Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while maint... [more]

Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The... [more]

In this paper, a hybrid heuristic rule-based and deterministic optimization-driven process decision framework is presented for the analysis and optimization of process flowsheets for end-to-end optimal (E2E0) pharmaceutical manufacturing. The framework accommodates various operating modes, such as batch, semi-batch and continuous, for the different unit operations that implement each manufacturing step. To address the challenges associated with solving process synthesis problems using a simulation-optimization approach, heuristic-based process synthesis rules are employed to facilitate the reduction of the superstructure into smaller sub-structures that can be more readily optimized. The practical application of the framework is demonstrated through a case study involving the end-to-end continuous manufacturing of an anti-cancer drug, lomustine. Alternative flowsheet structures are evaluated in terms of the sustainability metric, E-factor while ensuring compliance with the required pro... [more]

Explicitly incorporating the effects of chemical phenomena such as chemical pretreatment and mineral scaling during the design of treatment systems is critical; however, the complexity of these phenomena and limitations on data have historically hindered the incorporation of detailed water chemistry into the modeling and optimization of water desalination systems. Thus, while qualitative assessments and experimental studies on chemical pretreatment and scaling are abundant in the literature, very little has been done to assess the technoeconomic implications of different chemical pretreatment alternatives within the context of end-to-end water treatment train optimization. In this work, we begin to address this challenge by exploring the impact of pH control during pretreatment on the cost and operation of a high-recovery desalination train. We compare three pH control methods used in water treatment (H2SO4, HCl, and CO2) and assess their impact on the operation of a desalination plant... [more]

This paper proposes an AI-assisted approach aimed at accelerating chemical process design through causal incremental reinforcement learning (CIRL) where an intelligent agent is interacting iteratively with a process simulation environment (e.g., Aspen HYSYS, DWSIM, etc.). The proposed approach is based on an incremental learnable optimizer capable of guiding multi-objective optimization towards optimal design variable configurations, depending on several factors including the problem complexity, selected RL algorithm and hyperparameters tuning. One advantage of this approach is that the agent-simulator interaction significantly reduces the vast search space of design variables, leading to an accelerated and optimized design process. This is a generic causal approach that enables the exploration of new process configurations and provides actionable insights to designers to improve not only the process design but also the design process across various applications. The approach was valid... [more]

Design problems for process systems engineering applications often require multi-scale modeling integrating detailed process models. Consequently, black-box optimization and surrogate modeling have continued to play a fundamental role in mission-critical design applications. Inherent in surrogate modeling applications, particularly those constrained by “expensive” function evaluations, are the questions of how to properly balance “exploration” and “exploitation” and how to do so while harnessing parallel computing in techniques. We devise and investigate a one-step look-ahead GRASP heuristic for balancing exploration and exploitation in a parallel environment. Computational results reveal that our approach can yield equivalent or superior surrogate quality with near linear scaling in the number of parallel samples.

Chemical recycling of plastics is a promising technology to reduce carbon footprint and ease the pressure of waste treatment. Specifically, highly efficient conversion technologies for polyolefins will be the most effective solution to address the plastic waste crisis, given that polyolefins are the primary contributors to global plastic production. Significant challenges encountered by plastic waste valorization facilities include the uncertainty in the composition of the waste feedstock, process yield, and product price. These variabilities can lead to compromised performance or even render operations infeasible. To address these challenges, this work applied the robust optimization-based framework to design an integrated polyolefin chemical recycling plant. Data-driven surrogate model was built to capture the separation units’ behavior and reduce the computational complexity of the optimization problem. It was found that when process yield and price uncertainties were considered, wa... [more]

Solvent-based carbon capture processes typically suffer from the temperature rise of the solvent due to the heat of absorption of CO2. This increased temperature is not thermodynamically favorable and results in a significant reduction in performance in the absorber column. As opposed to interstage coolers, which only remove, cool, and return the solvent at discrete locations in the column, internal coolers that are integrated with the packing can cool the process inline, which can result in improved efficiency. This work presents the modeling of these internal coolers within an existing generic, equation-oriented absorber column model that can cool the process while allowing for simultaneous mass transfer. Optimization of this model is also performed, which is capable of optimally choosing the best locations to place these devices, such that heat removal and mass transfer area are balanced. Results of the optimization have shown that optimally placed cooling elements result in a signi... [more]

Cyclic adsorption processes attain a cyclic-steady state (CSS) condition by undergoing repeated cycles in time, owing to their transient and modular nature. Mathematically, solving a set of underlying nonlinear partial differential equations iteratively for different steps in a cycle until the CSS condition is attained presents a computational challenge, making the simulation and optimization of cyclic adsorption processes time-consuming. This paper focuses on expediting the CSS convergence in adsorption process simulations by implementing two vector-based acceleration methods that offer quadratic convergence akin to Newton’s methods. These methods are straightforward to implement, requiring no prior knowledge of the first derivatives (or Jacobian). The study demonstrates the efficacy of accelerated convergence by considering two adsorption processes that exhibit complex dynamics, namely, a four-step vacuum swing adsorption and a six-step temperature swing adsorption cycles for post-co... [more]

Developing methods for rapid, large-scale deployment of carbon capture systems is critical for meeting climate change goals. Optimization-based decisions can be employed at the design and manufacturing phases to minimize the costs of deployment and operation. Manufacturing standardization results in significant cost savings due to economies of numbers. Building on previous work, we present a process family design approach to design a set of carbon capture systems while explicitly including economies of numbers savings within the formulation. Our formulation optimizes both the number and characteristics of the common components in the platform and simultaneously designs the resulting set of carbon capture systems. Savings from economies of numbers are explicitly included in the formulation to determine the number of components in the platform. We show and discuss the savings we gain from economies of numbers.

In this work, we present recent algorithmic and implementation advances of the nonconvex two-stage robust optimization solver PyROS. Our advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the formulations and/or initializations of the various subproblems used by the underlying cutting set algorithm, and extensions to the pre-implemented uncertainty set interfaces. The effectiveness of PyROS is demonstrated through the results of an original benchmarking study on a library of over 8,500 small-scale instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. To demonstrate the utility of PyROS for large-scale process models, we present the results of a carbon capture case study. Overall, our results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

The determination of the design space (DS) in a pharmaceutical process is a crucial aspect of the quality-by-design (QbD) initiative which promotes quality built into the desired product. This is achieved through a deep understanding of how the critical quality attributes (CQAs) and process parameters (CPPs) interact that have been demonstrated to provide quality assurance. For computational inexpensive models, the original process model can be directly deployed to identify the design space. One such crucial process is the Tablet Press (TP), which directly compresses the powder blend into individual units of the final product or adds dry or wet granulation to meet specific formulation needs. In this work, we identify the design space of input variables in a TP such that there is a (probabilistic) guarantee that the tablets meet the quality constraints under a set of operating conditions. A reduced-order model of TP is assigned for this purpose where the effects of lubricants and glidan... [more]

Within an Industry 4.0 framework, a variety of new considerations are of increasing importance, such as securing processes against cyberattacks on the control systems or utilizing advances in image processing for image-based control. These new technologies impact relationships between process design and control. In this work, we discuss some of these potential relationships, beginning with a discussion of side channel attacks and what they suggest about ways of evaluating plant design and instrumentation selection, along with controller and security schemes, particularly as more data is collected and there is a move toward an industrial Internet of Things. Next, we highlight how the 3D computer graphics software tool set Blender can be utilized to analyze a variety of considerations related to ensuring safety of plant operation and facilitating the design of assemblies with image-based sensing.

Superstructure optimization for process synthesis is a challenging endeavour typically leading to large scale MINLP formulations. By the combination of phenomena-based building blocks, accurate thermodynamics, and structural screening we obtain a new framework for optimal process synthesis, which overcomes prior limitations regarding solution by deterministic MINLP solvers in combination with accurate thermodynamics. This is facilitated by MOSAICmodeling’s generic formulation of models in MathML / XML and subsequent decomposition and code export to GAMS and C++. A branch & bound algorithm is implemented to solve the overall MINLP problem, wherein the structural screening penalizes instances, which are deemed nonsensical and should not be further pursued. The general capabilities of this approach are shown for the distillation-based separation of a ternary system.

Adsorption-based Atmospheric Water Extraction (AWE) is an energy-efficient distributed freshwater supply method. This research focuses on AWE's kinetic analysis and stochastic optimization, investigating the impact of ambient conditions, kinetics, and weather variability. A one-dimensional fixed-bed system was numerically analyzed using the validated isotherm of MIL-100 (Fe), assuming different kinetic parameters within the linear driving force model. Stochastic optimization, based on annual weather data from Georgia (GA), illustrates the influence of weather conditions on AWE process performance, operation, and cost. Our study offers valuable insights for future research, including site selection, adsorbent material development, and process design. We outline three critical areas for further exploration: experimental verification, material screening, and meteorological site selection.

Early stage exploration of reaction systems, including catalyst selection, operating conditions’ specifications, reactor design, and optimization, is critical in the engineering field. It is general practice in the reaction engineering field to explore systems against certain performance metrics, of which yield is one of the most commonly utilized objectives. While the yield provides a quantitative measure of how efficiently reactants are converted into target product(s), its definition is ambiguous, particularly in the presence of side/ incomplete reactions, and multiple products. Most of the yield definitions focus on a specific target product; however, conditions within the reactor search space that provide a maximum yield for one product may not be the same as those for another. Moreover, the presence of other undesired products that are not considered may reduce the overall efficiency of the system. This necessitates the utilization of a more holistic metric that encompasses the v... [more]

Although global efforts for CO2 capture are underway, large-scale CO2 capture projects still face economic risks and technical challenges. The Rotating Packed Bed (RPB) provides an alternative solution by mitigating location constraints and enabling a gradual increase in the scale of CO2 capture through compact modular sizes. However, the main challenge in RPB-based CO2 capture processes lies in the limited experience with implementing industrial-scale RPB processes. The intricate relationship between RPB unit design, operating conditions, and process performance further complicates the process-level analysis for scale-up. To address these challenges, we propose an optimization-based process design for RPB-based CO2 capture. Leveraging rigorous process modeling and simulation, we aim to make simultaneous decisions on RPB unit design and operating conditions. Ultimately, our goal is to develop a cost-effective and optimal RPB-based CO2 capture process, supported by comprehensive cost ev... [more]

Optimization-based process design is a central task of process systems engineering. However, solely relying on steady-state models may potentially lead to dynamic constraint violations, hinder robust performance, or simply reduce the controllability of a process. This has led to the consideration of process dynamics in the design phase, which is commonly termed integration of design and operation / control. Recently, we proposed a framework to carry out this integrative task by formulating a large-scale nonlinear programming problem that is solved simultaneously. To this end, the dynamic process model was discretized, and dynamic variability and parametric uncertainty were included. However, the proposed framework only operates on constant lengths of the finite elements. The discretization error was not assessed. Within this contribution, a method for quantifying this discretization error and adapting the number of finite elements accordingly is incorporated into the recently proposed... [more]

We present new modifications to superstructure optimization paradigms to i) enable their robust solution and ii) extend their applicability. Superstructure optimization of chemical process flowsheets on the basis of rigorous and detailed models of the various unit operations, such as in the state operator network (SON) paradigm, is prone to non-convergence. A key challenge in this optimization-based approach is that when process units are deselected from a superstructure flowsheet, the constraints that represent the deselected process unit can be numerically singular (e.g., divide by zero, logarithm of zero and rank-deficient Jacobian). In this paper, we build upon the recently-proposed modified state operator network (MSON) that systematically eliminates singularities due to unit deselection and is equally applicable to the context of both simulation-based and equation-oriented optimization. A key drawback of the MSON is that it is only applicable to the design of isobaric flowsheets... [more]

Maintaining product integrity in multi-product oil pipelines is crucial for efficiency and profit. This study presents a strategy combining design and process improvement to enhance flushing protocols, addressing the challenge of residual batch contamination. A pilot plant, mirroring industrial operations through dimensionless residence time distribution, was developed to identify and rectify bottlenecks during product transition. The pilot plant’s success in replicating industrial operations paves the way for targeted experiments and modelling to enhance optimized flushing, ensuring product quality and operational excellence.

Rapid and robust convergence of a process flowsheet is critical to enable large-scale simulations that address core scientific questions related to process design, optimization, and sustainability. However, due to the highly coupled and nonlinear nature of chemical processes, efficiently solving a flowsheet remains a challenge. In this work, we show that graph representations of the underlying physical phenomena in unit operations may help identify potential avenues to systematically reformulate the network of equations and enable more robust topology-based convergence of flowsheets. To this end, we developed graph abstractions of the governing equations of vapor-liquid and liquid-liquid equilibrium separation equipment. These graph abstractions consist of a mesh of interconnected variable nodes and equation nodes that are systematically generated through PhenomeNode, a new open-source library in Python developed in this study. We show that partitioning the graph into separate mass, en... [more]

Phthalates are the most widely used plasticizers in the polymers industry; however, their toxicity and environmental impacts have led to their ban in various applications. This has driven the search for more sustainable alternatives, including biobased citrate esters, especially tributyl citrate (TBC) and its acetylated form. TBC is typically produced by refined citric acid (CA) esterification with 1-butanol (BuOH). However, the high energy and materials-intensive downstream purification of fermentation-derived CA involves high production costs, thus limiting the widespread adoption of TBC as a plasticizer. This work presents an innovative approach for TBC production using calcium citrate as feedstock instead of pure CA. The process involves a simultaneous acidification-esterification stage and further hydration of calcium sulfate, thus reducing costs by avoiding multiple CA refining steps. The approach proceeds via a solid-solid-liquid reaction of calcium citrate with sulfuric acid in... [more]

Alternative formulations for the optimization of chemical process flowsheets are presented that leverage surrogate models and implicit functions to replace and remove, respectively, the algebraic equations that describe a difficult-to-converge Gibbs reactor unit operation. Convergence reliability, solve time, and solution quality of an optimization problem are compared among full-space, ALAMO surrogate, neural network surrogate, and implicit function formulations. Both surrogate and implicit formulations lead to better convergence reliability, with low sensitivity to process parameters. The surrogate formulations are faster at the cost of minor solution error, while the implicit formulation provides exact solutions with similar solve time. In a parameter sweep on the autothermal reformer flowsheet optimization problem, the full-space formulation solves 33 out of 64 instances, while the implicit function formulation solves 52 out of 64 instances, the ALAMO polynomial formulation solves... [more]

Process simulation problems often involve systems of nonlinear and nonconvex equations and may run into convergence issues due to the existence of recycle loops within such models. To that end, surrogate models have gained significant attention as an alternative to high-fidelity models as they significantly reduce the computational burden. However, these models do not always provide a guarantee on the prediction accuracy over the domain of interest. To address this issue, we strike a balance between computational complexity by developing a data-driven branch and prune-based framework that progressively leads to a guaranteed solution to the original system of equations. Specifically, we utilize interval arithmetic techniques to exploit Hessian information about the model of interest. Along with checking whether a solution can exist in the domain under consideration, we generate error-bounded convex hull surrogates using the sampled data and Hessian information. When integrated in a bran... [more]

This paper presents an algorithm for developing sparse surrogate models that satisfy mass/energy conservation even when the training data are noisy and violate the conservation laws. In the first step, we employ the Bayesian Identification of Dynamic Sparse Algebraic Model (BIDSAM) algorithm proposed in our previous work to obtain a set of hierarchically ranked sparse models which approximate system behaviors with linear combinations of a set of well-defined basis functions. Although the model building algorithm was shown to be robust to noisy data, conservation laws may not be satisfied by the surrogate models. In this work we propose an algorithm that augments a data reconciliation step with the BIDSAM model for satisfaction of conservation laws. This method relies only on known boundary conditions and hence is generic for any chemical system. Two case studies are considered-one focused on mass conservation and another on energy conservation. Results show that models with minimum bia... [more]