A Hybrid Method for Stochastic Performance Modeling and Optimization of Chemical Engineering Processes

As chemical engineers seek to improve plant safety, reliability, and financial performance, a wide range of uncertaintyladen decisions need to be made. It is widely agreed that probabilistic approaches provide a rational framework to quantify such uncertainties and can result in improved decision making and performance when compared with deterministic approaches. This article proposes a novel method for design and performance analysis of chemical engineering processes under uncertainty. The framework combines process simulation tools, response surface techniques, and numerical integration schemes applied in structural reliability problems to determine the probability of a process achieving a performance function of interest. The approach can be used to model processes in the presence or absence of performance function(s), with or without parameter interactions, at both design and operational phases. With this, process behavior can be quantified in terms of stochastic performance measures such as reliability indices and the associated most probable process design/operating conditions, providing a simple way to analyze a wide range of decisions. To validate the applicability of the proposed framework, three case study systems are considered: a plug flow reactor, a heat exchanger, and finally a pump system. In each case, performance criteria based on the original physical model and the surrogate model are set up. Reliability analysis is then carried out based on these two models and the results are assessed. The results show that the proposed framework can be successfully applied in chemical engineering analysis with additional benefits over the traditional deterministic methods.     

Robust PI controller design for integrator plus dead-time process with stochastic uncertainties using operational matrix

To increase the precision and reliability of process control, random uncertainty factors affecting the control system must be accounted for. We propose a novel approach based on the operational matrix technique for robust PI controller design for dead-time processes with stochastic uncertainties in both process parameters and inputs. The use of the operational matrix drastically reduces computational time in controller design and statistical analysis with a desired accuracy over that of the traditional Monte-Carlo method. Examples with deterministic and stochastic inputs were considered to demonstrate the validity of the proposed method. The computational effectiveness of the proposed method was shown by comparison with the Monte-Carlo method. The proposed approach was mainly derived based on the integrator plus dead-time process, but can be easily extended to other types of more complex stochastic systems with dead-time, such as a first-order plus dead-time or a second-order plus dead-time system.     

Designing sustainable alternatives for batch operations using an intelligent simulation–optimization framework

The drive towards sustainability has compelled the batch process industries to implement the concept of environmentally friendly plants. However, the temporal nature of processing in these processes obviates the application of traditional waste minimization, material recycling, or energy integration schemes. Further, most of the existing methodologies for generating sustainable alternatives are restricted to specific problems, such as reaction byproduct, wastewater, or solvent minimization. In this paper, we propose an intelligent simulation–optimization framework for identifying comprehensive sustainable alternatives for batch processes. We differentiate between wastes generated by the reaction–separation process and cleaning wastes. A P-graph-based approach is used for identifying the root cause of process waste generation and generating broad design alternatives. Specific variable-level design solutions are then identified and evaluated using process simulation. The cleaning wastes resulting from the optimized process are also minimized using a source-sink allocation method that allows design of recycle network structure. A multi-objective stochastic optimization method is used to integrate the analysis so that the overall process economic and environmental footprint is optimized. We illustrate the proposed methodology using a well-known literature case study involving reaction, distillation and washing operation.     

SIMOP: Efficient reactive distillation optimization using stochastic optimizers

A methodology to improve the efficiency of stochastic methods applied to the optimization of chemical processes with a large number of equality constraints is presented. The methodology is based on two steps: (a) the optimization of the simulation step, which involves the optimum choice of design variables and subsystems to be simultaneously solved; (b) the optimization of the nonlinear programming (NLP) problem using stochastic methods. For the first step a flexible tool (SIMOP) is used, whereby different numerical procedures can be easily obtained, taking into account the problem formulation and specific characteristics, the need for specific initialization schemes and the efficient solution of systems of nonlinear equations. This methodology was applied to the optimization of a reactive distillation process for the production of ethylene glycol. Due to the complexity of the mathematical model, several different numerical procedures were generated, and their influence on the computational burden and on the reliability and accuracy of the optimization to reach the global optimum were studied. The results obtained suggest that in addition to the choice of design variables, the structure of subsystems associated to numerical procedures has a considerable impact on the performance of the optimizers.     

Uncertainty‐conscious methodology for process performance assessment in biopharmaceutical drug product manufacturing

This work presents an uncertainty‐conscious methodology for the assessment of process performance—for example, run time—in the manufacturing of biopharmaceutical drug products. The methodology is presented as an activity model using the type 0 integrated definition (IDEF0) functional modeling method, which systematically interconnects information, tools, and activities. In executing the methodology, a hybrid stochastic–deterministic model that can reflect operational uncertainty in the assessment result is developed using Monte Carlo simulation. This model is used in a stochastic global sensitivity analysis to identify tasks that had large impacts on process performance under the existing operational uncertainty. Other factors are considered, such as the feasibility of process modification based on Good Manufacturing Practice, and tasks to be improved is identified as the overall output. In a case study on cleaning and sterilization processes, suggestions were produced that could reduce the mean total run time of the processes by up to 40%. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1272–1284, 2018     

Design and assessment of delay timer alarm systems for nonlinear chemical processes

In process and manufacturing industries, alarm systems play a critical role in ensuring safe and efficient operations. The objective of a standard industrial alarm system is to detect undesirable deviations in process variables as soon as they occur. Fault detection and diagnosis systems often need to be alerted by an industrial alarm system; however, poorly designed alarms often lead to alarm flooding and other undesirable events. In this article, we consider the problem of industrial alarm design for processes represented by stochastic nonlinear time‐series models. The alarm design for such complex processes faces three important challenges: (1) industrial processes exhibit highly nonlinear behavior; (2) state variables are not precisely known (modeling error); and (3) process signals are not necessarily Gaussian, stationary or uncorrelated. In this article, a procedure for designing a delay timer alarm configuration is proposed for the process states. The proposed design is based on minimization of the rate of false and missed alarm rates—two common performance measures for alarm systems. To ensure the alarm design is robust to any non‐stationary process behavior, an expected‐case and a worst‐case alarm designs are proposed. Finally, the efficacy of the proposed alarm design is illustrated on a non‐stationary chemical reactor problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 77–90, 2018     

Probabilistic reactor design in the framework of elementary process functions

Computational process models in combination with innovative design methodologies provide a powerful reactor design platform. Yet, model-based design is mostly done in a pure deterministic way. Possible uncertainties of the underlying model parameters, prediction errors due to simplifying assumptions regarding the reactor behavior and suboptimal realizations of the design along the reaction coordinate are in general not considered. Here we propose a systematic design approach to directly account for the impact of such variabilities during the design procedure. The three level design approach of Peschel et al. (2010) based on the concept of elementary process functions (EPF) serves as basis. The dynamic optimizations on each level are extended within a probabilistic framework to account for different sources of randomness. The impact of these sources on the performance prediction of a design is quantified and used to robustify the reactor design aiming at a more reliable performance and thus design prediction. The uncertainties of model parameters, non-idealities of the reactor behavior and inaccuracies in the design are included via statistical moments. By means of the sigma point method (Julier and Uhlmann, 1996) random variables are mapped to the design objective space via the nonlinear process model. Importantly, this work introduces a full probabilistic orthogonal collocation approach, i.e. random and stochastic variables can be described. Whereas the former one relates to randomness independent on the reaction time (e.g. kinetic model parameters or initial conditions), the latter one describes stochasticity along the reaction time (e.g. fluctuating pressure or temperature control). As an example process the hydroformylation of 1-dodecene in a thermomorphic solvent system consisting of n-decane and N,N-dimethylformamide is considered.Our probabilistic EPF approach allows designing robust optimal reactors, which operate within an estimated confidence at their expected optimum considering almost any kind of randomness arising in the design procedure. An additional value is that with increased predictive power of the reactor performance its embedding in an overall process is strongly simplified.     

Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach

Uncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol’s sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.     

Analysis of Design Parameters in Anode‐Supported Solid Oxide Fuel Cells Using Response Surface Methodology

Achieving high performance from a solid oxide fuel cell (SOFC) requires optimal design based on parametric analysis. In this paper, design parameters, including anode support porosity, thicknesses of electrolyte, anode support, and cathode functional layers of a single, intermediate temperature, anode‐supported planar SOFC, are analyzed. The response surface methodology (RSM) technique based on an artificial neural network (ANN) model is used. The effects of the cell parameters on its performance are calculated to determine the significant design factors and interaction effects. The obtained optimum parameters are adopted to manufacture the single units of an SOFC through tape casting and screen‐printing processes. The cell is tested and its electrochemical characteristics, which show a satisfactory performance, are discussed. The measured maximum power density (MPD) of the fabricated SOFC displays a promising performance of 1.39 W cm^–2. The manufacturing process planned to fabricate the SOFC can be used for industrial production purposes.     

OPTIMAL DESIGN AND OPERATION OF BATCH PROCESSES

The economical design of continuous chemical processes to produce commodity products has reached an advanced state of development. Modern computer tools are used routinely to simulate and optimize these processes. This is not the case, however, for the manufacture of speciality products which must be made in batch operations. The continuing shift towards the production of higher value-added specialty products by the CPI has stimulated efforts aimed at developing good computer assisted design strategies for batch processes.

This paper discusses the formulation of the problem for the optimal design and operation of batch processes. The batch problem differs from the continuous one in a number of important ways. First, batch plants do not operate at steady state. There are important trade-offs between the processing time and the severity (intensity) of processing in single units. Cycle time and performance trade-offs also exist among the various units in the process. Second, batch plants produce multiple products in many cases. There is often a competition for shared resources (labor, utilities, and equipment) among the various products. This paper presents a hierarchical solution approach for the design and optimization of a batch process. The approach is demonstrated by solving an example problem which illustrates the fundamental economic trade-offs.     

Novel operability‐based approach for process design and intensification: Application to a membrane reactor for direct methane aromatization

This article introduces a novel operability‐based approach for process design and intensification of energy systems described by nonlinear models. This approach is applied to a membrane reactor (MR) for the direct methane aromatization (DMA) conversion to benzene and hydrogen. The proposed method broadens the scope of the traditional path of the operability approaches for design and control, mainly oriented to obtain the achievable output set (AOS) from the available input set, and compare the computed AOS to a desired output set. In particular, an optimization algorithm based on nonlinear programming tools is formulated for the calculation of the desired input set that is feasible considering process constraints and intensification targets. Results on the application of the operability method as a tool for process intensification show reduction of the DMA‐MR footprint (≈77% reactor volume and 80% membrane area reduction) for an equivalent level of performance, when compared to the base case. This case study indicates that the novel approach can be a powerful tool for process intensification of membrane reactors and other complex chemical processes. © 2016 American Institute of Chemical Engineers AIChE J, 63: 975–983, 2017     

Multiobjective supply chain design under uncertainty

In this article, the design and retrofit problem of a supply chain (SC) consisting of several production plants, warehouses and markets, and the associated distribution systems, is considered. The first problem formulation modifies and extends other previously presented models, in order to include several essential characteristics for realistically representing the consequences of design decisions on the SC performance. Then, in order to take into account the effects of the uncertainty in the production scenario, a two-stage stochastic model is constructed. The problem objective, i.e., SC performance, is assessed by taking into account not only the profit over the time horizon, but also the resulting demand satisfaction. This approach can be used to obtain different kinds of solutions, that may be valuable at different levels. On one hand, the SC configurations obtained by means of deterministic mathematical programming can be compared with those determined by different stochastic scenarios representing different approaches to face uncertainty. Additionally, this approach enables to consider and manage the financial risk associated to the different design options, resulting in a set of Pareto optimal solutions that can be used for decision-making.     

Use of CAPE-OPEN standards in the interoperability between modelling tools (MoT) and process simulators (Simulis Thermodynamics and ProSimPlus)

Computer-aided design, analysis and/or operation of chemical products and processes that manufacture them require a number of computational tools. As these tools may come from different sources and disciplines, an important issue is how they can be used simultaneously and efficiently for the design, analysis and/or simulation of a specific process-product? One alternative is to employ CAPE-OPEN standard interfaces for integration of the set of diverse computational tools that may be needed to solve the problem. The objective of this paper is to highlight, through examples, the integration of different computational tools according to problem specific work-flows/data-flows. The reliability of the integration of different tools is illustrated through two case studies. In case study 1, the tools Simulis^® Thermodynamics (PME) and ICAS-MoT (PMC) are combined for the calculation of thermodynamic properties through the use of a standard middleware (DLL file). In case study 2, the interoperability between ProSimPlus simulator (PME) and ICAS-MoT (PMC) is highlighted for simulation of a new unit operation and combined with other unit operations that can be found in the host simulator. A ProSimPlus-ICAS-MoT–COFE interoperability is also carried out successfully to proof the interoperability of the different computational entities. Furthermore, the introduction of the multiscale modelling concept and its application through the CAPE-OPEN standards is highlighted.     

Retrofit of complex and energy intensive processes--I

Thermodynamic methods of process synthesis are very useful for the design of complex and energy intensive processes, but they cannot be used simultaneously with material balances. Algorithmic methods are simultaneous, but they are difficult to solve for complex and energy intensive processes because the number of variables increases with the number of combinations. We can approach the optimal design for complex and energy intensive processes if we combine the two methods. The combined approach is composed of two steps, the thermodynamic and the algorithmic one. In the first one we eliminate unpromising structures and we include new, potentially good ones by studying an Extended Grand Composite Curve. In the second one we can optimize the superstructure obtained by using Mixed-Integer Nonlinear Programming. The combined approach can be used for optimal design of energy and material parameters of continuous processes as well as for energy recovery. In a retrofit case study we have targeted energy saving using rigorous models and fixed amount flow rates to find two promising structures, and then we have used parameter and simultaneous structural optimization to determine the best alternative and its parameters.     

设计余量对运行优化和化学过程控制性能的影响简

Operation optimization is an effective method to explore potential economic benefits for existing plants. The m.aximum potential benefit from operationoptimization is determined by the distances between current operating point and process constraints, which is related to the margins of design variables. Because of various ciisturbances in chemical processes, some distances must be reserved for fluctuations of process variables and the optimum operating point is not on some process constraints. Thus the benefit of steady-state optimization can not be fully achied（ed while that of dynamic optimization can be really achieved. In this study, the steady-state optimizationand dynamic optimization are used, and the potential benefit-is divided into achievable benefit for profit and unachievable benefit for control. The fluid catalytic cracking unit （FCCU） is used for case study. With the analysis on how the margins of design variables influence the economic benefit and control performance, the bottlenecks of process design are found and appropriate control structure can be selected.     

Deterministic vs. stochastic performance assessment of iterative learning control for batch processes

The performance assessment of linear time‐invariant batch processes when iterative learning control (ILC) is implemented has been discussed. Previous literatures show that conventional performance assessment cannot be directly applied to batch processes due to the nature of batch operations. Chen and Kong have suggested a new method to assess the control performance of batch processes using optimal ILC as the benchmark. In their work, ILC controllers are assumed to affect either stochastic or deterministic performance but without considering their interaction. This work elaborates the controllers effects on both stochastic and deterministic control performance of batch processes. It is shown that the optimal solution based on the minimum variance control law has a trade‐off between deterministic and stochastic performance, which can be shown by a trade‐off curve. Furthermore, a method is proposed to estimate this curve from routine operating data, against which the performance of ILC controllers can be assessed. Simulation studies are conducted to verify the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 457–464, 2013     

Capturing dynamics in integrated supply chain management

A major challenge for an enterprise to stay competitive in today’s highly competitive market environment is to be able of capturing and handling the dynamics of its entire supply chain (SC). This work incorporates uncertainty and process dynamics into enterprise wide models which also contemplate cross-functional decisions. The SC integrated solution developed includes a design–planning and a financial formulations. A model predictive control (MPC) methodology is proposed that comprises a stochastic optimization approach. A scenario based multi-stage stochastic mixed integer linear programming (MILP) model is employed to address the problem. The novel control framework introduced constitutes a step-forward in closing the loop for the dynamic supply chain management (SCM) and a supporting platform for the supervisory module handling the incidences that may arise in the SC. The potential of the presented approach is highlighted through a case study, where the results of the deterministic MPC and the joint control framework are compared. It is emphasized the significance of merging uncertainty treatment and control strategies to improve the SC performance.     

Industrial wastewater desalination using electrodialysis: evaluation and plant design

Industrial processes usually generate streams enriched with high organic and inorganic components. Due to the complexity of these streams sometimes it is not quite straightforward to predict the performance of desalination technologies. Some technologies are available for the selective removal of salts from aqueous stream, but in general these technologies are applied in high value applications where salts are either the product or limit further purification of the final product is required. These technologies are, however, not widely used in low value applications like wastewater treatment. The aim of this article is to review, improve and perform the design of electrodialysis processes for relevant industrial wastewater applications. It is focused on the determination of the critical design parameters like membrane resistance, current efficiency and limiting current density through lab scale experiments and its further use for industrial scale first approximation design. In this article, the basic equations for design are reviewed and a practical approach to obtain the number of stacks required for a certain separation is introduced. An industrial wastewater stream has been used for lab batch experiment and its following continuous plant design. The results show that it is possible to separate monovalent ions in a high rate (more than 70 %) and divalent ions were less separated (less than 50 %). The energy required for the particular case was evaluated in a range from 6 to 11 kWh/m³ of feed stream depending on the water reclamation rate.     

Lactic acid production by electrodialysis Part II: Modelling

One interesting alternative to the usual end-of-pipe processes for treating waste water produced during cheese-making involves its fermentation to sodium lactate. Then, electrodialysis can be used to recover free lactic acid from the fermentation broth. The design and optimization of such a process is aided by a suitable mathematical model. This work presents a model of the performance of an electrodialysis stack to be used in such a process. Its reliability has been assessed by comparison with experimental data for free lactic acid recovery from sodium lactate solutions. A suitable procedure for estimating some process-dependent parameters is also discussed.     

Efficient integration of optimal solvent and process design using molecular clustering

We present a molecular clustering approach for the efficient incorporation of solvent design information into process synthesis in the integrated design of solvent/process systems. The approach is to be used in conjunction with an integrated solvent/process design approach where the solvent design stage utilises multi-objective optimisation in order to identify Pareto optimal solvent candidates that are subsequently evaluated in a process synthesis stage. We propose to introduce the solvent design information into the process synthesis stage through the use of molecular clusters. The partitioning of the original Pareto optimal set of solvents leads to smaller compact groups of similar solvent molecules from which representative molecules are introduced into the process synthesis model as discrete options to determine the optimal process performance associated with the optimal solvent. We investigate two clustering strategies, serial and parallel clustering, that allow to effectively exploit the solvent-process design interactions to minimise the computational demands of the process synthesis stage. We further propose a clustering heuristic probability that can aid decision making in clustering and can significantly accelerate the search for the best integrated solvent-process systems. The presented method is illustrated with case studies in the design of solvents for liquid-liquid extraction, gas-absorption and extractive distillation systems.