Crude Slate Planning When Supply Routes Change: Assays, Constraints and LP Modelling

Planners usually spot a supply route change when a cargo nobody modelled turns up on the schedule: a different grade, loaded at a different terminal, with a different arrival window. The LP still solves and still returns a slate. But if its assays describe a crude that no longer matches what arrives, and its constraints reflect last year's logistics, the recommendation is wrong. The error tends to show up at the unit, not in the spreadsheet. The usual symptoms are a crude unit held back by overhead corrosion or desalter performance, a hydrotreater short of capacity for the sulfur load, a product off specification, or a tank farm with no segregation left for the next parcel. The money goes one of two ways: margin given away to a conservative slate, or a run the plant cannot deliver. This article covers how to re-optimise the slate when origin and quality shift materially: which data to refresh first, how to structure the constraints, and how to separate the LP question from the scheduling question.

Standards and data context

An LP is only as good as the assay data behind it, so the relevant standards are laboratory methods. These are the ones I can vouch for:

• ASTM D2892 covers distillation of crude petroleum using a 15-theoretical-plate column, and underpins the light-end true boiling point (TBP) cuts.
• ASTM D5236 covers distillation of heavy hydrocarbon mixtures by the vacuum potstill method, and extends the TBP curve into the residue range.
• ASTM D664 covers acid number of petroleum products by potentiometric titration, used to measure total acid number (TAN) relevant to corrosion risk assessment.

The standards fix how cut yields and properties are generated. They do not decide how often the data must be refreshed, how to treat a blended parcel, or which properties you must carry. Those are site decisions, and they belong in the model's management-of-change process.

What actually changes when a supply route changes

A new route rarely changes just one thing. Treat it as five separate questions.

1. Quality. Gravity, sulfur, acidity, metals, salt, pour point and vapour pressure may all differ from the crude it replaces, even when the grade name looks similar.
2. Cut structure. Two crudes with similar density can yield very different amounts of naphtha, distillate and vacuum residue. That moves the load across the downstream units.
3. Logistics. Parcel size, arrival frequency, receiving terminal and tank availability all change. Pipeline or marine blending may produce a delivered quality that differs from the load-port assay.
4. Commercial terms. Price basis, freight and lead time shift, and that changes which opportunity crudes are worth evaluating.
5. Contamination and variability. A new route can bring different co-mingling, salt or sediment behaviour.

Only the first three change the physical constraint set. The other two change the objective. Keep them in separate data tables, so a price update never silently overwrites a quality update.

Assay management

Refresh before you optimise

Don't run the optimiser on an assay that predates the route change. Get a current assay for the crude as it will be delivered, not as loaded. If a full assay won't arrive in time, use a recent one with a clearly flagged confidence level, and run sensitivity cases around its uncertain properties. A planner should be able to see at a glance which crudes have a full recent assay and which are running on an analogue or estimate.

Assay administration is a bottleneck in its own right. Getting a new crude into the model quickly is part of the planning capability. If building a crude takes weeks, you won't evaluate the opportunity cargoes a route change opens up.

Which properties to carry

At minimum, the model needs the following for each crude:

• Cut yields on a mass and volume basis across the TBP range, from ASTM D2892 and ASTM D5236 data.
• Density and sulfur by cut, so product quality and unit loads can be calculated.
• Acidity and metals, used for corrosion and catalyst-poison constraints.
• Cold-flow and vapour pressure properties wherever they limit blending or storage.

Some properties don't blend linearly. Viscosity, pour point and flash point need blend indices or correlations. Without them the LP will report a feasible blend that fails in the tank.

LP structure for slate re-optimisation

The core formulation

In plain terms, the model chooses crude volumes to maximise margin:

Maximise: Σ (product value × product yield) − Σ (crude delivered cost × crude volume) − processing costs

subject to:

• crude availability: each crude volume lies between a minimum commitment and a maximum parcel availability;
• crude unit throughput: total charge does not exceed unit capacity;
• cut-based unit capacities: naphtha, distillate and residue loads respect the downstream units;
• quality limits: blended properties of unit feeds and finished products meet limits;
• material balance: all streams are accounted for.

Yields are linear in crude volume, so the structure suits LP well. After a route change, though, the binding limits are usually not crude unit capacity. They are the secondary constraints: sulfur load on hydroprocessing, residue handling, acid tolerance of crude unit metallurgy, desalter limits, and tank segregation.

Make the constraints carry operating knowledge

A constraint that reads "maximum acid number of the blended charge" should come from your corrosion engineers and your materials of construction, not from a model default. The same goes for a limit on the share of a single crude in the blend. It should reflect real compatibility or desalting experience, not caution inherited from a crude you no longer run. Review each of these limits when the origin changes, and record who owns it.

Handling non-linearity

Where unit yields depend on feed quality, planning models normally use recursion. A simulation or correlation updates the yield vectors between LP passes. After a large shift in slate, though, vectors built around the old operating point can mislead you. Re-base them on the new expected blend before trusting the result. Then check that successive passes settle on a stable slate instead of oscillating.

From a monthly slate to cargo decisions

An LP gives the best slate for a defined period. Purchase decisions are discrete, though. A cargo is bought whole and arrives on a date. Evaluating each cargo alone against a base case misses the interactions. Two cargoes can be good together and poor separately, or the reverse.

The scheduling layer then asks a different question: given the chosen cargoes, can the tanks, pipelines and unit campaigns deliver the feed in time? A paper in Computers & Chemical Engineering (volume 145, 2021) proposes a mixed-integer linear programming (MILP) clustering strategy to integrate the operational management of crude oil supply. I cite it for its scope, which is integrating supply decisions with operations, not for any specific performance claim.

The three layers should share assay and constraint data. If each keeps its own copy, they will diverge after the first update.

Illustrative scenario

This scenario is constructed for illustration and does not describe a real plant or event.

A coastal refinery has run a medium sour crude from a single regional supplier through a pipeline and terminal. A route disruption removes that supply. The planner's alternatives are a lighter, lower-sulfur grade by ship and a heavier, higher-acid grade at a discount.

The planning team follows this sequence:

1. Pull current assays for both alternatives as they will be delivered, and flag any that rely on analogue data.
2. Update the delivered-cost table separately, including freight and lead time.
3. Re-base the recursion vectors on a blend close to the expected new charge, rather than the old one.
4. Run the LP with the old limits to see which constraints bind, then ask unit engineers to confirm each binding limit.
5. Run cases that vary the heavy crude's share and the assay uncertainty.
6. Pass the shortlisted cargo combinations to the scheduler to test tank segregation and arrival timing.

The qualitative outcome is common. The lighter grade relieves residue-handling and acid limits, but it loads the light-end units and may weaken the margin. The heavier grade improves the crude price but pushes against the acid and residue constraints, so the LP caps its share. The best answer is usually a blend, and whether it's viable depends on whether the tank farm can keep the parcels apart long enough to blend at the charge point. That physical check often decides the plan.

Checklist for re-optimising after a route change

• Confirm each new crude has an assay representing the delivered material, and mark the confidence level of each.
• Check that the assay includes the full cut range, supported by ASTM D2892 and ASTM D5236 data, plus acidity from ASTM D664 where relevant.
• Keep quality, logistics and price data in separate tables with separate owners.
• Review every blend-share and quality limit with the unit or corrosion engineer who owns it.
• Re-base recursion vectors on the expected new blend, and confirm convergence.
• Add blend indices for any non-linear property that governs a product or storage limit.
• Run sensitivity cases on assay uncertainty and on the share of any unfamiliar crude.
• Evaluate cargoes in combination, not only one at a time against the base case.
• Pass the shortlisted slate to scheduling to test tank segregation, line transfers and arrival timing.
• After the first cargoes are processed, compare the model's predicted yields and qualities with the plant's actuals, and correct the vectors.
• Record every limit changed and the reason, so the next route change starts from an audit trail.

Conclusion

When supply routes change, the biggest risks are stale assays, inherited constraints and a slate the logistics can't deliver. Refresh the data first, then challenge the limits with the engineers who own them, and keep the LP, cargo selection and scheduling layers on a common dataset. Next steps: audit your current model for crudes whose assay no longer matches delivered quality, list the constraints with no named owner, and schedule a validation against actual yields from the first cargo of any new origin. A formal model health check, as Becht recommends, gives you a structured way to do this before the next disruption forces the decision.