appear months later as a shortened run length rather than immediately as a cost.
The recurring theme is that the value of a crude depends on the specific configuration processing it. There is no universal ranking, and a grade that is excellent for a complex refinery with deep conversion may be poor for a simple one, which is why generic crude value tables are of limited use for an actual decision.
Two grades, worked
Take two crudes offered for the same delivery month, with a product price set you can swap for your own.
Grade A is light and sweet. Per barrel it yields 0.42 gasoline and naphtha, 0.33 distillate, 0.17 residue and 0.05 LPG and fuel gas, with 0.03 lost in processing. Grade B is medium and sour, yielding 0.34 gasoline, 0.31 distillate, 0.29 residue, 0.04 LPG, and 0.02 loss.
Value gasoline at 95 dollars a barrel, distillate at 105, residue at 58 and LPG at 60.
Grade A gross product worth is 0.42 times 95, or 39.90, plus 0.33 times 105, or 34.65, plus 0.17 times 58, or 9.86, plus 0.05 times 60, or 3.00. Those add to 87.41.
Grade B is 32.30 plus 32.55 plus 16.82 plus 2.40, which is 84.07.
Now the processing. Grade A costs 3.10 a barrel to run. Grade B costs 4.60, from the extra hydrotreating and the hydrogen that goes with the sulphur. Subtract those and the value at the plant gate is 84.31 for A and 79.47 for B.
The gap is 4.84 dollars a barrel, and that is the number the crude discount has to beat. If Grade B is offered at 3.50 under Grade A, which reads as a substantial saving on a purchase order, buying it costs 1.34 dollars a barrel. Two million barrels of it is 2.68 million dollars, booked as a procurement win.
The breakeven discount of 4.84 moves with the product price set rather than with anything about the crude. Widen the distillate crack and A's advantage grows, so the discount B needs rises. Firm the residue market and B's disadvantage narrows. A procurement team carrying a fixed differential against a benchmark grade is holding a number that was correct on the day somebody computed it.
If the hydrotreater is already at its limit, the 4.60 understates Grade B further, because each incremental sour barrel displaces throughput that would otherwise have gone through the same unit. Adding the shadow price of the binding unit to the processing cost is the correct treatment, and it typically pushes the required discount past five dollars.
Blending as the decision variable
Refineries rarely run a single crude. They run a blend, and the blend is where the optimisation lives.
The attraction is that blending lets you hit a target set of properties that no available single crude provides, and buy the components at the best available prices. A blend of a cheap heavy sour grade with a light sweet one can land on the same processed properties as a mid-grade that trades at a premium, and the spread between the blend cost and the mid-grade price is the prize.
The optimisation itself is old and settled. Charnes, Cooper and Mellon published their aviation gasoline blending study in Econometrica in 1952, one of the first applications of linear programming to an industrial problem of any kind, and the formulation has not needed much repair since. The trouble comes from applying it to properties that refuse to behave linearly.
Two things complicate this and both matter operationally.
Not all properties blend linearly. Density and sulphur blend roughly on a volume or weight basis, which makes them easy. Viscosity does not, and neither do several other properties that matter to the units, so these need blending indices rather than simple weighted averages. The standard treatment for viscosity converts each component onto a viscosity blending index, averages on that scale, and converts back. Using a linear approximation where one does not apply produces a blend that meets specification on paper and does not in the tank.
Compatibility is a hard constraint. Certain crude combinations precipitate asphaltenes when mixed, which fouls equipment and is expensive to recover from. This is a feasibility constraint, not a cost, and it has to be enforced as a rule rather than traded off against economics.
Where the value is left on the table
Three patterns recur in refineries that have not been through this exercise recently.
Selection is anchored on a historical slate. The plant has run a particular set of grades for years, the operating team knows how to handle them, and alternatives get evaluated rarely. Meanwhile the relative pricing of grades moves continuously, and a slate that was optimal three years ago is unlikely to be optimal now.
The constraint that binds is not the one being managed. Refinery optimisation attention tends to go to the crude unit. Frequently the binding constraint is somewhere else, at the hydrotreater, the hydrogen plant, or a sulphur recovery limit, and until that is identified the selection is being optimised against the wrong limit. Locating it takes one model run per candidate limit, relaxing each by a small amount on its own and recording which relaxation moved the objective. Units with a shadow price of zero are constraining nothing, however busy they look on a control screen, and the unit carrying the largest shadow price is where the crude decision is really being made.
Product value is taken from a price sheet rather than from realisable value. A product is only worth the marker price if you can actually sell it into that market. If a product is length in your system and moves at a discount, the netback calculation should use the discounted value. Using the marker overstates the value of grades that produce more of it, and the error is systematic. The symptom is a model that keeps recommending a grade the commercial team quietly resists. Check it against last year's realised price per product versus the marker over the same period: a product that ran twenty cents under has been inflating every yield vector containing it by twenty cents times its yield fraction, which is enough to reorder a close ranking.
The horizon question
Crude selection decisions are made weeks or months ahead of the operation they affect, because of voyage times and term arrangements. That gap creates its own problem, since the product prices that determine netback are not known when the crude is bought.
The practical treatments are the standard ones for decisions under price uncertainty. Evaluate the slate against forward curves rather than against spot, since the forward is the price you could actually lock. Run the selection across a small number of price scenarios and prefer choices that hold up across them, because a slate that is optimal only under one price path is a bet rather than a plan. And where a hedge is available and the position is material, price the hedged and unhedged versions separately so the decision is explicit rather than absorbed.
There is a one-line check that comes out of this and is worth running every cycle. Compare the netback spread between your top two candidate slates against the difference between spot and the forward curve for the delivery month. Where the price movement between now and delivery is larger than the spread between the candidates, the ranking is being decided by your price assumption rather than by the crude, and the honest presentation says so before the cargo is fixed.
What a decision output should contain
A crude selection recommendation that people will act on has four elements.
The recommended blend with its component volumes, and the resulting processed properties against every relevant constraint.
The netback per barrel with the calculation shown: product yields, product values, processing costs, and the cost of the crude itself.
Which constraint binds, and what the marginal value of relaxing it would be. This is frequently the most useful output, because it tells the capital planning discussion where debottlenecking would pay. A shadow price of forty cents a barrel on hydrogen capacity, at 200 thousand barrels a day, is about 29 million dollars a year before any capital cost, and that supports a completely different conversation than a shadow price of two cents.
The alternatives considered and how close they were. A recommendation that is one cent per barrel better than the runner up should be treated differently from one that is eighty cents better, and without the ranking there is no way to tell.
The limits
Linear programming on a refinery model is a well-established tool with a known weakness: the model is a linear approximation of a non-linear plant, and its accuracy depends on the yield vectors being valid near the operating point. Push the solution far from where the vectors were estimated and the plan will not reproduce in operation. Comparing planned yields against realised yields, run by run, and updating the vectors, is the maintenance that keeps the model honest, and it is often the first thing to lapse.
Assay data ages too. Crude streams change composition over time as fields mature and as blending upstream changes, and a five year old assay for a stream that has shifted will produce a plan that misses. Periodic reassay of the grades you actually run is unglamorous and directly affects plan quality.
There is also an operational constraint that no economic model captures well, which is the plant's tolerance for change. A slate that switches grades frequently imposes transition costs, tank management complexity and operator load that do not appear in the netback calculation. Some of the theoretical optimisation gain is consumed by that friction, and a plan that is slightly worse on paper and stable in operation is frequently the better one.
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