Methanation in a fluidized bed reactor with high initial CO partial pressure: Part II— Modeling and sensitivity study

A model of a bench-scale methanation reactor was set-up by modifying the classical two-phase model approach and introducing an additional bulk flow from bubble to dense phase to consider the volume contraction of the methanation reaction. The model uses experimentally determined kinetics and hydrodynamic correlations from literature. It was satisfyingly validated by comparing the calculated gas concentration profiles with the experimental data, especially with respect to initial reaction rates and reactor exit concentrations.A sensitivity study with respect to different bubble size correlations, mass transfer rates and considering or neglecting the bulk flow (influence of volume contraction caused by the methanation reaction) was carried out. It showed that the bubble size correlation by Werther and the resulting gas concentration profiles fit the measured data better than the computed gas concentration profiles using the bubble size correlation by Rowe.Neither a variation of the mass transfer coefficient nor neglecting the bulk flow in the fluidized bed model did yield further improvement of the calculated concentration profiles.     

Extraction liquide-liquide. Transfert de matiére et dispersion axiale dans une colonne à pulvérisation

Mass transfer has been studied in two spray columns with dense and loose packing flows using Heptane-DMSO-Benzene and Heptane-Water-Acetone ternary systems.The existence of dense packing flow mainly depends on the mass transfer direction. When mass transfer occurs from the continuous phase to the drops, the dense packing flow exists and is stable. On the contrary, a large coalescence takes place when the transfer occurs from the drops to the continuous phase.Concentration profiles in the continuous phase have been obtained and interpreted with the model of piston flow with axial mixing. The two parameters of the model-transfer unit number and Peclet number-lead to the mass transfer conductance and the axial dispersion coefficient that can be related to the relative velocity of the two phases which was found to be a characteristic value for hydro-dynamic behaviour.     

Modeling the axial distribution of mass transfer coefficient in an agitated-pulsed extraction column

The dispersed phase holdup and drop size in solvent extraction columns vary along the column height and this affects the mass transfer coefficient and interfacial area. In this article, mass transfer study was performed experimentally using a 25 mm diameter agitated pulsed column. The axial distribution of mass transfer coefficient was determined by coupling population balance equation and axial dispersion model by taking the longitudinal variation in hydrodynamic performance into consideration. Feasibility of different mass transfer models in predicting concentration profiles was evaluated and a novel correlation based on effective diffusivity was developed. The results showed that both overall and volumetric mass transfer coefficients have significant change along the column height and greatly depends on the agitation speed and pulsation intensity. Increasing dispersed phase velocity also augments the overall mass transfer coefficient. The maximum number of transfer unit was measured to be 10 m⁻¹ at agitation speed of 1000 rpm.     

Experimental study of Gas—liquid transfer rates using an inclined perforated tray without downcomer

Gas—liquid interfacial area, liquid phase and gas phase mass transfer coefficients are measured for an inclined perforated plate without downcomer. The influence of geometric and hydrodynamic parameters is investigated experimentally.The existence of optimal geometries and hydrodynamic conditions which yield maximal mass transfer rates is shown. A techno—economic study is carried out which compares usual equipment with the present technique. Possible applications are suggested.     

Hydrodynamics and mass transport in rotary disk contactors

This paper reports a detailed study of the hydrodynamics involved in the operation of rotary disk contactors (RDC). New information is presented regarding the ‘critical rotor speed’ which divides the two hydrodynamic regimes of near constant and varying characteristic velocity of the dispersed droplet phase. Generalized correlations for prediction of characteristic velocity both above and below the critical rotor speed have been proposed under conditions of no solute transfer as well as solute transfer between the dispersed and continuous phases. Experimental data on mass transfer obtained in the two hydrodynamic regimes of RDC operation have also been correlated by the application of mass transport theory taking into account the factors affecting the interfacial area of contact, drop size, characteristic velocity and dispersed phase holdup.     

Auslegungskonzept für pulsierte Siebboden-Extraktoren

A concept for the design of pulsed sieve-plate extractors . A concept is presented for the design of pulsed sieve-plate extractors (PSE) according to which the column diameter is calculated via the flooding load and the column length by concentration profiles using the well known backmixing models. This concept requires some parameters to describe the hydrodynamic and mass transfer behaviour. The parameters depend on physical properties, operating conditions, and extractor geometry and subject to mutual influence. It is now possible to present correlations and models for prediction of these parameters. The mass transfer term can be determined by Sherwood correlations for single drops, using the Sauter mean drop diameter. The total mass transfer coefficient can be given as a function of column lenght. The calculated concentration profiles agree well with the measured profiles and thus the concept is confirmed.     

A Novel Model for Predicting the Dense Phase Behavior of 3D Gas‐Solid Fluidized Beds

A novel phenomenological discrete bubble model was developed and tested for prediction of the hydrodynamic behavior of the dense phase of a 3D gas‐solid cylindrical fluidized bed. The mirror image technique was applied to take into account the effects of the bed wall. The simulation results were validated against experimental data reported in the literature that were obtained by positron emission particle tracking. The time‐averaged velocity profiles of particles predicted by the developed model were found to agree well with experimental data. The initial bubble diameter had no significant influence on the time‐averaged circulating pattern of solids in the bed. The model predictions clearly indicate that the developed model can fairly predict the hydrodynamic behavior of the dense phase of 3D gas‐solid cylindrical fluidized beds.     

Performance of Fixed Bed Reactors with Two-Phase Upflow and Downflow

A time and space dependent model was developed to analyse the performance of two-phase upflow and downflow fixed bed bioreactors and was applied to biological phenol degradation. The hydrodynamic parameters were determined from residence time distribution measurements, using an imperfect pulse method for time–domain analysis of non-ideal pulse tracer response. A transient diffusion model of the tracer in the porous particle coupled with the PDE model was used to interpret the obtained RTD curves. Gas–liquid mass transfer parameters were determined by a stationary method based on the least square fit of the calculated concentration profiles in gas phase to the experimental values. The analysis of the performance of fixed bed bioreactors used for phenol biodegradation shows that for the same operating conditions two-phase upflow gives much higher conversions. Gas–liquid mass transfer is the limiting step in the rate of phenol biodegradation when the inlet phenol concentration is high. © 1997 SCI.     

循环流化床气固传质实验研究

This study is devoted to gas-solid mass transfer behavior in heterogeneous two-phase flow. Experiments were carried out in a cold circulating fluidized bed of 3.0m in height and 72mm in diameter with naphthalene particles. Axial and radial distributions of sublimated naphthalene concentration in air were measured with an online concentration monitoring system HP GC-MS. Mass transfer coefficients were obtained under various operating condition, showing that heterogeneous flow structure strongly influences the axial and radial profiles of mass transfer coefficients. In the bottom dense region, mass transfer rate is high due to intensive dynamic behavior and higher relative slip velocity between gas and clusters. In the middle transition region and the upper diluter region, as a result of low mass transfer driving force and the influence of flow structure, mass transfer rate distribution becomes non-uniform. In conclusion, among the operating parameters influencing mass transfer coefficients, the superficial gas velocity is the most important factor and the solid circulation rate should be also taken into account.     

Modeling of core flow in a gas-solids riser

The heterogeneous flow structure in gas-solids riser reactors is typically represented by an upward solids flow in the core region and a back-mixing downward solids flow in the wall region. The hydrodynamic and reaction characteristics in these two regions are highly different, as most reactions with fresh catalyst solids occur in the core region and mostly spent catalyst solids are found in the wall region. Gross understanding on gas-solids riser flow can be conveniently obtained from a cross-section averaged one-dimensional modeling approach, which is probably only valid for the core region. The success of such an approach, however, has to rely on the appropriate modeling of controlling mechanisms of riser flows. Our recent studies show that commonly-employed Richardson-Zaki equation overestimates the hydrodynamic forces in the dense phase and acceleration regimes; there is also a non-negligible effect of solids collision on solids acceleration, and the wall effect should be taken into account in terms of wall boundary and back flow mixing. In this paper we propose a new mechanistic modeling to describe the hydrodynamics of upward flow of solids in a gas-solids riser, with new formula of hydrodynamic phase interactions. The modeling results are validated against published measurements of pressure and solids volume fraction in a wide range of particle property, gas velocity and solid mass flux. Parametric effects of operation conditions such as transport gas velocity and solid mass flux on hydrodynamic characteristics of riser flows are predicted.     

Interfacial area and mass transfer in carbon dioxide absorption in TEA aqueous solutions in a bubble column reactor

The hydrodynamic behaviour and mass transfer of carbon dioxide removal process by aqueous solutions of triethanolamine (TEA) are analysed. The experiments were made in a bubble column reactor (BCR) as gas–liquid contactor. The interfacial area and mass transfer coefficient were calculated by using a photographic method based on the bubble diameter determination. The influence of operation conditions, liquid phase nature and chemical reaction on the mass transfer coefficient and gas–liquid interfacial area has been also analysed.     

Droplet population balance modelling—hydrodynamics and mass transfer

The hydrodynamic and mass transfer behavior of a rotating disc contactor extraction (RDC) column based on a bivariate population balance model is investigated using the generalized fixed-pivot technique for the discretization of droplet internal coordinate. Single-droplet and swarm-droplet studies in small lab-scale devices were used to evaluate breakage and coalescence parameters necessary for column simulations. The breakage probability of single droplets was measured and a new correlation was developed, which also takes viscosity effects into account. Coalescence probability studies resulted in chemical system dependent parameters, which were obtained by an inverse solution of a simplified balance model. In a final study, the hydrodynamic and mass transfer behavior of pilot plant RDC columns have been simulated based on the parameter set derived from the lab-scale units. The simulated mean Sauter diameter, hold-up values and concentration profiles were found to be well predicted at different operating conditions. The relative error for the simulated mean Sauter diameters is about 15%, for the hold-up about 20% and for the concentration profiles about 20%.     

Modelling of fluidized bed reactors—VI(b): The nonisothermal bed with stochastic bubbles

Two stochastic nonisothermal fluidized bed reactor models are developed to investigate the significance of the fluctuating nature of fluidized beds on reactor performance. Fluctuating bubble size distributions within the bed are simulated by stochastic mass and heat transfer coefficients. Results of hybrid computer simulations indicate that randomness can enhance or inhibit reactor performance depending on the operating parameters of the nonisothermal model. Bubble and dense phase concentration statistics are fairly similar to those of corresponding isothermal models because dense phase temperatures are relatively insensitive to transfer coefficient fluctuations due to the high dense phase beat capacity. However, the corresponding stochastic isothermal models predict decreases in conversion with increasing variance in the transfer coefficients for all operating conditions. Results indicate that a deterministic system with two stable steady states may have fewer stable random stationary solutions. The existence of the stationary states is dependent on fluctuation frequency and variance of the transfer coefficients.     

Numerical analysis of heat transfer mechanisms to pneumatically conveyed dense phase flow

Mass and energy balances are required in power generation, chemical, pharmaceutical, food and commodity transfer processes in order to achieve efficient utilization of energy and raw materials. There is a need for accurate, reliable, on-line, continuous and non-invasive measurement of solids' mass flow rate in many industrial processes mentioned above. Thermal flowmeters, in theory, provide a true indication of the mass flow of solids in pneumatic conveying pipelines.A complicated heat transfer between a pipe wall and a gas-solid flow in a conveying pipeline inevitably takes place in a thermal solids' mass flow measurement process. A study of heat transfer mechanisms to pneumatically conveyed gas-solid dense phase flow as a means to mass flow rate measurement has been conducted experimentally and numerically to evaluate the heat transfer coefficient between the hot wall and the gas-solid dense phase flow. The prediction of the heat transfer coefficient is compared with the experimental findings. It was found that the heat transfer coefficient between the pipe wall and the gas-solid dense flow is a function of solids loading ratio. Increasing the gas stream velocity significantly augments the heat transfer between the hot wall and the gas-solid dense phase flow.     

Toward Understanding of Two‐Phase Eccentric Helical Reactor Performance

Mass transfer investigations in a two‐phase gas‐liquid Couette‐Taylor flow (CTF) reactor and a numerical flow simulation are reported. The CTF reactor is characterized by high values of the mass transfer parameters. Previous mass transfer investigations have yielded high values of the volumetric mass transfer coefficients (of the order of 10^–1 s^–1) and the specific interfacial area, compared to those obtained in a stirred tank (10³ m² m^–3). In order to intensify mass transfer in the CTF reactor, an eccentric rotor (rotating inner cylinder) was used. In the eccentric annulus with rotating inner cylinder, due to frequent variation of the hydrodynamic flow field parameters, nonlinear hydrodynamic conditions occurred. These conditions can influence the rate of mass transfer. The experimental results of benzaldehyde oxidation in an eccentric CTF reactor confirmed an increase in mass transfer, as against a concentric CTF reactor. Numerical simulation of the Couette‐Taylor (helical) flow was performed in a concentric and in an eccentric annulus. Calculation of parameters such as velocity, static pressure, kinetic energy and energy dissipation rate revealed a significant effect of gap eccentricity on the flow behavior.     

PERFORMANCE OF A PACKED-BED REACTOR

We examined the conversion rates in a packed bed catalytic reactor with a two phase upward flow in a wide range of operating conditions. The oxidation of ethanol to acetic acid in the liquid phase on a Pd-Alumina catalyst was chosen as the test reaction.

Global reaction rates were measured by changing gas velocities, temperature, and feed concentrations of ethanol in the liquid phase. The observed rates were compared with those calculated using two models, assuming a total external wetting of the catalyst. In the first model, a “kinetic” conversion rate was calculated by neglecting any interphase mass transfer resistance. In the second model the interphase mass transfer resistance was considered and expressed by an overall coefficient evaluated from published correlations. The results show that there is an hydrodynamic influence, probably due to the mass transfer and/or to the partial effective wetting of the catalyst. Mass transfer, on the other hand, is better than that observed in other cases. A comparison with the performances of a downflow trickle-bed reactor operating at the same tested conditions showed a much smaller influence of mass transfer and hydrodynamics on the overall conversion rate for the upflow reactor.     

Modelling of the coupling hydrodynamic transfer for a gas-liquid countercurrent flow on a wavy surface

This paper concerns laminar countercurrent gas-liquid flow over a wavy wall column, in the case of a falling liquid film. The modelling concerns the coupling of hydrodynamic and heat and mass transfer for an absorption as an example of application. The falling liquid film interacts, through the free interface, with the gas phase. The wavy surface generates particular hydrodynamic conditions with the presence of a vortex in both phases. The consequence of these vortices is an increase of transfers compared to the smooth wall.     

Mass transfer during dissolution of solids using hydrodynamic cavitation devices

Experimental investigations are performed to explore the mass transfer during dissolution of solids under hydrodynamic cavitation conditions and to evaluate the effect of cavitation on the dissolution rate after pretreatment of the liquid phase. The results obtained are compared with theoretical data.     

On the relevance of mass transfer limitations in the Fischer-Tropsch slurry process

Satterfield and Huff[1] reported recently on significant mass transfer resistances in the FT slurry process. However, their conclusions are at least partly based on a study with an unsuitable catalyst. In the present communication FT studies with 8 different catalysts and bubble columns, respectively, were analyzed using new and reliable results on hydrodynamic properties. In all cases, mass transfer resistances were found to be small compared to reaction resistances. As long as much more active catalysts are not developed significant mass transfer limitations cannot be expected in the bubble column if operated under appropriate conditions. The absence of mass transfer limitations is mainly a result of the high gas holdups attainable with molten paraffin as liquid phase.