Optimization of pipeline scheduling operations: efficient formulations and hydraulic considerations. / Otimização da programação de operações dutoviárias: formulações eficientes e considerações hidraúlicas.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

Pipeline systems correspond nowadays to the most efficient mode for the transportation of large amounts of liquid and vapor products for long distances. Pipelines are utilized by the Petroleum Industry to transport petroleum and its product derivatives. The present work addresses the scheduling of pipeline distribution of a system that operates with a pipeline that transports products from a refinery to depots at different geographical locations by mathematical programming models. The system is composed by the Planalto Refinery (REPLAN) from Petrobras. A pipeline (OSBRA) is connected to the refinery that extends for approximately 1000 kilometers. A higher level of detail in the mathematical model for pipeline operations developed by Rejowski Jr. (MS Dissertation, EPUSP São Paulo, 2001) becomes essential in this complex logistic operation. A factor of extreme importance is product contamination inside the pipeline. Therefore, special constraints are developed that impose the segments of the pipeline to operate continuously when they do not contain interfaces. These constraints help the proposed formulation to find the optimal solution of the problem. The improvement of logical formulations becomes paramount because the generated models encompass a large number of decisions to be optimized. Logical relations involving the initial inventory at the depots and at the pipeline, as well as the demands for each product are proposed. These relations improve the computational performance of the proposed models in scenarios of high-demand. Then, the special constraints and the demand satisfaction at the depots at the end of the operational horizon are relaxed and added as penalties in the objective function. These penalties increase the solution effort of the proposed models and at the same time have great influence on the operational results of the system. Another factor of extreme importance for the pipeline operation scheduling is its continuous time representation. Additionally, this representation enables the models to incorporate simplified hydraulic constraints. Therefore, a simplified and efficient strategy to determine the pipeline flow rate is to include the yield curves of the pumping stations. This formulation, that is modeled as an MINLP (Mixed Integer Non Linear Programming), is compared to an MILP (Mixed Integer Linear Programming) with discrete time and fixed flow and yield rates proposed by Rejowski Jr. and Pinto (Computers and Chemical Engineering, 2004, v.28/8 p.1511-1528). It is shown that the present formulation provides better quality results. The MILP formulation with discrete time is characterized as a particular case of the proposed formulation. The MINLP is greatly influenced by the number of time intervals that compose it and this factor has always to be considered so that the best solution can be found with feasible computational effort. This formulation is also applied to a case with several pumping station configurations with different unit costs and yield curves. Two formulations that consider the scheduling of pipeline operations with the incorporation of the hydraulic aspects calculated rigorously are presented. The first one results in an MINLP model and considers variations on the time interval durations and in the pipeline flow rate. A second MILP formulation is developed. Computational results for both models are shown as well as the generated solutions discussed. The impact of variations on the topographical profile of the pipeline system is analyzed in the obtained results by the models. Changes in the flow rate of the pipeline, in the decision of the time intervals that the system is activated, in the pumping station yields and in the time interval durations were detected. Then, in another example it is shown that the changes in the topographical profile can alter the sequence of products sent by the refinery to the pipeline. Finally, both formulations have their results compared to models with simplified hydraulic considerations, whose results can lead to suboptimal and even to infeasible solutions.

ASSUNTO(S)

pipelines programação matemática otimização matemática mathematical optimization mathematical programing dutos

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