The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D
 T and D
 L) over the entire range of practical values of Sc and Pem, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.

https://paginas.fe.up.pt/~jdelgado/2006_HMT__JD.pdf

A critical review of dispersion in packed beds

Optical measurements of porosity and fluid motion in packed beds

Fundamentals of Porous Structures.- Flow in Porous Media.- Transport Phenomena in Porous Structures.- Modeling of Transport Processes in Porous Materials.- Experimental Investigation of Transport in Porous Media.- Applications & Examples.- Conclusions & Recommendations.

Transport Processes in Porous Media

Direct air capture (DAC) is a developing technology for removing carbon dioxide (CO2) from the atmosphere or from low-CO2-containing sources. In principle, it could be used to remove sufficient CO2 from the atmosphere to compensate for hard-to-decarbonize sectors, such as aviation, or even for polishing gas streams containing relatively low CO2 concentrations. In this paper, the performance of lime-based sorbents for CO2 capture from air in a fixed bed was investigated. The effects of sorbent type, particle diameter, air flow rate, and relative humidity on the breakthrough time, breakthrough shape, and global reaction rate over a series of capture and regeneration cycles were examined. The greatest reaction rates and conversions were obtained when the sorbents were pre-hydrated and inlet air was humidified to 55% relative humidity. Humidifying the air alone leads to axial carbonation gradients since there is competition between CO2 and water with the available CaO. Negligible conversion, over the duration of the experiment, is obtained in a dry system without pre-hydration and humid air. A shrinking-core gas–solid reaction model was fitted to the breakthrough curves in order to estimate the surface reaction and effective diffusion constants. Although the surface reaction constants of the two sorbents were similar, the pelletized limestone had a greater effective diffusivity due to its greater porosity. At mild calcination conditions with air at 850 °C, the pelletized particles maintained their activity over nine carbonation–calcination cycles with a conversion drop of only 9% points. However, calcination under oxy-fuel conditions (CO2 at 920 °C) reduced the pellet carbonation conversion from 81 to 59% and pore surface area from 12.01 to 3.20 m2/g after only 4 cycles. This research clearly shows that DAC using lime-based sorbents is technically feasible, and that regeneration schemes compatible with technologies like calcium looping (CaL) are applicable for the air capture option. Finally, this study demonstrates that DAC using lime-based materials can be in the future a strategy to address emissions from transportation and distributed CO2 sources and to mitigate climate change.

/pdf/direct-capture-of-carbon-dioxide-from-air-via-lime-based-9hjky2geck.pdf

Direct capture of carbon dioxide from air via lime-based sorbents

Experimental studies have been made with the help of laboratory-scale distillation columns of the startup and product switchover operations of distillation columns. The object of these studies was to minimize the time necessary from initial startup or product switchover for steady-state operations to be attained. It has been shown that the time needed can be clearly reduced by a specific mode of operation. Theoretical studies support the experimental findings. Dynamic simulation has proved to be a suitable aid for the preparation and planning of experimental studies. As a result, the time needed to reach steady state can be considerably reduced, and consequently the costs.

Experimental and theoretical studies of the dynamics of startup and product switchover operations of distillation columns

Flow Distribution in Packed Beds

Studies were made on the rate of mass transfer to single spheres, with the aid of a diffusioncontrolled electrode reaction:Microelectrodes used as anode were platinum spheres having 1.66mm and 2.74mm diameters respectively, each with PVC-coated platinum wire of 0.6mm diameter. The reference electrode used as cathode was a thin platinum plate of 50×120mm. The experimental apparatus employed was as shown in Fig. 1. To obtain uniform distribution of liquid velocity over the entire column cross-section, glass beads of 5mm diameter were packed to a height of 30mm, topped with 10 sheets of Saran screen of about 12 meshes. Below the packing and 8mm above the spherical electrode, a Saran screen of about 150 meshes was placed.From the measurements of limiting current 6), 8) at various liquid flow rates, the mass transfer coefficients, kf, were calculated by the equation:kf=i/nFAc (7)The experimental results are shown in Table 1. It was found that neither the results thus obtained nor those by previous investigators3), 9), 10), 14), 16) showed good agreements with the Ranz-Marshall's eq. (2)14).Thereupon, assuming that the empirical equation might be presented as:Sh-2=kRepScq (8)the authors determined the values of the constants k, p and q (Figs. 3, 4 and 5), obtaining an equation:Sh=2.0+0.52Re0.54Sc0.35 (9)The value of the exponent of the Schmidt group, 0.35, agrees well with 0.348 obtained by Frossling3) from his experimental data.

Mass Transfer to Single Spheres

For the fixed-bed reactors such as adiabatic multistage reactors, autothermic reactors and externally cooled reactors, the authors studied on the process optimum condition. which means the condition where the necessary amount of catalyst in VR/F is minimized when the conversion is specified.Considering the reaction whose rate at a given composition of the reaction mixture have maximum at a temperature, as in the ammonia synthesis and the catalytic oxidation in sulphur dioxide, the authors extended Konoki's treatment for the adiabatic multistage reactor3, 4) in whose operation maximum temperature is fixed, into the more general form, Eq. (18) through Eq. (21). These results were sucessfully applied to the sulphur dioxide convertor of adiabatic 3-stage.For the autothermic process with two flow paths (Fig. 5), the authors using the simpler design equation (30) instead of Eq.(24), proposed a graphical method of solution based on Picard's method.10) By this method we can easily determine optimum Γ and T10 As an example the authors showed the result of trial and error for the determination of T and T10 for the autothermic ammonia synthesis process. The basic equations (32) for the externally cooled reactor can be also reduced to the simpler form, Eq. (35), and so the same method above described will be employed.

Process Optimum Condition for Gas-Solid Catalytic Reaction Process in Fixed-Bed

It is well known that, in the high temperature region, the diffusional resistances within the boundary film and that within the pores of catalyst pellet have an important effect on the overall effective reaction rate. In reactor design, it is essential to analyze the experimental data and to distinguish the effect of diffusion from the chemical reaction rate so as to predict the over-all effective reaction rate for the given industrial conditions.Previously, Kubota and Shindo5) presented a method for calculating effectiveness factor of the porous catalyst, which is applicable to any reaction but which involves considerable complicated computations.In this paper, the authors present a new method for calculating effectiveness factor, based on the approximation of reaction rate to a kind of first-order reaction as expressed by Eq. (6) or (7). When this method was applied to ammonia synthesis, whose rate was expressed by Eq. (13) and which was far from the first-order reaction, the value of Ef' obtained was found to be a very good approximation to the value of Ef obtained by the previous method (Fig. 2).Other proposals the authors make in this paper are (i) a general analytical procedure for predicting the effective reaction rate by taking into account the diffusional resistances within the boundary film and that within pores of catalyst pellet, and (ii) two other methods for estimating the chemical reaction rate from the experimental data, by taking into account the above-mentioned diffusional resistances. Of these two methods, the first one is applicable when veA (pAG) can be obtained from the reaction, viz. when the reaction is carried on in a differential reactor, and the second one is applicable when veA (pAG) cannot be obtained directly from the experiment, viz., when the reaction is carried on in an integral reactor. When the latter was applied to the ammonia synthesis data, obtained by one of the authors4), great difference was found in the range of above 475°C or so, between the apparent values of reaction rate constant and their corrected values given according to this procedure.

Takashi Akehata

Papers

Flow Distribution in Packed Beds

Mass Transfer to Single Spheres

Process Optimum Condition for Gas-Solid Catalytic Reaction Process in Fixed-Bed

On the Over-all Effective Reaction Rate of Gas-Solid Catalytic Reaction Process