Break-even prices

As crude prices vary, it is important to calculate the actual beneficial value that different crude types give to a plant. One way of doing this is to calculate the break-even price. This is the maximum price that could be paid for a beneficial crude while keeping its processing more economic than a reference case. Beneficial in this scenario is defined as the addition of the particular crude type to the reference case resulting in an increase in the objective function.

Imagine a simple plant separating crude oil into a distillate and residue.

The plant then takes the distillate and sells it.

The plant can process three crudes: Arab Heavy, Arab Light and Forties.

The CDU is constrained to process 150 kbbl/d of crude.

If the plant is free to obtain any of these crudes which have minimal cost, then the optimal solution is to process pure Forties, as this has the most distillate and so will yield the most saleable product, and make about $94,000 per day.

However the plant may be forced to process pure Arab Light. This gives a lower objective function of about $79,000 per day. Imagine this is the normal state of operations at the plant.

Suppose though that Forties could be processed, but at an increased price, say 5 cents per barrel. We know that running pure Forties (at 3 cents per barrel) is the most economic way of running the plant, but when you have to pay more for Forties is it still a better choice? By pricing Forties at 5 cents per barrel and running the problem, the plant now makes about $91,000 per day: less money than when Forties was 3 cents per barrel, but still more money than when processing pure Arab Light. The extra distillate yield from Forties offsets the small amount of money that has to be paid for the crude, so Forties is still the best choice of crude to purchase.

While negotiating the price of Forties, the price may rise to 10 cents per barrel. Is Forties still a better choice? Running the problem again, we find that even at 10 cents per barrel Forties results in an objective function of about $84,000 per day, higher than pure Arab Light.

How far does this behavior extend? There must be some point where the extra value obtained by Forties distillate no longer offsets the increased cost, assuming a constant price of Arab Light. At this point, there is no benefit in buying the candidate crude, or in paying any more for the candidate crude. In fact, paying more would reduce the objective function. The candidate crude cost is said to break-even.

Running the problem again with Forties at 15 cents per barrel we find the objective function is now about $76,000 per day, less than the pure Arab Light case. Thus somewhere between 10 and 15 cents per barrel the price of Forties breaks even.

Calculating the break-even price

The break-even price is defined as follows:

Break-Even Price = Candidate Price + (Candidate Objective - Parent Case Objective) / Candidate Quantity

In the above example the parent case is with Arab Light alone, and the candidate case is processing pure Forties. From the equation, remembering that the crude amount needs to be per barrel:

Break-Even Price = 0.03 + (94309.33 - 78786.52)/(150,000) = 0.133 $/bbl

Thus the break-even price for Forties is 13 cents per barrel.

Break-even prices in blends

Break-even prices are most useful when working with blends of crudes. They help show the value of a crude in the blend, helping to factor out the increase in value that the crude gives to the blend, and allowing you to see the increase in value the crude would give by itself (which is the possible extra amount you should be willing to pay for the pure crude).

For example, in a blend Forties may give 2 cents per barrel increase in value, but in the blend Forties only represents 20% of the actual mix. The break-even price can thus be used to determine what extra value Forties would contribute at 100% - that is, the most one should be willing to pay for the crude to result in operations that were still more economic than the base case:

Break-Even Price = 0.03 + (81891.08 - 78786.52)/(30,000) = 0.133 $/bbl

Another way to examine the effect of Forties in the blend is to look at the change in objective function as the proportion of Forties varies. As the amount of Forties in the blend changes, the objective function increases. However, when looking at the blend as a whole this information is not very useful.

Instead it is possible to look at the change in objective function relative to the amount of material processed. At 20% Forties in the blend we can see that this results in a 2 cents per barrel increase in the objective function. From this graph it is possible to project this increase (at 20% Forties) back to 100% Forties (that is, extend the trend line to 100% Forties). This gives us the extra-value price for pure Forties, which we can see is $0.10 per barrel, or 0.13 $/bbl, including the original 3 cents per barrel Forties crude cost:

Break-Even Price = Candidate Price + ((Candidate Objective - Parent Case Objective) / Crude Flow) * (100 / Percentage Candidate Crude in Blend)

Break-even prices in the Crude Evaluation analytic

The Economics Detail page of the Crude Evaluation analytic shows the break-even prices for each crude analyzed in the analytic. In the Crude Evaluation analytic each of the candidate crudes is separately added into the base blend and the new problem re-optimized. The result of this new problem with the candidate crude is then compared to the analytic parent case to determine the break-even price for the crude.

We can define our refinery base blend, in this case pure Arab Light, but at only 120 kbbl/d, less than the maximum capacity of the refinery, 150 kbbl/d.

We can separately bring in each of the three candidate crudes, that is, process 120 kbbl Arab Light & 30 kbbl Arab Heavy, or 120 kbbl Arab Light & 30 kbbl Arab Light (that is, pure Arab Light again), or 120 kbbl Arab Light & 30 kbbl Forties.

Running these three scenarios we can compare the results to the parent case (running 150 kbbl Arab Light), and then calculate the break-even price.

• Running with Arab Heavy results in decrease in profitability for the plant (because it has less distillate), so this crude has a negative break-even price. That is, even if someone were paying you to process the crude it would still be uneconomic.

• Arab Light has the same break-even price. This is logical, as topping up the extra capacity with more Arab Light wouldn't increase the objective function relative to pure Arab Light alone.

• Processing Forties increases the objective function, up until we have to pay more than $0.13 per barrel for Forties. This is the same answer as the manual calculation above for the worth of Forties.

  

To make it easier to compare crudes it is possible to compare each candidate crude to a reference crude. The reference crude can be chosen using the Reference menu in the Data group of the Home ribbon tab.

Selecting Arab Light as a reference shows the values relative to this reference crude. The relative actual price shows the difference between the candidate crude price and the reference crude price. The relative break-even price shows the difference between the break-even value for the candidate crude and the break-even value for the reference crude. In this example the reference delta to Arab Light for Forties is 11 cents per barrel, the same value as manually calculated for the value of Forties alone (relative to Arab Light alone).

The Economics Detail page also shows the actual objective function value for each of the case stack solutions. The difference between the case stack solution and the parent case is shown. Where a reference crude is selected from the Data group, the difference between the single case solution and the reference case solution is shown in the Relative to Reference Crude column.

Another piece of information shown for the Marginal Economics column group is the Incremental Profit Per Barrel. This is similar to the break-even price, but without the original crude cost included:

Incremental Profit per barrel = ((Candidate Objective - Parent Case Objective) / Candidate Quantity)

Thus the incremental profit per barrel says how much extra profit is obtained from processing each extra barrel of the candidate crude. Also shown is the marginal value (Marginal Values) of the crude in the parent case.

Shading in marginal economics

The marginal economics are shaded when they do not abide by the following rule (in $/bbl):

Candidate Marginal - 0.5 < Incremental Profit < Base Blend Marginal + 0.5

That is the incremental profit is expected to be greater than the candidate marginal value, or the last drop marginal value is expected to be greater than the first drop marginal value. Where this is not the case it may indicate a non-convex solution which may require further investigation to confirm the behavior.