Reboiling optimization

This section is a companion to the section titled Fractionators-Optimization Techniques. In that section the Smith-Brinkley method is recommended for optimization calculations and its use is detailed. This section gives similar equations for simple and reboiled absorbers. 

The results of the computer calculation are as summarized by copies of the printouts. Note that Stage one is the product from an overhead condenser and is hquid, as is the bottoms or reboiler outlet product. The results show that the initial criteria have been met for recovery of component 5 however, this does not reflect any optimization of reflux or final number of stages (theoretical trays) that might be required to accomplish the separation in a final design. 

The best designs provide for the percentage vaporization per pass to have been completed by the time the fluid mixture reaches the upper end of the tube and the mixture is leaving to enter the bottom chamber of the distillation column. In order to assist in accomplishing this, the initial reboiler elevation should be set to have the top tubesheet at the same level as the liquid in the column bottom section. A liquid-level control adjustment capability to raise or lower this bottoms level must exist to optimize the recirculation. Sometimes, the level in the bottom of the column may need to be 25-30% of the reboiler tube length above the elevation of the tubesheet. Therefore, the vapor nozzle return from the reboiler must enter at sufficient elevation to allow for this possibility. 

S Entropy (kJ-K-1, kJkg-1-K-1, kJkmol-1-K-1), or number of streams in a heat exchanger network (-), or reactor selectivity (-), or reboil ratio for distillation (-), or selectivity of a reaction (-), or slack variable in optimization (units depend on application), or solvent flowrate (kg s-1, kmol-s-1), or stripping factor in absorption (-)... 

This example focuses on the design and optimization of a steady-state staged column. Figure El 2.1 shows a typical column and some of the notation we will use, and Table El2.1 A lists the other variables and parameters. Feed is denoted by superscript F. Withdrawals take the subscripts of the withdrawal stage. Superscripts V for vapor and L for liquid are used as needed to distinguish between phases. If we number the stages from tihe bottom of the column (the reboiler) upward with k= 1, then V0 = L1 = 0, and at the top of the column, or the condenser, Vn = Ln+l = 0. We first formulate the equality constraints, then the inequality constraints, and lastly the objective function. 

PALEN, J. W. and Taborek, J. J. Chem. Eng. Prog. 58, No. 7 (July 1962) 37-46. Refinery kettle reboilers proposed method for design and optimization. 

Varying the enthalpy, or heat content, of the feed is an additional independent variable that an operator, or process design engineer, can use to optimize fractionation efficiency. An additional benefit of feed preheat is that a lower-level temperature heat source can be used. If valuable 100-psig steam is required for the reboiler, then low-value 20-psig steam might be adequate for the feed preheat exchanger. 

Estimation of column costs for preliminary process evaluations requires consideration not only of the basic type of internals but also of their effect on overall system cost. For a distillation system, for example, the overall system can include the vessel (column), attendant structures, supports, and foundations auxiliaries such as reboiler, condenser, feed neater, and control instruments and connecting piping. The choice of internals influences all these costs, but other factors influence them as well. A complete optimization of the system requires a full-process simulation model that can cover all pertinent variables influencing economics. 

Some distillation columns must handle two or more feed streams simultaneously. Furthermore, alternative feed nozzles are often provided to allow the actual feed-point locations to be altered. By optimizing the feed-point locations, energy consumption in the reboiler can often be minimized. 

Feed flow optimization (a) maximizing throughput by fully loading the condenser (b) maximizing throughput against a reboiler constraint (c) maximum recovery of the heat content of bottom product by economizer. 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

Reduction in hatch time For a given fresh feed and a given separation, the column performance is measured in terms of minimum batch time required to achieve a desired separation (specified top product purity (x D]) and bottom product purity (x B2) for binary mixture). Then an optimal amount and composition of recycle, subject to physical bounds (maximum reboiler capacity, maximum allowable purity of the off-cut) are obtained in an overall minimum time to produce the same separation (identical top and bottom products as in the... 

In all the case studies presented here it is assumed that the amount of fresh feed to be processed in the long production campaign is fixed for every batch cycle, but the reboiler is oversized to some extent. The optimal amount of recycle is obtained within this bound so that maximum benefit can be achieved out of a given column. 

Referring to Figure 8.2 and given a batch charge (BO, xB0)> a desired amount of distillate DI of specified purity x D1 and final bottom product B2 of specified purity x b2 Mujtaba (1989) determined the amount and composition of the off-cut (Rl, x R1) and the reflux rate policy r(t) which minimised the overall distillation time. In this formulation instead of optimising Rl, xR1) the mixed charge to the reboiler (Bc, xBC) was optimised and at the end of the solution the optimal (Rl, x RI) was evaluated from the overall balance around the mixer in Figure 8.2. The dynamic optimisation problem is formulated as ... 

This study was done for case 2 and case 4 of Table 8.1 (for a low and high value of q). The results are summarised in Table 8.6. The purpose of this study is to show that recycling is beneficial even on a fixed reboiler capacity basis. Although these scaled results will in general not be strictly optimal, the benefits of recycling in terms of productivity are quite clear from Table 8.6. Also the benefit increases with q as before. 

Mujtaba and Macchietto (1997) have considered a maximum conversion problem for BREAD, subject to given product purity constraints. The reflux ratio is selected as the control parameters to be optimised for a fixed batch time so as to maximise the conversion of the limiting reactant. The optimal product amount, condenser and reboiler duties are also calculated. Referring to Figure 4.5 for CBD column the optimisation problem can be stated as ... 

For a given product purity of x D = 0.70, Mujtaba and Macchietto (1997) solved the maximum profit problem for a number of cost parameters using the method described above. The results are presented in Table 9.3. For each case, Table 9.3 also shows the optimal batch time, amount of product, reflux ratio, total reboiler duty and maximum conversion (calculated using the polynomial equations). 

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