Historically, the petroleum industry has used linear programming (LP) to address its planning and optimization needs (Favennec, 2001; Li et al 2005). The CDU yield prediction is modeled using linear functions of the crude feed. The linear function can be the simple fixed-yield equation or the enhanced swing cut equation (Zhang, 2001, Trierwiler, & Tan, 2001). The latter approach is currently used in many refineries. The simplicity, robustness and convenience of the linear approach are tradeoffs for the true optimal and accurate solution to the planning model. Attempts to add nonlinearity to CDU yield prediction in the planning models focused on fitting parameters of different crude oil feedstocks in addition to parameters for the operating variables (Alhajri et al, 2008, Lopez et al, 2009, Gueddar et al, 2009).
The goal of our work is to incorporate and evaluate nonlinear modeling approaches for CDU yield prediction. Our proposed CDU models range from the simple fractionation index (FI) model, to the moderate aggregate distillation model to the more rigorous tray-by-tray distillation model. These models are designed so they are fit for the optimization model of refinery planning by incorporating the appropriate simplifying assumptions and initialization procedure. The models are lastly evaluated to assess their impact and benefit in terms of accuracy, robustness and simplicity and computation effort.
The FI model is our first and simplest CDU model. The model employs the fractionation index defined by Geddes (Jakob, 1971). The CDU is represented by a series of separation units where the bottom products are the CDU product streams and the top products are fed to the next stage. Each stage will have two FI parameters representing the stripping and the rectifying sections of the separation unit (Wagner, 1978; Gilbert, 1966). The model is an equivalent short-cut approach to calculate the component distribution in the top and bottom product streams of each unit. The model lacks more details on the operating conditions, but its benefits include calculating the cut point temperatures while using column-characteristic parameters.
The next complex model, the aggregate model, decomposes the CDU into a set of simple and thermodynamically equivalent cascade of conventional distillation columns and steam distillation columns. The conventional distillation column uses reboilers as the energy-separating agent. On the other hand, steam replaces the reboiler in the steam distillation columns as a mass-separating agent. Steam distillation uses different mechanism for generating the vapor phase, and therefore, it displays unique characteristics from the more common conventional distillation (Suphanit, 1999). The conventional distillation column can be modeled using an aggregate model approach based on the work of Caballero & Grossmann (1999) for the synthesis of distillation columns. The principle of their approach is to treat the column sections above and below the feed tray as two integrated heat and mass exchangers. On the other hand, the unique characteristics of steam distillation require modifying the aggregate model of the conventional distillation. The modified aggregate model for steam distillation is significantly more difficult and requires more steps in the initialization phase for the model to converge. The results of the model successfully predict the inverse temperature profile in the stripping section of steam distillation columns.
The last CDU model in our comparison is the rigorous tray-by-tray calculations. The CDU decomposition used for the aggregate model is extended to the tray-by-tray model to simplify the calculations. Careful initialization and simplification assumptions are used to ensure convergence. The results of the three proposed models are presented and compared to CDU simulation model.
The proposed nonlinear CDU models, FI model, aggregate model and tray-by-tray model, are separately integrated into a refinery production planning model. The results of the new NLP production planning model are compared to each others and with the current LP models. The benefits of introducing the NLP models and the level of NLP complexity are assessed in terms of accuracy, robustness and simplicity and computation effort. As will be shown, the main advantage of the proposed nonlinear models is their potential of predicting higher profit in refinery planning operation.
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