Crude oil cargo selection and time frame of LP optimisation
Combinatorial selection is the most rigorous and theoretically correct method of crude oil cargo evaluation. Efficient algorithms are key to its implementation
M D Pawde and Sachin Singh
Hindustan Petroleum Corporation Ltd (HPCL), India
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Linear programming (LP) models of refineries are used for capital investment decisions, evaluation of crude oil for term and spot procurement, production planning, scheduling and supply chain optimisation. A good refinery LP model accurately captures unit configuration, yields, properties, stream blending, extent of constraints on product specifications, flexibility on crude and product cargo sizes, and so on.
The methodology of crude oil evaluation using an LP model is as critical as a good LP model itself. Each refiner has their own unique requirements from the LP, which depend upon the environment in which the refinery operates and the market to which it caters. The methodology of evaluation should address, among other concerns, the time horizon of optimisation, unit of optimisation of crude and products quantities, and prices and norms for inventory pricing.
In a previous article (PTQ, Q2 2010), we addressed how unit of optimisation (the choice between weight-based and volume-based optimisation) of crude oil and finished products could affect the LP output and, hence, the decisions taken by a refiner. This article discusses the challenges in selecting spot crude oil cargoes and the time frame of LP optimisation.
Selection of spot crude oil cargoes
The crude oil requirement of most refineries is met partly through term contracts with suppliers, with the balance met through purchases on the spot market. Crude oil cargoes from term contracts are lifted on a uniform basis throughout the year. Liftings of spot cargoes are on an as and when required basis. Most refiners maintain a balance between term and spot crude oil purchases. Term contracts offer security and uniformity of supply. However, there is a loss of flexibility in month-to-month operations if the entire requirement is termed up. Hence, a certain percentage of the total requirement is always planned to be fulfilled from the spot market.
Crude oil is available on the spot market in parcel sizes ranging from about 500–2000 kbbl. Selection â€¨of the right spot crude oil is a â€¨challenging task. The following example illustrates the possible ways a refiner can select spot cargoes once term cargoes are firmed up. Table 1 lists the crude oil available in the opening inventory and the cargoes expected to be received in the month. We call this the base crude oil basket. Over and above this base basket, 2000 kbbl of spot crude is required to meet the refinery’s planned throughput for the month.
Three sweet crude oils from West Africa, ranging from heavy to medium light to very light, are used as sample spot crudes in this example. Any one of the three, or any combination, is acceptable in the refinery for the period under consideration. Major stream properties and distillation yields of these crudes are listed in Table 2.
Of the three grades, Amenam Blend has the least amount of resid and the highest naphtha content; on the other hand, Cabinda has the highest amount of resid and the least amount of light ends. Qua Iboe is rich in middle distillates —kerosene and gas oil — which have a good requirement for upliftment from the refinery. However, there are throughput limitations in the gas oil hydrotreater. Naphtha has a limited customer base, and surplus production will have to be exported at a loss. The refinery’s catalytic cracker can absorb only a limited amount of vacuum gas oil (VGO) and, hence, high VGO-yielding crude oils are usually not attractive in this configuration. The refinery does not have a bottoms upgrading facility and there is limited demand for bottoms product. However, because of the very high margin on this product, this small demand should nonetheless be fully met.
Multiple cargoes of these crude oil grades are available in 1000 kbbl parcel sizes. The delivered price of all the cargoes of a particular grade is the same. The supplier can choose two cargoes, either a single grade or a combination of two grades, to meet its requirement of 2000 kbbl. The objective is to find a combination of cargoes that maximises the refinery’s margin within the constraints of its hardware and product demand.
Three possible ways of selecting the crude oils can be:
Ranked selection Evaluate the three grades in the LP model and prepare the pecking order (ranked in decreasing order of margin), then select the top two cargoes in the ranking
Sequential selection First select Spot Cargo 1; next, include the selected cargo in the base basket (which may now be called the extended base basket); then re-evaluate all the grades in the LP to select Spot Cargo 2
Combinatorial selection Evaluate all possible two-cargo combinations; six such combinations are possible in this example.
Results of each of these selection methodologies are tabulated in Tables 3a, 3b and 3c. Incremental margin is the margin of the spot cargo barrels. Whole basket margin is the overall margin of the entire crude mix including the spot cargo bought.
Cargoes are evaluated for increments of 1000 kbbl. Since Qua Iboe gives the maximum margin, two Qua Iboe cargoes are selected by this method. Whole basket margin is the margin of the base basket plus two cargoes of each of the spot grades.
After selecting the first cargo of Qua Iboe, it is put into the base basket; the margin of this extended base basket is $5.70/bbl. By selecting Amenam Blend as the second cargo, the total margin of $5.84/bbl is higher than the achievable margin had the second cargo also been Qua Iboe ($5.76/bbl).
Combinatorial selection recommends purchase of one cargo each of Cabinda and Amenam Blend, as the margin achievable by the combination is the highest ($5.87/bbl), higher than the Amenam + Qua Iboe combination ($5.84/bbl) recommended by the sequential selection method.
Which of these methods is correct?
We first need to explore why these methods give different recommendations. The weighted average production pattern of the six possible combinations is shown in â€¨Table 4.
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