(664f) Product-Centric Continuous-Time Formulation for Straight Pipelines

Technologies such as horizontal drilling
and hydraulic fracking are yielding new supplies of crude oil and natural gas
liquids and so, pipelines, which represent the most reliable and cost-effective
way of transporting large volumes over long distances, are expanding. In the
U.S., the total mileage of 192,396,
reflects a 9.3% increase over the last 5 years [1]. In 2013, pipeline operators
delivered 6.6 million barrels of refined products (e.g., gasoline, diesel, jet
fuel) and natural gas liquids (propane, ethane). Increased mileage and volumes
represents a challenge for operators to deliver the benefits of increased
energy production to consumers.

Most pipeline scheduling models rely on a
continuous-time and -volume representation to better adapt to segments of
different length and diameter. They allow the flowrate to vary between given
lower and upper bounds, to better utilize the capacity of the pipeline. Since
flowrates need not be defined as model variables, models are typically of the
mixed-integer linear programming type (MILP) unless an accurate representation
of the pumping cost is needed [2]. Another classification criterion is related
to the handling of materials as they move through the pipeline. The most
popular option is to work with batches [3-5] that need to be related to the
actual products. This is because it facilitates the calculation of the left and
right coordinates needed to exactly locate products inside the pipeline, which
trigger entry and exiting events.

This paper presents a new formulation that
does not need to define batches. It is derived from Generalized Disjunctive
Programming (GDP) [6-8], building on recent work for a batch-centric
formulation [5] that was the subject of last year AIChE annual meeting. The
main challenge is that coordinates need to be reset following a product
complete exit from a segment, so that a new lot of the same product can enter
at the other end (it is not an issue in batch-centric models since batches
never re-enter a segment). The new coordinate constraints prevent multiple
products to enter/leave a segment during a time slot, which can lead to more
time slots being required to represent a schedule. One advantage, is that there
are no other decisions that can compromise solution quality, contrary to the
batch centric model that has a few tuning parameters related to the definition
of old batches from the initial pipeline status and new batches injected. The
other advantage, is that it becomes possible to rigorously enforce forbidden
product sequences, very common in practice to reduce product contamination.

Results over a set of seven benchmark problems
from [5], involving straight pipelines with unidirectional flow and multiple
intermediate dual purpose nodes, show that the new formulation can reduce the
makespan of Ex2 by 8%. On the other hand, it fails for Ex3 since all feasible
schedules involve multiple batches of a product simultaneously on a segment,
which is not currently allowed, and returns a suboptimal solution for Ex1
(dealing 345 km of the Iranian pipeline system). Thus, there is not a single
best performer amongst the GDP-based formulations.

The GDP product-centric formulation has
also been compared to a Resource-Task Network (RTN) counterpart [9]. After
minor modifications to the RTN, both models were found identical, i.e. they can
generate the same schedule using the same number of event points. The benefit of
the new formulation, is that it reduces problem size by a factor of 3-5,
resulting in orders of magnitude improvements in performance.

The new formulation is modular and can
easily be extended to other configurations (tree-like, mesh). Furthermore, it
can tackle problems with reversible flow.

Given the segment volumes, flowrate range
(same for all segments), product supply and demand of the three products (P1-P3)
at nodes N1, N3-N4 (node N2 is just a connection node), and initial status of
the pipeline, can you find the minimum makespan for this reversible flow problem?

Acknowledgments: Financial support from Funda‹o para
a Cincia e Tecnologia (FCT) through projects IF/00781/2013 and UID/MAT/04561/2013.

References:

[1] Association of Oil Pipe Lines, 2014. U.S. Liquids
Pipeline Usage & Mileage Report. http://www.aopl.org/wp-content/uploads/2014/10/U.S.-Liquids-Pipeline-Usage-Mileage-Report-Oct-2014-s.pdf (accessed 30.01.2017).

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