Continuous Stirred Tank Reactor Research Articles

Generalization of Liu–Zhou Method for Multiple Roots of Applied Science Problems

Some optimal and non-optimal iterative approaches for computing multiple zeros of nonlinear functions have recently been published in the literature when the multiplicity θ of the root is known. Here, we present a new family of iterative algorithms for multiple zeros that are distinct from the existing approaches. Some special cases of the new family are presented and it is found that existing Liu-Zhou methods are the special cases of the new family. To check the consistency and stability of the new methods, we consider the continuous stirred tank reactor problem, isentropic supersonic flow problem, eigenvalue problem, complex root problem, and standard test problem in the numerical section and we find that the new methods are more competitive with other existing fourth-order methods. In the numerical section, the error of the new methods confirms their robust character.

Mesophilic anaerobic digestion of mixed sludge in CSTR and AnMBR systems: A perspective on microplastics fate.

Most microplastics (MPs) end up in the biosolids produced in wastewater treatment plants (WWTPs) and can pose contamination risks when the biosolids are applied to agriculture. This study evaluated the impact of mesophilic anaerobic digestion on the fate of MPs in WWTP sludge. For this, two laboratory-scale anaerobic digesters were operated in parallel, consisting of a continuous stirred tank reactor (CSTR) and a membrane bioreactor (AnMBR) equipped with an ultrafiltration membrane to decouple the hydraulic and sludge retention times. Both digesters were continuously fed with mixed sludge from a municipal WWTP. The results showed a significant reduction in the MP concentration, with the AnMBR having the higher MP removal efficiency (88.6% vs. 62.1%) and obtaining a higher percentage of biomethanisation (58.3% vs. 43.7%). Polypropylene (PP) and polyacrylonitrile were the main polymers in the mixed sludge, while PP and polyethylene were the dominant polymers in the digested samples. The MP particles in all the samples were predominantly in the 500-104μm size range. Microbiological analysis indicates a greater species diversity in the microbial community of the AnMBR, the results also revealed a symbiotic relationship between the Firmicutes and Patescibacteria phyla in this digester.

Novel MGWO-Based FOPID Controller for CSTR System

In this paper, the performance of a jacketed and series Continuous Stirred Tank Reactor (CSTR) system is studied. The fractional-order proportional–integral–derivative (FOPID) controller has been implemented and to achieve better performance, independent control parameters must be tuned. In order to tune these parameters, a novel Modified Grey Wolf Optimizer (MGWO) technique is proposed in this work. This optimally tuned controller parameters enhance the performance of the system and achieves an optimal fitness function. To demonstrate the effectiveness of the proposed controller, comparisons are made with other techniques. Time-domain characteristics, frequency responses, and robust analysis of the proposed controller are presented. The simulation results justify the superiority of the proposed method by improving the performance of the system.

Design of Fractional‐Order Sliding Mode Controller for an Unstable Three‐State Model Jacketed CSTR

ABSTRACTControl of a jacketed continuous stirred tank reactor (CSTR) is challenging due to nonlinear dynamics, complexity, and rapid reactor dynamics under imperfect mixing in the jacket. Current controller designs mainly focus on the two‐state model, neglecting the potential of three‐state models in scenarios with nonperfect mixing and fast reactor dynamics. This study proposes a sliding mode controller (SMC) design scheme based on the transfer function model using a newly developed jellyfish optimisation algorithm. Further, a fractional‐order sliding mode control (FO‐SMC) strategy is proposed, which integrates modifications to the SMC to mitigate chattering, enhance control robustness, and provide better disturbance rejection capability. PID and fractional‐order PID (FOPID) controllers were also designed for comparative analysis. The simulation results demonstrated that FO‐SMC outperformed other designed controllers, shown by a 37.14% reduction in settling time, 10.69% reduction in integral absolute error (IAE), and 19.06% reduction in time‐weighted absolute error (ITAE) compared to SMC and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under dynamic conditions.

A novel dynamic machine learning-based explainable fusion monitoring: application to industrial and chemical processes

Abstract The complexity and fusion dynamism of the modern industrial and chemical sectors have been increasing with the rapid progress of IR 4.0–5.0. The transformative characteristics of Industry 4.0–5.0 have not been fully explored in terms of the fundamental importance of explainability. Traditional monitoring techniques for automatic anomaly detection, identifying the potential variables, and root cause analysis for fault information are not intelligent enough to tackle the intricate problems of real-time practices in the industrial and chemical sectors. This study presents a novel dynamic machine learning based explainable fusion approach to address the issues of process monitoring in industrial and chemical process systems. The methodology aims to detect faults, identify their key causes and feature variables, and analyze the root path of fault propagation with the time and magnitude of one cause variable to another impact. This study proposed using a time domain multivariate granger-entropy-aided dynamic independent component analysis (DICA)—distributed canonical correlation analysis approach, incorporating the dynamics time wrapping supported time delay-signed directed graph. The proposed methodology utilized the application to industrial and chemical processes and verified using the continuous stirred tank reactor and Tennessee Eastman process as practical application benchmarks. The framework’s validations and efficiency are evaluated using established techniques such as classic computed ICA and DICA as standard model scenarios. The outcomes and results showed that the newly developed strategy is preferable to previous approaches regarding explainability and robust detection and identification of the actual root causes with high FDRs and low FARs.

Asynchronous Resilient Filtering for Singular Perturbation Stochastic Semi‐Markov CPSs Against Stochastic Cyber Attacks

ABSTRACTThe article investigates the problem of asynchronous resilient filter design for cyber‐physical systems (CPSs) under multiple cyber‐attacks, which are characterized by singular perturbation and stochastic semi‐Markov jump systems (SPSS‐MJSs) with a dynamic‐memory event‐triggered (DMET) scheme. Firstly, we consider the vulnerability of communication network and establish a unified cyber‐attack framework to address the occurrences of deception attacks and denial‐of‐service (DoS) attacks, simultaneously. Then, we introduce the function of the memorizer and propose the DMET scheme, which can effectively save network resources in bandwidth‐limited environments. Since the mode information of the resilient filter is often unavailable, we employ a hidden Markov model (HMM) to describe the asynchronous relationship between the modes of the original system and the constructed filter. Furthermore, we judiciously select a stochastic Lyapunov functional concerning the internal dynamic variable, which results in the stochastically admissible criterion for filtering error systems under complex cyber‐attacks. The co‐design approach is adopted to obtain the gains of the asynchronous resilient filter and the DMET scheme. Finally, a continuous stirred‐tank reactor (CSTR) system is offered to validate the effectiveness of the developed method.

Modeling of a Continuous Stirred Tank Reactor and Controller Design Using LMI Approaches

ABSTRACTThe design of non‐linear control systems remains a challenge today, therefore through this work a procedure to obtain a vertex‐reduced multi‐model representation, without loss of convexity, is proposed as a suitable solution. That is, a novel approach which considers all parameter variations around the Continuous Stirred Tank Reactor (CSTR) system operating region is developed, resulting in a unique polytopic representation. After that, based on the linear matrix inequalities approach, a control scheme is developed to compute the optimal matrix gains, while the operating, states and inputs, constraints are satisfied and the stability conditions are ensured. Finally, the realistic simulation results highlight the model representation effectiveness in capturing the CSTR dynamic behavior in the operating region, despite parameter variations, allowing the optimal control law design, overcoming the non‐linear system nature, to achieve the desired closed‐loop system performance.

An identification-based robust H∞ control of fouling in chemical reactor

In this article, a robust control algorithm is proposed for a nonlinear and time-varying continuous stirred tank reactor (CSTR) with sediment formation in the cooling jacket. The existing control schemes may fail, as deposition measurement or estimation is a challenge in such a process. As a main contribution, the deposition phenomenon is modeled here as the system uncertainty. Then, an identification-based robust integral controller is constructed for the underlying CSTR. Applying the loop-shaping procedure here is also a novelty to satisfy the performance objectives in the frequency domain. In a comprehensive scenario, which includes the set-point tracking in the presence of system uncertainties and external disturbance, the performance of the proposed robust control system is evaluated and discussed from a comparison viewpoint. The numerical study shows that fouling control and robust performance are ensured by the developed H∞-based technique.

Comparative enrichment of complete ammonium oxidation bacteria in floccular sludge reactors: sequencing batch reactor vs. continuous stirred tank reactor

Comparative enrichment of complete ammonium oxidation bacteria in floccular sludge reactors: sequencing batch reactor vs. continuous stirred tank reactor

Optimising medium chain carboxylate production in xylan mixed-culture monofermentation.

This work investigates the optimization of medium-chain carboxylate (MCC) production through xylan mixed-culture monofermentation. The pH screening in batch assays showed that the hydrolysis stage and selectivity towards MCC precursors were optimised at pH 6. Subsequently, a continuous stirred tank reactor (CSTR) and a Sequential Batch Reactor (SBR) were operated at different Hydraulic Retention Times (HRT), revealing that the SBR at HRT 2 days yielded the highest caproic acid since lactic acid availability and chain elongation process were balanced. An enriched medium with yeast extract and vitamins favoured the growth of chain elongators, and therefore, the MCC production. Moreover, cross-feeding interaction between bacteria in xylan fermentation was observed, and Pseudoramibacter was present in the highest caproic acid yields. This work highlights the impact of selecting the proper operational window to optimise one-stage MCC production.

A Cross-Layer Game-Theoretic Approach to Resilient Control of Networked Switched Systems Against DoS Attacks.

This article investigates the resilient control strategies of networked switched systems (NSSs) against denial-of-service (DoS) attacks and external disturbance. In the network layer, both the defender and the attacker allocate energy over multiple channels. Considering the impact of switching characteristic in the physical layer on the network layer, a dynamic regulating factor is proposed to adjust the total energy of the defender. To optimize the signal-to-interference-noise ratio and energy consumption simultaneously at each player's side, a multiobjective game problem is formulated. Furthermore, a nondominated sorting genetic algorithm framework is employed, incorporating the knee point selection mechanism to attain the Pareto-Nash equilibrium, based on which the optimal defense strategy can be derived to achieve resilience against DoS attacks. In the physical-layer, taking the dynamic packet loss caused by DoS attacks and external disturbance into account, an H∞ minimax controller containing control inputs and the switching signal is designed to guarantee the optimal performance for NSSs through the dynamic game-theoretic approach. Finally, the networked continuous stirred tank reactor system is provided to verify the effectiveness of the proposed method.

Analysis of observability and detectability for CSTR model of biochemical processes under uncertain system dynamics and various sets of measured outputs

An analysis of observability and detectability for continuous stirred tank reactor model of selected biochemical processes has been addressed in this paper. In particular, properties of observability or detectability of the considered system model have been proved under uncertain system dynamics in view of various sets of system measured outputs. It is related to considering system dynamics depending on initial conditions and the impact of inputs taking into account a given measured output. The method of indistinguishable state trajectories (indistinguishable dynamics) and tools based on the Lyapunov second method were used to investigate the observability and detectability properties. The analysis was performed for eight cases of different sets of measured outputs with association to the realistic features of measuring devices. The obtained research results are essential for system state estimation that involves the synthesis of state observers. The proposed approach may be successfully applied to the complex biochemical non-linear uncertain systems modelled as continuous stirred tank reactors.

Internal model control based sliding mode controller design for unstable second order delayed processes with a case study on CSTR

Controlling the unstable processes is challenging since one or more poles are located on the right side of the s-plane. The existence of dead time in these systems makes control much more difficult. In this paper, internal model control based sliding mode control has been proposed for the control of unstable processes with dead time. Two sliding surfaces based on PID and PIDPI are used to design of the proposed controller. The parameters of continuous and discontinuous control law are obtained using differential evolution optimization technique. An objective function is constituted in terms of performance measure (integral absolute error) and control effort measure (total variation of controller output). Illustrative examples demonstrate the superiority of the proposed controller over earlier reported work in this realm, especially in terms of load disturbance rejection. A case study on temperature management of a continuous stirred tank reactor during an irreversible exothermic process also serves to highlight the applicability of the proposed system. Furthermore, robustness of the proposed controller is also investigated by inclusion of perturbations in the parameters. The obtained results clearly show how well the suggested controller works.

Adaptive Proportional-Integral Control Design for a Class of Continuous Stirred Tank Reactors with Uncertain Parameters

Mathematical model of reaction systems contains experimental parameters such as reaction enthalpies, which may be inaccurate and, therefore, severely affect the computation as well as the implementation of feedback control laws. This paper aims to design an adaptive PI-like controller to regulate a chemical reaction system by means of the Lyapunov theory. More precisely, uncertain model parameters are updated online by solving a set of ordinary differential equations while the global asymptotic convergence of closed-loop system trajectories towards the desired equilibrium is ensured by using the proposed adaptive PI-like controller under the assumption of stability of isothermal conditions. The applicability of theoretical developments is illustrated with an irreversible first-order reaction system having multiple steady states and taking place in a non-isothermal continuous stirred tank reactor. Simulation results show that system trajectories initiated at different conditions are asymptotically stabilized at the desired values and the closed-loop system is robust against the uncertainty of heat exchange coefficient and dilution rate.

Synergistic Promotion of Direct Interspecies Electron Transfer by Biochar and Fe₃O₄ Nanoparticles to Enhance Methanogenesis in Anaerobic Digestion of Vegetable Waste

When vegetable waste (VW) is used as a sole substrate for anaerobic digestion (AD), the rapid accumulation of volatile fatty acids (VFAs) can impede interspecies electron transfer (IET), resulting in a relatively low biogas production rate. In this study, Chinese cabbage and cabbage were selected as the VW substrates, and four continuous stirred tank reactors (CSTRs) were employed. Different concentrations of biochar-loaded nano-Fe3O4(Fe3O4@BC) (100 mg/L, 200 mg/L, 300 mg/L) were added, and the organic loading rate (OLR) was gradually increased during the AD process. The changes in biogas production rate, VFAs, and microbial community structure in the fermentation tanks were analyzed to identify the optimal dosage of Fe3O4@BC and the maximum OLR. The results indicated that at the maximum OLR of 3.715 g (VS)/L·d, the addition of 200 mg/L of Fe3O4@BC most effectively promoted an increase in the biogas production rate and reduced the accumulation of VFAs compared to the other treatments. Under these conditions, the biogas production rate reached 0.658 L/g (VS). Furthermore, the addition of Fe3O4@BC enhanced both the diversity and abundance of bacteria and archaea. At the genus level, the abundance of Christensenellaceae_R-7_group, Sphaerochaeta, and the archaeal genus Thermovirga was notably increased.

Unlocking higher methane yields and digestate nitrogen availability in soil through thermal treatment of feedstocks in a two-step anaerobic digestion

BackgroundThere is an increasing interest in using lignocellulosic feedstocks for biogas production. Treatment of these feedstocks prior to anaerobic digestion (AD) can enhance their accessibility to microorganisms involved in the process. To improve the digestion of recalcitrant feedstocks and boost biogas yields, many biogas plants now employ two-step AD systems, extending substrate residence times. However, the combined effect of feedstock treatment and two-step AD on methane yield and fertiliser value of digestates are underexplored. This study, therefore, evaluated the effectiveness of thermal treatment (TT) of pre-digested agricultural feedstocks before a secondary AD step on the carbon (C) and nitrogen (N) dynamics of digestates following application to soil. It also investigated the effects of TT on methane yields. Pre-digested feedstock (PDF) was treated at three different temperatures (70 °C, 120 °C and 180 °C) for 60 min, followed by parallel secondary AD steps using lab-scale continuous stirred-tank reactors (CSTR) and a batch test. Thermally treated feedstocks with and without a secondary AD step were applied to soil to study C and N dynamics and turnover for 2 months.ResultsTT at 180 °C increased ultimate CH4 yields by 7.2%; however, it decreased the net mineral N release in soil from 42 to 34% (of N input). Adding a secondary AD step increased the net mineral N release in soil from an average of 39% to 47% (of N input), with the effect of TT levelling off. Moreover, the secondary AD step significantly reduced C mineralisation rates from an average of 37% to 26% (of C applied).ConclusionsOverall, TT at 120–180 °C can improve biogas yields of recalcitrant feedstocks, but it may lead to the formation of refractory nitrogen compounds resistant to further degradation during AD, potentially resulting in a lower N fertiliser value of digestates.Graphical

Maximum sensitivity constrained modified Smith predictor for delayed integrating type stirred tank reactors model

Abstract A maximum sensitivity constrained modified Smith predictor consisting of two PD controllers is developed for integrating type continuously stirred tank reactors (CSTRs) model. This CSTR type model approximated as integrating first order plus time delay with and without inverse response processes is challenging to control as it contains integrating term, process time delay and a zero lying in the right half of s-plane. The inner and outer loop PD blocks are tuned to achieve the desired set-point tracking and load disturbance rejection responses using direct synthesis approach. The proposed control is free from integrating action and therefore, smooth setpoint tracking response with no overshoot is obtained which is highly desirable in the process industries. Two design parameters λ and τ are involved in the suggested control whose suitable values are recommended to achieve the desired robustness level by specifying the maximum sensitivities of the inner and outer loop transfer functions. Various illustrative models are considered to show the effectiveness and superiority of the proposed control structure. The system robustness towards process parameter perturbations and load disturbances are investigated in all the examples. Performance of the suggested modified Smith predictor is found superior as compared to the other recently published works.

Nonlocal modeling of continuously stirred tank reactors with residence time distribution

Abstract The residence time distribution (RTD) has an important impact in the performance of chemical reacting systems. The segregated fluid assumption is commonly used to assess the analysis and design of chemical reactors. Models derived from the segregated fluid assumption for continuously stirred tank reactors (CSTR) rely on batch reactor models. A drawback of such assumption is that the CSTR model structure is not recovered in the limit when the RTD becomes very narrow (e.g., a Dirac delta). The aim of the present work is to propose a nonlocal modeling approach that is consistent with the CSTR model structure. The main idea is to represent the reactor as a continuum of tiny differential CSTRs determined by the RTD. The resulting nonlocal model is expressed as integrodifferential equations representing the interaction of reactive molecules of a given residence time with molecules of all residence times. By doing this, the nonlocal model is reduced to the usual CSTR model in the limit when the RTD is very narrow. The methodology was illustrated with three worked cases of dimerization, autocatalytic and series reaction schemes, and the results were compared with that obtained with the segregated fluid assumption. It was found that nonlocal models predict lower conversions than the segregated fluid models.

Decentralized Finite‐Time Adaptive Neural Output‐Feedback Quantized Control for Switched Nonlinear Large‐Scale Delayed Systems

ABSTRACTThis paper considers the problem of decentralized finite‐time adaptive neural output‐feedback quantized control for a class of switched nonlinear large‐scale delayed systems. A switched high‐gain quantized state observer is therefore constructed for each subsystem to estimate unavailable system states. Different from the traditional Lyapunov–Krasovskii functional method, multiple Lyapunov–Krasovskii functions are introduced to develop the decentralized adaptive output‐feedback control strategy with neural network approximation for the switched nonlinear large‐scale delayed systems. Under a category of switching signals with persistent dwell time, all signals in the closed‐loop switched system are semi‐globally uniformly ultimate bounded. Meanwhile, the tracking errors can remain in a small domain of origin in finite time. Case studies are finally used to illustrate the flexibility and effectiveness of the proposed control approach, including the switched two continuous stirred tank reactor delayed systems.

Kinetic Modelling of Ralstonia eutropha H16 Growth on Different Substrates

Due to environmental pollution and the depletion of fossil fuels, there is growing interest in the development and use of biofuels as environmentally friendly alternatives. One of the most promising biofuels is biohydrogen, hydrogen produced through sustainable processes using microorganisms such as bacteria and algae. One of the most interesting bacteria for hydrogen production is Ralstonia eutropha H16, known for its ability to produce oxygen-tolerant hydrogenases. These enzymes play a crucial role in biohydrogen metabolism and production. The aim of this work was to determine the optimal conditions (reactor type and synthetic medium composition) for the cultivation of R. eutropha H16. The culture media contained different concentrations of fructose and glycerol (mono- or double-substrate cultivation) and the experiments were carried out in a batch reactor. The initial experiments were carried out with 4 g/L fructose or glycerol in the culture medium at pH 7, T = 30 °C, and 120 rpm. The mathematical model, consisting of the growth kinetics (described by the Monod’s model) and the corresponding mass balances, was proposed. The developed model was validated using two independent experiments with different initial substrate concentrations: 2 g/L glycerol and fructose in one medium and 4 g/L fructose and 1 g/L glycerol in the second. In order to propose the optimal cultivation procedure for future research, the mathematical model simulations were performed for different reactor types (batch, fed-batch, and continuous stirred tank reactors) and different initial substrate concentrations. The most successful experiment was the one with 4 g/L glycerol, where γX = 0.485 ± 0.001 g/L of biomass was achieved. Further calculations showed that the most biomass would be produced at higher glycerol concentrations (at γG = 6.358 g/L, γX = 1.311 g/L should be achieved after 200 h of cultivation) and when using a fed-batch reactor (γX = 0.944 g/L after 200 h of cultivation).