Detailed Scheduling of Single-Source Pipelines with Simultaneous Deliveries to Multiple Offtake Stations

Abstract

Continuous formulations for the scheduling of single-source refined-product pipelines with multiple distribution terminals have already been published. They help the scheduler make key operating decisions such as the sequence of batch injections at the input station, the batch sizes, the start and end times of pumping runs, and the set of aggregate product deliveries to perform during each run. In this way, the aggregate pipeline schedule is defined. However, the scheduler has yet to decide not only on the order of execution of such product extractions but also the number of batch cuts to make to accomplish each aggregate delivery. Therefore, it becomes necessary to refine the aggregate schedule. Most previous contributions providing a refined delivery plan have assumed that product withdrawals at receiving locations over a single-source pipeline should be made one at a time. However, such pipelines do not actually work in this way because their operators usually perform simultaneous product deliveries to cut down on pump operating and maintenance costs. By doing so, they seek to reduce the number of pipeline segments where the liquid flow should be restarted. This article presents a new mixed-integer linear programming (MILP) continuous formulation for developing the detailed schedules of single-source pipelines assuming that simultaneous deliveries to multiple receiving terminals can be performed. The problem goal is to minimize the overall flow restart and stoppage volumes through the smallest number of pipeline operations. Solutions to two examples obtained with the proposed approach present significant reductions in both the operating cost and the CPU time with respect to previous contributions.

Improving the Mathematical Formulation for the Detailed Scheduling of Refined Products Pipelines by Accounting for Flow Rate Dependent Pumping Costs

“…Results obtained were compared to those reported in a previous work (CAFARO et al, 2012) in which the pumping costs were assumed to be independent from the pump rate. When pumping energy charges associated to the head loss inside the pipeline are taken into account, the flow rate is more stable all along the time-horizon, and important savings are obtained.…”

“…As stated by the objective function, the aim is to minimize energy consumption, stoppage and restart costs. To demonstrate the efficiency of the proposed approach, the given solution will be compared with that obtained by Cafaro et al (2012), in which the pumping costs were not taken into account. Figure 2 presents the aggregate schedule to be decomposed into detailed operations through the proposed MILP model.…”

Transportation planning for petroleum products and integrated inventory management

“…Also, MirHassani et al [14] presented an MILP model for scheduling a unidirectional pipeline with one source and multiple DCs, some of which were able to receive and inject the products. Cafaro et al [15] provided a new model for scheduling a pipeline with single source and many DCs, which could receive batches simultaneously. Recently, the pipeline systems with more complexity have been studied.…”

A mathematical model for scheduling of real-world tree-structured multi-product pipeline system

“…The proposed mathematical formulation is based on the work of Cafaro et al (2012). The main differences between this work and the model of Cafaro et al (2012) are as follows: (a) Our approach relies on a system with a single-source tree-structured pipeline network, whereas their approach assumes a single source pipeline network without any branch, (b) Our approach treats the case of multi-delivery to output terminals, whereas their approach considers the single delivery, and (c) their approach performs the pipeline input and output operations in two steps, whereas our approach seeks to find both of them in a single step.…”

“…Cafaro et al (2012) presented a new MILP continuous formulation for the scheduling of a single-source pipeline considering the simultaneous deliveries at the output terminals to reduce the number of stoppages and restarts of the pipeline segments. However, the model they proposed has focused on the single-delivery for all depots, i.e., in each pumping run, just a single product can be transferred to each active output terminal.…”