Mathematical model of supercritical extraction applied to oil seed extraction by CO2+saturated alcohol — I. Desorption model

Supercritical fluid extraction of solutes from solid matrix is represented by the extraction curve, where cumulated extracted oil is plotted versus time. Experimental data obtained in laboratory scale and pilot plant is adjusted with different extraction models; in order to predict extraction curves for full-scale extractors. Sometimes, a shortcut method is useful to adjust experimental data; these correlations are typical in most of engineering processes. In this paper, three shortcut methods are reviewed. First, a model based on flux models considering residence time distribution curves for serially interconnected perfectly mixed tanks and plug flow in series or in parallel with them. It could be used to analyze extractor behavior taking into account bed distribution (preferential ways, dispersion). Second, fast adjusting or ‘t^n’ model considers a differential mass balance where mass transfer coefficient is an ‘nth^’ potential function of time; analytical solution gives an explicit equation. Third, it is presented a linear shortcut method by intervals based on Sovovà model; it predicts considering four extraction periods: delay, rapid extraction, slow extraction and depletion; delay time and solubility are evaluated using the ‘t^n’ model. This model gives a process transfer function (Laplace domain). Supercritical fluid extraction of sunflower seed oil with carbon dioxide was performed in a pilot plant at 30.0 MPa and 40°C, using different amounts of methanol, ethanol, butanol and hexanol as cosolvents. Experimental data are fitted with proposed shortcut methods. Fitting error is less than 5% except in linear shortcut method by intervals which is higher.     

On minimal models of process systems

Minimal representations are known to have no redundant elements, and are therefore of great importance. Based on the notions of performance and size indices and measures for process systems, the paper proposes conditions for a process model being minimal in a set of functionally equivalent models with respect to a size norm.Generalized versions of known procedures to obtain minimal process models for a given modelling goal, model reduction based on sensitivity analysis and incremental model building are proposed and discussed.The notions and procedures are illustrated and compared on a simple example, that of a simple nonlinear fermentation process with different modelling goals and on a case study of a heat exchanger modelling.     

Oxidative Stress Evaluation in Ischemia Reperfusion Models: Characteristics,Limits and Perspectives

Ischemia reperfusion injury is a complex process consisting of a seemingly chaotic but actually organized and compartmentalized shutdown of cell function, of which oxidative stress is a key component. Studying oxidative stress, which results in an imbalance between reactive oxygen species (ROS) production and antioxidant defense activity, is a multi-faceted issue, particularly considering the double function of ROS, assuming roles as physiological intracellular signals and as mediators of cellular component damage. Herein, we propose a comprehensive overview of the tools available to explore oxidative stress, particularly in the study of ischemia reperfusion. Applying chemistry as well as biology, we present the different models currently developed to study oxidative stress, spanning the vitro and the silico, discussing the advantages and the drawbacks of each set-up, including the issues relating to the use of in vitro hypoxia as a surrogate for ischemia. Having identified the limitations of historical models, we shall study new paradigms, including the use of stem cell-derived organoids, as a bridge between the in vitro and the in vivo comprising 3D intercellular interactions in vivo and versatile pathway investigations in vitro. We shall conclude this review by distancing ourselves from “wet” biology and reviewing the in silico, computer-based, mathematical modeling, and numerical simulation options: (a) molecular modeling with quantum chemistry and molecular dynamic algorithms, which facilitates the study of molecule-to-molecule interactions, and the integration of a compound in a dynamic environment (the plasma membrane...); (b) integrative systemic models, which can include many facets of complex mechanisms such as oxidative stress or ischemia reperfusion and help to formulate integrated predictions and to enhance understanding of dynamic interaction between pathways.     

An effective voidage model for sedimentation of bidisperse solid suspension

An effective voidage model of a liquid-fluidized bed that takes into account particle–particle interaction has been used to predict the slip and interface velocities of sedimenting zones for bidisperse solid–liquid systems. The model visualizes that a ‘test particle’ in the bed is surrounded by particles of ‘average size’ but enjoys an effective voidage different from the average voidage. The model was successfully used before to interpret and predict phase inversion as well as mixing and segregation in a liquid-fluidized bed. A little modification of the original model was done to make it suitable for interpreting batch sedimentation data. The model does not necessarily need the experimental values of the relevant parameters. Predictions of the model over a range of particle sizes and liquid properties are more accurate than those of the previous models.     

Agent-based supply chain management—2: a refinery application

The refinery business involves tasks that span several departments and process large amount of data. Among others, these include crude procurement, logistics and scheduling (storage, distillation units, etc.). Current refinery decision support systems (DSSs) fail to integrate all the decision-making processes of a refinery, to interface with other systems in place, to incorporate dynamic data from various sources and to assist different departments concurrently. In part 1 of this two-part paper, we proposed an agent-based framework for supply chain DSSs. Here, we demonstrate its application through a prototype DSS, called petroleum refinery integrated supply chain modeler and simulator or PRISMS, for crude procurement. PRISMS serves as a central DSS through which all processes of a refinery can be studied and enables integrated decisions with respect to the overall refinery business. In particular, PRISMS can be used to study the effects of internal policies of the refinery and its various departments. We illustrate this through three detailed ‘what-if’ studies that provide an insight into how the business responds to changes in policies, exogenous events and plant modifications.     

A chemical engineer's perspective on health and disease

Chemical process systems engineering considers complex supply chains which are coupled networks of dynamically interacting systems. The quest to optimize the supply chain while meeting robustness and flexibility constraints in the face of ever changing environments necessitated the development of theoretical and computational tools for the analysis, synthesis and design of such complex engineered architectures. However, it was realized early on that optimality is a complex characteristic required to achieve proper balance between multiple, often competing, and objectives. As we begin to unravel life's intricate complexities, we realize that that living systems share similar structural and dynamic characteristics; hence much can be learned about biological complexity from engineered systems. In this article, we draw analogies between concepts in process systems engineering and conceptual models of health and disease; establish connections between these concepts and physiologic modelling; and describe how these mirror onto the physiological counterparts of engineered systems.     

The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure

In a global economy, the key to success is providing products around the world at the right time in the right quantity and quality, at a low cost. Efficient supply chains have an important role in guaranteeing this success. Optimized planning of such structures is required and uncertainties regarding product demands and prices, amongst other supply chain conditions, should also be considered. In this paper, we look into supply chain planning decisions that account for uncertainty on product portfolios demand and prices. A multi-period planning model is developed where the supply chain operational decisions on supply, production, transportation, and distribution at the actual period consider the uncertainty on products’ demand and prices. Different decision scenarios, involving the evaluation of the supply chain economical performance, are analyzed (e.g. global operating costs/profit realized) for different criteria on the importance of the partners within the global chain (i.e. partners’ structure). A Mixed Integer Linear Programming (MILP) formulation is formulated for each planning scenario and the optimal solution is reached using a standard Branch and Bound (B&B) procedure. The final results provide details on the supply chain partners production, transportation and inventory, at each planning period, while accounting for the importance of each partner in the global chain as well as demand/price uncertainties. The applicability of the developed formulation is illustrated through the solution of a real case-study involving an industrial chain in the pharmaceutical sector.     

Data-driven distributionally robust optimization of shale gas supply chains under uncertainty

This article aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two-stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first-stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second-stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data-driven approach is applied to construct the ambiguity set based on principal component analysis and first-order deviation functions. By taking advantage of affine decision rules, a tractable mixed-integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a small-scale illustrative example and a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models, including the deterministic and stochastic programming counterparts, are investigated as well. © 2018 American Institute of Chemical Engineers AIChE J, 65: 947–963, 2019     

Semi-supervised dynamic latent variable modeling: I/O probabilistic slow feature analysis approach

Modeling of high dimensional dynamic data is a challenging task. The high dimensionality problem in process data is usually accounted for using latent variable models. Probabilistic slow feature analysis (PSFA) is an example of such an approach that accounts for high dimensionality while simultaneously capturing the process dynamics. However, PSFA also suffers from a drawback that it cannot use output information when determining the latent slow features. To address this lacunae, extension of the PSFA by incorporating outputs, resulting in Input-Output PSFA (IOPSFA) is proposed. IOPSFA can use both input and output information for extracting latent variables. Hence, inferential models based on IOPSFA are expected to have better predictive ability. The efficacy of the proposed approach with an industrial and a laboratory scale soft sensing case studies that have both complete and incomplete output measurements is evaluated, respectively. © 2018 American Institute of Chemical Engineers AIChE J, 65: 964–979, 2019     

Approximate dynamic programming based approach to process control and scheduling

Multi-stage decision problems under uncertainty are abundant in process industries. Markov decision process (MDP) is a general mathematical formulation of such problems. Whereas stochastic programming and dynamic programming are the standard methods to solve MDPs, their unwieldy computational requirements limit their usefulness in real applications. Approximate dynamic programming (ADP) combines simulation and function approximation to alleviate the ‘curse-of-dimensionality’ associated with the traditional dynamic programming approach. In this paper, we present the ADP as a viable way to solve MDPs for process control and scheduling problems. We bring forth some key issues for its successful application in these types of problems, including the choice of function approximator and the use of a penalty function to guard against over-extending the value function approximation in the value iteration. Application studies involving a number of well-known control and scheduling problems, including dual control, multiple controller scheduling, and resource constrained project scheduling problems, point to the promising potentials of ADP.     

A Reptation-Based Lattice Model with Tube-Chain Coupling for the Linear Dynamics of Bidisperse Entangled Linear Polymer

A reptation-based lattice model for simulating the linear dynamics of entangled linear polymers that accounts for an essential coupling in tube-chain motions during constraint release is proposed. The predictions are tested against a representative set of dynamic oscillatory data on bidisperse polybudadiene (PBd) melts. The special feature of the current model lies in that the motion of the primitive chain coincides exactly with that of the ‘tube,’ so that it is possible to mimic the longitudinal relaxation that is cooperative with the lateral one (i.e., double reptation) during constraint release. The simulation is shown to capture the central feature of constraint release for the investigated system without demanding factorizability for the stress relaxation function, as usually enforced in existing tube theories. Furthermore, the simulation suggests that the longitudinal chain relaxation currently incorporated might account for an important partition of stress relaxation that had customarily been attributed to the effect of double reptation or similar tube motions alone.     

Resilient supply chain design and operations with decision-dependent uncertainty using a data-driven robust optimization approach

To addresses the design and operations of resilient supply chains under uncertain disruptions, a general framework is proposed for resilient supply chain optimization, including a quantitative measure of resilience and a holistic biobjective two-stage adaptive robust fractional programming model with decision-dependent uncertainty set for simultaneously optimizing both the economic objective and the resilience objective of supply chains. The decision-dependent uncertainty set ensures that the uncertain parameters (e.g., the remaining production capacities of facilities after disruptions) are dependent on first-stage decisions, including facility location decisions and production capacity decisions. A data-driven method is used to construct the uncertainty set to fully extract information from historical data. Moreover, the proposed model takes the time delay between disruptions and recovery into consideration. To tackle the computational challenge of solving the resulting multilevel optimization problem, two solution strategies are proposed. The applicability of the proposed approach is illustrated through applications on a location-transportation problem and on a spatially-explicit biofuel supply chain optimization problem. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1006–1021, 2019     

Structural solvability analysis of dynamic process models

The variable structure of dynamic process models is represented by a directed graph termed as the representation graph for the purpose of solvability analysis in this paper. Structural solvability analysis, the determination of the structural differential index and the structural decomposition of the differential–algebraic equations (DAE) model set can be performed using the representation graph. The characteristic features of the representation graph for both index 1 and high index semi-explicit DAE models are presented. Based on the above a novel index reduction procedure for high index models is proposed. The notions and methods are illustrated on simple process examples.     

Decision support for integrated refinery supply chains: Part 1. Dynamic simulation

Supply chain studies are increasingly given top priority in enterprise-wide management. Present-day supply chains involve numerous, heterogeneous, geographically distributed entities with varying dynamics, uncertainties, and complexity. The performance of a supply chain relies on the quality of a multitude of design and operational decisions made by the various entities. In this two-part paper, we demonstrate that a dynamic model of an integrated supply chain can serve as a valuable quantitative tool that aids in such decision-making. In this Part 1, we present a dynamic model of an integrated refinery supply chain. The model explicitly considers the various supply chain activities such as crude oil supply and transportation, along with intra-refinery supply chain activities such as procurement planning, scheduling, and operations management. Discrete supply chain activities are integrated along with continuous production through bridging procurement, production, and demand management activities. Stochastic variations in transportation, yields, prices, and operational problems are considered in the proposed model. The economics of the refinery supply chain includes consideration of different crude slates, product prices, operation costs, transportation, etc. The proposed model has been implemented as a dynamic simulator, called Integrated Refinery In-Silico (IRIS). IRIS allows the user the flexibility to modify not only parameters, but also replace different policies and decision-making algorithms in a plug-and-play manner. It thus allows the user to simulate and analyze different policies, configurations, uncertainties, etc., through an easy-to-use graphical interface. The capabilities of IRIS for strategic and tactical decision support are illustrated using several case studies.     

Hybrid modelling of yeast production processes – combination of a priori knowledge on different levels of sophistication

Process models are used to formulate knowledge about process behaviour. They are applied, e.g., to predict the process' future behaviour and for state estimation when reliable on-line measuring techniques to monitor the key variables of the process are not available. There are different sources of information available for modelling, which provide process knowledge in different representations. Some elements or aspects may be described by physically based mathematical models and others by heuristically obtained rules of thumb, while some information may still be hidden in the process data recorded during previous runs of the process. Heuristic rules are conveniently processed with fuzzy expert systems, while artificial neural networks present themselves as a powerful tool for uncovering the information within the process data without the need to transform the information into one of the other representations. Artificial neural networks and fuzzy technology are increasingly being employed for modelling biotechnological processes, thus extending the traditional way of process modelling by mathematical equations. However, a sufficiently comprehensive combination of all these techniques has not yet been put forward. Here, we present a simple way of combining all the available knowledge relating to a given process. In a case study, we demonstrate the development of a hybrid model for state estimation and prediction on the example of a yeast production process. The model was validated during a cultivation performed in a standard pilot-scale fermenter.     

Sustainable supply chain network design for the optimal utilization of municipal solid waste

The growing waste generation, increasing environmental regulations, and limited land area for waste disposal necessitate an effective and efficient waste supply chain management solution in terms of both socioeconomic perspectives and environmental sustainability. Waste management is connected to supply chain decisions as it involves waste generation, collection, separation, transportation, processing, and disposal. Accordingly, this article develops a mixed integer linear programming model for the optimal planning of a waste management system in a multi-echelon supply chain network, which aims to find a trade-off between supply chain costs, depletion of waste, and efficient use of generated waste while considering the environmental impacts. Various recycling and waste-to-energy technologies are used to convert plastic and mixed waste into value-added products including fuel, electricity, and heat. Although recycling is preferable from an environmental point of view, it is shown that the waste-to-energy option is more economically efficient. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16464 2019     

A model predictive control strategy for supply chain optimization

This paper describes a model predictive control strategy to find the optimal decision variables to maximize profit in supply chains with multiproduct, multiechelon distribution networks with multiproduct batch plants. The key features of this paper are: (1) a discrete time MILP dynamic model that considers the flow of material and information within the system; (2) a general dynamic optimization framework that simultaneously considers all the elements of the supply chain and their interactions; and (3), a rolling horizon approach to update the decision variables whenever changes affecting the supply chain arise. The paper compares the behavior of a supply chain under centralized and decentralized management approaches, and shows that the former yields better results, with profit increases of up to 15% as shown in an example problem.     

Inventory policies and safety stock optimization for supply chain planning

In this article, traditional supply chain planning models are extended to simultaneously optimize inventory policies. The inventory policies considered are the (r,Q) and (s,S) policies. In the (r,Q) inventory policy an order for Q units is placed every time the inventory level reaches level r, while in the s,S policy the inventory is reviewed in predefined intervals. If the inventory is found to be below level s, an order is placed to bring the level back to level S. Additionally, to address demand uncertainty four safety stock formulations are presented: (1) proportional to throughput, (2) proportional to throughput with risk-pooling effect, (3) explicit risk-pooling, and (4) guaranteed service time. The models proposed allow simultaneous optimization of safety stock, reserve, and base stock levels in tandem with material flows in supply chain planning. The formulations are evaluated using simulation. © 2018 American Institute of Chemical Engineers AIChE J, 65: 99–112, 2019     

Capture and rebound of dust in granular bed gas filters

Experimental data for the efficiency of filtration of gases by fixed beds of granular solids are used to evaluate the reliability of the ‘cell’ and ‘constricted tube’ models for gas flow and aerosol transport. The dominant capture mechanisms are Brownian diffusion and inertial deposition. For Brownian diffusion, both models give sensible estimates for capture efficiency, but this process is shown to be insensitive to the model assumptions. Inertial deposition provides a much more sensitive test, and it is shown that neither model gives satisfactory predictions for the efficiency of inertial capture. Whether a dust particle adheres or rebounds on contacting a filter granule depends on the relative importance of kinetic and adhesion energies. An approach is proposed which enables the theoretical analyses to be applied to predict the limits of adhesion.     

Extracting dynamic features with switching models for process data analytics and application in soft sensing

In recent decades, soft sensors have been profoundly studied and successfully applied to predict critical process variables in real‐time. While dealing with various application scenarios, data‐driven methods with representation learning possess great potentials. Latent features are formulated in these approaches to predict outputs from correlated input variables. In this study, a probabilistic framework of feature extraction is proposed in the context of process data analysis. To address switching behaviors in industrial processes, multiple emission models are utilized to construct latent space. To address temporal correlations from continuously operating processes, a dynamic model is implemented in latent space. Bayesian learning strategy is then developed for parameters estimation, where modeling preferences and uncertainties from multiple models are considered. The effectiveness and practicability of the proposed feature extraction algorithm are illustrated through numerical simulations, as well as an industrial case study. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2037–2051, 2018