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470225 A Mathematical Model to Synthesize and Integrate Distillation Columns into Overall Processes

Multiple-effect distillation involves the use of parallel separation effects, which share the initial feed mixture and operate at different pressures. Under these conditions, available heat from the condensers of higher pressure effects can be used by the reboilers of lower pressure effects provided that the minimum temperature difference between heat sources (condensers) and sinks (reboilers) is secured. Energy consumption of the distillation system can be significantly reduced according to the number of effects, the operating pressures and the strategy of splitting the feed mixture among effects. Additional benefits can be succeeded by appropriately integrating the distillation effects with the heat exchangers involved in the rest process; the latter are also called background process needs.

Energy integration of hot/cold streams, either they belong to the multiple-effect distillation system or the background, naturally relates to the use of Pinch analysis. The procedure requires the appropriate placement of separation effects within the Grand Composite Curve of the integrated background needs over or under the pinch point [1]. The appropriate placement rule offers the guidelines for the selection of number, pressures and feed split fractions of effects. In particular, the number of effects defines the split of the overall distillation energy consumption among the multiple levels, while the feed split fraction defines the capacity of effects and, thus, the amount of energy that is required per effect. The operating pressures determine the temperature ranges of added effects and accordingly the temperature difference that is required for heat exchange among the effects and between the effects with the background. In a common multiple-effect distillation scheme, the higher pressure effect receives heat from hot utilities (or the background), while heat is cascaded to lower pressure effects until it is rejected to the background (or the cold utilities).

Both temperature ranges and duties determine the integration potential of the selected effects. At first, the temperature ranges of effects that need to get integrated should not overlap; moreover, the ranges should secure the minimum temperature difference for heat exchange. The temperature ranges also define whether the effects can get integrated with the background process over or below the pinch. Secondly, the number and split fractions define the energy consumption of each effect and, thus, the range of energy savings by integrating each other or with the background. The efficiency of multiple-effect integration schemes is graphically tested using the appropriate placement technique within the Grand Composite Curve as a trial an error procedure. In general the procedure involves the following steps: (1) add an effect, (2) change pressures of effects until effects are appropriately placed over/below the pinch of the background, (3) change the feed split fractions of effects until they are fully (or almost fully) integrated among them and with the background; otherwise go back to step (1). This procedure has been extensively used to integrate distillation columns [2,3], while other rigorous distillation models [4,5] have been also presented in literature to select operating pressures and split fractions; however, they assume fixed number of effects.

This paper presents a shortcut and linear optimization model to select the best synthesis plan of number, pressures and split fractions of distillation effects that minimize distillation energy cost securing the minimum capital cost of added effects. A transshipment model is used to debottleneck energy consumption of the overall process considering the needs of background hot/cold streams to be fixed and variable duties for the condensers/reboilers of effects.

The methodology assumes a pre-selected range of candidate pressures, where a distillation effect is capable to operate at each pressure level. Given the pressure of each candidate effect, the temperature ranges as well as the maximum reboilers and condensers duties can be estimated in advance assuming that each effect receives the whole feed mixture. Moreover, assuming that distillation duties are linearly depended on feed flowrate, the actual duties of effects can be linearly approximated as a fraction of their maximum duties; the fraction relates to the feed split fraction (variable) that is assigned to each candidate. Non-zero split fractions apparently denote the selection of an effect. Linear models are used for the estimation of capital costs of effects according to the selected fractions; the parameters of models were estimated by regressing distillation capital cost in the range of split fractions at each pressure.

The heat demands of candidate effects can be incorporated into the heat cascade of the overall process as additional variable hot/cold streams, whose contribution is managed through the associated split fractions. The hot/cold streams of the background are also incorporated in intervals of the cascade with fixed duties, since their energy contents are not affected by the choices made for effects. A transshipment model is used to debottleneck heat flows along the cascade using additional terms for the selection and contribution of effects to intervals. The model involves the equations of the transshipment model, constraints for selection of effects and the objective function, which is a cost function involving energy cost and distillation capital expenses; the latter is included to avoid solutions, which though they secure minimum energy cost, they aimlessly use more than the needed effects to succeed this target.

The proposed optimization model was used in the courses of a real-life biorefinery which fractionates lignocellulosic biomass into C5 Sugars, C6 Sugars and lignin. The Sugars are further fermented to produce bio-ethanol. The model was used to simultaneously integrate three different distillation columns – one for solvents recovery and two for ethanol purification – with the overall process resulting in high energy savings up to 82 % and zero distillation energy cost. Two effects have been selected for the solvents recovery distillation and one effect for each ethanol purification case. The operating pressures of all four distillations were appropriately changed to secure maximum integration with the background. The model not only detected promising multiple-effect structures for the solvents recovery by examining interactions among the synthesis specifications (number, pressures, split fractions) but also proceeded in re-engineering of operating pressures of ethanol distillations without aimlessly adding effects to secure fully integrated effects with the overall process.

**References**

- B. Linnhoff, H. Dunford and R. Smith, 1983, Heat Integration Of Distillation Columns Into Overall Processes, Chemical Engineering Science, 38, 8, 1175–1188
- M. Dias, M. Modesto, A. Ensinas, S. Nebra, R. Filho, C. Rossell, 2011, Improving bioethanol production from sugarcane: evaluation of distillation, thermal integration and cogeneration systems, Energy, 36, 6, 3691–3703
- P. Kravanja, A. Modarresi, A. Friedl, 2013, Heat integration of biochemical ethanol production from straw – A case study, Applied Energy, 102, 32–43
- M. Martín and I. Grossmann, 2011, Energy Optimization of Bioethanol Production via Gasification of Switchgrass, AIChE Journal, 57, 12, 3408–3428
- M. Martín and I. Grossmann, 2013, On the Systematic Synthesis of Sustainable Biorefineries, Ind. Eng. Chem. Res., 52, 9, 3044–3064

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