Compartmental Modelling in chemical engineering: A critical review

A full-scale operational digital twin for a water resource recovery facility-A case study of Eindhoven Water Resource Recovery Facility

Digital transformation for the water sector has gained momentum in recent years, and many water resource recovery facilities modelers have already started transitioning from developing traditional models to digital twin (DT) applications. DTs simulate the operation of treatment plants in near real time and provide a powerful tool to the operators and process engineers for real-time scenario analysis and calamity mitigation, online process optimization, predictive maintenance, model-based control, and so forth. So far, only a few mature examples of full-scale DT implementations can be found in the literature, which only address some of the key requirements of a DT. This paper presents the development of a full-scale operational DT for the Eindhoven water resource recovery facility in The Netherlands, which includes a fully automated data-pipeline combined with a detailed mechanistic full-plant process model and a user interface co-created with the plant's operators. The automated data preprocessing pipeline provides continuous access to validated data, an influent generator provides dynamic predictions of influent composition data and allows forecasting 48 h into the future, and an advanced compartmental model of the aeration and anoxic bioreactors ensures high predictive power. The DT runs near real-time simulations every 2 h. Visualization and interaction with the DT is facilitated by the cloud-based TwinPlant technology, which was developed in close interaction with the plant's operators. A set of predefined handles are made available, allowing users to simulate hypothetical scenarios such as process and equipment failures and changes in controller settings. The combination of the advanced data pipeline and process model development used in the Eindhoven DT and the active involvement of the operators/process engineers/managers in the development process makes the twin a valuable asset for decision making with long-term reliability. PRACTITIONER POINTS: A full-scale digital twin (DT) has been developed for the Eindhoven WRRF. The Eindhoven DT includes an automated continuous data preprocessing and reconciliation pipeline. A full-plant mechanistic compartmental process model of the plant has been developed based on hydrodynamic studies. The interactive user interface of the Eindhoven DT allows operators to perform what-if scenarios on various operational settings and process inputs. Plant operators were actively involved in the DT development process to make a reliable and relevant tool with the expected added value.

Syndromic Surveillance Using Structured Telehealth Data: Case Study of the First Wave of COVID-19 in Brazil

BACKGROUND

Telehealth has been widely used for new case detection and telemonitoring during the COVID-19 pandemic. It safely provides access to health care services and expands assistance to remote, rural areas and underserved communities in situations of shortage of specialized health professionals. Qualified data are systematically collected by health care workers containing information on suspected cases and can be used as a proxy of disease spread for surveillance purposes. However, the use of this approach for syndromic surveillance has yet to be explored. Besides, the mathematical modeling of epidemics is a well-established field that has been successfully used for tracking the spread of SARS-CoV-2 infection, supporting the decision-making process on diverse aspects of public health response to the COVID-19 pandemic. The response of the current models depends on the quality of input data, particularly the transmission rate, initial conditions, and other parameters present in compartmental models. Telehealth systems may feed numerical models developed to model virus spread in a specific region.

OBJECTIVE

Herein, we evaluated whether a high-quality data set obtained from a state-based telehealth service could be used to forecast the geographical spread of new cases of COVID-19 and to feed computational models of disease spread.

METHODS

We analyzed structured data obtained from a statewide toll-free telehealth service during 4 months following the first notification of COVID-19 in the Bahia state, Brazil. Structured data were collected during teletriage by a health team of medical students supervised by physicians. Data were registered in a responsive web application for planning and surveillance purposes. The data set was designed to quickly identify users, city, residence neighborhood, date, sex, age, and COVID-19-like symptoms. We performed a temporal-spatial comparison of calls reporting COVID-19-like symptoms and notification of COVID-19 cases. The number of calls was used as a proxy of exposed individuals to feed a mathematical model called "susceptible, exposed, infected, recovered, deceased."

RESULTS

For 181 (43%) out of 417 municipalities of Bahia, the first call to the telehealth service reporting COVID-19-like symptoms preceded the first notification of the disease. The calls preceded, on average, 30 days of the notification of COVID-19 in the municipalities of the state of Bahia, Brazil. Additionally, data obtained by the telehealth service were used to effectively reproduce the spread of COVID-19 in Salvador, the capital of the state, using the "susceptible, exposed, infected, recovered, deceased" model to simulate the spatiotemporal spread of the disease.

CONCLUSIONS

Data from telehealth services confer high effectiveness in anticipating new waves of COVID-19 and may help understand the epidemic dynamics.

Reactor performance estimation in microscale flow calorimeter for rapid characterization of exothermic reactions

Abstract

Continuous flow calorimeters are a promising tool in process development and safety engineering, especially for flow chemistry applications to characterize the heat release and kinetic parameters of rapid chemical reactions. In this study, the digital accompaniment of an isoperibolic flow calorimeter for characterization of exothermic reactions is presented. To support experimental planning and evaluation, computational fluid dynamic simulations are carried out for single-phase flow in the microreactor. The residence time distribution is obtained and used for estimation of conversion and temperature profiles along the microreactor channel. This leads to an integration of CFD simulations into the calorimeter’s software-guided workflow reducing the experimental effort regarding the determination of thermokinetic data. The approach is tested for a highly exothermic test reaction, which provides further hints for future investigations.

Article highlights

• Estimation of conversion and temperature profiles within a microscale calorimeter

• Combination of CFD simulations and reactor performance estimation

• Approach was tested for highly oxidation of sodium thiosulfate

• Estimated conversion and temperature profiles are in good agreement with experimental data

Graphical abstract

Hydrodynamics and mass transfer of concentric-tube internal loop airlift reactors: A review

The concentric-tube internal loop airlift reactor is a typical reactor configuration which has been adopted for a myriad of chemical and biological processes. The reactor hydrodynamics (including mixing) and the mass transfer between the gas and liquid phases remarkably affect the operational conditions and thus are crucial to the overall reactor performance. Hence, this study aims at providing a thorough description of the basic concepts and a comprehensive review of the relevant reported studies on the hydrodynamics and mass transfer of the concentric-tube internal loop airlift reactors, taking microalgae cultivation as an exemplary application. In particular, the reactor characteristics, geometry, CFD modeling, experimental characterization, and scale up considerations are elucidated. The research gaps for future research and development are also identified.

Predicting Mass Transfer in Liquid–Liquid Extraction Columns

In this work, the GEneralised Multifluid Modelling Approach (GEMMA) is applied to the simulation of liquid–liquid extraction in a Rotating Disc Column (RDC) and a Pulsed Sieve-plate Extraction Column (PSEC). A mass transfer modelling methodology is developed, in which the multiphase flows, droplet size distribution and dispersed phase holdup predicted with computational fluid dynamics are coupled to mass transfer correlations to predict the overall mass transfer. The numerical results for the stage-averaged dispersed phase holdup, Sauter mean droplet diameter and axial solute concentration in the RDC and PSEC agree with experimental observations. The proposed modelling method provides an accurate predictive tool for complex multiphase flows, such as those observed in intensified liquid–liquid extraction, and provides an alternative approach to column design using empirical correlations or pilot plant study.

Investigation of Oxy-Fuel Combustion through Reactor Network and Residence Time Data

Oxy-fuel combustion is a promising strategy to minimize the environmental impact of combustion-based energy conversion. Simple and flexible tools are required to facilitate the successful integration of such strategies at the industrial level. This study couples measured residence time distribution with chemical reactor network analysis in a close-to-reality combustor. This provides detailed knowledge about the various mixing and reactive characteristics arising from the use of the two different oxidizing streams.

Hybrid multi-zonal compartment modeling for continuous powder blending processes

To modernize drug manufacturing, the pharmaceutical industry has been moving towards implementing emerging technologies to enhance manufacturing robustness and process reliability for production of regulation compliant drug products. Although different science and risk based technologies, like Quality-by-Design, have been used to illustrate their potential, there still exist some underlying obstacles. Specifically, for the production of oral solid drug products, an in-depth process understanding, and predictive modeling of powder mixing in continuous powder blenders is one such major obstacle and originates from the current limitations of the experimental and modeling approaches. Though first principle based discrete element modeling (DEM) approach can address the above issues, it can get very computationally intensive which limits its applications for predictive modeling. In the proposed work, we aim to address this limitation using a multi-zonal compartment modeling approach, which is constructed from DEM. The approach provides a computationally efficient and mechanistically informed hybrid model. The application of the proposed approach is first demonstrated for a periodic section of the blender, followed by its extension for the entire continuous powder blender and the obtained model predictions are validated. The proposed approach provides an overall assessment of powder mixing along axial and radial directions, which is an important requirement for the quantification of blend uniformity. Given the low computational cost, the developed model can further be integrated within the predictive flowsheet model of the manufacturing line.

Computational Fluid Dynamics Simulation of Hydrodynamics in a Two-Stage Internal Loop Airlift Reactor with Contraction-Expansion Guide Vane

Global circulation and liquid back mixing adversely affect the continuous production of a multistage internal airlift loop reactor. A contraction-expansion guide vane (CEGV) is proposed and combined with a two-stage internal loop airlift reactor (TSILALR) to suppress the liquid back mixing between stages. A computational fluid dynamics (CFD) simulation is conducted to evaluate the performance of the CEGV in the TSILALR. The bubble size distribution and turbulent flow properties in the TSILALR are considered in the CFD simulation by using the population balance model and RNG k-ε turbulence model. The CFD model is validated against the experimental results. The deviations in the gas holdup and mean bubble diameter between the simulation and experimental results are less than 8% and 6%, respectively. The streamlines, flow pattern, bubble size distribution, and axial liquid velocity in the TSILALRs with and without the CEGV at superficial velocities of 0.04 and 0.08 m/s are obtained by CFD simulation. It has been shown that the CEGV generated local circulation flows at each stage instead of a global circulation flow in the TSILALR. The average global gas holdup in the TSILALR with a CEGV increased up to 1.98 times. The global gas holdup increased from 0.045 to 0.101 and the average axial velocity in the riser decreased from 0.314 to 0.241 m/s when the width of the CEGV increased from 50 to 75 mm at the superficial gas velocity of 0.08 m/s.

Residence time distribution (RTD) revisited

Residence Time Distribution (RTD) theory is revisited and tracer technology discussed. The background of RTD following Danckwerts ideas is presented by introducing "distribution" functions for residence time, internal age and intensity function and how to experimentally obtain them with tracer techniques (curves C and F of Danckwerts). Compartment models to describe fluid flow in real reactors are reviewed and progressive modeling of chromatographic processes discussed in some detail. The shortcomings of Standard Dispersion Model (SDM) are addressed, the Taylor-Aris model discussed and the Wave Model of Westerterp's group introduced. The contribution of Computational Fluid Dynamics (CFD) is highlighted to calculate RTD from momentum and mass transport equations and to access spatial age distribution and degree of mixing. Finally smart RTD and future challenges are discussed.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

Understanding gradients in industrial bioreactors

Gradients in industrial bioreactors have attracted substantial research attention since exposure to fluctuating environmental conditions has been shown to lead to changes in the metabolome, transcriptome as well as population heterogeneity in industrially relevant microorganisms. Such changes have also been found to impact key process parameters like the yield on substrate and the productivity. Hence, understanding gradients is important from both the academic and industrial perspectives. In this review the causes of gradients are outlined, along with their impact on microbial physiology. Quantifying the impact of gradients requires a detailed understanding of both fluid flow inside industrial equipment and microbial physiology. This review critically examines approaches used to investigate gradients including large-scale experimental work, computational methods and scale-down approaches. Avenues for future work have been highlighted, particularly the need for further coordinated development of both in silico and experimental tools which can be used to further the current understanding of gradients in industrial equipment.

How can process safety and a risk management approach guide pandemic risk management?

The coronavirus disease (COVID-19) brought the world to a halt in March 2020. Various prediction and risk management approaches are being explored worldwide for decision making. This work adopts an advanced mechanistic model and utilizes tools for process safety to propose a framework for risk management for the current pandemic. A parameter tweaking and an artificial neural network-based parameter learning model have been developed for effective forecasting of the dynamic risk. Monte Carlo simulation was used to capture the randomness of the model parameters. A comparative analysis of the proposed methodologies has been carried out by using the susceptible, exposed, infected, quarantined, recovered, deceased (SEIQRD) model. A SEIQRD model was developed for four distinct locations: Italy, Germany, Ontario, and British Columbia. The learning-based approach resulted in better outcomes among the models tested in the present study. The layer of protection analysis is a useful framework to analyze the effect of different safety measures. This framework is used in this work to study the effect of non-pharmaceutical interventions on pandemic risk. The risk profiles suggest that a stage-wise releasing scenario is the most suitable approach with negligible resurgence. The case study provides valuable insights to practitioners in both the health sector and the process industries to implement advanced strategies for risk assessment and management. Both sectors can benefit from each other by using the mathematical models and the management tools used in each, and, more importantly, the lessons learned from crises.

Linking CFD and Kinetic Models in Anaerobic Digestion Using a Compartmental Model Approach

Understanding mixing behavior and its impact on conversion processes is essential for the operational stability and conversion efficiency of anaerobic digestion (AD). Mathematical modelling is a powerful tool to achieve this. Direct linkage of Computational Fluid Dynamics (CFD) and the kinetic model is, however, computationally expensive, given the stiffness of the kinetic model. Therefore, this paper proposes a compartmental model (CM) approach, which is derived from a converged CFD solution to understand the performance of AD under non-ideal mixing conditions and with spatial variation of substrates, biomass, pH, and specific biogas and methane production. To quantify the effect of non-uniformity on the reactor performance, the CM implements the Anaerobic Digestion Model 1 (ADM1) in each compartment. It is demonstrated that the performance and spatial variation of the biochemical process in a CM are significantly different from a continuously stirred tank reactor (CSTR) assumption. Hence, the assumption of complete mixed conditions needs attention concerning the AD performance prediction and biochemical process non-uniformities.