CSTRs In Series Research Articles

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

AbstractIn this work, we propose a /methodology for the selection and refinement of finite elements for the integration of process design and control. The proposed methodology is based on the selection criteria of the Hamiltonian function through the implementation of the Pontryagin's minimum principle. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes, which is exploited in this work for the refinement of the discretization. Furthermore, the residuals at noncollocation points are evaluated to estimate the collocation error, this is used as a second refinement criterion in the proposed framework. The methodology is illustrated using two case studies featuring a reaction system with two CSTRs in series and the Williams–Otto reactor, respectively. The results showed that an accurate selection of the finite elements return economically attractive designs with fewer elements than those obtained with equidistributed finite element strategies.

An assessment of a multipoint dosing approach for exothermic nitration in CSTRs in series

Multipoint dosing strategy for scale-up of exothermic aromatic nitration.

Optimum Design of N Continuous Stirred-Tank Bioreactors in Series for Fermentation Processes Based on Simultaneous Substrate and Product Inhibition

Optimization of the continuous fermentation process is important for increasing efficiency and decreasing cost, especially for complicated biochemical processes described by substrate and product inhibition. The optimum design (minimum volume) of CSTRs in series assuming substrate and product inhibition was determined in this study. The effect of operating parameters on the optimum design was investigated. The optimum substrate concentration in the feed to the first reactor was determined for N reactors in series. The nonlinear, constrained optimization problem was solved using the MATLAB function “fmincon”. It was found that the optimum design is more beneficial at high substrate conversion and at a medium level of feed substrate concentration. The best number of reactors is two to three for optimum arrangements and two for equal-size arrangements. The presence of biomass in the feed to the first reactor reduces the reactor volume, while the presence of product in the feed slightly increases the required total volume. The percentage reduction in the total volume using the optimum design compared to equal-volume design (R%) was determined as a function of substrate conversion and substrate concentration in the feed to the first reactor. The obtained R% values agree with experimental data available in the literature for ethanol fermentation.

An explicit reduced-order model of Cu-Zeolite SCR catalyst for embedding in ECM

A piecewise analytical solution is developed as part of an explicit reduced-order model for a state-of-the-art Cu-SSZ-13 SCR catalyst in the degreened state (550 °C-4 h). Simplifying the species, coverage and energy balance equations by treating the monolithic catalyst as an array of CSTRs in series, along with additional approximations based on intrinsic catalyst behavior allow for the decoupling of the conservation equations. This yields analytical solutions for all relevant catalyst states and outputs, which can be integrated using a simple fixed step explicit Euler scheme. The reduced-order model utilizes the same reaction kinetics as the high-fidelity 1D plug flow reactor model, developed using NH3-temperature programmed desorption (TPD) and 4-step [40] reactor data on the degreened catalyst. SCR kinetics are modeled here using a global single-site approach, accounting for ammonia (NH3) and ammonium nitrate (AN) dynamics. Washcoat diffusion is considered using the overall mass transfer approach [39], and in the case of SCR catalysts, we demonstrate the applicability of the asymptotic internal Sherwood number for realistic reaction rates and washcoat diffusivities. Model results show the ability of the piecewise analytical solution to produce nearly identical results as the high-fidelity model, which in turn is validated with experimental reactor data. The reduced-order model is also translated to a full-size catalyst under transient engine drive cycle conditions. SCR outlet temperature, NH3 and AN coverage, along with outlet NOx and N2O slip predictions are in line with the high-fidelity model and experimental measurements. The simplified model presented here is generally applicable to all single-layer monolithic catalysts utilizing linear reaction rate expressions for solved species. This model allows for the tracking of catalyst states (such as NH3 coverage) and outputs (such as NOx) onboard the engine control module (ECM), enabling the development of model-based estimators and control strategies necessary to meet the upcoming emission and durability requirements.

Simulation of a Plant for the Production of Polyethylene

The simulation of a 270 KTA capacity polyethylene plant was performed using Aspen Hysys version 8.8. A Hysys model of the polyethylene was developed using the polyethylene plant layout of Indorama Eleme Petrochemical Company. A material and energy balance for the various components of the plant was performed manually and with Hysys for comparison. The design of the various components of the Hysys model was performed. The polyethylene reactor was simulated to study the effect of process functional parameters such as reactor dimensions, temperature and pressure. The effect of reactor size and number on polyethylene output was studied by simulating the plant with five continuous stirred tank reactors (CSTRs) in series and a single reactor. The results of the material and energy balance of the various components of the plant were performed manually and with Hysys which showed a maximum deviation of 0.8%. The design results of the sizing parameters for the Multiple and single CSTRs were compared in terms of Volume, Diameter, Height, Spacetime, Space Velocity, and Volumetric flowrate respectively. At 90% Conversion, the multiple CSTRs gave 600 dm3, 0.7668 m, 1.198 m, 0.052 hr, 195.83 hr-1, and 117.5 m3/h for the above listed parameters, while the single CSTR gave 6000 dm3, 1.721 m, 2.581 m, 0.056 hr, 17.867 hr-1 and 107.2 m3/h for the same conversion. The sizing results for each of the five compressors were also compared in terms of the following parameters: Adiabatic Head, Polytropic Head, Adiabatic fluid Head, polytropic Fluid Head, Adiabatic Efficiency, power consumed, polytropic head factor, polytropic exponent and isentropic exponent. The effect of reactor size and number showed that At 90% conversion the multiple CSTRS in series gave a lower volume than the single CSTR for the same conversion, and more Economical than the single CSTR for the same conversion.

Maximizing the Intermediate Product for 3 CSTRs in Series

Maximizing the Intermediate Product for 3 CSTRs in Series

Incipient Actuator Fault Handling in Nonlinear Model Predictive Control

This paper presents a reconfigurable nonlinear model predictive control (NMPC) scheme for handling of incipient actuator faults in nonlinear plants. The scheme seeks to ensure recoverability from an incipient actuator fault in plants where the input redundancy is insufficient to stabilize the faulty system at the nominal operating point, thereby requiring transition to a safe control-invariant set. To this end, the proposed scheme takes into account an estimate of the decrease in remaining actuator capacity from the time of detection of an incipient actuator fault, and minimizes the required control input to steer the plant to the safe set. We provide conditions for stability and fault recoverability of the proposed scheme, and demonstrate its applicability on a numerical example with two CSTRs in series.

The Maximum Mixedness Model Applied with Detailed Reaction Mechanisms

Abstract The Zwietering maximum mixedness model (MMM) is extended for use with detailed chemical reaction mechanisms in a combustion setting. Both MMM species and energy balances are offered with a Chemkin-consistent nomenclature. The solution algorithm is discussed. Several reactor residence time distributions are currently offered for use with the MMM program. The MMM is used here to simulate observed literature species concentration data in a turbulent, jet-stirred combustor. For comparison, the results are also compared to simulations from perfectly stirred reactor (PSR) and partially stirred reactor (PaSR) models. The MMM model predicts the observed higher-than-PSR fuel conversions using a residence time distribution based on two unequal CSTRs-in series.

On Single Compartment Pharmacokinetic Model Systems that Obey Free Radical Copolymerization Kinetics and Multiplicity

This study examines the issues in development of pharmacokinetic single compartment model for systems that obey free radical copolymerization kinetics. Copolymer composition as a function of reactivity ratios of comonomers for well mixed case was derived. For some cases, such as DEF-AN, diethyl fumarate and acrylonitrile system multiplicity in composition were found. The analysis is extended to n monomers. State space model expressions are used and the QSSA assumption is stated in state space equation form. Conditions when damped oscillations can be expected are noted. In addition to multiplicity in product composition, an account of reactivity ratios and other instances of multi- plicity were found during the pharmacodynamics of the free radical polymerization reactions. A careful study of initiated case, thermal case, 1 CSTR and 2 CSTRS was undertaken and results were presented. Numerical integration techniques were employed on the desktop computer. Steady state and transient state conversion for initiated case and thermal case for 1 CSTR and 2 CSTRs were calculated and plotted in Figures 7-9 and 12. No multiplicity was found in the thermal case for 1 CSTR in the dynamics of transient monomer conversion. Multiplicity was found in the initiated case for 1 CSTR in the dynamics of transient conversion of monomer. The multiplicity was found in the second CSTR for the case of 2 CSTRs in series. No multiplicity was found in the case of initiator decay.

Sludge exchange process on two serial CSTRs anaerobic digestions: Process failure and recovery

The sludge exchange process using two anaerobic digesters (CSTRs) in series was investigated under the mesophilic condition (36–38 °C). At first, the digesting sludge of the CSTRs in series with different TVFA/alkalinity ratios was tested in the laboratory by mixing the digesting sludge of two CSTRs from 6.5% to 50% based on volume. The sludge exchange test was then performed using the same CSTRs under batch and continuous processes. The change in the TVFA/alkalinity ratio was found to be linear with the digesting sludge exchange volume. The CSTR of TVFA/alkalinity ratio 1.970 recovered completely failed within 11 days for the batch process and the CSTR of TVFA/alkalinity ratio 1.514 within 3 weeks for the continuous feeding process at a sludge exchange volume of 13%. The reactor operation was stable when the TVFA/alkalinity ratio was less than 1.0 and when the TVFA concentration was lower than 10,000 mg L −1.

Modeling the Effects of Reactor Backmixing on RAFT Polymerization

AbstractThe effects of reactor backmixing on the outcome of RAFT polymerizations are examined. The kinetic model for the RAFT reaction is based on the first principle of mass balances and the method of moments. Two reactor models were applied for the simulation of backmixing, i.e., a PFTR with loop and multiple CSTRs in series. The models predict the behavior of monomer conversion, molecular weights, their distributions as well as the polydispersities for various chain types at different levels of backmixing. Both models demonstrated that a significant impact of reactor backmixing on RAFT kinetics and polymer molecular weight development exists. magnified image

Synthesis of cationic flocculants in continuous reactors

The synthesis of cationic flocculants by inverse microemulsion copolymerization of acrylamide and [2-(acryloyloxy)ethyl]-trimethylammonium chloride in continuous reactors (single CSTR and two CSTRs in series) was investigated. It was found that the particular microstructure of the polymers strongly depended on the process. The polymer synthesized in two CSTRs in series presented the best performance as flocculant because it contained both short (polymer produced in the second reactor) and branched long (polymer produced in the first reactor) polymer chains.

Modeling dry-scrubbing of gaseous HCl with hydrated lime in cyclones with and without recirculation

A mathematical model describing the dry-scrubbing of gaseous hydrogen chloride (HCl) with solid hydrated lime particles (Ca(OH)(2)) was developed and experimentally verified. The model applies to cyclone systems with and without recirculation, where reaction and particle collection occurs in the same processing unit. The Modified Grain Model was selected to describe the behavior of the reaction process and it was assumed that the gas and the solid particles flow in the reactor with a plug flow. In this work, this behavior is approximated by a cascade of N CSTRs in series. Some of the model parameters were estimated by optimization taking into account the experimental results obtained. A good agreement was observed between the experimental results and those predicted by the model, where the main control resistance is the diffusion of the gaseous reactant in the layer of solid product formed.

A mixed-integer formulation for back-off under constrained predictive control

The steady-state economic optimum in chemical process plants generally lies at the intersection of constraints. However, in order to maintain feasible operation in the face of disturbances, the steady-state operating point needs to be moved some distance from the constraints into the feasible region. The optimal back-off is a function of the plant dynamics, the type and magnitude of the expected disturbances, and the plant control system. This paper considers calculation of the optimal back-off with regulation under constrained predictive control. The resulting optimization problem is multilevel in nature, and is formulated and solved as a mixed-integer quadratic or linear programming problem for which global optimality is guaranteed. Case studies comprising CSTRs in series and a fluid catalytic cracking unit illustrate the application of the strategy.

Performance test of a 6-stage continuous reactor for palm methyl ester production

Effects of residence time (3–12 min), stirrer speed (0–800 rpm), and NaOH concentration (0.25–1.0 wt% of oil) on the production performance of the designed 6-stage continuous reactor (2.272 l) for transesterification of palm oil were investigated at molar ratio of methanol to oil of 6:1 and temperature of 60 °C. Higher stirrer speed increased the reaction rate up to an appropriate speed but excessive stirrer speed decreased the reaction rate. Inappropriate stirrer speed runs dramatically decreased the production capacity of the reactor. Higher NaOH concentration significantly increased reaction rate and production capacity of the reactor. The reactor had a residence time distribution equivalent to 5.98 ideal CSTRs in series and a production performance equivalent to a plug flow reactor. At NaOH of 1.0 wt% of oil, the reactor could produce saleable biodiesel within residence time of 6 min in which a production capacity was 17.3 l/h and a power consumption of stirrer was 0.6 kW/m 3.

An Optimization-Based Approach for the Operability Analysis of Continuously Stirred Tank Reactors

A generalized methodology for examining the inherent operability characteristics of chemical reactors is presented. This approach is developed by extending the operability framework proposed by Vinson and Georgakis (In DYCOPS-5, 5th IFAC Symposium on Dynamics and Control of Process Systems; Pergamon Press, 1998 and J. Process Control 2000, 10, 185−194) and Uzturk and Georgakis (Ind. Eng. Chem. Res. 2001, manuscript submitted) to nonsquare systems. This extension is motivated by the fact that operability problems with more control variables than set-point-controlled outputs are more common. In this formulation, both the steady-state and dynamic operability analyses require the solution of families of optimization problems. The proposed methodology is employed to investigate the integration of the design and control of systems of a single CSTR and two CSTRs in series. Results obtained show that (i) reactors operating at higher temperatures are inherently faster than reactors operating at lower temperatures,...

Development and Performance of an Alternative Biofilter System

ABSTRACT Step tracer tests were carried out on lab-scale biofilters to determine the residence time distributions (RTDs) of gases passing through two types of biofilters: a standard biofilter with vertical gas flow and a modified biofilter with horizontal gas flow. Results were used to define the flow patterns in the reactors. “Non-ideal flow” indicates that the flow reactors did not behave like either type of ideal reactor: the perfectly stirred reactor [often called a "continuously stirred tank reactor" (CSTR)] or the plug-flow reactor. The horizontal biofilter with back-mixing was able to accommodate a shorter residence time without the usual requirement of greater biofilter surface area for increased biofiltration efficiency. Experimental results indicated that the first bed of the modified biofilter behaved like two CSTRs in series, while the second bed may be represented by two or three CSTRs in series. Because of the flow baffles used in the horizontal biofilter system, its performance was more similar to completely mixed systems, and hence, it could not be modeled as a plug-flow reactor. For the standard biofilter, the number of CSTRs was found to be between 2 and 9 depending on the airflow rate. In terms of NH3 removal efficiency and elimination capacity, the standard biofilter was not as good as the modified system; moreover, the second bed of the modified biofilter exhibited greater removal efficiency than the first bed. The elimination rate increased as biofilter load increased. An opposite trend was exhibited with respect to removal efficiency.

Modelling of the periodic anaerobic baffled reactor (PABR) based on the retaining factor concept

The fact that the active biomass is continuously removed from the continuously stirred anaerobic digesters, leading to long retention times, has been overcome in a number of high rate systems based on immobilisation of the active biomass, such as the Upflow Anaerobic Sludge Blanket Reactor (UASBR) and the Anaerobic Baffled Reactor (ABR). A kinetic model of glucose consumption, which was developed based on a batch kinetic experiment, was used for the development of a dynamic model for the prediction of the behaviour of the recently developed flexible reactor called the Periodic Anaerobic Baffled Reactor (PABR) [(1998) Wat. Sci. Technol. 38(8–9), 401–408]. The PABR may be operated as a UASBR, an ABR or at an intermediate mode. The key assumption of the model is that the hydraulic behaviour of a PABR is equivalent with the behaviour of CSTRs in series as concerning the dissolved matter, whereas the biomass is allowed to be retained in the PABR through a retention factor accounting for precipitation. The model adequately predicted the experimental behaviour of a glucose fed PABR. The model was subsequently used to examine the behaviour of the PABR as a function of operating conditions, both for constant and varying loading rates. It was shown that for different cases, the reactor should best be operated as a UASBR or as an ABR.

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investi- gated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the re- actor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor op- timization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the re- versible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K 0 that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (w 0 ) of product to sub- strate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a re- versible Michaelis-Menten kinetics, is chosen as a model for the numerical examples. List of symbols CE;0 (mg/l) initial concentration of active enzyme

Application of controllability analysis tools during the conceptual design stage

This paper presents an extension to KBDS (Bañares-Alcántara and Lababidi, 1995), a prototype design support system for process engineering, that will enable the application of controllability and dynamics studies at the early stages of design. The underlying object-oriented knowledge representation structure of KBDS is flexible enough to accommodate such extension. The proposed extension focuses on design models creation and representation, and means of evaluating these models. This includes the addition of steady-state and dynamic modeling capabilities and the provision of communication to external packages to support the analysis and evaluation of design alternatives. Two systems were considered for integration with KBDS: MATLAB (Math Works, Inc., 1993a) and Omola (Andersson, 1995). Communication with these external tools is provided in the first instance through object-oriented message passing; we are planning to use é p é e (Ballinger et al., 1994) in the future. The integrated tools have been tested on the controllability of multiple CSTRs in series and effects of recycle streams. The control analysis sessions are found vital in supporting the evolution of design alternatives. They also highlight some features of KBDS in the support of the design process itself, i.e. the identification of design versions with the output generated by the control tools and the maintenance of decisions made during their application.