Axial Dispersion Model Research Articles

Performance of an Industrial Pulsed Disc-and-Doughnut Extraction Column

ABSTRACTAxial-dispersion and plug-flow models have been used to describe the solvent extraction performance of a 18 m high and 4 m diameter industrial pulsed disc-and-doughnut column. Uranium extraction phase-equilibrium data were fitted with the Langmuir model. Using the industrial column dimensions, operational parameters, physical properties, and the Langmuir parameters, the axial-dispersion model was shown to predict the organic-phase outlet concentration and the aqueous-phase outlet concentration, respectively, while the plug-flow model exhibited a poorer predictive ability.,

Experimental mass transfer coefficients in a pilot plant multistage column extractor

The volumetric overall mass transfer coefficients in a multistage column have been measured using axial dispersion model for toluene–acetone–water system. The effect of operating parameters on the volumetric overall mass transfer coefficients has been investigated for both mass transfer directions. The results show that the mass transfer performance is strongly dependent on rotor speed and mass transfer direction, although only slightly dependent on phase flow rates. In addition, empirical correlations to predict the overall mass transfer coefficients have been developed. The proposed correlations based on dimensionless numbers can be considered as a useful tool for the possible scale up of the multistage column extractor.

Dispersion characteristics of a spiral symmetry stream anaerobic bio-reactor

The dispersion characteristics of an anaerobic reactor affect its flow patterns and consequently impact its removal efficiency η (assumed). The dispersion characteristics of a spiral symmetry stream anaerobic bio-reactor (SSSAB) were investigated under overall and local dispersion conditions, which were well described by the axial dispersion model and increasing-sized CSTRs model, respectively. The flow patterns of the SSSAB under super-high (hydraulic loading rate L=18.45LL−1d−1, biogas production rate G=80.24LL−1d−1) and high loadings (L=9.23LL−1d−1, G=40.12LL−1d−1) tended to the completely mixed flow, while under middle (L=4.61LL−1d−1, G=20.06LL−1d−1) and low loadings (L=2.31LL−1d−1, G=10.03LL−1d−1) tended to the plug-flow. The axial dispersion decreases along the height of the SSSAB. The fluid in the reactor mixed completely after the actual completely mixed time θacm, which decreases from 1.54 to 0.44 with the loading rate increases. The maximum and minimum values of the mean increasing rate vm are 14.00 and 0.72 at super-high and loading rate, respectively. And η positively correlates to the number of tanks N and negatively to vm. Reducing vm and enlarging N are the favorable method to further improve the treatment efficiency for the reactor operated under low or medium loading and high or super-high loading conditions, respectively.

A combined method to facilitate the high dispersion modeling for wastewater treatment bioreactors with closed boundaries

Two tanks in series and axial dispersion models are used frequently for bioreactors flow regime modeling, especially the wastewater treatment reactors. Using the tanks in series model is simple, but the axial dispersion model is dependent on the boundary conditions. In case of high dispersion and closed boundaries, axial dispersion model will be a complicated method. In this paper by combination of tanks in series and axial dispersion models, a new simple model is presented to facilitate the axial dispersion solution for closed boundary condition. For the various studied Peclet numbers, the maximum peak concentration error is calculated by combined method equal to 3% in comparison with the error for open solution that increases progressively and exceeds 14%. Furthermore the combined model peak time errors are zero for all the Peclet numbers while are more than 10% for the open solution.

Batch and Continuous Flow Adsorption of Phenolic Compounds from Olive Mill Wastewater: A Comparison between Nonionic and Ion Exchange Resins

The goals of this work were (i) to compare two anion ion exchange resins (IRA958 Cl and IRA67) and a nonionic resin (XAD16) in terms of phenolic compounds adsorption capacity from olive mill wastewater and (ii) to compare the adsorption capacity of the best resin on columns of different length. The ion exchange resins performed worse than nonionic XAD16 in terms of resin utilization efficiency (20% versus 43%) and phenolic compounds/COD enrichment factor (1.0 versus 2.5). The addition of volatile fatty acids did not hinder phenolic compounds adsorption on either resin, suggesting a noncompetitive adsorption mechanism. A pH increase from 4.9 to 7.2 did not affect the result of this comparison. For the best performing resin (XAD16), an increase in column length from 0.5 to 1.8 m determined an increase in resin utilization efficiency (from 12% to 43%), resin productivity (from 3.4 to 7.6 gsorbed phenolics/kgresin), and phenolics/COD enrichment factor (from 1.2 to 2.5). An axial dispersion model with nonequilibrium adsorption accurately interpreted the phenolic compounds and COD experimental curves.

Axial dispersion and mixing phenomena of the gas phase in a packed pebble-bed reactor

The knowledge and proper analyses of axial dispersion and the mixing phenomena of the coolant gas flow in the dynamic core of pebble-bed nuclear reactors are useful for safe design and efficient operation of these reactors. These processes can be characterized in terms of the residence time distribution and quantified in terms of the axial dispersion coefficient. Therefore, in this work, the axial dispersion coefficients of the gas phase and their residence time distributions were measured experimentally in a separate effect pilot-plant scale and cold-flow experimental setup of 0.3m in diameter, using a sophisticated and advanced gaseous tracer technique. The non-ideal flow of the gas phase in the pebble bed was described using the axial dispersion model (ADM). The effect of the gas velocity on the axial dispersion was investigated using a range of velocities from 0.01 to 2m/s, covering both the laminar and turbulent flow regimes. The effect of the bed structure (pebble size) on the axial dispersion coefficient was investigated, and the results indicate that the pebble size strongly affects axial dispersion and mixing in the packed pebble-bed reactor. The results show that the flow pattern of the gas phase does not deviate much from the idealized plug-flow condition at high flow rate, which depends on the gas flow rate and the bed structure of the pebble-bed. The present work provides insight on the extent of mixing and dispersion in the gas phase in the studied bed using an advanced gas dynamics technique and methodology that properly accounts for the external dispersion.

Hydrodynamic study of a novel membrane aerated biofilm reactor (MABR): Tracer experiments and CFD simulation

The membrane-aerated biofilm reactor (MABR) is a promising technology for wastewater treatment, especially for simultaneous organic and nitrogen removal. The mass transfer phenomena induced by flow velocity and flow pattern is required in order to improve the reactor design and the removal pollutants efficiency. Tracer experiments and residence time distribution (RTD) theory were used to characterize the flow in a special MABR. The liquid phase flow patterns were investigated through tracer pulse stimulus-response technique using dextran blue as model tracer. RTD curves were analyzed by cold-model tests (axial dispersion model ADM, tanks in series model TIS and mixing cell model MCM). The detailed flow pattern of the reactor was obtained from computational fluid dynamic (CFD) simulation. According to experimental results of RTD studies and CFD simulation, the flow patterns were demonstrated to be analogous to completely mixed flow with deviations of the ideal hydrodynamic behavior; stagnant zones (low fluid velocity) in 85% of its volume, being the remainder a channeling trouble (high fluid velocity). These deviations were quantitatively described (macromixing level-global mixing) with a minimum quadratic error function value of (S) 0.01. The local mixing flow pattern (micromixing level) obtained by CFD allowed determining the location of each zone; the stagnant zone is situated in the area where membranes are located; therefore it is possible to assume that degradation reactions of pollutants would take place in this area.

Axial Mixing and Mass Transfer Performance of an Annular Pulsed Disc-and-Doughnut Column

The annular pulsed disc-and-doughnut column (APDDC) is an important type of extraction equipment in the PUREX process, which has been used in several commercial reprocessing plants. As there are few mass transfer experimental results reported in the literature, the axial mixing and mass transfer performance of an APDDC was studied for both extraction and stripping processes in the present work. Two parameters in the axial dispersion model (ADM), namely, the axial dispersion coefficient of the continuous phase and the number of mass transfer units, were regressed by correlating ADM with experimental concentration profiles. The influence of flow rate and pulsation intensity on these parameters was also investigated. Models developed for the PDDC were tested for correlation with APDDC experimental data and suitable models and conditions were determined. The height of a mass transfer unit was also calculated, which highlights the impact of axial mixing on mass transfer performance. Moreover, the influence of internal wettability on mass transfer performance was discussed.

Effect of interfacial mass transfer on the dispersion in segmented flow in straight capillaries

The effect of interfacial mass transfer on the extent of dispersion in liquid‐liquid segmented flow in straight capillaries is studied. In the absence of interfacial mass transfer, dispersion coefficient was seen to go through a minimum with increasing flow rates. In the presence of mass transfer, physicochemical properties of both the phases and slug lengths were seen to vary along the capillary length. The extent of dispersion was always higher in the presence of interfacial mass transfer. The predictions using axial dispersion model deviated noticeably for larger capillaries as the model does not account for varying buoyancy, dynamic contacting, and Marangoni convection. Simulations of a first‐order interfacial reaction considering varying slug lengths showed a significant change in optimum operating parameters than the conventional approach. A special case of “drop‐on‐demand” type of controlled two‐phase flow in capillaries was also studied. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4294–4308, 2015

Column flotation cell design by drift flux and axial dispersion models

A common problem in column flotation research is designing the appropriate cell which provides all the requirements of the desired tests. The drift flux model and the axial dispersion model were used in this paper for designing a column flotation cell for research purposes. To validate the approach, a column with required values of axial mixing coefficient (E), vessel dispersion number (Nd), bubble diameter (db), column height (Hc) and gas holdup (εg) equal to 0.003 (m2/s), 0.32, 1.7 (mm), 1.15 (m) and 7.2 (%) were assumed respectively and the column diameter was calculated as 5.42 (cm) by the developed methodology. The flotation column was constructed based on the calculated value of column diameter and required values of above-mentioned variables. Residence time distribution (RTD) of the liquid phase was measured for the column using the tracer impulse response method. Vessel dispersion number (Nd) was measured from the RTD statistics equal to 0.32, which was completely similar to its required value. One other set of information from the literature was also used for validation and it was found that the methodology is capable of designing of columns with required specifications.

Residence time distribution measurements in a pilot-scale poison tank using radiotracer technique

Various types of systems are used to control the reactivity and shutting down of a nuclear reactor during emergency and routine shutdown operations. Injection of boron solution (borated water) into the core of a reactor is one of the commonly used methods during emergency operation. A pilot-scale poison tank was designed and fabricated to simulate injection of boron poison into the core of a reactor along with coolant water. In order to design a full-scale poison tank, it was desired to characterize flow of liquid from the tank. Residence time distribution (RTD) measurement and analysis was adopted to characterize the flow dynamics. Radiotracer technique was applied to measure RTD of aqueous phase in the tank using Bromine-82 as a radiotracer. RTD measurements were carried out with two different modes of operation of the tank and at different flow rates. In Mode-1, the radiotracer was instantaneously injected at the inlet and monitored at the outlet, whereas in Mode-2, the tank was filled with radiotracer and its concentration was measured at the outlet. From the measured RTD curves, mean residence times (MRTs), dead volume and fraction of liquid pumped in with time were determined. The treated RTD curves were modeled using suitable mathematical models. An axial dispersion model with high degree of backmixing was found suitable to describe flow when operated in Mode-1, whereas a tanks-in-series model with backmixing was found suitable to describe flow of the poison in the tank when operated in Mode-2. The results were utilized to scale-up and design a full-scale poison tank for a nuclear reactor.

Simulation of Direct Dimethyl Ether Synthesis in a Slurry Reactor by Recirculation and Axial Dispersion Models

Dimethyl ether is an environmentally friendly alternative to diesel fuel. This fuel can be produced directly from synthesis gas in a slurry bubble column reactor. We predicted the performance of the slurry bubble column reactor for dimethyl ether synthesis using a recirculation model and comparison with axial dispersion results. The differential equations of recirculation and axial dispersion models for the dimethyl ether synthesis are solved for a similar kinetic equation. A comparison of the results with experimental data from the literature confirms that the recirculation model better represents the reactor behavior. Finally, the effects of operating variables are studied using a simulation framework.

Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

AbstractThis paper presents an extensive review of the kinetics, hydrodynamics, mass transfer, heat transfer and mathematical as well as computational fluid dynamics (CFD) modeling of Low-Temperature Tropsch Synthesis (LTFT) synthesis in Slurry Bubble Column Reactors (SBCRs), with the aim of identifying potential research and development areas in this particular field. The kinetic expressions developed for F-T synthesis over iron and cobalt catalysts along with the water gas shift (WGS) reactions are summarized and compared. The experimental data and empirical correlations to predict the hydrodynamics (gas holdup, Sauter mean bubble diameter, and bubble rise velocity), mass transfer coefficients and heat transfer coefficients are presented. The effects of various operating variables, including pressure, temperature, gas velocity, catalyst concentration, reactor geometry, and reactor internals on the hydrodynamic and transport parameters as well as the performance of SBCRs are discussed. Additionally, modeling efforts of SBCRs, using axial dispersion models (ADM), multiple cell recirculation models (MCCM) and computational fluid dynamics (CFD), are addressed. This review revealed the following:(1)Numerous F-T and WGS kinetic rate expressions are available for cobalt and iron catalysts and one must be careful in selecting the appropriate expressions for LTFT. Iron catalyst suffers from severe attrition and subsequent deactivation in SBCRs and accordingly building a costly catalyst manufacturing facility onsite is required to maintain a steady operation of the F-T reactor;(2)Experimental data on the hydrodynamic and transport parameters at high pressures and temperatures, typical to those of actual F-T synthesis, remain scanty when compared with the plethora of studies conducted using air–water systems in small reactors at ambient conditions;(3)Several empirical correlations for predicting the hydrodynamic and mass as well heat transfer parameters are available and one should select those which consider the reactor diameter, gas mixtures and the potential foamability of the F-T liquids;(4)The effect of cooling internals configuration and sparger design on the hydrodynamic and transport parameters, local turbulence, mixing and catalyst attrition are yet to be seriously addressed;(5)The impact of operating variables on the hydrodynamic and transport parameters as well as the overall performance of the SBCRs should be investigated using actual F-T fluid–solid systems under typical pressures and temperatures using a large-scale reactor (>0.15 m ID) in the presence of gas spargers and cooling internals;(6)Significant efforts are still required in order to advance CFD modeling of SBCRs, particularly those pertaining to the relevant closure models, such as drag, lift and turbulence. Also, cooling internals configuration and the design as well as orientation of gas spargers should be accounted for in the CFD modeling; and(7)Proper validations of the CFD formulations using actual systems for F-T SBCR are needed.

Characterization Method for Separation Devices Based on Micro Technology

AbstractDesign of microstructured process modules based on empirical approaches is time‐ and cost intensive. This becomes especially important for complex continuous operations, where several unit operations have to be efficiently combined for maximum process efficiency and economy. A concept for a model‐based design by an axial dispersion model is presented as a contribution to simplification and cost reduction. Simple microchannel structures with varying cross sections are evaluated with volume flows up to 20 mL min−1. The predictive accuracy of the model is demonstrated and assessed by selected examples.

A one-parameter model for describing the residence time distribution of closed continuous flow systems characterized by nonlinear reaction kinetics: Rod and ball mills

For evaluation of the performance of a continuous flow reactor, a description of the residence time distribution (RTD) of the reactants is required in the form of a suitable mathematical expression. For closed reactors, the analytic expression obtained from the well known axial dispersion model is too complicated for practical use. The \ wo-parameter empirical model that involves one large and two small perfectly mixed sub-reactors along with a small plug flow sub-reactor provides an accurate description of RTD in the form of a relatively much simpler mathematical expression. However, due to the lack of specification of the sequence in which the sub-reactors are arranged, this model cannot be used for modeling of systems characterized by nonlinear reaction kinetics. Therefore, in this paper we propose a new one-parameter empirical model that meets both the requirements. The model involves partitioning the process unit into a number of unequal-volume perfect mixers arranged in a definite order. The first perfect mixer at the feed end is the largest, and the volumes of the successive smaller perfect mixers form a geometric progression, the inverse of the common ratio being the sole parameter of the model. Several sets of available experimental RTD data on two closed reactors, rod mills and ball mills, were analyzed using the proposed model. In most cases the model was found to fit the experimental data on a par with the dispersion and two-parameter models. Moreover, the proposed order of arrangement of different perfect mixers could be validated by demonstrating that the simulated trend of variation in the particle size distribution along the mill matches closely with that observed in practice.

Axial dispersion model in predictive mass transfer correlation for random pulsed packed column

The continuous phase volumetric overall mass transfer coefficient in a ceramic intalox saddle pulsed packed extraction column using axial dispersion model was studied for two different liquid-liquid systems containing water/acetone/toluene and water/acetone/n-butyl acetate. The effects of pulsation intensity, continuous and dispersed phase flow rates on mass transfer coefficient were investigated. The experimental results indicated that the mass transfer coefficient was enhanced by increasing pulsation intensity and dispersed and continuous phase flow rates. The utilization of nonlinear least square method provided a new predictive correlation for the continuous phase overall mass transfer coefficient. The developed mass transfer model was validated via the comparison of the modeling data with experimental results with 18.7% average absolute relative error (AARE). Furthermore, one empirical correlation was developed for prediction of the continuous phase overall mass transfer coefficient as the function of the aforementioned operating variables.

CFD analysis and flow model reduction for surfactant production in helix reactor

Flow pattern analysis in a spiral Helix reactor is conducted, for the application in the commercial surfactant production. Step change response curves (SCR) were obtained from numerical tracer experiments by three-dimensional computational fluid dynamics (CFD) simulations. Non-reactive flow is simulated, though viscosity is treated as variable in the direction of flow, as it increases during the reaction. The design and operating parameters (reactor diameter, number of coils and inlet velocity) are varied in CFD simulations, in order to examine the effects on the flow pattern. Given that 3D simulations are not practical for fast computations needed for optimization, scale-up and control, CFD flow model is reduced to one-dimensional axial dispersion (AD) model with spatially variable dispersion coefficient. Dimensionless dispersion coefficient (Pe) is estimated under different conditions and results are analyzed. Finally, correlation which relates Pe number with Reynolds number and number of coils from the reactor entrance is proposed for the particular reactor application and conditions.

MODELING OF LAMINAR FLOW TUBULAR REACTOR USING VELOCITY PROFILE

Design of reactor using traditional performance equations is inadequate as it does not take into account non-ideality in the reactors. Quantification of non-ideality is done using Residence Time Distribution studies (RTD). But RTD studies can be carried out on already existing reactor. Therefore this technique will not help in incorporating non-ideality in the design stage. Another method is to use Computational Fluid Dynamics (CFD) packages and predict RTD. The methods used to predict reactor performance using RTD involves modeling, fitting the RTD data to the model to determine the model parameters such as number of tanks in tanks in series model or dispersion number in axial dispersion model. These models are inadequate as the RTD may not be a proper fit. After the model fit, using the model parameter to determine the performance of the reactor is cumbersome and in some cases it is not possible. There are several models that predict reactor performance which use Convection – Diffusion – Reaction (CDR) equations and these methods are computationally intensive. Simpler models that are less computationally intensive but adequate enough to predict reactor performance are to be developed. In the present paper a model is developed which makes use of only velocity profile to predict homogeneous reactor performance. Algorithm of the model is then applied to Laminar Flow Tubular Reactor (LFTR). Testing of the model is done by comparing the results of the model with those predicted by well established analytical methods for LFTR. The results of the model and those of LFTR agree well.

Flow Characterization of Vapor Phase of Geothermal Fluid in Pipe Using Isotope <sup>85</sup>Kr and Residence Time Distribution Modeling

Measurement of vapor flow in geothermal pipe faces great challenges due to fast fluids flow in high-temperature and high-pressure environment. In present study the flow rate measurement has been performed to characterization the geothermal vapor flow in a pipe. The experiment was carried out in a pipe which is connected to a geothermal production well, KMJ-14. The pipe has a 10 ” outside diameter and contains dry vapor at a pressure of 8 kg/cm 2 and a temperature of 170 o C. Krypton-85 gas isotope ( 85 Kr) has been injected into the pipe. Three collimated radiation detectors positioned respectively at 127, 177 and 227 m from injection point were used to obtain experimental data which represent radiotracer residence time distribution (RTD) in the pipe. The last detector at the position of 227 m did not respond, which might be due to problems in cable connections. Flow properties calculated using mean residence time (MRT) shows that the flow rate of the vapor in pipe is 10.98 m/s, much faster than fluid flow commonly found in various industrial process plants. Best fitting evaluated using dedicated software developed by IAEA expert obtained the P e clet number Pe as 223. This means that the flow of vapor of geothermal fluids in pipe is plug flow in character. The molecular diffusion coefficient is 0 . 45 m 2 /s, calculated from the axial dispersion model. Received: 21 November 2013; Revised: 16 May 2014; Accepted: 23 May 2014

Enhancement of CO conversion in a novel slurry bubble column reactor for methanol synthesis

This paper is dealing with the simulation of a commercial size slurry bubble column reactor (SBCR) for catalytic conversion of synthesis gas (CO + CO2 + H2) to methanol and comparison of the results especially carbon monoxide removal with gas-phase model in the quasi-steady state condition. For this purpose it was assumed that the flow pattern of gas is plug, and axial dispersion model was considered for liquid–solid phase. The results of the model for Shiraz petrochemical complex feedstock show that the production rate of methanol in a commercial SBC reactor is lower than conventional gas-phase methanol synthesis. This disadvantage is corrected by the modified feed which includes 5% CO and the 95% of the conventional feed. This novelty results in the same methanol production rate with the conventional gas-phase reactor. Besides the same methanol production rate, CO injection to the feed, causes water production noticeably reduced during methanol synthesis via CO2 hydrogenation. Consequently lower catalyst deactivation rate and higher methanol production rate are achieved.