Continuous Chemical Reactor Research Articles

Observer-Based High Order Sliding Mode Control of a Continuous Chemical Reactor

Observer-Based High Order Sliding Mode Control of a Continuous Chemical Reactor

Sinusoidal control strategy applied to continuous stirred‐tank reactors: Asymptotic and exponential convergence

AbstractThe main goal of this proposal is to present a class of nonlinear controllers for regulation and set point changes in continuous chemical reactors. The proposed control law has in its mathematical structure a proportional term of the regulation error to provide closed‐loop stability and a sinusoidal term, which can compensate for the nonlinearities of the plant. The closed‐loop stability of the plant is demonstrated via Lyapunov analysis, which reveals an asymptotic convergence of the control output to the required set points. Furthermore, the analysis of the regulation error's dynamic under the considered assumptions leads us to conclude that exponential stability is also reached. The controller is implemented via numerical experiments in two examples to generalize the applicability of the proposed approach by considering continuous stirred‐tank reactors models. The first case considers autocatalytic chemical oscillatory reactions that induce chaotic behaviour. For the second case, a process of acetone, butanol, and ethanol (ABE) fermentation through Clostridium acetobutylicum is considered. The proposed strategy shows an adequate performance because it can reach the required set point without long time settings and overshoot. A comparison with a smooth sliding‐mode and a standard proportional‐integral (PI) controller indicates the advantages of the proposed control approach.

Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations. Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator

This paper presents a concise and orderly methodology to obtain universal solutions to different problems in science and engineering using the nondimensionalization of the governing equations of the physical–chemical problem posed. For its application, a deep knowledge of the problem is necessary since it will facilitate the adequate choice of the references necessary for its resolution. In addition, the application of the methodology to examples of coupled ordinary differential equations is shown, resulting in an interesting tool to teach postgraduate students in the branches of physics, mathematics, and engineering. The first example used for a system of coupled ordinary differential equations is a model of a continuous flow chemical reactor, where it is worth noting; on the one hand, the methodology used to choose the reference (characteristic) time and, on the other, the equivalence between the characteristic times obtained for each one of the species. The following universal curves are obtained, which are validated by comparing them with the results obtained by numerical simulation, where it stands out that the universal solution includes an unknown that must be previously obtained. The resolution of this unknown implies having a deep knowledge of the problem, a common characteristic when using the methodology proposed in this work for different engineering or physicochemical problems. Finally, the second example is a coupled oscillator, where it is worth noting that the appearance of characteristic periods that implicitly or explicitly affect the particles’ movement is striking.

Fitness Dependent Optimizer Based Computational Technique for Solving Optimal Control Problems of Nonlinear Dynamical Systems

This paper presents a pragmatic approach established on the hybridization of nature-inspired optimization algorithms and Bernstein Polynomials (BPs), achieving the optimum numeric solution for Nonlinear Optimal Control Problems (NOCPs) of dynamical systems. The approximated solution for NOCPs is obtained by the linear combination of BPs with unknown parameters. The unknown parameters are evaluated by the conversion of NOCP to an error minimization problem and the formulation of an objective function. The Fitness Dependent Optimizer (FDO) and Genetic Algorithm (GA) are used to solve the objective function, and subsequently the optimal values of unknown parameters and the optimum solution of NOCP are attained. The efficacy of the proposed technique is assessed on three real-world NOCPs, including Van der Pol (VDP) oscillator problem, Chemical Reactor Problem (CRP), and Continuous Stirred-Tank Chemical Reactor Problem (CSTCRP). The final results and statistical outcomes suggest that the proposed technique generates a better solution and surpasses the recently represented methods in the literature, which eventually verifies the efficiency and credibility of the recommended approach.

Reactive PLIF Method for Characterisation of Micromixing in Continuous High-Throughput Chemical Reactors

This work aimed to test and optimise reactive Planar Laser-Induced Fluorescence (PLIF) methods for the visualisation of the micromixing regions in chemical reactors using standard PLIF and Particle Image Velocimetry (PIV) equipment with the laser source 512 nm. Two methods were tested: (i) an acid–base reaction with fluorescein as the reaction-sensitive tracer and (ii) Fenton’s reaction, with Rhodamine B as the reaction tracer. Both test-reactions were studied in stopped-flow equipment to define suitable operational conditions, namely the chemical composition of the inflow streams, the concentration of reagents and fluorophore, and suitable excitation light wavelength. The visualisation of the micromixing regions was tested in a continuous flow reactor with a T-jet geometry. A laser light sheet emitted from an Nd:YAG laser illuminated the axial section of the demonstration reactor. The mixing dynamics and the reaction course were visualised with the acid–base reactive PLIF images. Fenton’s reactive PLIF method showed the overall distribution of mixing and reaction regions. The main contribution of this work is benchmarking two methods with costs that enable the visualisation of micromixing regions in continuous high-throughput reactors.

Congruence Study between the Continuous Chemical Reactor (CSTR) and the Maturation Oxidation Ponds within Wastewater Treatment

People who are involved in managing wastewater treatment face the challenge of achieving conservation goals with limited funds, and also of balancing needs for nature conservation. This context has been motivated with finding logic explanations of wastewater treatment by oxidation ponds. Description of progressive we have made with developing methods is for understanding how, when and where had done to apply the oxidation ponds for protecting biodiversity. The Rashid oxidation pond facility was highlighted as a model plant for utilizing this technology in wastewater treatment in the city of Rashid, El-Beheira Governorate, Egypt. The main concept is based on the interaction of chemical pollutants NO2, NO3, BOD5-in, and BOD5-out and heavy metals with microorganisms as Chlorophyta Green and cyanophyta, and how these oxidation ponds imitate the Continuous Chemical Reactor (CSTR) to build its core architecture for maximum usefulness. By applying the theoretical equation of (CSTR) on the experimental results of the oxidation pond according to Thirumurthi equation, it was discovered that (CSTR) and oxidation pond are matching together with a satisfactory ratio of congruence (85% - 88%). Also, the heavy metals as (iron, Zinc and copper) are high percentage removal by the algae rules. This investigation established that the oxidation ponds may function as a Continuous Chemical Reactor under ultimate conditions and precautions.

A TITO Control Strategy to Increase Productivity in Uncertain Exothermic Continuous Chemical Reactors

In this manuscript, a two-input two-output (TITO) control strategy for an exothermic continuous chemical reactor is presented. The control tasks of the continuous chemical reactor are related to temperature regulation by a standard proportional-integral (PI) controller. The selected set point increases reactor productivity due to the temperature effect and prevents potential thermal runaway, and the temperature increases until it reaches isothermal operating conditions. Then, an optimal controller is activated to increase the mass reactor productivity. The optimal control strategy is based on a Euler-Lagrange framework, in which the corresponding Lagrangian is based on the model equations of the reactor, and the optimal controller is coupled with an uncertainty estimator to infer the unknown terms required by the proposed controller. As a benchmark, a continuous stirred tank reactor (CSTR) with a Van de Vusse chemical reaction is considered as an application case study. Notably, the proposed methodology is generally applicable to any continuous stirred tank reactor. The results of numerical experiments verify the satisfactory performance of the proposed control strategy.

Microcapillary film reactor outperforms single-bore mesocapillary reactors in continuous flow chemical reactions

Meso- and micro-flow reactors are routinely used in continuous flow chemistry, however the role of capillary diameter, D, on conversion and reaction rates is often overlooked during scale-up. Volume, pressured drop and diffusion distances/times must be delicately balanced to fully realize the hydrodynamic capabilities of continuous chemical flow reactors. We carried out a comprehensive Computational Fluid Dynamics analysis experimentally validated with detailed fluid tracing, residence time distributions and continuous chemical reactions (neutralization and 4th Bourne reaction) to fully elucidate the role of D and molecular diffusion in reagents dispersion and chemical conversion. To our understanding, we captured and reported both numerically and experimentally for the first time the transition from convective, segregated flow to plug flow and dispersed flow, which we propose is linked to a dimensionless ratio between the time scales of diffusion to convection, tdiff/tconv. We tested three tubular systems: a small-bore (i.d. ~1100 µm) and large-bore (i.d. ~2400 µm) capillary reactor and a novel multiplexed (10-bore) Microcapillary Film Reactor (MFR) with mean i.d. 363 ± 32.2 µm. In the MFR’s narrow microcapillaries we observed excellent radial diffusion linked to the small diffusion distance, with low dimensionless axial dispersion coefficient values (Dax/uL) ranging from 0.0015 ± 0.0005 to 0.0033 ± 0.0006 (for flow rates 0.5–5.0 mL/min), exhibiting all the desired features of a high-performance ‘plug’ flow system. Dax/uL remained mostly independent of the Reynolds number, whereas for the single, large bore capillary the Dax/uL values (0.032–0.057) increased linearly with the Reynolds numbers (19.4–48.5), shifting towards very dispersive flow. We propose splitting flow through multiple parallel microcapillaries as in the MFR is a superior strategy for scaling-up continuous flow reactions compared to increasing D, which neglects diffusive effects.

Heterogeneous photocatalysis in flow chemical reactors.

The synergy between photocatalysis and continuous flow chemical reactors has shifted the paradigms of photochemistry, opening new avenues of research with safer and scalable processes that can be readily implemented in academia and industry. Current state-of-the-art photocatalysts are homogeneous transition metal complexes that have favourable photophysical properties, wide electrochemical redox potentials, and photostability. However, these photocatalysts present serious drawbacks, such as toxicity, limited availability, and the overall cost of rare transition metal elements. This reduces their long-term viability, especially at an industrial scale. Heterogeneous photocatalysts (HPCats) are an attractive alternative, as the requirement for the separation and purification is largely removed, but typically at the cost of efficiency. Flow chemical reactors can, to a large extent, mitigate the loss in efficiency through reactor designs that enhance mass transport and irradiation. Herein, we review some important developments of heterogeneous photocatalytic materials and their application in flow reactors for sustainable organic synthesis. Further, the application of continuous flow heterogeneous photocatalysis in environmental remediation is briefly discussed to present some interesting reactor designs that could be implemented to enhance organic synthesis.

Kinetics-free process intensification: From semi-batch to series of continuous chemical reactors

A kinetics-free procedure is developed to transform a reaction recipe carried out in an isothermal discontinuous semi-batch reactor into one based on a series of continuous tubular or tank reactors. Using a suitable number of reactors and a correct feeding policy, it is possible to reproduce any discontinuous recipe in flow reactors without knowing the kinetics of the system. The developed procedure allows to determine the number of reactors in series (either tubular or stirred tank) able to reproduce the performance of a semi-batch recipe in terms of selectivity, keeping the same productivity of the original semi-batch process. It was found that using 15 reactors in series allows to keep unchanged the performance of a large number of semi-batch processes once a correct policy of intermediate reactant feeding is implemented. This large number of reactors in series with intermediate feeding can be easily implemented using tubular reactors instead of stirred tank ones. Finally, the synthesis of an amine/epoxy resin was investigated as a case study, fully supporting the reliability of the proposed procedure.

Evaluation of four different coagulants used for chemical dephosphorization of membrane bioreactor effluent

A continuous flow chemical reactor was constructed to study the dephosphorization effect on the effluent of the oxygen-limited internal-loop fluidized membrane bioreactor (IF-MBR) for domestic sewage treatment. Removal effect of total phosphorus (TP) by four coagulants of AlCl3, FeCl3, polyaluminum ferric chloride (PAFC) and polyaluminium chloride (PAC) was evaluated. Results showed that when the ratio of coagulants to TP was 5 (coagulants in terms of Fe and Al), the removal efficiency of TP by FeCl3 was 92.5% and the addition of FeCl3 resulted in an increase in the chromaticity of the effluent. PAC and PAFC had good removal of TP, and the removal percentage achieved 96.2 and 97.4, respectively. However, the flocs they produced were small and light, and the performance in settlement was poor. AlCl3 performed well as a phosphorus removal agent, the removal rate of TP reached 97.4%, and the flocs were large and dense. Based on this, AlCl3 was the best choice for IF-MBR and then the experiment further optimized the Al/P ratio. Results showed that when the Al/P ratio was above 1:1, the effluent TP concentration was lower than 1mg/L; when the ratio was higher than 2.5:1, the effluent TP was lower than 0.5mg/L.

A saturated feedforward/cascade controller for passive continuous reacting systems using entropy production shaping

A control scheme is proposed for adiabatic continuous chemical reactors using thermodynamic properties. This control scheme is inspired by the general advantages of cascade control and Passivity-based Control, using the internal entropy production as a storage function, leading to a transparent physical interpretation. The inner loop shapes the entropy production function (the potential that generates the dynamics) to guarantee stability, while the outer loop regulates process variables such as temperature, pressure, or conversion. The resulting control scheme is equivalent to a feedforward/PI control with control saturations, subject to the available potential and the bounds of the manipulated variable. The controller parameters are given by the physical properties of the system and only a single proportional parameter needs to be tuned to regulate a process variable to its desired value.

Experimental and modelling aspects of the reactive extrusion process

Reactive extrusion consists in using an extruder as a continuous chemical reactor. It is not a recent process, but it has been rapidly developed during the last thirty years and is more and more used today for the chemical modification of existing polymers. Among the various extrusion systems (single screw extruders, counter- and corotating twin-screw extruders, co-kneaders), the corotating twin-screw extruders are today the most widely used in reactive extrusion. After a presentation of the main advantages and drawbacks of the reactive extrusion, we will describe the way to control the process through on-line and in-line monitoring. Then, a modelling approach based on continuum mechanics will be presented, followed by an example of industrial applications of this particular process.

Chaos Suppression via Euler-Lagrange Control Design for a Class of Chemical Reacting System

In this work the problem of chaos suppression for a class of continuous chemical reactor with chaotic dynamics is tackled via a nonlinear control strategy. The proposed controller is developed under the framework of optimal control theory, where a functional is proposed to maximize the chemical reaction rate via a proposed Lagrangian-type which contains directly the state equation of the reacting system, avoiding the problems of Lagrange, the Hamiltonian formulation, and consequently the explicit constraints to the system. This allows solving in an easier form the optimization problem in comparison with the standard methods. This procedure allows suppressing the chaotic behavior of the reacting system by stabilizing the reaction rate term by leading it to an extreme value. Numerical experiments are done in order to show the satisfactory performance of the proposed methodology.

Global-nonlinear stochastic dynamics of a class of two-state two-parameter non-isothermal continuous stirred tank reactors

The global-nonlinear stochastic dynamics of a class of two-state two-parameter continuous exothermic chemical reactors subjected to noise disturbances is studied with Fokker-Planck’s (FP’s) partial differential equation (PDE) theory. The dependency of the stochastic on deterministic dynamics is formally established, and the fundamental characteristics of the associated two-state probability density function (PDF) are described in analytic form, including: (i) stationary state PDF, (ii) convection, diffusion, and metastability time scales along which the state PDF transient occurs, as well as (iii) conditions for PDF metastability. The correspondence between the determination of stochastic stationary state PDF and the assessment of deterministic multiplicity via Van Heerden’s (VH) diagram is established. The developments and results are illustrated with numerical solution of FP’s PDE, and put in perspective with typical and atypical results drawn with Monte Carlo (MC) method.

The membrane-assisted chemical looping reforming concept for efficient H2 production with inherent CO2 capture: Experimental demonstration and model validation

In this work a novel reactor concept referred to as Membrane-Assisted Chemical Looping Reforming (MA-CLR) has been demonstrated at lab scale under different operating conditions for a total working time of about 100 h. This reactor combines the advantages of Chemical Looping, such as CO2 capture and good thermal integration, with membrane technology for a better process integration and direct product separation in a single unit, which in its turn leads to increased efficiencies and important benefits compared to conventional technologies for H2 production. The effect of different operating conditions (i.e. temperature, steam-to-carbon ratio or oxygen feed in the reactor) has been evaluated in a continuous chemical looping reactor, and methane conversions above 90% have been measured with (ultra-pure) hydrogen recovery from the membranes. For all the cases a maximum recovery factor of around 30% has been measured, which could be increased by operating the concept at higher pressures and with more membranes. The optimum conditions have been found at temperatures around 600 °C for a steam-to-carbon ratio of 3 and diluted air in the air reactor (5% O2). The complete demonstration has been carried out feeding up to 1 L/min of CH4 (corresponding to 0.6 kW of thermal input) while up to 1.15 L/min of H2 was recovered.Simultaneously, a phenomenological model has been developed and validated with the experimental results. In general, good agreement is observed, with overall deviations below 10% in terms of methane conversion, H2 recovery and separation factor. The model allows better understanding of the behavior of the MA-CLR concept and the optimization and design of scaled-up versions of the concept.

Enhanced fuel conversion by staging oxidization in a continuous chemical looping reactor based on iron ore oxygen carrier

Natural iron ore as an oxygen carrier for chemical looping combustion (CLC) has recently attracted increasing attention. However, low fuel conversion efficiency is the major issue for the CLC process based on iron ore. The unconverted gaseous fuel causes energy loss and degrades CO2 purity. Based on the technology of interconnected fluidized bed, a new 2kW CLC reactor was constructed with a two-stage fuel reactor. Staging oxidization of fuel was proposed in the special fuel reactor to promote fuel conversion. The fuel oxidation primarily occurs in the 1st stage fuel reactor, and the remaining unconverted combustible gas is further oxidized by fresh oxygen carrier in the 2nd stage fuel reactor. This CLC reactor was tested using an Australian iron ore as oxygen carrier and syngas and CH4 as gaseous fuels, respectively. The staging oxidization of gaseous fuel in this new configuration was evaluated by comparing with the results from a 1kW reactor with one stage fuel reactor. For the syngas tests, fuel conversion efficiency in the 2kW reactor maintained between 92.9% and 98.3%, while that in the 1kW reactor maintained at only about 80%. For the CH4 tests with thermal power input of 1–2kW, up to 92.9% CH4 was converted and CO2 yield reached around 88% at 980°C. Finally, the oxygen carrier particles were characterized by XRD and SEM. Overall, staging oxidation of fuel is an effective method to enhance fuel conversion when using a Fe-based oxygen carrier.

Cascade control of a class of chemical reactors based on entropy production shaping

On this contribution a cascade control for a class of continuous chemical reactors is presented. Given that the internal entropy production of the reacting systems under study can be considered as a storage function, the inner loop is designed to shape the entropy production using the outflow rate as the control variable. The tracking reference for the entropy production of the inner loop is computed by an outer loop that regulates a typical process variable such as temperature or pressure inside the reactor. In the resulting cascade control structure, the inner loop guarantees the stability of the reacting system, while the outer loop can be used to fulfil safety or operational conditions.

Influence of ligament shape and thickness on vortex shedding in highly porous structures

Highly porous structures (porosity ≥75%) used as inserts in continuous chemical reactors with characteristic length scale in the millimeter range exhibit at industrial relevant throughputs the transport phenomenon vortex shedding. The dependency of the ligament shape and thickness of the porous media on vortex shedding is investigated in two geometries: a highly porous structure consisting of round ligaments and a highly porous structure whose ligaments are thicker and have a square cross section. The contribution of vortex shedding to the total turbulent kinetic energy is determined from proper orthogonal decompositions (POD) of fluctuating velocity fields measured with particle image velocimetry (PIV). The spatial structure of the vortex shedding phenomenon is addressed by POD eigenfunctions and by the wake length extracted by the position of zero mean streamwise velocity along the wake axis. Shedding frequencies are evaluated for a large Reynolds number range (6≤ReD≤1500) by a dye injection technique. The vortex shedding phenomenon is more intense in case of the highly porous structure with square and thicker ligaments. This means that larger vortices are created and detached, Strouhal numbers are larger and the contribution of vortex shedding to the total turbulent kinetic energy is more substantial in this case compared with the structure with round and thinner ligaments.

Vortex shedding in a highly porous structure

Highly porous media (with a porosity ≥85%), like metal foams, fins or designed porous inserts are widely used in industrial flow applications. Motivated by the use of highly porous inserts in continuous chemical reactors, the time dependent behavior of flows through a highly porous structure is investigated experimentally and numerically for Reynolds numbers ReD=33 and 330 (based on the ligament diameter and the bulk velocity). The experimental studies are based on the Particle Image Velocimetry (PIV), whereas the numerical studies are conducted by using the Large Eddy Simulation (LES) approach with the dynamic Lagrangian subgrid closure. The vortex shedding phenomena is observed for both values of Reynolds number. It is demonstrated that the length of the wake and the orientation of the shedded vortices are dependent on the position within the highly porous structure.