Search Results (14)

The hydrodynamic and reaction characteristics of poly-alpha-olefin (PAO) polymerization in a continuous stirred tank reactor (CSTR) under Eulerian–Eulerian multiphase flow and a finite-rate chemical kinetics model were studied in this paper. A mathematical framework correlating 1-decene conversion with operational and structural parameters was established. Numerical simulations revealed an axial circulation flow pattern driven by combined impellers, with internal coils enhancing heat exchange and flow guidance. The gaseous catalyst, injected below the turbine impeller, achieved rapid dispersion and low gas holdup. The results demonstrated that 1-decene conversion exhibited insensitivity to impeller speed under fully turbulent mixing (mixing time <0.15% of space time), suggesting limited mass transfer benefits from further speed increases. Conversion positively correlated with temperature and space time, albeit with diminishing returns at prolonged durations. Series reactor configurations improved conversion efficiency, though incremental gains decreased with additional units. Optimal reactor design should balance conversion targets with economic factors, including energy consumption and capital investment. These findings provide critical insights into scaling PAO polymerization processes, emphasizing the interplay between reactor geometry, mixing dynamics, and reaction kinetics for industrial applications. Full article

The depletion of fossil fuel reserves and their environmental impact have driven the search for sustainable energy alternatives. Biodiesel has emerged as a promising substitute. Being a major byproduct of the coffee industry, spent coffee grounds (SCGs) offer a viable feedstock due to their abundance, high fatty acid content, and calorific value. This study explores biodiesel production from SCGs. First, oil was experimentally extracted from SCGs using Soxhlet extraction with hexane as the solvent. The oil yield varied between 12 and 13.4% with a density of 0.9 g/mL. Reactor modeling and kinetic analysis were performed, showing that CSTRs in series are favorable for the esterification and transesterification reactions. Furthermore, Aspen Plus was used to simulate the extracted oil conversion into biodiesel through a two-step esterification and purification process. The simulation results are verified against previous experimental research. Sensitivity analyses were performed to evaluate the influence of key process parameters, including methanol-to-oil ratio, reactor residence time, and transesterification temperature. The simulation results indicate an optimal biodiesel mass yield of 90.31%, with a purity of 99.63 wt%, at a methanol-to-oil ratio of 12:1 and a transesterification temperature of 60 °C. Full article

Unlike on Fe and Co catalysts, the CO conversion effect on Ru catalyst performance is little reported. This study is undertaken to explore the issue using a series of Ru/NaY catalysts under 200–230 °C, 2.0 MPa, H₂/CO = 2, and 10–60% CO conversion in a 1 L continuous stirred tank reactor (CSTR). The results are comparatively studied with those of Fe and Co catalysts reported previously. The NaY support and four 1.0%, 2.5%, 5.0%, and 7.5% Ru/NaY catalysts were characterized by BET, H₂ chemisorption, H₂O-TPD, XRD, HRTEM, and XANES/EXAFS techniques. The BET and XRD results suggest a high surface area (730 m²/g), high degree of crystallinity of the NaY support, and high dispersion of Ru, while an hcp Ru structure and well-reduced Ru were reflected in the HR-TEM FFT and XANES/EXAFS results. The reaction results indicate that the CO conversion effect on CH₄ and C₅₊ selectivities on the Ru is the same as that on the Fe and Co catalysts, with CH₄ selectivity decreasing and C₅₊ selectivity increasing with increasing CO conversion. However, the CO conversion effect on olefin formation for the Ru catalyst was found to be opposite to that of the Fe and Co; increasing CO conversion enhanced olefin formation but suppressed secondary reactions of 1-olefins. The H₂O cofeeding experiments showed that H₂O impacted olefin formation by suppressing hydrogen adsorption and hydrogenation. The H₂O-TPD experiment evidenced a much stronger H₂O adsorption capacity (6.8 mmol/g-cat) on Ru followed by Co (1 mmol/g-cat), and then Fe (0.2 mmol/g-cat)., which showed only a very low H₂O adsorption capacity.This finding may explain the opposite CO conversion effect on olefin formation observed on the Ru catalyst, and may also explain why low CH₄ selectivity (i.e., 3%) occurred on the Ru catalyst and high CH₄ selectivity (i.e., 6–8%) occurred on the Co catalyst, both of which possess low water gas shift (WGS) activity. Full article

This study examines the asymptotic stability of a continuous stirred tank reactor (CSTR) used for poly(methyl methacrylate) (PMMA) polymerisation, utilizing nonlinear fractional-order mathematical models. By applying Taylor series and Laplace transform techniques analytically and incorporating real plant data, we focus exclusively on the chemical reaction effects in the kinetic constants, disregarding mass transport phenomena. Our results confirm that fractional derivatives significantly enhance the stability and performance of dynamic models compared to traditional integer-order approaches. Specifically, we analyze the stability of a linearized fractional-order system at steady state, demonstrating that the system maintains asymptotic stability within feasible operational limits. Variations in the fractional order reveal distinct impacts on stability regions and system performance, with optimal values leading to improved monomer conversion, polymer concentration, and weight-average molecular weight. Comparative analyses between fractional- and integer-order models show that fractional-order operators broaden stability regions and enable precise tuning of process variables. These findings underscore the efficiency gains achievable through fractional differential equations in polymerisation reactors, positioning fractional calculus as a powerful tool for optimizing CSTR-based polymer production. Full article

The effects of wastewater step-feeding (SF) on the performance of horizontal subsurface flow constructed wetlands (HSF CWs) are numerically investigated. The purpose is to check if this alternative feeding technique increases the ability of HSF CWs to remove pollutants. Two methodologies are used: Initially, the tanks-in-series (TIS) methodology, based on the finite volume method (FVM), is analyzed using the volumetric degradation coefficient λ. In this case, the operation of a CW is similar to a series of continuous stirred-tank reactors (CSTRs) operating under steady conditions. Then, the step-feeding (SF) procedure is presented, in which the CW is operated like a plug flow reactor (PFR). For the numerical investigation, the available experimental data for five existing HSF CWs are used. The results show that SF does not improve the performance of HSF CWs in removing biochemical oxygen demand (BOD) operating under Mediterranean conditions. When the HSF CWs operate without the SF procedure, the performance is between 55 and 81% for the TIS method and 60 and 89% for the PFR method, while the ability of the CW tank to remove the BOD decreases and varies from 48 to 79% (TIS) and from 54 to 86% (PFR), respectively. Full article

The present study evaluates the removal of micropollutants from water/wastewater contaminated sources through the application of a heterogeneous catalytic ozonation process, using a pilot-scale continuous operation unit, composed of a membrane module for the diffusion and effective dilution of ozone into the liquid phase to be treated and a plug flow reactor/continuous stirred tank reactor (PFR/CSTR) contact reactor system in series, where the catalyst is recirculated in dispersion mode. The solid materials tested as catalysts are natural and calcined zeolite, Bayoxide and alumina, whereas the examined micropollutants, used in this case as probe compounds, are p-chlorobenzoic acid (p-CBA), atrazine, benzotriazole and carbamazepine. A high-performance liquid chromatography system was used to determine the removal of micropollutants. In the case of p-CBA, an ozone-resistant compound, the addition of catalyst was found to significantly enhance its degradation rate, leading to >99% removal under the optimum defined conditions, i.e., in terms of catalyst concentration, pH, temperature, and process time. On the other hand, in the case of atrazine, a different ozone-resistant compound, the introduction of examined catalysts in the ozonation process was found to reduce the degradation of micropollutant, when compared with the application of single ozonation, indicating the importance of specific affinity between the pollutant and the solid material used as catalyst. Benzotriazole, a moderately ozone-reactive compound was degraded by more than 95% under all experimental conditions and catalysts tested in the pilot unit, while carbamazepine, a highly ozone-reactive compound, was completely removed even during the first stage of treatment process (i.e., at the membrane contactor). When increasing the pH value (in the range 6–8) and the contact time, the performance of catalytic ozonation process also improved. Full article

The performances of four different designs for a pilot-scale spray dryer have been evaluated and compared based on experimentally measured particle residence time distributions (RTD), recovery rates and physical properties of spray-dried fresh skim milk. The RTDs have been measured using a dye pulse injection method, and the measurements have been fitted to models using continuous stirred-tank reactors in series (CSTR-TIS) for quantitative performance evaluation and comparison. Conical drying chambers and a box connection design have been used in the latest dryer design to reduce the amount of wall deposition and provide a smoother gas flow pattern. The particle-to-gas mean residence time ratio for the latest design is significantly closer to unity (1.6 s/s to 1.0 s/s) compared with earlier designs (2.6 s/s to 1.5 s/s). The latest design has a wider spread of RTD (n = 5–8) compared with earlier designs (n = 13–18), which may be linked to the recirculation zone in the box connection. Although the latest design has a wider spread of RTD, the conical design has shown promising results compared with a cylindrical drying chamber in terms of overall wall deposition behaviours. Full article

A numerical model for the wet torrefaction of poultry litter in a pilot unit was developed in this study. The model accounted for the following process steps: preheating biomass in a feed hopper, feeding biomass into the reactor, fluidized-bed generation using superheated steam, and the supply of additional heat by the electric heating of the reactor walls. Following a “black box” approach, a major assumption of the model is that the behavior of the fluidized-bed reactor is similar to a completely stirred tank reactor (CSTR). Under this assumption, the properties of the particles and gases do not depend on their location inside the reactor. During wet torrefaction, poultry-litter biomass was heated to a predetermined temperature and decomposed, generating biochar along with a gas phase (torgas), whose amounts depended on the content of inert ash in the biomass particles. Variable optimization in the model was performed using MATLAB software. The model successfully estimated the optimal duration required for the completion of wet torrefaction under various conditions: temperature, batch weight, reactor dimensions, etc. The model was validated using experimental data obtained from a series of wet torrefaction experiments performed in a fluidized bed, and provided reliable estimations of the duration of the process depending on material properties, reactor size and feedstock characteristics. Full article

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. Full article

In order to develop an iron-based catalyst with high attrition resistance and stability for Fischer–Tropsch synthesis (FTS), a series of experiments were carried out to investigate the effects of SiO₂ and its hydroxyl content and a boron promoter on the attrition resistance and catalytic behavior of spray-dried precipitated Fe/Cu/K/SiO₂ catalysts. The catalysts were characterized by means of N₂ physisorption, nuclear magnetic resonance (NMR), X-ray diffraction (XRD), Raman spectrum, X-ray photoelectron spectroscopy (XPS), H₂-thermogravimetric analysis (H₂-TGA), temperature-programmed reduction and hydrogenation (TPR and TPH), and scanning and transmission electron microscopy (SEM and TEM). The FTS performance of the catalysts was tested in a slurry-phase continuously stirred tank reactor (CSTR), while the attrition resistance study included a physical test with the standard method and a chemical attrition test under simulated reaction conditions. The results indicated that the increase in SiO₂ content enhances catalysts’ attrition resistance and FTS stability, but decreases activity due to the suppression of further reduction of the catalysts. Moreover, the attrition resistance of the catalysts with the same silica content was greatly improved with an increase in hydroxyl number within silica sources, as well as the FTS activity and stability to some degree. Furthermore, the boron element was found to show remarkable promotion of FTS stability, and the promotion mechanism was discussed with regard to probable interactions between Fe and B, K and B, and SiO₂ and B, etc. An optimized catalyst based on the results of this study was finalized, scaled up, and successfully applied in a megaton industrial slurry bubble FTS unit, exhibiting excellent FTS performance. Full article

In this paper, we study the convergence properties of a network model comprising three continuously stirred tank reactors (CSTRs) with the following features: (i) the first and second CSTRs are connected in series, whereas the second and third CSTRs are connected in parallel with flow exchange; (ii) the pollutant concentration in the inflow to the first CSTR is time varying but bounded; (iii) the states converge to a compact set instead of an equilibrium point, due to the time varying inflow concentration. The practical applicability of the arrangement of CSTRs is to provide a simpler model of pollution removal from wastewater treatment via constructed wetlands, generating a satisfactory description of experimental pollution values with a satisfactory transport dead time. We determine the bounds of the convergence regions, considering these features, and also: (i) we prove the asymptotic convergence of the states; (ii) we determine the effect of the presence of the side tank (third tank) on the transient value of all the system states, and we prove that it has no effect on the convergence regions; (iii) we determine the invariance of the convergence regions. The stability analysis is based on dead zone Lyapunov functions, and comprises: (i) definition of the dead zone quadratic form for each state, and determination of its properties; (ii) determination of the time derivatives of the quadratic forms and its properties. Finally, we illustrate the results obtained by simulation, showing the asymptotic convergence to the compact set. Full article

The present work aims at investigating the residence time distribution (RTD) of a multiple spouted bed reactor, which will be applied for the pyrolysis and gasification of residual biomass. The unit is composed of square-based spouted beds, placed in series and at descending heights, and communicating with each other through an opening in the lateral wall. The gas is fed evenly in parallel. The experimental analysis is based on tracer experiments in cold-flow units, assessing the influence of the number of units and the bed height. The tests proved the good mixing properties of the spouted beds, which create a stable fluidization regime and do not feature dead zones. Each spouted bed can generally be well assimilated to an ideal continuous stirred tank reactor (CSTR). The RTD of the device seems adequate for the application, and also seems to be well tuneable through the selection of the bed height and number of units. Given the good similarity with ideal reactor networks, these represent a valid tool to estimate the final behavior in terms of RTD. Full article

This manuscript addresses a novel output model predictive controller design for a representative model of continuous stirred-tank reactor (CSTR) and axial dispersion reactor with recycle. The underlying model takes the form of ODE-PDE in series and it is operated at an unstable point. The model predictive controller (MPC) design is explored to achieve optimal closed-loop system stabilization and to account for naturally present input and state constraints. The discrete representation of the system is obtained by application of the structure properties (stability, controllability and observability) preserving Cayley-Tustin discretization to the coupled system. The design of a discrete Luenberger observer is also considered to accomplish the output feedback MPC realization. Finally, the simulations demonstrate the performance of the controller, indicating proper stabilization and constraints satisfaction in the closed loop. Full article

The tanks-in-series model (TIS) is a popular model to describe the residence time distribution (RTD) of non-ideal continuously stirred tank reactors (CSTRs) with limited back-mixing. In this work, the TIS model was generalised to a cascade of n CSTRs with non-integer non-negative n. The resulting model describes non-ideal back-mixing with n > 1. However, the most interesting feature of the n-CSTR model is the ability to describe short recirculation times (bypassing) with n < 1 without the need of complex reactor networks. The n-CSTR model is the only model that connects the three fundamental RTDs occurring in reactor modelling by variation of a single shape parameter n: The unit impulse at n→0, the exponential RTD of an ideal CSTR at n = 1, and the delayed impulse of an ideal plug flow reactor at n→∞. The n-CSTR model can be used as a stand-alone model or as part of a reactor network. The bypassing material fraction for the regime n < 1 was analysed. Finally, a Fourier analysis of the n-CSTR was performed to predict the ability of a unit operation to filter out upstream fluctuations and to model the response to upstream set point changes. Full article