Kishalay Mitra

Mathematical Modeling and Optimization of Two-Layer Sintering Process for Sinter Quality and Fuel Efficiency Using Genetic Algorithm

ABSTRACT Two-layer sintering by charging a green sinter mix with normal coke rate in the upper layer and reduced coke rate in the lower layer can substantially reduce the coke rate and improve the sinter quality by producing more uniform thermal profile throughout the bed height. The two-layer sintering process has been analyzed by numerical simulation using a detailed CFD-based model, considering all the important phenomena (i.e., gas-solid reaction, melting and solidification, flow through porous bed, heat, and mass transfer etc.). A genetic algorithm optimization technique is then applied to evaluate the optimum coke rate in the two layers of the bed to produce the ideal thermal profile and melting fraction in the sinter bed for optimum sinter quality. By this optimization method a high-quality sinter with minimum return fines can be achieved along with reduced coke rate. Application of genetic algorithm for this type of process optimization has several advantages over traditional optimization techniques, because it can identify the global optimum condition and perform multiobjective optimization very easily for a complex industrial process such as iron ore sintering.

Multiobjective dynamic optimization of a semi-batch epoxy polymerization process

Abstract Multiobjective Pareto optimal solutions for epoxy semi-batch polymerization process are obtained by adapting nondominated sorting genetic algorithm II (NSGA II). The objective is to produce polymer of maximum possible number average molecular weight ( M n ) with a specified value of polydispersity index (PDI) and number average molecular weight in minimum possible time. The M n and reaction time are, therefore, taken as two objectives where the first one is maximized and the second one is minimized. The decision variables are addition profiles of various reactants and the reaction time itself and PDI is treated as a constraint. In another optimization study, the time intervals are also been changed from hourly addition assumptions to equal interval additions for an optimized time frame. Additionally, similar analysis has been performed with a new addition strategy with total additions of reactants very close to available experimental conditions. Sensitivity analysis for estimated kinetic parameters and analysis for stabilization of products are also studied. A validated model, taking care of required physico-chemical aspects of the proposed reaction mechanism, is a prerequisite for this kind of study.

Multicriteria Optimal Control of Polypropylene Terepthalate Polymerization Reactor

Tetrabutoxytitanium (TBOT) is a proven catalyst for the esterification step of the polypropylene terepthalate (PPT) polymerization process. Previous studies show that the performance of TBOT is superior in terms of the enhanced degree of polymerization and less processing time to other competitive catalysts. But, interesting observation left was to investigate whether with other process objectives like by-product minimization and controlled growth of desired functional groups, any other catalyst offers better system performance or not. Present study carries out the exercise of searching other catalytic options along with TBOT for the process improvements and gives a detailed process analysis through different sets of optimized operations. A well-validated kinetic model for esterification step of PPT polymerization process and the advanced Real-Coded Nondominated Sorting Genetic Algorithm-II (Real-Coded NSGA-II) optimization routine have been used in this current effort. For process objectives like by-product minimization, TBOT though become a marginal winner, Sn- and Zn-based catalysts compete with each other. Zn-based catalyst is found probably the most suitable catalyst in terms of the overall process performance with excellent by-product minimization (∼10 times better), higher degree of polymerization (∼1.75 times better), and tight quality control (∼5 times better).

Control of Meniscus-Level Fluctuation by Optimization of Spray Cooling in an Industrial Thin Slab Casting Machine Using a Genetic Algorithm

Abstract Meniscus-level fluctuation is a common problem during thin slab casting and can lead to breakout. Because meniscus-level fluctuation increases with increase in casting speed, it restricts high-speed casting. It is now known that the meniscus-level fluctuation is caused by fluctuation in bulging and decreasing the total bulging can control it. Increasing the spray cooling reduces the total bulging and hence the meniscus-level fluctuation. However, the increase in spray cooling poses other problems. The midwide surface temperature at the slab exit may fall excessively, requiring significant reheating and thus fuel consumption in the reheating furnace. Also, the temperature at the unbending point may fall below a critical value causing crack formation. Thus, an optimization procedure was adopted to find the optimum combination of spray cooling, which will minimize the total bulging, keeping the midwide surface temperature at the slab exit more than a minimum and user-specified value. To do so, a genetic algorithm was used in conjunction with a model for estimation of temperature at different locations of strand and total bulging in the strand (thermal-bulge model). Based on the results of optimization, the casting speed in a plant could be enhanced by more than 30%.

Multiobjective Pareto Optimization of an Industrial Straight Grate Iron Ore Induration Process Using an Evolutionary Algorithm

Multiobjective optimization of an industrial straight grate iron ore induration process is carried out in this study using an evolutionary algorithm. A simultaneous maximization of throughput and pellet quality indices like cold compression strength (CCS) and Tumbler index (TI) is adopted for this purpose, which leads to an improved optimal control of the induration process as compared to the conventional practice of controlling the process based on burn-through point (BTP) temperature. Discretized pressure and temperature profiles, grate speed, and bed height are used as decision variables whereas the bounds on CCS, abrasion index (AI), maximum pellet temperature, and BTP temperature are treated as constraints. The optimization results show that it may be possible to achieve significant improvement in the throughput with similar TI values and without violating any operational constraints. Commonality among decision variables corresponding to various Pareto optimal (PO) solutions obtained as a result of this multiobjective optimization study helps in unveiling the embedded relationship amongst them, which, in turn, can reveal the operating principles of running the process in an optimal fashion. The methodology is quite generic in nature and can be adopted for similar processes. The results of this optimization exercise can be used as a set of operating target points for the underlying model based predictive control algorithms to control and optimize the process.

Unveiling Salient Operating Principles for Reducing Meniscus Level Fluctuation in an Industrial Thin Slab Caster Using Evolutionary Multicriteria Pareto Optimization

Achieving higher speed to attain higher productivity in continuous casting process is not an easy task as perturbations in casting speed may lead to inter-roll bulging causing the meniscus level to fluctuate leading to increase in chances of breakout. However, increasing the spray cooling in a random manner as a measure of reducing the bulging and thereby controlling meniscus level fluctuation is not the way to achieve higher production rate because this would lower the exit temperature of the slab from the rollers. In that case, the temperature of the slab entering the reheating furnace, which is placed just ahead of the roll caster, would have to be increased leading to higher fuel consumption. The objective of any thin slab casting practitioner who wants to reduce meniscus level fluctuation by eliminating the sources of the fluctuation, therefore, is to find the optimal spray distribution that minimizes the bulging, maximizes the slab exit temperature, and maximizes casting speed simultaneously. This three-objective (mutually conflicting) optimization problem is solved here adapting the elitist version of the nondominated sorting genetic algorithm (NSGA II). An industrial continuous casting case study has been formulated under the above mentioned optimization framework, solved and analyzed in full details to unveil embedded salient operating principles for the casting process under consideration. In this way, the nominal casting speed and productivity could be increased by more than 30% and 10%, respectively, with a return on investment of one month along with few other intangible benefits. This problem formulation methodology is very generic in nature and can be applied to many complex problems from various fields.

Handling Uncertainty in Kinetic Parameters in Optimal Operation of a Polymerization Reactor

In deterministic optimization of the epoxy polymerization system, kinetic parameters for the assumed reaction scheme, once tuned with experimental data during the model building exercise, are assumed constant henceforth during the entire course of optimization studies. However, the important fact that these parameters are subjected to experimental and regression errors and thereby some level of uncertainty are embedded in them has been ignored by assuming them as constants. This further leads to emergence of suboptimal solutions that cannot fully utilize the true potential of the situation in hand. It is, therefore, realistic to consider the uncertainty associated with these parameters. Different methodologies from the paradigm of optimization under uncertainty have been generally used to formally tackle these problems where uncertainty propagation of these parameters through model equations is reflected in terms of system constraints and objectives that facilitate a designer to unveil the trade-off between solution optimality and robustness. Chance constrained programming (CCP) is one such methodology and is adopted here to carry out an analysis in determining optimal performance of a semibatch epoxy polymerization reactor under uncertainty in kinetic parameters. This multiobjective optimal control study aims to find out the trade-off among optimal growth of the desired species, solution robustness, and productivity of the reactor achieved through optimal discrete addition rates of different manipulated variables, e.g., bisphenol-A, epichlorohydrin, and sodium hydroxide. Various system requirements on the control variables are expressed in terms of bounds on number average molecular weight, polydispersity index, and other constraints that express the experimental conditions realistically.

Unveiling optimal operating conditions for an epoxy polymerization process using multi-objective evolutionary computation

The optimization of the epoxy polymerization process involves a number of conflicting objectives and more than twenty decision parameters. In this paper, the problem is treated truly as a multi-objective optimization problem and near-Pareto-optimal solutions corresponding to two and three objectives are found using the elitist non-dominated sorting GA or NSGA-II. Objectives, such as the number average molecular weight, polydispersity index and reaction time, are considered. The first two objectives are related to the properties of a polymer, whereas the third objective is related to productivity of the polymerization process. The decision variables are discrete addition quantities of various reactants e.g. the amount of addition for bisphenol-A (a monomer), sodium hydroxide and epichlorohydrin at different time steps, whereas the satisfaction of all species balance equations is treated as constraints. This study brings out a salient aspect of using an evolutionary approach to multi-objective problem solving. Important and useful patterns of addition of reactants are unveiled for different optimal trade-off solutions. The systematic approach of multi-stage optimization adopted here for finding optimal operating conditions for the epoxy polymerization process should further such studies on other chemical process and real-world optimization problems.

Supply Chain Planning under Uncertainty: A Chance Constrained Programming Approach

Uncertainty issues associated with a multi-site, multi-product supply chain planning problem has been analyzed in this paper using the chance constraint programming approach. In literature, such problems have been addressed using the two stage stochastic programming approach. While this approach has merits in terms of decomposition, computational complexity even for small size planning problem is large. This problem is overcome in our paper by adopting the chance constraint programming approach for solving the mid term planning problem. It is seen that this approach is generic, relatively simple to use, and can be adapted for bigger size planning problems as well. We demonstrate the proposed approach on a relatively moderate size planning problem taken from the work of McDonald and Karimi (1997) and discuss various aspects of uncertainty in context of this problem.

EVOLUTIONARY ALGORITHMS FOR OPTIMAL CONTROL OF PPT POLYMERIZATION REACTOR

Abstract Synthesis of Poly(propylene terepthalate) (PPT) is normally carried out (in batch as well as semi-batch mode) in a combined mixture of TPA (terephthalic acid) and PG (1,3-propanediol) with a suitable catalyst in two steps: esterification and polycondensation. Functional group modeling technique is used here to analyse the semibatch PPT formation system. Objectives of multiobjective optimization are to maximize productivity and the proportionality among desired functional groups at minimum possible processing time. But these conflicting objectives lead to an undesired population of other undesired functional groups. Several constraints are incorporated into the system to tackle this situation. Real-coded NSGA-II (Non-dominated Sorting Genetic Algorithm) has been utilized as an evolutionary optimization technique to solve the problem.