The process synthesis problem can also be formulated and solved as an optimization problem. In this case, all the possible flowsheets are combined into one, normally called a superstructure. The superstructure contains more streams and unit operations than would be needed in reality, but by selectively removing unit operations and specific streams, the superstructure can be reduced to a practical flowsheet. The optimization problem is reduced to continuous design variables, such as pressure and temperature and to integer variables that indicate if a specific stream or unit operation is or not included. Figure 12.11 shows a very simple example of a superstructure generated to represent two alternative reactors, where the squares represent logical choices (e.g., it is either reactor 1 or reactor 2) and the triangle represents the convergence of the hypothetical choices (e.g., after the reactor, the process continues to the next unit operation through the exit stream).
The objective of the optimization is to remove those aspects of the flowsheet that are not going to render the best options. To solve this optimization problem, computer-aided and mathematical approaches have been used. Given the type of problem, the mathemati- cal approaches utilize algorithms that solve mixed-integer nonlinear problems (MINLP).
Questions Alternatives
Level 2: input–output structure of the flowsheet
1. Purify the feed streams? 1. Use pure oxygen instead of air to eliminate nitrogen oxide production.
2. Do not recover and recycle some reactants?
2. Recycle back unreacted species.
3. Use a gas recycle and purge stream, or vent gaseous
reactants? 3. Purge recycled streams to reduce accumulation of impurities in the system.
4. Recover and recycle or remove a by-product formed by a
secondary reversible reaction? 4. Use pure oxygen to eliminate nitrogen oxide formation and recycle back carbon dioxide.
R1
y2 R2 y1
FIGURE 12.11 Example of a superstructure generated to represent two alternative reactors. If y1ẳtrue, then y2ẳfalse and reactor 1 is used. If y2ẳtrue, then y1ẳfalse and reactor 2 is used.
To illustrate the optimization problem, we can loosely follow Grossmann’s MINLP definition.23Let’s assume that we want to minimize the total environmental impact of our process superstructure flowsheet; we can describe the optimization problem as follows:
FobjẳMinfCTyỵfðxịg
subject to: ð1ị CxỵDyd ð2ị Eye ð3ị x0 ð4ị y2 f0;1gp
What this set of mathematical equations means is that the total environmental impact of our flowsheet would depend on a combination of process-driven equations [orf(x)], while the definition of the flowsheet would be guided by which combination of unit operations are considered [CTy]. Our objective function (Fobj) would be minimized through the relationship, as that would minimize the total environmental impact. In constraint (3) we state thatxrepresents a vector of continuous variables, such as temperature and pressure.
In constraint (4) we state thatyrepresents the logical variables that will tell us if a unit operation in the superstructure is either kept or not (0 value if it is not kept, 1 if it is). Logical constraints are set in constraint (2), and constraint (1) represents the overall types of process constraints, such as mass and energy balances and process design specifications.
A number of approaches have been developed in this area,24,25with a series of accompa- nying computer tools, algorithms, solvers, and simulators to expedite the solution of these types of optimization problems, which can be rather complex for some chemical systems.
Early in the state of the art of process synthesis, the role of superstructure optimization was not as prominent, but with improvements in computer capabilities and the development of better algorithms, both by chemical engineers and by mathematical programmers, the approach has become more practical. One of the limitations of this method, however, is that the initial superstructure in most cases is limited by the imagination of the engineer who prepares the first draft. In recent times, engineers have used other techniques, such as artificial intelligence and thermodynamic pinch to generate the first superstructure.
Multiobjective optimization, alone or in combination with other approaches in hybrid methods, has been used in the recent past to integrate green engineering and sustainability concepts into process synthesis and design, as most of the optimization techniques have focused on the economics of the process, which don’t allow for implementation of the full aspects of green engineering.26As we saw earlier, the areas of green engineering represent a balance between several seemingly competing objectives. A promising theory for the inclusion of green engineering and sustainability principles in the optimization of alter- natives is the inclusion of sustainability and life cycle impact assessment metrics into the design, using a life cycle framework in the definition of the multiobjective optimization problem for chemical plants process design, synthesis, and integration.27–29
Perhaps the best way to introduce green engineering aspects into process synthesis methodology is to utilize hybrid systems that can combine several of the best aspects of the various techniques and integrate green engineering concepts as seamlessly as possible. For example, an approach proposed by Hostrup et al. explores a hybrid system that integrates mathematical optimization techniques, heuristic approaches, and thermodynamic insights into process synthesis to determine a flowsheet that optimizes separation efficiency, energy
flowsheet generated by heuristics and thermodynamic insight techniques is taken as the first iteration of the superstructure, and this superstructure is optimized with the mathemati- cal technique to determine the optimal flowsheet. The optimal flowsheet is obtained by solving the optimization problem through a suitable MINLP model.
Let’s follow an example of a hybrid system proposed by Hostrup et al. to illustrate how solving process synthesis through superstructure optimization would work. In this case, we seek to find the optimal flowsheet and the best solvent to separate a mixture. The proposed steps for the methodology are:
1. Determine the number and type of separation techniques based on solvent property differences.
2. Identify separation alternatives using external materials (e.g., membranes).
3. Define the initial superstructure based on pure-component properties analysis to determine which separation techniques are feasible and which are not.
4. Perform a binary mixture property analysis to eliminate unfeasible separation techniques from the superstructure.
5. Generate solvent alternatives based on process and environmental constraints.
6. Perform a multicomponent mixture property analysis with the solvents identified to eliminate unfeasible separation techniques from the superstructure.
7. Solve the remaining optimization problem. The problem statement can be formulated mathematically as follows:
FobjẳMaxfCTyỵfðxịg sets optimization function subject to
h1ðxị ẳ0 process design specifications h2ðxị ẳ0 mass and energy balances h3ðxị ẳ0 solvent design constraints l1g1ðxị u1 process design specifications
l2g2ðxị u2 environmental and property constraints l3ByþCxu3 enforces logical conditions
x0 sets continuous variables
y2 f0;1gp sets logical variables
Example 12.6 Benzene is used to separate acetone from a well-known binary azeotropic mixture between acetone and chloroform. Given the health and safety issues associated with benzene, the desire is to replace benzene and find the optimal design to accomplish this.
In this instance the problem can be stated: “Given a chemical species that must be separated from a mixture, determine the flowsheet design that optimizes separation efficiency, cost of energy requirements, process issues, and environmental constraints.”
Solution A detailed solution can be found in a publication by Hostrup et al.31Note that once the problem is solved, the “optimal” flowsheet design will not have a minimal
environmental impact, but it will satisfy a set of environmental constraints in that the solvent selected will not have the same concerns as benzene.
Step 1. The separation techniques considered as a starting point were adsorption, absorption, pervaporation, filtration, crystallization, distillation, distillation plus decanter, extractive distillation, azeotropic distillation, liquid–liquid extraction, and supercritical extraction.
Step 2. No membrane system is known for this mixture, so membrane-based techniques are eliminated.
Step 3. There is no interest in a solid-state product, so crystallization is eliminated.
Step 4. Binary mixture properties analysis validates the presence of an azeotrope and confirms the feasibility of pressure swing distillation, since the location of the azeotrope changes with the pressure. High-pressure distillation is feasible but would probably require very large amounts of energy, so it is eliminated as an alternative.
Miscibility analysis also eliminates distillation plus decanter as an alternative, since there are no miscibility gaps.
Step 5. For this step the desired outcome is to replace benzene as a separating agent. For this problem, the solvent design problem is set first, thus reducing the number of alternatives for subsequent optimization. The design criteria for the solvent search is to include acyclic alcohols, aldehydes, ketones, acids, ethers, and esters with the following property constraints:
g2ðxị
340 K < Tb <420 K bðselectivityị>3:5 Spðsolvent powerị>2:0 S1ðsolvent lossị < 0:9 8>
>>
><
>>
>>
:
h3ðxị No azeotrope with any component in the binary feed mixture
Binary feed mixture molar composition:acetone 34:4%;chloroform 65:6%
After designing the solvent, Hostrup et al. found two potential solvents from the molecular design exercise: 1-hexanal and amyl methyl ether. They checked the EHS data on both solvents and found that 1-hexanal did not have the carcinogenicity problems that benzene has. There was, however, very limited data on methyl amyl ether, but they decided not to exclude this solvent from the analysis at this point, although they indicated that additional exploration was necessary. Note that if the solvent selection criteria are changed, a different set of solvents or even more solvents might be found as alternatives. However, for the purpose of illustration, two alter- natives plus the baseline (benzene) for comparison would be sufficient.
Step 6. The two solvents identified form homogeneous systems with the acetone–
chloroform mixture; therefore, liquid–liquid extraction and azeotropic distillation are eliminated. Since carbon dioxide is found to have low solubility with acetone and poor selectivity in relation to chloroform, supercritical fluid extraction is also eliminated.
Therefore, the reduced superstructure will only consider pressure swing distillation and extractive distillation with the three solvent alternatives (the two additional solvents plus benzene as a baseline for comparison). Note that both separation
alternatives include two distillation columns. A simplified version of the superstruc- ture is presented in Figure 12.12.
Step 7. The optimization problem was based on maximizing profits. The optimization problem can be expressed as follows:
Fobj ẳ Maxfprofitg
ẳ Maxfsales-cost of solvent-cost of steam-cost of electricity-cost of coolingg subject to
h1ðxị
column 1 pressureẳ 1 atm if extractive distillation 10 atm if pressure swing distillation
outlet pressure of pumpẳcolumn 1 pressure Feedẳ5 kmol=h acetoneỵ5 kmol=h chloroform 8>
>>
<
>>
>:
h1ðxị
mass and energy balances for the mixer energy balance for the pump
energy balance for the heat exchanger mass and energy balances for columns 1 and 2
total mass and energy balances for the entire flowsheet 8>
>>
>>
><
>>
>>
>>
:
g1ðxị
composition of acetone in the distillate of column 1>0:99 recovery of acetone in column 1>99%
composition of chlorofrom in the distillate of column 2>0:98 recovery of chloroform in column 2>90%
8>
>>
<
>>
>:
D1
EX
D2 Decanter
Feed
Solvent Makeup
P1
P2
Benzene 1-Hexanal Methyl, n-pentyl ether
FIGURE 12.12 Simplified representation of the reduced superstructure for Example 12.6. (From Hostrup and Gani, ref 30. Copyright1999, with permission from Elsevier.)
After solving the optimization problem, the alternative that exhibits the largest value for the objective function was the extractive distillation using amyl methyl ether.
Additional Points to Ponder What is a possible reason to have chloroform as part of a binary mixture? What other green engineering constraints could have been added to the optimization solvent definition? Is there any other issue with the solvents used in this example?
Even though the extractive distillation alternative was found as optimal in Example 20.6 under the conditions and constraints described, Hastrup et al. point out that since pressure swing distillation in the superstructure flowsheet did not include heat integration, there is still some room for optimization as an alternative in comparison with the extractive distillation flowsheet. Heat integration was not part of the scope of the optimization at that point;
however, with the two flowsheets to compare it is possible to run some “what if” scenarios.
For example, if heat integration is considered and more than 25% of the energy requirements required can be saved or recovered, pressure swing distillation will become the optimal flowsheet design for this objective function. The system under study in the example was really a subsystem of a larger flowsheet; therefore, heat integration (covered next Chapter 13) should be considered for the entire process. It is also important to point out that changing the constraints in the solvent selection criteria would lead to a different set of solvents, or changing the conditions of the separation techniques might have changed the reduced superstructure (e.g., by adding a cosolvent to carbon dioxide to increase the solubility of the substrate might have made supercritical fluid extraction an attractive alternative).
Finally, it is very important to point out that the formulation of the optimization function in this case was based purely on an economic objective that was maximized while attempting to satisfy environmental, health, and safety constraints. In this case the objective function was not minimization of the environmental impact, and this provides a very interesting contrast with the methodology presented by Carvalho et al. If the objective function had been written to minimize the environmental impact using one or a series of green engineering metrics, it might have been possible to obtain another solution for the optimal flowsheet.