Mass Transfer Correlations Research Articles

Assessment of the gas discharge characteristics during gas recovery by hydrate decomposition

Hydrate-based gas separation is a novel approach for the capture and recovery of hydrofluorocarbons. The gas discharge characteristics during hydrate decomposition need to be clarified for the efficient recovery of hydrofluorocarbons. In this study, we investigated the mass transfer characteristics during the gas recovery from hydrate particles by decomposing the HFC134a hydrates. First, the volumetric mass transfer coefficient was estimated from the gas recovery rate during the HFC134a hydrate slurry. The hydrate particles enhanced the gas recovery performance of the overall apparatus. Next, the mass transfer coefficient between hydrate and liquid was calculated. Ascending bubbles and the resulting change in the dispersion state of the particles significantly affected the mass transfer. Finally, we developed a mass transfer correlation equation between the solid and liquid phases by dimensionless numbers based on Kolmogorov’s theory. The experimental equation predicted the Sherwood number with ±40 % accuracy and an average absolute relative error of 19.0 %. The dispersion state of the hydrate particles was a significant factor in the estimation.

An efficient technology for dye intermediate production: Process intensification of catalytic hydrogenation of aromatic nitrocompounds in a rotating packed bed reactor

AbstractThe rotating packed bed (RPB) is suitable for catalytic hydrogenation of aromatic nitrocompounds whose reaction rate is limited by the mass transfer rate. However, the matching mechanism between the mass transfer rate and intrinsic reaction rate in the RPB reactor is still unclear. In this work, the matching relationship in the RPB reactor is studied by combining the characteristics of mass transfer and reaction in detail. Effects of various operating conditions on the gas–liquid mass transfer coefficient up to 0.31/s, under working conditions were studied and the mass transfer correlation was proposed. The hydrogenation of p‐nitroanisole was used as a probe reaction to analyze the matching mechanism. Various aromatic nitrocompounds in the RPB and stirred tank reactors were investigated. The reaction efficiency of the former is 5–20 times that of the latter, which further explained the universality of the matching mechanism in the RPB reactor.

Experimental study of cryogenic oxygen–nitrogen mass transfer characteristics on microtextured plates

The detailed effects of microtexture on the distillation performance of the cryogenic fluids are seldom reported. In this work, sinusoidal microtextured plate was applied to carry out falling film visualization and mass transfer experiments of cryogenic oxygen–nitrogen system. The flow pattern and wetting of LN2 on the microtextured plate and the flat plate were analyzed through the recorded images. Gas-liquid countercurrent mass transfer experiments of oxygen–nitrogen system on the microtextured plate were conducted. Results show that the F-factor in cryogenic distillation operation should be lower than that of common chemical processes to avoid the deterioration of mass transfer performance. Furthermore, experiments on the effect of microtexture size on oxygen–nitrogen mass transfer performance were conducted. Results show that increasing the amplitude and decreasing the periodic length can optimize the interfacial mass transfer performance of cryogenic distillation. Finally, new mass transfer correlations for cryogenic distillation are proposed.

Sensitivity to heat and mass transfer correlations of the model for an evaporative condenser

Evaporative condensers have established themselves in refrigeration plants for food process and storage owing to the combination of air and water cooling, with an overall reduction in energy (pumping) and fluid (water) consumption. Given the steep rise of electricity prices, the need to develop conduction strategies at the plant level which are less energy-intensive has driven the need for models to carry out simulations of the new strategies without actually impacting normal plant operations. This paper describes the development of a distributed-parameter model of an evaporative condenser with fill-pack, based on Merkel’s pioneering works on evaporative cooling. Several correlations are available for the heat and mass transfer coefficients, but none that satisfies the operating conditions of the case at hand, yet they are the most critical set of parameters for the model, therefore a sensitivity study has been carried out, to ascertain which combinations of transport coefficients out of a total of 288 would yield a total cooling power closest to the value declared by the manufacturer for a real-life evaporative condenser under rating conditions. This work demonstrates the applicability of the correlations examined, and also twenty of the examined combinations allow the model to reach a good agreement with the reference data (within ±5%). Further, the distributed-parameter structure of the model allows highlighting the reasons for good or bad performance of the correlations by determining the spatial distribution in the cooling coil and fill-pack of quantities such as moist air enthalpy and water temperature. The model and methodologies are a little cost-intensive in terms of computational time and can be applied to the study and design of any similar piece of equipment.

Process intensification for production of dispersants via integration of reaction and separation in a horizontal thin film evaporator

Process intensification can be achieved in specialty chemicals manufacturing via transition from batch-to-continuous processing. However, the absence of headspace in a continuous tubular reactor limits the ability to remove volatile byproducts from the reacting liquid flow. Previous studies showed that the production of succinimide dispersants follows a two-step amidation-dehydration pathway in which water is formed as a by-product. The inability to remove this water imposed a thermodynamic equilibrium limitation on the dehydration step, and hence necessitated a downstream drying step to obtain a dehydrated dispersant product within commercial specifications. In the present study, the use of an agitated, horizontal thin film evaporator (TFE) was investigated as a continuously operated reactive separator which combines reaction and dehydration into a single operating unit, reducing the overall cost and physical footprint of the process. The continuous TFE unit was first experimentally investigated as a stand-alone, integrated reactor-separator. Using this configuration, the obtained imide yield consistently exceeded the maximum thermodynamic yield at each operating temperature, confirming the efficiency of the integrated reaction and separation steps in the TFE. Next, the unit was modeled by integrating reaction kinetics with mass and energy balance equations, using appropriate correlations for heat and mass transfer from the literature which were verified for the experimental set-up. This model provided insights into the system behavior across different operating conditions, including the role of forward and reverse reactions along the TFE unit length. The model was then used to confirm the feasibility of replacing the two-step tubular reactor-evaporator process with a single TFE unit as an intensified reactive separator, further reducing the physical footprint of the process by enabling compact modular process designs.

Dimensionless correlation of mass transfer on a frosted flat plate with thickness, mass, heat flux measurements

The aim of the study is to investigate frosting on the horizontal flat plate which has uniform air velocity distribution upstream. While the air temperature is 21.9 °C, the relative humidity is 80% and the air velocity is 0.7 m/s; frost is formed on the flat plate at surface temperatures of −15.1, −11.2, −7.1 °C, then under these conditions frost thickness, frost mass are measured. Continuous heat flux measurements under frosting which is very rare in literature are performed, too. Considering only the initial part of the frosting process at high plate temperature first an increase in heat flux then a continuous decrease is observed. A new dimensionless mass transfer correlation that does not require frost surface temperature and additionally includes dimensionless plate length is presented. The mass transfer correlation is based on dimensionless numbers of Reynolds, Fourier, specific humidity, dimensionless temperature, and dimensionless plate length which are derived from air temperature, air velocity, air relative humidity, plate temperature, plate length, plate width, and time information. In obtaining the correlation, frost mass measurements from previous researchers were added to the presented experimental results to develop a correlation valid over a wide range. As a result of the broad data set, the ranges at which the correlation is valid; air velocity of 0.7–2.5 m/s, air temperature of 5–22 °C, plate temperature of −5 to −25 °C, air relative humidity of 50%–83.73% and plate length of 85.6–300 mm. Nondimensionalizing the plate length has increased the prediction capability of the correlation.

Mass transfer studies on the solvent-free lipase-catalyzed partial hydrolysis of palm oil in packed-bed reactor

Packed-bed reactor (PBR) is widely employed for enzyme-mediated reactions at an industrial scale because the reactor configuration enables reusability of the biocatalyst with ease, thereby reducing the overall operating expenses. However, mass transfer limitation remains a key challenge in fixed-bed column systems, especially at large scale. Therefore, the present study investigated the external mass transfer effects on solvent-free lipase-catalyzed partial hydrolysis reaction and aimed to develop a mass transfer model for the operation. The influence of volumetric flow rate, one of the crucial operating parameters affecting the external mass transfer resistance, was examined. Results demonstrated increasing the flow rate led to an increase in hydrolysis reaction with the highest reaction rate observed at 5 ml min-1 . A dimensionless mathematical mass transfer model of Colburn factor, JD = K(Re)n-1 which is a function of Reynolds and Schmidt numbers, was then proposed to simulate the enzymatic partial hydrolysis reaction of palm oil in PBR. The mass transfer model was analyzed with different n values and results revealed that the mass transfer correlation of JD=0.92(Re)-0.2 was able to predict the experimental data accurately. The model developed could describe the dominance of mass transfer effects besides providing useful information for the scale-up design of industrial reactor.

Towards more predictive correlations for conjugated mass transfer across a droplet interface

Most studies of heat or mass transfer in dispersed, two-phase flows are either analytical or empirical, and therefore limited to simplified or specific operating conditions. In this frame, Direct Numerical Simulations (DNS) can be a powerful tool to address the needs arising from the development of new liquid–liquid solvent extraction processes, involving e.g., more viscous solvents or different hydrodynamic conditions. In this study, a large parametric study, in the range: Reynolds number Re∈[1,500], Péclet number Pee∈[10,1000], viscosity ratio μ∗∈[0.05,20] and a thermodynamic equilibrium coefficient k∈[0.1,10] , of mass transfer from an isolated droplet is achieved by DNS to propose a physically based correlation of the apparent Sherwood number, Sh, that is sufficiently generic to apply to emerging and future applications. The updated correlations derive first from a solid analysis of the features, in terms of concentration fields inside and outside the droplet and interface properties, to challenge the validity of the assumptions of mass transfer correlations. Then, we propose proper modifications in the formulation of existing models. In a second step, the accuracy and the robustness of the new models have been assessed by comparison with Sh obtained from DNS. The proposed correlations are applicable for mass transfer as well as for heat transfer problems, in most configurations encountered in chemical plants.

Numerical study of falling film dehumidification performance on corrugated plates

Due to a number of benefits, liquid desiccant dehumidification has received a lot of attention lately. In comparison to previous improvement strategies, corrugated plates have demonstrated higher efficacy in liquid desiccant dehumidification. This study employs computational fluid dynamics to examine the dehumidification performance of falling film liquid desiccant dehumidification on over sinusoidally shaped corrugated plates. The effects of plate geometries, solution parameters, and moist air (concentration of humidity, temperature, and flow rate) were discussed. Additionally, a mass transfer correlation was proposed based on the current numerical data. It is indicated that the corrugated plate significantly enhances dehumidification performance due to the liquid film waves intensification, mass transfer area expansion, and induction of vortexes close to the gas-liquid interface. The most effective falling film dehumidification is achieved using a corrugated plate with a wavelength of 5.0 mm and an amplitude of 0.5 mm. By raising the solution or air inlet temperature, the dehumidification rate is reduced while being strengthened by raising the solution or air inlet concentration, velocity, or air humidity. While decreasing when solution intake concentration or air velocity rises, the efficacy of dehumidification rises as solution velocity does. The proposed mass transfer correlation accurately predicts 93.3 % of the 45 data, with an error of 11 % or less. In the current parameter scopes, the magnitude has a more significant effect on Shair than the wavelength. Adjustments to air velocity and solution concentration can cause significant fluctuations in Shair, while air and solution temperature have little effect on Shair.

Heat and mass transfer correlations of supercritical n-decane considering the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes

The convective heat and mass transfer characteristics of the supercritical pressure (SCP) fuel in the regenerative cooling channel of hypersonic vehicles are significantly affected by pyrolysis reactions. In this study, we proposed a novel method to develop the Nusselt number (Nu) and Sherwood number (Sh) correlation of SCP fuel that considers the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes based on the differential global reaction (DGR) model of pyrolysis. The convective heat and mass transfer and pyrolysis characteristics of n-decane were investigated experimentally and numerically in a vertical downward-flow heated tube at pressures of 3-7 MPa. Theoretical analysis of the experimental conditions was conducted sequentially according to the partial differential equations (PDEs) of species continuity and energy, in which the internal source terms of heat and mass due to pyrolysis reactions were simplified and predicted using the DGR model of n-decane pyrolysis. A semi-empirical Sh correlation for predicting the radial distribution of fuel conversion was proposed associated with computational fluid dynamics (CFD) data by equivalently simplifying the internal mass source as pseudo-wall mass flux. A Nu correlation for convective heat transfer was proposed using the same methodology considering the influences of pyrolysis. The correction terms consider pyrolysis endothermicity and thermophysical property variation due to the conversion differences between the pipe wall and the bulk flow. Finally, the Nu correlation was compared to the experimental data, and the influence of heat transfer deterioration (HTD) due to pyrolysis coking was also analyzed quantitatively and empirically.

Investigating Mass Transfer Relationships in Stereolithography-Based 3D Printed Electrodes for Redox Flow Batteries

Redox flow batteries are a promising option for large-scale energy storage but remain too costly for widespread deployment. One approach to increase cost competitiveness is to improve the power density and efficiency of the electrochemical cell. Porous electrodes determine the performance of the cell, and their three-dimensional structure determines the electrolyte transport, fluid pressure drop, and the available surface area for electrochemical reactions [1]. Conventional porous electrodes are fibrous mats assembled in coherent structures [2]; however, they are repurposed from fuel cell gas diffusion electrodes and have not been tailored for redox flow batteries. Hence, an effective means to improve the performance of redox flow batteries is by engineering porous electrode structures to sustain the requirements of liquid-phase electrochemistry. To this purpose, there is a need to develop new manufacturing techniques affording a higher degree of control over the electrode microstructure and resulting properties. Additive manufacturing, or 3D printing, can be employed to manufacture customized, controlled, and deterministic architectures, enabling the fine-tuning of the electrical and hydraulic performance of porous electrodes [3].In this study, we manufacture model grid structures using stereolithography 3D printing followed by carbonization (Figure 1a) to tune the physiochemical properties of electrodes to be used in redox flow batteries. We employ a suite of microscopy, tomography, spectroscopy, fluid dynamics, and electrochemical diagnostics to understand the impact of the electrode structure on the mass transport and hydraulic performance of ordered lattice structures in flow cells. Here, the influence of the printing direction, pillar geometry (Figure 1b), and flow field type on mass transport is investigated using an organic electrolyte. We elucidate correlations between the electrode structure and performance metrics, namely surface area, pressure drop, and mass transfer correlations. We find that the printing orientation impacts the electrode performance through a change in electrode morphology caused by resin spreading and surface roughness, affecting the shrinking direction upon carbonization, internal surface area, and thus the charge transfer, mass transfer, and hydraulic resistances. Furthermore, we find that mass transfer rates within the electrode are enhanced by using an interdigitated flow field or by altering the pillar shape to a helical or triangular design, which we hypothesize improves mixing. Compared to commercial carbon-fiber electrodes, the pressure drop is significantly reduced (Figure 1c) as expected due to larger pore sizes (~500 μm for the grids vs. 2-100 μm for the Freudenberg H23 paper electrode and 2-300 μm for the ELAT Cloth electrode). Even though the commercial electrodes feature a superior internal surface area compared to the 3D printed electrodes, their area normalized mass transfer coefficients are lower (Figure 1d). Going forward, the use of printing technologies enabling finer features in combination with carbonization at elevated temperatures can be used to manufacture multiscale electrodes simultaneously providing low hydraulic resistance and excellent electrochemical performance. Additive manufacturing in combination with emerging computational approaches in topology optimization [4] might enable the bottom-up design and manufacturing of advanced electrode materials.

Comparison of CO2 absorption in DETA solution and [bmim]-[PF6] using thermodynamic and process modelling

Non-conventional amines are being research around the world to overcome the problems associated with traditional and conventional amines such as monoethanolamine (MEA) and methyldiethanolamine (MDEA). Having appropriate and specific process and thermodynamic models for these amines is vital to recognize their applicability and performance for CO2 absorption. However, studies on process modelling of these types of amines are very limited. In this study, the rate-based modelling was utilized for a packed column to obtain profiles of operating variables for CO2 absorption by Diethylenetriamine (DETA) solution. Deshmukh-Mather (D-M) method as thermodynamic modelling was incorporated in the rate-based model. The process model was validated using experimental data from the literature. Additionally, a sensitivity analysis of mass transfer correlations was performed on the temperature and concentration profiles. The effect of different operational parameters on the CO2 removal efficiency was studied, and the CO2 absorption efficiency of DETA solution was compared with that of an ionic solvent, 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim]- [PF6]). The effect of different parameters on the CO2 removal efficiency highlights the need to find optimum operating parameters for absorber column to achieve the maximum absorption efficiency. Although the absorption efficiency of CO2 by ionic solvent was higher than that of DETA solution under the same operational conditions, the advantages, and the disadvantages of each solvent in CO2 capture processes should be considered without compromising the solvent performance.

Investigating Mass Transfer Relationships in Stereolithography 3D Printed Electrodes for Redox Flow Batteries

AbstractPorous electrodes govern the electrochemical performance and pumping requirements in redox flow batteries, yet conventional carbon‐fiber‐based porous electrodes have not been tailored to sustain the requirements of liquid‐phase electrochemistry. 3D printing is an effective approach to manufacturing deterministic architectures, enabling the tuning of electrochemical performance and pressure drop. In this work, model grid structures are manufactured with stereolithography 3D printing followed by carbonization and tested as flow battery electrode materials. Microscopy, tomography, spectroscopy, fluid dynamics, and electrochemical diagnostics are employed to investigate the resulting electrode properties, mass transport, and pressure drop of ordered lattice structures. The influence of the printing direction, pillar geometry, and flow field type on the cell performance is investigated and mass transfer vs. electrode structure correlations are elucidated. It is found that the printing direction impacts the electrode performance through a change in morphology, resulting in enhanced performance for diagonally printed electrodes. Furthermore, mass transfer rates within the electrode are improved by helical or triangular pillar shapes or by using interdigitated flow field designs. This study shows the potential of stereolithography 3D printing to manufacture customized electrode scaffolds, which could enable multiscale structures with superior electrochemical performance and low pumping losses.

Progress Toward a Comprehensive Model for Mass Transfer in Structured Packings

Significant effort has been devoted to the study of mass transfer in sheet metal structured packings over the past half century. A number of mass transfer correlations have appeared in the literature as a result of those efforts. Unfortunately, none of these correlations has shown itself to be reliable over the full range of chemical systems, column operating conditions, and packing topologies encountered today. In an attempt to rectify some of the shortcomings of earlier correlations for sheet metal structured packings, we have employed a new data analysis methodology which simultaneously fits ⟨HETP⟩ data and mass transfer area data. The correlation we report upon here includes 444 ⟨HETP⟩ values from a variety of systems, operating pressures, and packing designs, along with 409 mass transfer area measurements. We demonstrate that this correlation outperforms all others while remaining simple enough to implement in process simulation software.

Heat and mass transfer analysis and optimization of passive interfacial solar still

Due to the fast thermal response and high solar energy efficiency, the passive interfacial solar still has become a reliable scheme for distributed water supply. In this paper, the thermodynamic performance of the interfacial solar still under different structures and operating conditions is studied experimentally, which provides an optimization direction for strengthening the distillation process. Firstly, based on the different Ra numbers, the calculation correlations for diffusion and convective mass transfer in the air interlayer were established to accurately predict the thermodynamic model of the interfacial distillation process. Then, the temperature distribution of the condenser and the growth process of condensate droplets were analyzed with the constant evaporation temperature. Simultaneously, the influence of different condensing structures and external variables on the heat transfer performance was compared. The results show that the interfacial still could obtain maximum evaporation heat under the vertical operation condition. When the evaporation temperature is 70 °C, the temperature difference between the wick evaporator and condenser can be increased by 49.5 %, after coupling a finned condenser with the aspect ratio of 7.2. In addition, a narrower interlayer spacing and a larger evaporation temperature could bring a higher equivalent heat transfer rate and evaporation efficiency. In a sunny weather, the interfacial solar still coupled with an extended condenser can reach a 4.81 kg/m2/day water yield and a 0.486 daily gained output ratio under 1 cm interlayer spacing.

On the dissolution of a solid spherical particle

The dissolution of a solid spherical particle is a canonical problem that finds many areas of application. In this work, we provide a generalized theory that takes into account the role of forced convection in the solvent (or, alternatively, the relative motion of the particle in the solvent), showing that the problem can be formulated in terms of four dimensionless parameters. Focusing on the case when one of these (the Reynolds number) is small, we consider asymptotic and numerical approaches to the problem, with a key outcome being a numerical method, implemented in the finite-element software Comsol Multiphysics, that is able to solve the resulting axisymmetric moving-boundary problem, even when over 90% of the particle has dissolved and its shape is far from spherical. We also demonstrate how this approach relates to and supersedes earlier efforts, providing a quantitative assessment of the often unquestioningly used Ranz–Marshall correlation for mass transfer from a sphere. In particular, we find that this correlation may overpredict the dissolution time by a factor of four, whereas a correlation by Clift et al. that is cited and used less often performs considerably better, even in the highly convection-dominated regime for which it was not originally intended.

Hydrodynamic and mass transfer correlations for SiC ceramic foam monolithic trays used in distillation column

AbstractBACKGROUNDCellular foam materials are excellent engineering materials for many applications in chemical engineering, especially process intensification of chemical conversions and separation. Recently, a silicon carbide (SiC) ceramic foam monolithic tray was developed as an excellent mass transfer tool to improve distillation and it showed an improved operational flexibility. Previous studies have revealed the effects of open cell diameter and tray thickness on the hydraulic performance and mass transfer efficiency of SiC foam monolithic trays, but relevant correlations are still missing, limiting their practical uses.RESULTSIn this study, based on the published experimental data, empirical correlations were developed to predict the hydrodynamic performance and mass transfer efficiency of SiC ceramic foam monolithic trays. The new correlations include the influence of the tray structure parameters, such as open cell (or pore) diameter and tray thickness, and of the operation conditions (such as the liquid and vapor volumetric flow rates), and the data obtained agree well with the experimental results.CONCLUSIONThe availability of such empirical correlations can be beneficial for the chemical engineering design of practical distillation processes based on SiC foam monolithic trays. © 2023 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI).

Assessment of biodegradation kinetics and mass transfer aspects in attached growth bioreactor for effective treatment of brilliant green dye from wastewater

In this study, Bacillus licheniformis immobilized with low-density polyethylene (LDPE) was employed to degrade Brilliant Green (BG) dye from wastewater in a packed bed bioreactor (PBBR). Bacterial growth and extracellular polymeric substance (EPS) secretion were also assessed under different concentrations of BG dye. The impacts of external mass transfer resistance on BG biodegradation were also evaluated at different flow rates (0.3–1.2 L/h). A new mass transfer correlation JD=5.71NRe-0.3 was proposed to study the mass transfer aspects in attached-growth bioreactor. The intermediates, namely 3- dimethylamino phenol, benzoic acid, 1–4 benzenediol, and acetaldehyde were identified during the biodegradation of BG and, subsequently degradation pathway was proposed. Han - Levenspiel kinetics parameters μmax and Ks were found to be 0.185 per day and 115 mg/L, respectively. The new insight into mass transfer and kinetics support the design of efficiently attached growth bioreactor to treat a wide range of pollutants.

Condensation heat transfer between a vertical superhydrophobic aluminum surface and moist air under natural convection

Condensation heat transfer at superhydrophobic surfaces has raised a lot of interest due to their potential application in atmospheric water harvesting and air-conditioning. In moist air, the condensation heat transfer using a superhydrophobic surface can be negatively affected by the existence of a large amount of non-condensable gas, namely, the dry air. Besides, the air flow pattern would substantially affect the surface condensation rate due to the convective mass transfer of water vapor. In this study, the condensation regime of a superhydrophobic aluminum surface vertically positioned in quiescent moist air was visualized and the condensation rate was experimentally investigated. Condensation experiments were also performed by using hydrophobic, hydrophilic, and superhydrophilic surfaces for comparison. The condensation rate of the superhydrophobic surface was consistent with that of other surfaces, though the condensation regimes of the four surfaces were quite different. The average deviation between the experimental condensation rate and the empirical correlation of natural convection heat and mass transfer was within 12%. The result indicates that vapor transfer induced by diffusion and convection in the boundary layer rather than the heat transfer resistance associated with condensate dominates the condensation heat and mass transfer between the moist air and the superhydrophobic surface.

Mass transfer study of phenolic compound liquid-liquid extraction process from bio-oil of coffee shell pyrolysis product

Coffee shells are one of the potential renewable materials used in the pyrolysis process to produce bio-oil. However, the amount of phenolic compounds, which is roughly 36.74%, is one of the primary drawbacks of using coffee shell bio-oil as a fuel source. Only a little amount of research has been done on the mass transfer modeling and phenomena of phenol extraction from coffee shell bio-oil. The objectives of this study are to identify the best extraction circumstances, ascertain the empirical correlation of total mass transfer, and produce the empirical correlation of Sherwood number, which can be used to characterize the role of variables in this mass transfer process. The ratio of impeller diameter to tank diameter and the Sherwood number, as well as Reynolds, Schmidt, Weber, dispersed phase holdup, were studied as dimensionless numbers. This study used liquid–liquid extraction process at the temperature of 50 ℃, with chloroform–methanol 80% as a solvent with ratio of 2:1 v/v and use bio-oil to solvent ratio of 1:1 v/v. The extraction time has an interval of 30 min (20, 50, 80, 110 min), with varied impeller diameter (3.5 cm and 4 cm), vessels diameter (9 cm and 10 cm) and mixing speed (250 rpm, 300 rpm, 350 rpm). According to the findings, the greatest phenol yield was obtained at impeller diameter 3.5 cm, tank diameter 9 cm, and mixing speed 300 rpm, with a distribution coefficient of 0.848. The results demonstrate that the maximum overall mass transfer coefficient is 4.096 × 10-4 m/s and that the liquid diffusivity is 1.7965 × 10-9 m2/s. The equation model from this study could be applied to a liquid–liquid extraction process that is scaled up to extract more phenolic compounds from the the produced bio-oil.