Development of support vector regression (SVR)-based correlation for prediction of overall gas hold-up in bubble column reactors for various gas-liquid systems

The objective of this study was to develop a unified data-driven correlation for the overall gas hold-up for various gas-liquid systems using support vector regression (SVR)-based modeling technique. Over the years, researchers have amply quantified the hydrodynamics of bubble column reactors in terms of the overall gas hold-up. In this work, about 1810 experimental points were collected from 40 open sources spanning the years 1965-2007. The model for overall gas hold-up was established as a function of several parameters which include superficial gas velocity, superficial liquid velocity, gas density, molecular weight of gas, sparger type, sparger hole diameter, number of sparger holes, liquid viscosity, liquid density, liquid surface tension, operating temperature, operating pressure and column diameter of the gas-liquid system. For understanding the hold-up behavior, the data used for training the model was grouped into various gas-liquid systems viz., air-water, gas-aqueous viscous liquids, gas-organic liquids, gas-aqueous electrolyte solutions and gas-liquid systems operated over a wide range of pressure. A generalized model established using SVR was evaluated for its performance for various gas-liquid systems. Statistical analysis showed that the proposed generalized SVR-based correlation for overall gas hold-up has prediction accuracy of 97% with average absolute relative error (% AARE) of 12.11%. A comparison of this correlation with the selected system specific correlations in the literature showed that the developed SVR-based correlation significantly gives enhanced prediction of overall gas hold-up.     

Effect of geometrical parameters of draft tubes and clear liquid height on gas holdup in a bubble column for gas dispersion into tubes

The effects of the geometrical parameters of draft tubes and the clear liquid height on the average gas holdup E_G in a 0.16 m I.D. bubble column for gas dispersion into the tubes were experimentally studied in an airtap water system. The gas holdup depended on the superficial gas velocity U(ING), the kinds of gas spargers, the diameter and length of the draft tubes, clearance C_b between the lower end of the draft tube and the bottom of the bubble column, and the clear liquid height H_L. E_G increased with decreasing hole diameter of the gas sparger at a small gas velocity U_G, but did not depend on the kinds of gas spargers at a large U_G. E_G decreased with increasing clear liquid height H_L. The effect of H_L on E_G was well expressed by the modified three-region model. The experimental data of E_G were correlated.     

The effect of gas‐liquid counter‐current operation on gas hold‐up in bubble columns using electrical resistance tomography

BACKGROUND: In order to improve the performance of a counter‐current bubble column, radial variations of the gas hold‐ups and mean hold‐ups were investigated in a 0.160 m i.d. bubble column using electrical resistance tomography with two axial locations (Plane 1 and Plane 2). In all experiments the liquid phase was tap water and the gas phase air. The superficial gas velocity was varied from 0.02 to 0.25 m s^?1, and the liquid velocity varied from 0 to 0.01 m s^?1. The effect of liquid velocity on the distribution of mean hold‐ups and radial gas hold‐ups is discussed. RESULTS: The gas hold‐up profile in a gas–liquid counter‐current bubble column was determined by electrical resistance tomography. The liquid velocity slightly influences the mean hold‐up and radial hold‐up distribution under the selected operating conditions and the liquid flow improves the transition gas velocity from a homogeneous regime to a heterogeneous regime. Meanwhile, the radial gas hold‐up profiles are steeper at the central region of the column with increasing gas velocity. Moreover, the gas hold‐up in the centre of the column becomes steeper with increasing liquid velocity. CONCLUSIONS: The value of mean gas hold‐ups slightly increases with increasing downward liquid velocity, and more than mean gas hold‐ups in batch and co‐current operation. According to the experimental results, an empirical correlation for the centreline gas hold‐up is obtained based on the effects of gas velocity, liquid velocity, and ratio of axial height to column diameter. The values calculated in this way are in close agreement with experimental data, and compare with literature data on gas hold‐ups at the centre of the column. Copyright © 2010 Society of Chemical Industry     

A novel three‐phase airlift reactor without circulation of solids

A novel configuration of a three‐phase internal loop airlift reactor is proposed. The draft is divided in two sections: (top) gas–liquid contact section; (bottom) liquid–solid contact section. Solids particles are fluidized in the bottom section by liquid circulation. The main advantage compared with classic airlift or three‐phase fluidized bed is the reduced stress on particles as interference with bubbles is prevented. Experiments with silica sand (325 µm diameter) were carried out to characterise the hydrodynamics of the airlift. The influence of superficial gas velocity, overall solids hold‐up and sparger height were assessed. A theoretical analysis was proposed to derive simple design criteria.     

Hydrodynamics,Mass Transfer and Gas Scrubbing in a Co‐current Droplet Column Operating at High Gas Velocities

The main objective of this work was to propose a new process for household fume incineration treatment: the droplet column. A feature of this upward gas‐liquid reactor which makes it original, is to use high superficial gas velocities (13 m s^–1) which allow acid gas scrubbing at low energy costs. Tests were conducted to characterize the hydrodynamics, mass transfer performances, and acid gas scrubbing under various conditions of superficial gas velocity (from 10.0 to 12.0 m s^–1) and superficial liquid velocity (from 9.4·10^–3 to 18.9·10^–3 m s^–1). The following parameters characterized the hydrodynamics: pressure drops, liquid hold‐ups, and liquid residence time distribution were identified and investigated with respect to flow conditions. To characterize mass transfer in the droplet column, three parameters were determined: the gas‐liquid interfacial area (a), the liquid‐phase volumetric mass transfer coefficient (k_La) and the gas‐phase volumetric mass transfer coefficient (k_Ga). Gas absorption with chemical reaction methods were applied to evaluate a and k_Ga, while a physical absorption method was used to estimate k_La. The influence of the gas and liquid velocities on a, k_La, and k_Ga were investigated. Furthermore, tests were conducted to examine the utility of the droplet column for the acid gas scrubbing, of gases like hydrogen chloride (HCl) and sulfur dioxide (SO₂). This is a process of high efficiency and the amount of pollutants in the cleaned air is always much lower than the regulatory European standards imposed on household waste incinerators.     

Bubble size and radial gas hold‐up distributions in a slurry bubble column using ultrafast electron beam X‐ray tomography

Gas hold‐up and bubble size distribution in a slurry bubble column (SBC) were measured using the advanced noninvasive ultrafast electron beam X‐ray tomography technique. Experiments have been performed in a cylindrical column (D_T = 0.07 m) with air and water as the gas and liquid phase and spherical glass particles (d_P = 100 μm) as solids. The effects of solid concentration (0 ≤ C_s ≤ 0.36) and superficial gas velocity (0.02 ≤ U_G ≤ 0.05 m/s) on the flow structure, radial gas hold‐up profile and approximate bubble size distribution at different column heights in a SBC were studied. Bubble coalescence regime was observed with addition of solid particles; however, at higher solid concentrations, larger bubble slugs were found to break‐up. The approximate bubble size distribution and radial gas hold‐up was found to be dependent on U_G and C_s. The average bubble diameter calculated from the approximate bubble size distribution was increasing with increase of U_G. The average gas hold‐up was calculated as a function of U_G and agrees satisfactorily with previously published findings. The average gas hold‐up was also predicted as a function of C_s and agrees well for low C_s and disagrees for high C_s with findings of previous literature. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1709–1722, 2013     

Mass transfer and hydrodynamic characteristics in a co‐current downflow contacting column

Hydrodynamic and mass transfer characteristics of water–air system in a co‐current downflow contacting column (CDCC) were studied for various nozzle diameters at different superficial gas velocities and liquid re‐circulation rates. Gas hold‐up and liquid‐side mass transfer coefficient increased with increasing superficial gas velocity and liquid flow rate but decreased with increasing nozzle diameter. It is shown that correlations developed, which are based on liquid kinetic power per liquid volume present in the column, and superficial gas velocity explains gas hold‐up and the mass transfer coefficient within an error 20% for all gas and liquid flow rates and nozzle diameters used. The constants of correlations for gas hold‐up and mass transfer coefficient were found to be considerably different from other gas–liquid contacting systems. © 2003 Society of Chemical Industry     

Effect of Dual Impeller‐Sparger Geometry on the Hydrodynamics and Mass Transfer in Stirred Vessels

The understanding of the effect of impeller‐sparger configurations on gas dispersion and mass transfer is very important to improve the performance of gas/liquid contactor systems. The influence of the impeller positions, the upper turbine diameter, the sparger ring diameter and its location in regard to the lower impeller on the power consumption, the volumetric mass‐transfer coefficient and the overall oxygen transfer efficiency were studied in a nonstandard curved bottomed reactor with an agitated system with dual disk style turbines. In the range of the gas flow rates studied, the most efficient impeller‐sparger arrangement for the oxygen transfer is the impeller system with turbines of different diameters located at C = 0.25 and IC = 0.5, and with the sparger of smaller diameter than the lower impeller settled below the impeller. A new model to estimate the k_La with an average relative error of 8 %, which takes the reactor operation conditions and the influence of the impeller‐sparger geometry into account, was also proposed.     

外环流反应器的气含率及循环液速

研究了气体分布器的形式、体系的聚并特性及静液面高度对外环流反应器的气含率和环流液速的影响。实验结果显示,对于空气－１％乙醇体系（非聚并体系）,气体分布器的形式对外环流反应器的气含率及环流液速有显著的影响;在相同的操作条件下,空气－１％乙醇体系（非聚并体系）的气含率及环流液速明显高于空气－水体系（聚并体系）。静液面高度对下降区的气含率有较大影响。     

Liquid flow and phase holdup—measurement and CFD modeling for two-and three-phase bubble columns

Bubble columns are an important class of contacting devices in chemical industry and biotechnology. Their simple setup makes them ideal reactors for two- and three-phase operations such as fermentations or heterogeneous catalysis. Still, design and operation of these reactors is subject to widely empirical scale-up strategies. With recent advances in the development of measurement techniques, a more detailed approach to the development of optimized reactors for specific operations should become possible. This report is based on detailed measurements of local dispersed phase holdups in a pilot plant-sized bubble column operated at high superficial gas velocities and solid holdups. It deals with the influence of superficial gas velocity, solid loading and sparger geometry on measured and computed liquid flow velocities and holdup distributions. Liquid velocity measurements have been performed using the electrodiffusion method, modeling calculations have been carried out using the computational fluid dynamics (CFD) code CFX-4.3. Measurement results presented here give an insight into the development of liquid circulation and fluctuating velocity distribution depending on superficial gas velocity, solid loading and sparger geometry. CFD results implementing a multi-fluid model with k-ε turbulence and special momentum exchange terms for direct gas-solid interactions show that, even on standard PC workstations, this kind of computations can deliver qualitatively reasonable agreement with measurements.     

Hydrogenation of 2‐ethylanthraquinone under Taylor flow in single square channel monolith reactors

The hydrogenation of 2‐ethylanthraquinone (EAQ) to 2‐ethylanthrahydroquinone (EAHQ) was carried out under Taylor flow in single square channel monolith reactors. The two opening ends of opaque reaction channel were connected with two circular transparent quartz‐glass capillaries, where Taylor flow hydrodynamics parameters were measured and further used to obtain practical flow state of reactants in square reaction channels. A carefully designed gas‐liquid inlet mixer was used to supply steady gas bubbles and liquid slugs with desired length. The effects of various operating parameters, involving superficial gas velocity, superficial liquid velocity, gas bubble length, liquid slug length, two‐phase velocity and temperature, on EAQ conversion were systematically researched. Based on EAQ conversion, experimental overall volumetric mass transfer coefficients were calculated, and also studied as functions of various parameters as mentioned earlier. The film model, penetration model, and existing semi‐empirical formula were used to predict gas‐solid, gas‐liquid, and liquid‐solid volumetric mass transfer coefficients in Taylor flow, respectively. The predicted overall volumetric mass transfer coefficients agreed well with the experimental ones. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Population balance modeling of bubble size distributions in a direct-contact evaporator using a sparger model

The study of bubble size distributions in direct-contact evaporators was addressed both theoretically and experimentally. Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions. A sparger model was developed based on experimental data for a non-coalescing system and using bubble formation models for isothermal and non-isothermal conditions. Bubble size distributions in a direct-contact evaporator operating in the quasi-steady-state regime for four different gas superficial velocities, including the homogeneous and heterogeneous regimes, together with the sparger model, were used for estimating the three empirical parameters from the population balance model, which were observed to be functions of the gas superficial velocity. In all cases considered, the population balance model fitted the experimental data rather well and the regressed parameters exhibit the physically expected behavior with changes in the gas superficial velocity.     

Measurement of Local Phase Holdups in a Two‐ and Three‐Phase Bubble Column

A new invasive sensing probe for the measurement of local phase holdups in two‐ and three‐phase reactors is described. The local gas and solids holdups in a bubble column with a volume of V = 2 m³ at varying operating conditions (gas velocity, sparger design, solids content and density) are measured by means of differential pressure measurement in combination with either time domain reflectometry or electrical conductivity measurement. The phase distribution profiles at two‐ and three‐phase operating conditions are described. The influence of the sparger design on the shape of these profiles, the influence of the solid phase on the gas distribution, the solids distribution and the gas‐stow effect above the sparger because of a dense particle layer are capable of experimental proof for the first time.     

Assessing the performance of an industrial SBCR for Fischer–Tropsch synthesis: Experimental and modeling

The main objective of this study is to predict the performance of an industrial‐scale (ID = 5.8 m) slurry bubble column reactor (SBCR) operating with iron‐based catalyst for Fischer–Tropsch (FT) synthesis, with emphasis on catalyst deactivation. To achieve this objective, a comprehensive reactor model, incorporating the hydrodynamic and mass‐transfer parameters (gas holdup, ε_G, Sauter‐mean diameter of gas bubbles, d₃₂, and volumetric liquid‐side mass‐transfer coefficients, k_La), and FT as well as water gas shift reaction kinetics, was developed. The hydrodynamic and mass‐transfer parameters for He/N₂ gaseous mixtures, as surrogates for H₂/CO, were obtained in an actual molten FT reactor wax produced from the same reactor. The data were measured in a pilot‐scale (0.29 m) SBCR under different pressures (4–31 bar), temperatures (380–500 K), superficial gas velocities (0.1–0.3 m/s), and iron‐based catalyst concentrations (0–45 wt %). The data were modeled and predictive correlations were incorporated into the reactor model. The reactor model was then used to study the effects of catalyst concentration and reactor length‐to‐diameter ratio (L/D) on the water partial pressure, which is mainly responsible for iron catalyst deactivation, the H₂ and CO conversions and the C₅₊ product yields. The modeling results of the industrial SBCR investigated in this study showed that (1) the water partial pressure should be maintained under 3 bars to minimize deactivation of the iron‐based catalyst used; (2) the catalyst concentration has much more impact on the gas holdup and reactor performance than the reactor height; and (3) the reactor should be operated in the kinetically controlled regime with an L/D of 4.48 and a catalyst concentration of 22 wt % to maximize C₅₊ products yield, while minimizing the iron catalyst deactivation. Under such conditions, the H₂ and CO conversions were 49.4% and 69.3%, respectively, and the C₅₊ products yield was 435.6 ton/day. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3838–3857, 2015     

Gas‐Liquid Mass Transfer in a Slurry Bubble Column at High Slurry Concentrations and High Gas Velocities

The volumetric mass transfer coefficient k_La in a 0.1 m‐diameter bubble column was studied for an air‐slurry system. A C₉‐C₁₁ n‐paraffin oil was employed as the liquid phase with fine alumina catalyst carrier particles used as the solid phase. The n‐paraffin oil had properties similar to those of the liquid phase in a commercial Fischer‐Tropsch reactor under reaction conditions. The superficial gas velocity U_G was varied in the range of 0.01 to 0.8 m/s, spanning both the homogeneous and heterogeneous flow regimes. The slurry concentration ?_S ranged from 0 to 0.5. The experimental results obtained show that the gas hold‐up ?_G decreases with an increase in slurry concentration, with this decrease being most significant when ?_S < 0.2. k_La/?_G was found to be practically independent of the superficial gas velocity when U_G > 0.1 m/s is taking on values predominantly between 0.4 and 0.6 s^–1 when ?_S = 0.1 to 0.4, and 0.29 s^–1, when ?_S = 0.5. This study provides a practical means for estimating the volumetric mass transfer coefficient k_La in an industrial‐size bubble column slurry reactor, with a particular focus on the Fischer‐Tropsch process as well as high gas velocities and high slurry concentrations.     

Gas—Liquid Mass Transfer Coefficient in Stirred Tank Reactors

Volumetric gas—liquid mass transfer coefficient (k_La) data available in the literature for larger tanks (T = 0.39 m to 2.7 m) have been analyzed on the basis of relative dispersion parameter, N/N_cd. It was observed that at a given superficial gas velocity (V_G), k_La values were approximately the same irrespective of geometric configuration (size of the tank, type and size of the impellers, type of the sparger, etc.) at a particular N/N_cd. A single correlation based on N/N_cd is presented which shows satisfactory agreement with the k_La data of different workers.     

Process modeling and optimization of industrial ethylene oxide reactor by integrating support vector regression and genetic algorithm

This article presents an artificial intelligence‐based process modeling and optimization strategies, namely support vector regression–genetic algorithm (SVR‐GA) for modeling and optimization of catalytic industrial ethylene oxide (EO) reactor. In the SVR‐GA approach, an SVR model is constructed for correlating process data comprising values of operating and performance variables. Next, model inputs describing process operating variables are optimized using Genetic Algorithm (GAs) with a view to maximize the process performance. The GA possesses certain unique advantages over the commonly used gradient‐based deterministic optimization algorithms The SVR‐GA is a new strategy for chemical process modeling and optimization. The major advantage of the strategies is that modeling and optimization can be conducted exclusively from the historic process data wherein the detailed knowledge of process phenomenology (reaction mechanism, kinetics, etc.) is not required. Using SVR‐GA strategy, a number of sets of optimized operating conditions leading to maximized EO production and catalyst selectivity were obtained. The optimized solutions when verified in actual plant resulted in a significant improvement in the EO production rate and catalyst selectivity.     

Gas hold‐up in stirred tank reactors

Based on a study of the gas hold‐up data for stirred tank reactor generated in the present work and the data available in the literature for large stirred tank reactors (T = 0.57 m to 2.7 m) equipped with disc turbines and pitched blade downflow turbines a correlation is presented which reliably predicts gas hold‐up data over wide range of system configurations and operating parameters. The parameter used, N/N_cd, relates gas hold‐up at impeller speed N with respect to the gas hold‐up at minimum impeller speed for complete dispersion of the gas, N_cd. It is shown that the gas hold‐up data of different workers when compared on the basis of N/N_cd, shows unanimity.     

Diluted alcohol solutions in bubble columns and draft tube airlift reactors with a single orifice sparger: experiments and simple correlations

BACKGROUND: Bubble columns (BCs) and airlift reactors (ALRs) have important applications as bioreactors, chemical reactors and as contactors in waste‐water treatment. The liquid phase properties in these reactors significantly influence the main hydrodynamic and mass transfer characteristics. Dilute alcohol solutions can be used to simulate real industrial systems in bioreactors. However, only a few research studies have considered such systems. The aim of this paper is to broaden the existing experimental data related to the influence of alcohol addition on the main characteristics of draft tube airlift reactors (DT‐ALRs), and to propose simple correlations for their prediction. RESULTS: New experiments were conducted in a DT‐ALR with a single orifice sparger, and with dilute aliphatic alcohol solutions from methanol to n‐octanol. Also, simple correlations were developed to predict the gas hold‐up and volumetric mass transfer coefficients in BCs and DT‐ALRs, but also the downcomer liquid velocity and liquid circulation time DT‐ALRs with single orifice sparger and dilute alcohol solutions. The proposed correlations included, in addition to the superficial gas velocity, the surface tension gradient as the only factor to characterize the liquid phase. CONCLUSIONS: General conclusion can be made that the gas holdup increased, but the downcomer liquid velocity decreased in a DT‐ALR, with increase in surface tension gradient of the alcohol solutions. Also, very good agreement was achieved between experimental and calculated data, by applying the developed correlations, with relative average errors less than 5%, except for gas hold‐up, where it was in the range 8–32%. Copyright © 2009 Society of Chemical Industry     

Fault detection and isolation in hybrid process systems using a combined data‐driven and observer‐design methodology

A combined data‐driven and observer‐design methodology for fault detection and isolation (FDI) in hybrid process systems with switching operating modes is proposed. The main contribution is to construct a unified framework for FDI by integrating Gaussian mixture models (GMM), subspace model identification (SMI), and results from unknown input observer (UIO) theory. Initially, a GMM is built to identify and describe the multimodality of hybrid systems using the recorded input/output process data. A state‐space model is then obtained for each specific operating mode based on SMI if the system matrices are unknown. An UIO is designed to estimate the system states robustly, based on which the fault detection is laid out through a multivariate analysis of the residuals. Finally, by designing a set of unknown input matrices for specific fault scenarios, fault isolation is performed through the disturbance‐decoupling principle from the UIO theory. A significant benefit of the developed framework is to overcome some of the limitations associated with individual model‐based and data‐based approaches in dealing with the problem of FDI in hybrid systems. Finally, the validity and effectiveness of the proposed monitoring framework are demonstrated using a numerical example, a simulated continuous stirred tank heater process, and the Tennessee Eastman benchmark process. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2805–2814, 2014