An objective function is a mathematical function whose purpose is to increase or decrease a limited global characteristic of the process. Optimization of a chemical process is usually aimed at maximizing profit or minimizing cost, which means that the objective function generally has a unit of dollars. Since the objective function depends on the base case, the optimization results will be useless due to insufficient information about the base case.
It is therefore essential that the base case analysis provides an objective function that is affected by all relevant decision variables. The overall optimization objective function of unit 500 is to maximize the plant's net present value. In addition, the objective function can be further simplified by assuming, which may mean neglecting, the values of the decision variables based on sensitivity analysis.
The engineer must prioritize decision variables in the initial stages of optimization based on their impact on the objective function. Using sensitivity analysis, an engineer can easily identify the decision variables with the greatest impact on the objective function. By plotting the percentage change of a variable versus the value of the objective function, with each variable represented by a separate line, the decision variables with the greatest impact on the objective function can be easily identified.
This further proves the necessity of understanding the decision variables and their role in the value of the objective function and other decision variables.
Variation from Base Case
TYPES OF OPTIMIZATION
Not only does topology optimization have a more significant impact on overall profitability, but topology optimization further limits and reduces the possible operating conditions – the focus of parametric optimization. The extent to which topology optimization constrains parametric optimization depends largely on the stage of the design process. Since side reactions cannot be completely prevented, unwanted by-products and waste streams will be produced.
During optimization, investigate possible unwanted by-products, which are distinct from waste streams as they can be sold, and the consequences of any hazardous waste product. The unwanted by-products themselves will not be sold for a total profit, otherwise they would not be unwanted, so this additional revenue would serve as a partial economic credit. Minimize the production of waste and unwanted byproducts with the right catalyst and operating conditions.
Side reactions can be suppressed by reducing the conversion of the limiting reactant to the transition or by choosing a different catalyst. Besides the obvious changes, such as compressing gas instead of liquid, equipment redesign is usually the result of an in-depth analysis of the separation part and heat integration in the process. Alternative reaction configurations depend on the specific process and reactor configuration previously designed for the specific removal of unwanted byproducts.
Today, the separation of chemical components can be achieved using a wide variety of equipment and technologies. Heat integration is intended to heat and cool process streams to their desired temperature with other process pairs rather than utilities. Then determine if heat integration can be done by investigating the initial temperature and the desired final temperature and whether the process steam can supply or absorb heat.
HENSAD, which stands for Heat-Exchanger-Network-Synthesis-Analysis-Design, is a useful computer software tool for heat integration design validation. As discussed in Topological Optimization, parametric optimization is much more efficient when the topology is fixed. Since the efficiency of the optimization process depends on the allocation of time for key variables, the approach to parametric optimization must be well thought out and justified.
APPROACHES TO OPTIMIZATION
Many of the topological designs of a chemical process rely on the parametric model, so a successful optimization will often require optimizing the topology several times based on the parametric optimization. A recycling loop containing decision variables complicates the evaluation of the objective function and can only be correctly optimized with a complete understanding of the process. Most chemical process optimizations will require an objective function based on process simulations and mathematical functions.
Synthesizing a chemical process in any modern process simulator software involves first selecting individual steps in the process and then interconnecting these steps. If the simulation is invalid after adding a step, the problem is in the process. Essentially, the dependent variable or "output" is what the objective function desires to maximize or minimize and the input includes the independent or decision variables that are capable of change.
For original case study endpoints, typically use maximum/minimum process constraints or start at the initial value and probe in the direction known to improve the objective function. The input case study matrix variables, scope and step sizes must take into account total cycle time. Conducting a case study with a single variable changed can be an extremely useful step in creating a case study matrix.
By including too narrow a range or too large a step size, the designed case study can act as a filter. Oversimplification will produce case study results that do not capture the true relationship between a decision variable and an objective function, thereby invalidating optimization results. Case studies are not often an appropriate tool for the overall objective function, but can be very useful in optimizing the decision variables within that overall objective function.
For example, a chemical process simulation can perform case studies on reactors to increase conversion, even if the objective function is to increase profitability. As maximizing conversion minimizes costs associated with raw materials, recycling, separation, equipment and much more, a reactor case study alone can clearly impact overall profitability. Chemical process simulation can be an extremely useful tool, case studies can provide useful insight into defining decision variables, but this software only provides estimates and can often be a waste of time.
OPTIMIZATION OF UNIT 500 REACTOR
The reduced recycle rate consequently lowers utility costs associated with feed preheating, reactant cooling effluent, and reactor effluent separation, as less mass needs to be cooled, heated, and separated. It is desirable to use a fluidized bed reactor instead of the current packed bed reactor design, including two reactors in series with intermediate heating. It should be noted that the included optimized design of Unit 500 never explored this type of reactor.
An estimate that 10% of the feed bypasses the catalyst is due to the bubbly nature of the fluidized bed, meaning that the maximum conversion in one pass is 90% of the equilibrium conversion, even in an infinitely large reactor. The yield objective function for reactor design is defined in the following equations and is unitless. The optimal value, considering the bypass, of the objective function is equivalent to 90%, which would mean a 90% conversion of the ethylbenzene supplied to the reactor, without side reactions.
Restrictions for the reactor include a maximum temperature of 1000 K and an inlet and outlet pressure of at least 0.75 bar no and greater than 2.5 bar, as with the previous reactor design. Ar is Archimedes' number. dp is the particle diameter. µ is the viscosity of the process stream. However, examination of the simulation reactor should include only the feed, a separator to bypass 10% of the reactants, the reactor, and a mixer to combine the bypass with the reactor product.
The case study input included the identified decision variables and then provided not only the target revenue but also the superficial velocity as it determined the validity of a case study's results. To conduct the case studies, I first had to decide on the range of decision variables to implement in the case study matrix. This range had to be large enough so that the data could capture changes in yield caused by changes in a single variable.
An in-depth understanding of the effect of a variable on the objective function reduces the scope and step sizes required for an efficient case study matrix, thereby reducing simulation time. For any value of the decision variable, the reactor will only operate at certain values of the other two variables. Running the initial case study matrix with a large range and large step sizes to reduce computational time later reduced the range by finding results outside the speed limits.
Styrene Out (kmol/hr)
Temperature (K)
Pressure (bar)
Diameter (mm)
Superficial Velocity (m/s)
SUMMARY
To really justify the optimization results from the fluidized bed reactor example, all possible reactor setups must be optimized for maximum yield. Hopefully, this discussion has provided a clear method for calculating and evaluating chemical process optimization, even though it is endless and complicated.
