(595c) Integration of Nonlinear CDU Models in Refinery Planning Optimization | AIChE

# (595c) Integration of Nonlinear CDU Models in Refinery Planning Optimization

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## Authors

Carnegie Mellon University
Carnegie Mellon University
Argonne National Laboratory

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. Despite the improvement of the swing cut model, the model does not reflect the nonlinearity of the process, but it provides an incentive to further improve the planning model and calculate more accurate yields. The simplicity, robustness and convenience of the linear approach are tradeoffs for the true optimal and accurate solution to the planning model. In fact, planning technology is considered well developed and progress is expected in model refinement through the use of nonlinear programming (NLP) (Pelham & Pharris, 1996), which accommodates the use of nonlinear process models. This effort is an attempt to address this need with the goal to develop more accurate refinery planning models, using the latest NLP algorithms and implementing more accurate process modeling. The objective is to propose nonlinear process model equations for implementation into a refinery planning model.

A simple nonlinear model applied to the CDU is the fractionation index (FI) model. The model employs the fractionation index defined by Geddes (Jakob, 1971). For the purpose of utilizing the FI model, the CDU is represented by a series of binary separation stages where the bottom products are the CDU product streams and the top products are fed to the next stage. Each stage will have one or two FI parameters representing the stripping and the rectifying sections of the separation stages (Wagner, 1978; Gilbert, 1966). Using the model, the compositions of the components in the top and bottom product streams of each stage are calculated. The model calculates cut point temperature of each product along with the product flowrates. The model lacks more details on the operating conditions, but introduces a simple nonlinearity that can be implemented into a planning model. Different implementation and decisions for the FI model are examined. Results of the CDU FI model and the FI-based refinery planning model are presented.

Another nonlinear model for the CDU uses a decomposition technique to make the complex CDU more manageable modeling. The CDU is represented as 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). Most noticeably, the temperature profile reaches at a maximum at the feed stage in steam distillation column, as opposed to the monotonic profile of conventional distillation.

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. This aggregate representation, which includes a modest number of nonlinear equations, reflects the nonlinear nature of the process. The results of the aggregate model for conventional distillation are in good agreement with the results from simulation software. The aggregate model is extended to cascaded conventional distillation columns. The convergence of the cascaded columns is enhanced with a proposed flow analysis that generated additional constraints. However, good initialization is key to successful nonlinear programming model. The adapted initialization scheme involved staged LP & simple NLP mass balances around the column. The result model and the implemented computational strategies proved successful and gave us a robust model for conventional distillation.

Many of the distillation column models cannot be applied to steam distillation due to the models' inherent assumptions. Therefore, The unique characteristics of steam distillation require modifying the aggregate model. The modification includes the top and bottom sections above and below the feed stage, similar to the conventional distillation model. However, the feed stage is taken as an equilibrium stage, along with a bottom stage (stage #n) and the stage below the condenser (stage #1). In addition to the mass and enthalpy balances applied to the all sections and stages, equilibrium equations are applied to the three identified equilibrium stages. The modified aggregate model for steam distillation is more difficult and requires more steps in the initialization phase for the model to converge. The results of the model successfully predict the expected temperature profile in steam distillation columns. Similar to the conventional distillation columns, the steam distillation model is extended to cascaded columns using similar computational strategies. The conventional and steam distillation columns are then combined in the cascaded arrangement to represent and model the CDU. The proposed CDU NLP-based aggregate model and FI models 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 model and the level of NLP complexity are assessed in terms of accuracy, robustness and complexity. As will be shown, the main advantage of the proposed nonlinear model is its potential of producing more accurate production scenarios.

References

Caballero, J.A.; Grossmann, I.E. (1999). Aggregate models for integrated distillation systems. Industrial & Engineering Chemistry Research, 38(6), 2330-2344.

Favennec, JP. (2001). Refinery Operation & Management. Editions Technip. Paris.

Gilbert, R.J.H., Leather, J., Ellis, J.F.G. (1966). The Application of the Geddes fractionation index to the crude distillation units. AIChE Journal, 12(3), 432-437.

Jakob, R.R. (1971); Estimates number of crude trays. Hydrocarbon Processing, 50(5), 149-152.

Li, W.; Hui, C.W.; Li, A.X. (2005). Integrated CDU, FCC and product blending models into refinery planning. Computers and Chemical Engineering, 29, 2010-2028.

Pelham, R.; Pharris, C. (1996). Refinery operation and control: a future vision. Hydrocarbon Processing, 75(7), 89-94.

Suphanit, B. (1999). The design of complex distillation systems, PhD Thesis. UMIST. Manchester.

Trierwiler, D.; Tan, R.L. (2001) Advances in crude oil LP modeling. Hydrocarbon Asia, 8, 52-58

Wagner, H. (1978) Thermodynamic design of multi-component rectifications. International Chemical Engineering, 18 (3), 391-394.

Zhang, J.; Zhu, X.X.; Towler, G.P. (2001). A simultaneous optimization strategy for overall integration in refinery planning. Industrial & Engineering Chemistry Research, 40, 2640-2653.