Liquid Solid Mass Transfer Coefficient Research Articles

Novel Correlation for the Solid–Liquid Mass Transfer Coefficient in Stirred Tanks Developed by Interpreting Machine Learning Models Trained on Literature Data

Novel Correlation for the Solid–Liquid Mass Transfer Coefficient in Stirred Tanks Developed by Interpreting Machine Learning Models Trained on Literature Data

Quantifying Liquid-Solid Mass Transfer in a Trickle Bed Using {T}_{2}-{T}_{2} Relaxation Exchange NMR

Measurement of the liquid-solid mass transfer coefficient within a trickle bed (i.e. gas-liquid flow within a packed bed) of porous silica pellets is achieved through the use of {T}_{2}-{T}_{2} relaxation exchange nuclear magnetic resonance (NMR). Compared to many conventional measurement techniques, the NMR method enables measurement of mass transport using pellets of real commercial interest. Mass transfer coefficients measured using the NMR technique over a range of liquid Reynolds number, 0.2 le R{e}_{mathrm{L}}le 1.4, are compared to a number of literature correlations, with values measured using the NMR method falling within the range predicted by the correlations. The results demonstrate the importance of considering both the flow conditions and the type of pellets used to develop mass transport correlations in trickle beds. This novel NMR application may be utilized in the future to screen catalyst pellets in trickle beds for optimal mass transport properties.

Experimental study on the addition of pulsating flow to enhance liquid-solid mass transfer in the circulating fluidized bed

The addition of pulsating flow in the conventional liquid-solid circulating fluidized bed (CLSCFB) to enhance liquid-solid mass transfer efficiency has been proposed. A pulsating continuous liquid-solid circulating fluidized bed (PCLSCFB) experimental system was designed and constructed. The liquid-solid mass transfer coefficient (kSL) in the PCLSCFB was measured by the experimental method of dissolving the insoluble benzoic acid particles. The effects of superficial liquid velocity, superficial solids velocity and pulsation property on the liquid-solid mass transfer coefficient (kSL) in the PCLSCFB were thus determined. It was concluded that the liquid-solid mass transfer coefficient (kSL) increases with the increasing pulsation amplitude and frequency in the experimental range. The addition of pulsating flow significantly strengthens the liquid-solid interphase transfer efficiency in comparison with the CLSCFB. The correlation of the mass transfer coefficient (kSL) for the PCLSCFB has been proposed based on experimental data and main parameters.

Hydrodynamics and liquid–solid mass transfer in micropacked bed reactors with copper foam packing

Hydrodynamics and liquid–solid mass transfer in micropacked bed reactors (μPBRs) with copper foam packing are investigated. Effects of fluid superficial velocities, liquid viscosity, pore diameter of foam packing on the residence time distribution, liquid holdup, axial dispersion coefficient, and liquid–solid mass transfer coefficient are discussed. The liquid holdup of μPBRs can reach 0.23 ∼ 0.39, which is larger than that of packed bed reactors (0.05). The axial dispersion coefficient of μPBRs is 3.17 × 10-6 ∼ 2.30 × 10-5 m2/s, which is similar with that of packed bed reactors. The value of liquid–solid volumetric mass transfer coefficient with effect of axial dispersion coefficient in μPBRs can reach 0.033 ∼ 0.13 s−1, which is higher than that of packed bed reactors (0.006 ∼ 0.09 s−1). The empirical models of liquid holdup, axial dispersion coefficient, and liquid–solid mass transfer coefficient in single liquid phase flow and gas–liquid two phase flow of μPBRs are established and their predictions are in good agreement with experimental values.

Electron transfer-based peroxydisulfate activation by waste herb residue biochar: Adsorption versus surface oxidation

Waste herb residue biochar (WBC) was synthesized to activate peroxydisulfate (PDS) for the removal of different micropollutants. WBC prepared at 700 °C (WBC700) exhibits discrepant adsorption and PDS catalytic performance to three pharmaceuticals and four phenolic compounds. At 60 min reaction time, the adsorptive removal by 0.5 g/L WBC700 varied from 31.3% (clofibric acid) to 97.6% (4-chlorophenol), while the apparent removal ranged from 36.1% (clofibric acid) to 99.5% (4-chlorophenol) when 0.5 g/L WBC700 and 1.0 mM PDS were applied. The oxidation of the micropollutants involves electron transfer mechanism via the surface-confined metastable reactive complexes (WBC-PDS*), which was verified by electrochemical tests, quenching experiments, electron paramagnetic resonance, Fourier transform infrared and in-situ Raman spectroscopy. The observed pseudo first-order kinetic constant (kobs) of organic removal did not exhibit a good correlation with its electrochemical redox descriptor (half-wave potential, φ1/2, for example) as reported in the previous studies. Instead, the surface oxidation rate constant (koxid), determined from a dynamic model considering liquid-solid mass transfer of micropollutant and the sequent surface oxidation by WBC-PDS* complexes, was highly related to φ1/2. In parallel, the liquid-solid mass transfer coefficient (KLa) of micropollutant was obtained from a similar model excluding the surface oxidation, and kobs showed a more significant association with KLa than with adsorption capacity (Qe). This study provides a promising approach to understand the role of adsorption and surface oxidation in an electron transfer-dominated persulfate activation process.

Mass transfer intensification by means of resonance oscillations in a pulsation apparatus with a central tube with and without nozzles

An experimental study of resonance and non-resonance oscillations in a pulsating apparatus with a central tube was performed. Pulsating apparatus in two configurations was thoroughly investigated in the following way: (i) pulsating resonance apparatus with central tube, without nozzles and (ii) pulsating resonance apparatus with central tube, an additional tube, and nozzles. The following parameters were investigated as criteria for the onset of resonance: the liquid surface oscillations amplitude, the gas pressure oscillations amplitude in a gas-filled elastic element, the solid particles dissolution rate. A comparative analysis showed that the resonance frequencies, determined by the maximum amplitude of the liquid surface oscillations, by the gas pressure fluctuations and the dissolution rate of solid particles, are in good agreement with each other and with the theoretical value. The pressure pulsations were found as an easy and reliable for resonance identification. The dissolution rate of KOH particles increases up to 4–6 times at resonance frequency. At the same energy dissipation rate possesses approximately 10 times larger values of the liquid-solid mass transfer coefficient compared to the stirred tanks. With a decrease in the volume of a gas-filled elastic element, the amplitude of the oscillations at resonance increases, which is consistent with theory.

Measuring the liquid-solid mass transfer coefficient in packed beds using [formula omitted] relaxation exchange NMR

Direct measurement of the liquid–solid mass transfer coefficient in packed beds is achieved using T2-T2 relaxation exchange NMR. This method directly probes molecular exchange between intra- and inter-pellet fluid, rather than requiring a net flux between phases as in conventional methods. Mass transfer coefficients measured using the NMR method are compared with literature values and two widely used correlations. For Reynolds number, Re, less than 0.2, the mass transfer coefficients measured using NMR show excellent agreement with the correlations over the flow conditions for which they were developed. The approach also enables the quantification of mass transfer in the limit of, and at, zero flow. At Re= 0, the Sherwood number in packed beds with voidage of 0.41 determined by NMR is found to approach 9, in good agreement with previously reported results, but significantly greater than that predicted by extrapolating well-known correlations beyond their range of validity to Re= 0.

Liquid–Solid Mass Transfer in Adsorption Systems—An Overlooked Resistance?

In liquid-solid adsorption, fluid film diffusion is typically faster than intraparticle diffusion, especially for microporous adsorbents. However, fluid film diffusion might play a significant role in the overall rate of the process for mesoporous-macroporous and non-porous solids. In most adsorption modeling studies, the fluid film diffusion step is typically ignored, which is not always justified. This article critically discusses the theory behind the liquid-solid mass-transfer coefficient in stirred vessels and presents the dissolution and adsorption methods adopted for estimating its value. Then, starting from the definition of the Biot number, an original analysis is developed with reference to selected studies. Surface versus pore diffusion of the adsorbate in the adsorbent is taken into account, and external versus internal mass-transfer resistance is considered to put the fluid film resistance back in the picture when needed. Iso-Biot charts where the operating points can be visualized are presented as well.

Liquid-solid mass transfer in a rotating packed bed reactor with structured foam packing

A rotating packed bed (RPB) reactor has substantially potential for the process intensification of heterogeneous catalytic reactions. However, the scarce knowledge of the liquid–solid mass transfer in the RPB reactor is a barrier for its design and scale-up. In this work, the liquid–solid mass transfer in a RPB reactor installed with structured foam packing was experimentally studied using copper dissolution by potassium dichromate. Effects of rotational speed, liquid and gas volumetric flow rate on the liquid–solid mass transfer coefficient (kLS) have been investigated. The correlation for predicting kLS was proposed, and the deviation between the experimental and predicted values was within ± 12%. The liquid–solid volumetric mass transfer coefficient (kLSaLS) ranged from 0.04–0.14 1−1, which was approximately 5 times larger than that in the packed bed reactor. This work lays the foundation for modeling of the RPB reactor packed with structured foam packing for heterogeneous catalytic reaction.

Liquid-solid mass transfer in a rotating trickle-bed reactor: Mathematical modeling and experimental verification

Liquid-solid mass transfer model is significant but deficient for the design of a rotating trickle-bed reactor (RTBR), which has great potential for process intensification of heterogeneous catalytic reactions. In this work, a mathematical model considering the wetting efficiency was first established to describe the liquid-solid mass transfer process in the RTBR. External static liquid holdup was referred to give a reasonable initial value for calculation. The profile of concentration boundary layer was obtained by mass balance analysis of an Eulerian element on a single sphere. The above model was then extended to predict the liquid-solid mass transfer coefficient (kLS) in the RTBR. A copper dissolution method was employed to measure the kLS, considering the effects of particle diameter, rotational speed, and liquid superficial mass velocity. The comprehensive comparison between predicted and experimental values of kLS was conducted and deviations were within ±25%.

Mass Transfer Enhancement in GLS Fluidized Beds using Nanomaterials

Nanomaterial has unique physical property which made it important for many applications and that is why the use of nanomaterials rapidly increasing in the field of science and engineering.1. This work focuses on mass transfer of solids into liquid in three phase fluidized beds in presence of nanomaterial. This include the study of effect of gas velocity, time and different concentration of nanomaterials on mass transfer coefficient in stagnant liquid column in three phase fluidized bed system. To measure coefficient of the mass transfer, known quantity of solid pellets ie benzoic acid and known amount of nanomaterial fraction ie Arachitol nano were charged in the test column of three phase fluidized bed system. At the beginning of each run, test section was partially filled with water which prevent breakage of particles. The experiments were conducted by sequentially varying gas velocity for different volumes of nanomaterial and measuring the rate of mass transfer by collecting samples directly from the outlet ports at the top subsequently analysed by volumetric titration method. The results show enhancement in mass transfer coefficient by addition of nanomaterials. Arachitol nano has been taken in different volumes ie 3ml, 7ml, 10ml and 20ml in (GLS) gas ,liquid and solid fluidized bed with air, water and benzoic acid pellets as three phases respectively in the system. The presence of nanomaterial increases the solid liquid mass transfer coefficient value with increasing fraction of nanomaterial, increasing gas velocity and increasing time although experimental run has been taken only for one hour.

Determination of mass transfer resistances in trickle bed reactors

A methodology for determining the mass transfer resistances of three-phase reactions in trickle bed reactors is presented. The hydrogenation of styrene over Pd/C was used as a case study to demonstrate the methodology. The gas-liquid mass transfer resistance was experimentally approximated by changing the palladium content of the bed while the chemical reaction resistance was calculated by using the observed chemical reaction rate constant which has been experimentally approximated in two different stirred tank reactors by hydrogenating the same compound under the same temperature and using the same solvent and active catalytic metal. The liquid-solid mass transfer resistance was calculated by subtracting the gas-liquid mass transfer resistance and the chemical reaction resistance from the overall resistance. The wetting efficiency of the bed was estimated from the experimental data and it was compared to the literature by using the dimensionless numbers of Re, Fr, Mo, Ga, We and Stk. The specific gas-liquid and liquid-solid mass transfer coefficients found in agreement with the literature.

Two-Phase Flow Modeling of Solid Dissolution in Liquid for Nutrient Mixing Improvement in Algal Raceway Ponds

Achieving optimal nutrient concentrations is essential to increasing the biomass productivity of algal raceway ponds. Nutrient mixing or distribution in raceway ponds is significantly affected by hydrodynamic and geometric properties. The nutrient mixing in algal raceway ponds under the influence of hydrodynamic and geometric properties of ponds is yet to be explored. Such a study is required to ensure optimal nutrient concentrations in algal raceway ponds. A novel computational fluid dynamics (CFD) model based on the Euler–Euler numerical scheme was developed to investigate nutrient mixing in raceway ponds under the effects of hydrodynamic and geometric properties. Nutrient mixing was investigated by estimating the dissolution of nutrients in raceway pond water. Experimental and CFD results were compared and verified using solid–liquid mass transfer coefficient and nutrient concentrations. Solid–liquid mass transfer coefficient, solid holdup, and nutrient concentrations in algal pond were estimated with the effects of pond aspect ratios, water depths, paddle wheel speeds, and particle sizes of nutrients. From the results, it was found that the proposed CFD model effectively simulated nutrient mixing in raceway ponds. Nutrient mixing increased in narrow and shallow raceway ponds due to effective solid–liquid mass transfer. High paddle wheel speeds increased the dissolution rate of nutrients in raceway ponds.

Fluid dynamic characterization of a fluidized‐bed perfusion bioreactor with CFD–DEM simulation

AbstractBACKGROUNDIn the recent development of regenerative medicine, the low yields of progenitor cells have limited the large‐scale clinical applications. To overcome the limitation, a novel fluidized bed bioreactor has emerged. However, a detailed understanding of its fluid dynamics is still lacking.RESULTSA 3D modeling approach that couples computational fluid dynamics (CFD) and a discrete element method (DEM) was used to simulate the liquid and solid flows in a bioreactor being designed for stem cells expansion. The model was validated by comparing the simulation results with literature experimental data [Chem Eng Sci 60:1889–1900 (2005)], which showed a good agreement. Using the validated model, the effects of the superficial liquid velocity, particle size and particle density on the solids volume fraction, shear stress on the particles and liquid–solid mass transfer coefficient of dissolved oxygen and glucose were analyzed.CONCLUSIONSSimulation results show that particle size and density have an important impact on the shear stress distribution, and that the liquid velocity affects the shear stress distribution rather modestly when its value is beyond the minimum fluidization velocity. The liquid–particle mass transfer coefficient of dissolved oxygen and glucose can be improved by raising the liquid velocity, and the adoption of a high‐density material allows the reactor to operate with higher liquid velocities before reaching shear stress heterogeneities. Furthermore, the two objectives, (i) maintaining lower and homogeneously distributed shear stress and (ii) improving mass transfer, pose conflicting requirements on certain design parameters which need to be carefully considered in the reactor design. © 2018 Society of Chemical Industry

Esterification of maleic acid and butanol using cationic exchange resin as catalyst

Dibutyl maleate is a perfumery ester used as an intermediate in the production of paints, adhesives, and copolymers. Esterification of maleic acid and butanol was studied in presence of acidic cation exchange resin as a catalyst. The objective of this work was to test the suitability and efficacy of heterogeneous catalysts such as Indion 225H and Amberlyst-15 in the synthesis of dibutyl maleate. Various parameters deciding the conversion of reaction such as mole ratio, catalyst loading, molecular sieves, speed of agitation and effect of temperature were optimized for the maximum rate and conversion. The activation energy was calculated as 71.5 kcal/mol. Diffusivity value $$\hbox {D}_{\mathrm{AB}}$$ (maleic acid in n-butanol) at $$80\,^{\circ }\hbox {C}$$ was calculated as $$5.08\times 10^{-10}~\hbox {m}^{2}/\hbox {s}$$ and effective diffusivity ( $$\hbox {D}_{{\text {e-A}}})$$ was calculated as $$5.08\times 10^{-11}\,\hbox {m}^{2}/\hbox {s}$$ . Solid–liquid mass transfer coefficient ( $$\hbox {k}_{{\text {sl-A}}}$$ ) was calculated as $$6.77\times 10^{-6}\,\hbox {m/s}$$ for the particle size of Amberlyst-15 as 0.5 mm. Synopsis. Synthesis of dibutyl maleate was carried out using ion exchange resin as a catalyst. Effect of various parameters on the conversion of reaction like mole ratio, catalyst loading, molecular sieves, the speed of agitation and effect of temperature was studied.

Dynamic Liquid–Solid Mass Transfer in Solid Foam Packed Reactors at Trickle and Pulse Flow

The effective liquid–solid mass transfer (LSMT) has been investigated in solid foam packed reactors under cocurrent gas–liquid downflow. Based on a comprehensive literature analysis, the limiting current technique was adapted successfully to solid foam packings enabling measurements of dynamic mass transfer coefficients at different axial packing positions. The flexible reactor setup was used to analyze the appropriateness of various setup configurations. The LSMT coefficients are presented for two different solid foam pore densities for a wide range of gas and liquid velocities covering trickling and pulsing flow regime. To illustrate the difference in the LSMT dynamics in terms of electric current compared to the liquid holdup at pulse flow, a compartment model is developed. Excellent agreement is achieved between simulations and measurement data. Eventually, the effective mass transfer data are compared with conventional random and structured packings.

Theoretical estimation of mass transfer coefficients in solution crystallization

Generally, diffusion through film thickness is used for correlating data in the industrial crystallization processes. Furthermore, mass transfer is an important phenomenon in most chemical processes and studies involving determination of mass transfer coefficients are necessary for a better estimation of equipment performance. Solid-liquid mass transfer coefficients in stirred systems have received substantial attention in the past due to their practical applications. In contrast, little information is available on solid-liquid mass transfer in crystallization systems, despite the importance of crystallization. In this work, an expression for the mass transfer coefficients in solution crystallization has been developed based on the Stefan problem formulation. The model is able to predict a finite mass transfer coefficient when the layer thickness vanishes. The obtained mass transfer coefficients agree with previously reported experimental data. Furthermore, it is found that the stagnant film for mass transfer has oscillatory behavior, and this behavior is a function of residence time.

Enhancing Impeller Power Efficiency and Solid–Liquid Mass Transfer in an Agitated Vessel with Dual Impellers through Process Intensification

The effects of high volumetric solids concentration (CV), impeller type, and baffles on the impeller power input required for solids suspension and dispersion and the solid–liquid mass transfer coefficient (kSL) were studied in this work using an agitated vessel with dual impellers for the purpose of process intensification. It was found that at CV = 0.2 (v/v), the impeller power consumption required for solids suspension per unit mass solids (eJS = PJS/MS) is minimized while at the same time achieving maximum kSL values. Overall, it was observed that process intensification could be achieved using two radial flow impellers in a taller vessel under unbaffled conditions. A case study highlighting the benefits of adopting some of this study’s recommendations is presented. Mathematical correlations proposed to estimate eJS, impeller power consumption for solids dispersion, and kSL as a function of CV were found to fit experimental data reasonably well.

Operando determination of the liquid-solid mass transfer coefficient during 1-octene hydrogenation

Spatially-resolved and unresolved magnetic resonance measurements are used in combination with a partial least squares regression (PLSR) method to measure chemical composition within catalyst pellets during the 1-octene hydrogenation reaction occurring in a fixed bed of 0.3wt% Pd/Al2O3 catalyst pellets. The PLSR method is used to discriminate between chemical species within and external to the void space of the catalyst pellets. The spatially-resolved data show that the hydrogenation and isomerisation reactions are dominant in the upper and lower region of the reactor, respectively. The local intra-pellet compositions also show product accumulation inside catalyst pellets consistent with reaction occurring under conditions of mass transfer limitation. An average measure of the intra-pellet composition within the whole bed was then used to estimate the liquid-solid mass transfer coefficient during the course of the reaction. The values of kLS obtained from the NMR measurements were in the range 0.15×10−5ms−1<kLS<0.25×10−5ms−1, for reactor operating conditions characterised by gas and liquid Reynolds numbers 0.2<ReL<0.6 and 0.1<ReG<0.3; these values are shown to be consistent with those predicted by existing literature correlations. Closest agreement was found with values predicted from dissolution experiments performed under similar hydrodynamic conditions in trickle flow. In addition to introducing a method for the direct measurement of kLS, the data presented also confirm that estimates of kLS are more accurate when performed in an environment in which the hydrodynamics and fluid-solid contacting conditions are representative of the system of interest.

Experimental correlation of gas–liquid–solid mass transfer coefficient in a stirred tank using response surface methodology

In this paper, the three-phase (gas–liquid–solid) system in a stirred tank is experimentally studied. The response surface methodology (RSM) is used to analyze the three phase mass transfer coefficient under different conditions, i.e., rotation speeds (8, 10, and 12 s−1), volumetric solid content fractions (0, 6 and 12%), gas flow rates (6, 8, and 10 m3 h−1) and temperatures (40, 54, and 68 °C). With the RSM, it was found that all of these four operational parameters are significant in affecting the mass transfer coefficient, with the rotation speed being the most significant one. A new correlation is developed with a quadratic term for solid content fraction, indicating that there is a minimum value of mass transfer coefficient at a certain solid content fraction. Compared with traditional experimental design and correlation methods, the RSM in this study reduces experiment time and provides a better correlation to predict the mass transfer coefficient.