Number Pe Research Articles

Upscaling of dispersion in gas-liquid absorption on an inclined surface.

We extend the Taylor-Aris dispersion theory to upscale the gas absorption into a viscous incompressible liquid flowing along an inclined surface. A reduced-order model of advection-dispersion-reaction is developed with the aid of Reynolds decomposition and cross-sectional averaging techniques. The upscaled model allowed evaluation of the dispersion, advection, and absorption kinetics as a function of the Peclet number (Pe) and the Damköhler number (Da). The transport and kinetics parameters for the limiting cases of nonabsorption and absorption dominant are also evaluated. The upscaled model is solved analytically, and the obtained solution is used to evaluate the upscaled mass transfer between the gas and liquid. The results for the overall Sherwood number identify three regions: (i) advection dominant, (ii) transition where both advection and absorption play a role, and (iii) absorption dominant. The scaling relation between the Sherwood number (Sh) and the Da for the last region was determined to follow Sh∼Da^{1/2}. It is also revealed that in the first two regions, the Sherwood number versus the Peclet number exhibits a bell-shaped (or Gaussian) behavior, suggesting an optimal Pe that maximizes mass transfer between gas and liquid in these regions. The model and insights presented have the potential to be applied in a wide range of industrial separation processes involving the interaction of a gas exposed to a liquid flowing downward on an inclined surface under gravity.

Oscillating reaction in porous media under saddle flow

Pattern formation due to oscillating reactions represents variable natural and engineering systems, but previous studies employed only simple flow conditions such as uniform flow and Poiseuille flow. We studied the oscillating reaction in porous media, where dispersion enhanced the spreading of diffusing components by merging and splitting flow channels. We considered the saddle flow, where the stretching rate is constant everywhere. We generated patterns with the Brusselator system and classified them by instability conditions and Péclet number (Pe), which was defined by the stretching rate. The results showed that each pattern formation was controlled by the stagnation point and stable and unstable manifolds of the flow field due to the heterogeneous flow fields and the resulting heterogeneous dispersion fields. The characteristics of the patterns, such as the position of stationary waves parallel to the unstable manifold and the size of local stationary patterns around the stagnation point, were also controlled by Pe.

Stability of diffusion flames under shear flow: Taylor dispersion and the formation of flame streets

Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number (Le) fuels, provided that the flow Reynolds number, or the Peclet number Pe, exceeds a critical value. The underlying mechanisms behind these observations have not yet been fully understood. In the present paper, we identify the coupling between diffusive-thermal instabilities and Taylor dispersion as a mechanism which is able to explain the experimental observations above. The explanation is largely based on the fact that Taylor dispersion enhances all diffusion processes in the flow direction, leading effectively to anisotropic diffusion with an effective (flow-dependent) Lewis number in the flow direction which is proportional to 1/Le for Pe≫1. Validation of the identified mechanism is demonstrated within a simple model by investigating the stability of a planar diffusion flame established parallel to a plane Poiseuille flow in a narrow channel. A linear stability analysis, leading to an eigenvalue problem solved numerically, shows that cellular (or finite wavelength) instabilities emerge for high Lewis number fuels when the Peclet number exceeds a critical value. Furthermore, for Peclet numbers below this critical value, longwave instabilities with or without time oscillations are obtained. Stability regime diagrams are presented for illustrative cases in a Le−Pe plane where various instability domains are identified. Finally, the linear analysis is supported and complemented by time dependent numerical simulations, describing the evolution of unstable diffusion flames. The simulations demonstrate the existence of stable cellular structures and show that the longwave instabilities are conducive to flame extinction.

Thermophoresis migration of an aerosol spherical particle embedded in a Brinkman medium at small non-zero Péclet numbers

The method of matched asymptotic expansions is used to investigate the problem of thermophoresis migration of an aerosol spherical particle immersed in a porous medium saturated by a viscous fluid at a small non-zero Péclet number Pe. A uniform temperature gradient is imposed on the system parallel to the diameter of the particle in the opposite direction of z axis. It is assumed that the Knudsen number is in the range of the slip fluid flow through the pores of the porous medium and is compatible with the assumption of the continuum model. The porous medium is modeled by the Brinkman equation and is assumed to be homogenous and isotropic, and the solid matrix is in thermal equilibrium with the fluid through the voids of the medium. In the analysis of motion, the thermal stress slip is considered in addition to the temperature jump, the thermal creep, and the frictional slip. The thermophoretic velocity of the particle is obtained in the closed form up to order Pe3 as a function of the thermal properties of the system and the permeability of the porous medium. The present asymptotic analytical solutions can be viewed as an effective method for checking the numerical schemes for future work on arbitrary values of the Péclet number. The limiting case of the thermophoretic velocity for the Stokes clear fluid is recovered.

Unraveling instabilities and mixing behavior in two-layered flows: A quest for the optimum viscosity ratio

A two-layer miscible displacement of density-matched but viscosity-contrasted fluids through a channel is numerically investigated in a nonlinear regime. The flow is governed by Navier–Stokes equations, which are coupled to a convection-diffusion equation via viscosity dependent concentration. Instabilities in the form of roll-ups or ligament waves are observed when a less viscous fluid is sheared over a more viscous fluid. Through interfacial length calculations, we demonstrate that the temporal evolution of the interface can be divided into three regimes: the initial diffusion-dominated regime, the intermediate convection-dominated regime, and the final diffusion-dominated regime. With the unstable roll-up growth only in a convection-dominated regime, the growth of instability delays at later times in diffusion dominated regime. Moreover, onset time ton vs R plots for each Reynolds number (Re), Péclet number (Pe), initial interface location (h), and thickness of initial mixing zone (q) depict that the instability originates early for intermediate viscosity ratios (R) than larger R. In contrast to earlier studies in the linear regime, we showed that if the viscosity ratio between two fluids is very large or small, the instability doesn't trigger in the nonlinear regime. The analysis of the concentration's global variance-based degree of mixing allows us to find optimum parameters for maximum mixing. We show that the optimal mixing is obtained at an intermediate value of R (optimum R). Furthermore, the degree of mixing is found to increase for increasing Re and decreasing Pe.

Analysis of effects of moving wall direction in a one sided semi-circular porous cavity on mixed magneto-bioconvection in the presence of hybrid nanofluid with oxytactic bacteria

A computational analysis on the effects of direction of wall movement in a one sided semi-circular porous cavity on mixed magneto-bioconvection of hybrid nanofluid in the presence of oxytactic bacteria has been performed. The working fluid is the hybrid nanofluid. The enclosure is cooled from semi-circle side and heated from moving lid under the effect of uniform magnetic field in the horizontal direction. The numerical solution of governing equations is obtained by using the higher order finite element method (FEM). The reliability of designed solver is tested through the experimental and numerical data available in the literature. Two cases of the boundary conditions are considered related to the tendency of right vertical lid of the cavity. Other parameters are Richardson number, Darcy number, Hartmann number, Peclet number and porosity. It is found that moving lid direction is the most effective parameter for the flow field, isotherms, oxygen and microorganism distributions. Moreover, higher heat transfer rate is obtained in Case-I for different values of Darcy number. Around 10% increment is occurred on mass transfer with different Pe number in case of downward moving lid due to increment of convection mode of heat transfer inside the cavity.

Optimization on the performance of fibrous filter through computational fluid dynamic simulation coupled with response surface methodology

Fibrous-filtration media has been demonstrated with the ability to separate particulate matter in the gas. However, the complexity of involved parameters and the intricate interior structure of fibrous media pose great challenges for filter design and optimization. Herein, a novel numerical method was proposed to predict and optimize the fibrous-filtration progress by employing the computational fluid dynamic (CFD) simulation coupled with the response surface methodology (RSM). The involved filtration parameters exerted synergetic effects on filtration efficiency, which can be explained by the coupling effect of basic filtration principles with the variation of the Stk number and Pe number. Meanwhile, the pressure drop increased with the elevated solid volume fraction and airflow velocity but was not affected by the variation of particle diameters. This combined methodology of CFD simulation with RSM optimization paved a new path for the high-efficient screening of the filter design and optimization.

Heat transfer evaluation of liquid lead-bismuth eutectic cross flow tube bundle: Experimental part

Helical coil once-through tube steam generator (HCOTSG) is an excellent form of heat exchanger. HCOTSG is adopted in various industries, such as Lead-bismuth Fast Reactor (LFR). The flow and heat transfer in the shell side of HCOTSG are important for its design and optimization. It is of great significance to carry out relevant experiments to obtain empirical correlations. In this paper, experimental study on the lead-bismuth eutectic (LBE) cross flow around the tube bundle is carried out to investigate the thermal-hydraulic characteristics based on geometric approximation of local region. Three test sections with different inclination angles of 0°, 4°, 8° are adopted in the experiments with Peclect number (Pe) up to 350. The experimental sections are uniformly heated with heat flux ranging from 20 to 100 kW/m2. The heat transfer characteristic of LBE cross flow around inclined tube bundle is obtained, considering the effects of inclination angle of the test section. The heat transfer correlation of LBE cross flow around inclined tube bundle is proposed for the first time. By comparing the data of the experiments, the results are all within the error range of 10%. The correlation is appropriate for the program development of LBE HCOTSG. This study can provide essential experimental data for the design and code development of LBE HCOTSG.

Continuous flow extraction of biodiesel produced in a packed-bed reactor using supercritical carbon dioxide and tetrahydrofuran as solvents

The concurrent process of biodiesel (FAME) extraction and triglyceride methanolysis was carried out by using supercritical carbon dioxide (SC–CO2) and tetrahydrofuran (THF). This study explored the integration of SC-CO2 extraction facilitated catalyst-free transesterification efficiently at low temperatures with practical biodiesel productivity. The work started with studying the transesterification kinetics of triglycerides using different molar ratios of methanol under various SC-CO2 conditions in the presence of THF solvent. The elementary second-order kinetics associated with the mass transfer limiting factor satisfied the experimental results from all different mixing ratios. A four-factorial Box-Behnken Design (BBD) coupled with the ANOVA was employed to optimize the FAME recovery by the reaction-extraction processes with continuous two streams of SC-CO2 and 10% v/v THF-methanol mixture. The optimum predicted FAME recovery was 95.47% w/w at 71.93 °C, 186.67 bar using the substrate ratio 12.16. The supercritical fluid-assisted dispersion feature was characterized through the Peclect number (Pe) obtained from the volumetric dispersion model (VDM). The Pe could indicate suitable substrate mixing for the process operation and design to enhance production efficiency. The feasibility of upscaling the process to the commercial level was proposed with preliminary economic consideration, which could suggest process improvements in further research and technological development.

Theoretical study of supported ionic liquid membrane reaction and transport for CO2 cycloaddition reaction

Membrane reactors are promising for achieving a variety of thermodynamically limited reactions. However, few studies have focused on quantitative analysis of the coupling of reaction and separation matching of membranes. In this work, based on the experimental validation of the forced flow through principle of membrane reactors for catalytic CO2 cycloaddition, describes the membrane reaction performance of supported ionic liquid membranes (SILMs) in the presence of primary irreversible reactions, and draws on a dusty gas model to calculate fluxes within the gas pore space of the support. The degree of product separation is theoretically investigated in relation to the membrane permeation, the resistance difference between the ionic liquid membrane and the support, the liquid loading of the catalyst layer and the fluid flow rate, and adjustable parameters of the model are proposed to predict the SILM performance. In addition, two dimensionless numbers, namely Damköhler (Da) and Péclet (Pe) numbers, are introduced to correlate the equilibrium constant-conversion-DaPe relationship, and the reaction kinetics and permeate flux compatibility are analyzed with the help of CFD simulations, which incorporate parameters of operating conditions and stoichiometric coefficients of the reaction, as well as optimization of reactor geometrical, providing insights to achieve higher conversion improvements.

Magneto-bioconvection flow in a porous annulus between circular cylinders containing oxytactic microorganisms and NEPCM

PurposeThis paper aims to investigate magnetic impacts on bioconvection flow within a porous annulus between an outer cylinder and five inner cylinders. The annulus is filled by oxytactic microorganisms and nano-encapsulated phase change materials.Design/methodology/approachThe modified ISPH method based on the time-fractional derivative is applied to solve the regulating equations in Lagrangian dimensionless forms. The pertinent factors are bioconvection Rayleigh number Rab (1–100), circular cylinder’s radius Rc (0.1–0.3), fractional time derivative α (0.95–1), Darcy parameter Da (10−5–10−2), nanoparticle parameter ϕ (0–0.1), Hartmann number Ha (0–50), Lewis number Le (1–20), Peclet number Pe (0.1–0.75), s (0.1–0.9), number of cylinders NCylinders (1–4), Rayleigh number Ra (103–106) and fusion temperature θf (0.005–0.9).FindingsThe simulations revealed that there is a strong enhancement in the velocity field according to an increase in Rab. The intensity and location of the phase zone change in response to changes in θf. The time-fractional derivative a acting on a nanofluid velocity and flow characteristics in an annulus. The number of embedded cylinders NCylinders is playing a significant role in the cooling processes and as NCylinders increases from 1 to 4, the velocity field’s maximum reduces by almost 33.3%.Originality/valueThe novelty of this study is examining the impacts of the magnetic field and the presence of several numbers of embedded cylinders on bioconvection flow within a porous annulus between an outer cylinder and five inner cylinders.

Mass transfer rate in gas-liquid Taylor flow: Sherwood numbers from numerical simulations

Numerical simulations of Taylor flow are carried out using the unit cell approach. The hydrodynamics of two-phase flows are computed using COMSOL Multiphysics software and a moving mesh approach to track the interface. Gas-liquid mass transfer is then solved, by varying the diffusion coefficient. Surprisingly, this work shows that the global Sherwood number Sh∞ plateaus with the Péclet number Pe when it is larger than 1000, which was not previously reported. Local Sherwood numbers for transfer through the film (Shbf) and the caps (Shbs) allow to distinguish their contributions. Shbf evolves as given by the falling film theory, whereas Shbs follows the penetration theory only at moderate Péclet number. A dimensionless correlation to predict Sh∞ gathers results from contrasted configurations: Sh∞ is mainly sensitive to both Pe (before saturation) and the gas hold-up ϵG. The benefit of working with unit cells of small ϵG in milli-reactors is therefore highlighted.

Deriving analytical expressions of the spatial information entropy index on riverine water quality dynamics

Information entropy theory has been largely applied in hydrology and water resource engineering. Recently, entropy theory has received significant attention for describing reactive solute mixing and transport processes in ground water and surface water and for its applications in water quality management. However, analytical expressions of the entropy index of riverine water quality dynamics are often not included in the literature. In this study, the analytical expressions of the spatial information entropy index (Gx) in the 1D steady-state transport process under full-extent observation and tracking observations are derived after the definition of the system boundary and probability space. The expressions of Gx were successfully validated by field data from two tracer experiments, and the different characteristics of Gx under different riverine hydraulic situations were uncovered. The formula of Gx shows a reasonable linkage with the Peclet number (Pe) in hydrodynamics. This indicates that Gx is a physical quantity describing or linking to the real world more than a statistical index, and in practice, similar decision or management measurements based on entropy theory can be made for rivers with similar Pe conditions. Hydrologists will benefit in many ways from analytical expressions, such as theoretical analysis, quick calculation of the entropy index, preliminary engineering design, etc. A clearly defined example of maximum entropy time (tGmax) and its application in water quality evaluation, monitoring optimization and pollution source identification are demonstrated. These new findings will provide a convenient tool for catchment water quality management.

Prediction of Limiting Casting Speed in a Horizontal Direct-Chill Casting through Numerical Modeling and Simulation

Limiting casting expression speed was obtained and the flow redistribution and thermal history in a horizontal direct-chill (HDC) casting was predicted using the numerical modeling approach. The governing solidification equations were non-dimensionalized to understand the relevant contribution of each term in the solidification processes in the HDC system. The effect of an increase in the casting speed on the flow characteristics and sump length was represented by the Péclet number Pe. Details of the simulation reveal that at a low Pe, the natural convective flow creates minor counter-clockwise recirculating cells in the lower half of the HDC domain. However, at a Pe above 82.75, the minor recirculating cells disappear due to the strong forced convective flow from the upstream. Additionally, an increase in the Pe increases the sump length, strength, and spread of the turbulence field within and beyond the mold region. The limiting casting conditions are computed by predicting the sump length over which the alloy temperature is above the solidus temperature. This gives a simple relation for the casting speed as a function of the geometrical data and the alloy properties. The current work is useful to casting engineers who always rely on trial and error in choosing a new casting speed whenever a new alloy is to be produced. Hence, with the new information and the casting speed relations, it is possible and easy to predict the operating window over which melt break-out can occur during HDC.

Penguin Huddling: A Continuum Model

Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to heat loss to the huddle exterior and through the reorganisation of penguins as they seek to regulate their heat production within the huddle. These two heat transfer mechanisms, along with area, or penguin number, conservation, gives a free boundary problem whose dynamics depend on both the dynamics interior and exterior to the huddle. Assuming the huddle shape evolves slowly compared to the advective timescale of the exterior wind, the interior temperature is governed by a Poisson equation and the exterior temperature by the steady advection-diffusion equation. The exterior, advective wind velocity is the gradient of a harmonic, scalar field. The conformal invariance of the exterior governing equations is used to convert the system to a Polubarinova-Galin type equation, with forcing depending on both the interior and exterior temperature gradients at the huddle boundary. The interior Poisson equation is not conformally invariant, so the interior temperature gradient is found numerically using a combined adaptive Antoulas-Anderson and least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape. This shape is dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter beta which effectively measures the strength of the interior self-generation of heat by the penguins. The numerical method developed is applicable to a further five free boundary problems.

Isotopic fractionation of chlorine and potassium during chloride sublimation under lunar conditions

The Moon is depleted in volatile elements and compounds, and lunar samples exhibit a wide range of Cl isotopic compositions, which is believed to result from the volatilization of metal chlorides (e.g., NaCl, KCl, and FeCl2). However, the Cl isotopic fractionation behavior during volatilization is not well constrained, particularly for metal chlorides. Furthermore, the effect of metal chloride evaporation on metal isotopes is poorly known. In the present study, we performed NaCl and KCl sublimation experiments to study Cl and K isotopic fractionations at temperatures ranging from 923 K to 1061 K and at pressures of 7×10–5 bar to 1 bar in an N2 atmosphere. The isotope fractionation factors of 37/35Cl(αgas–solid) from NaCl sublimation experiments are 0.9985±0.0002, 0.9958±0.0004, and 0.99807±0.00004 at 1, 10–2, and 7×10–5 bar, respectively. Those of 41/39K(αgas–solid) and 37/35Cl(αgas–solid) from KCl sublimation experiments are 0.99884±0.00004 and 0.9988±0.0003 at 1 bar, 0.9977±0.0002 and 0.9972±0.0003 at 10–2 bar, and 0.9989±0.0002 and 0.9989±0.0001 at 7×10–5 bar, respectively. Chlorine and K isotopes fractionate more at 10–2 bar than at 7×10–5 bar and 1 bar. The saturation index in all the sublimation experiments was >95%, which resulted in near-equilibrium isotopic fractionation at the sublimation interface. Therefore, the isotopic fractionation was controlled by mass transfer processes in the gas and solid phases. The isotopic fractionation at 10–2 bar was controlled by the chemical diffusion of sublimated gas in an N2 atmosphere with almost no convection effect, (i.e., Pe number close to zero), whereas the isotopic fractionation at 1 bar was suppressed by atmospheric convection with a turbulence factor of 0.4±0.1 (i.e., Pe number >1). The extremely high sublimation rate and the very slow diffusion in the sublimating solid at 7×10–5 bar suppressed isotopic fractionations. Based on our experimental results, calculations using Cl/K and Na/K in lunar materials reveal that degassing of KCl contributed very little (<0.2‰) to the K isotopic fractionation (>0.58‰) during lunar magma ocean degassing. The Cl isotopic fractionation factor from lunar samples is similar to our results at 10–2 bar. This similarity of Cl isotope fractionation indicates that there may have been a transient atmosphere above the lunar magma ocean.

The morphology of dryout nanofluid droplet and underlying mechanisms based on coarse-grained molecular dynamic simulations

The evaporation of nanofluid droplet is an important process in nanofluid combustion, spray drying, and so on. We investigate the influence of nanoparticles on the evaporation behavior of spherical droplets by coarse-grained molecular dynamics simulations. The results show that the solid–liquid interaction and the initial volume fraction of the nanoparticles can greatly affect the crust formation. The underlying mechanisms can be characterized by multiplying the Peclet number(Pe) and initial particle concentration(φ0). Greater Pe·φ0 can result in morphologies with crust due to the quick movement of nanoparticles to droplet surface. Finally, a phase diagram is constructed to predict the morphology of the dryout nanofluid droplets. Our results extend the fundamental understanding of the mechanisms that control the drying of droplet suspensions.

Curvature and shape relaxation in surface-viscous domains.

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Study on Heat Transfer Characteristics of Graphene Nanofluids in Mini-Channels of Thermal Integrated Building.

Two kinds of rectangular mini-channels of different sizes were designed and fabricated for testing the convective heat transfer characteristics of graphene nanofluids. The experimental results show that the average wall temperature decreases with the increases in graphene concentration and Re number at the same heating power. Within the experimental Re number range, the average wall temperature of 0.03% graphene nanofluids in the same rectangular channel decreases by 16% compared with that of water. At the same heating power, the convective heat transfer coefficient increases with the increase in the Re number. The average heat transfer coefficient of water can be increased by 46.7% when the mass concentration of graphene nanofluids is 0.03% and the rib-to-rib ratio is 1:2. In order to better predict the convection heat transfer characteristics of graphene nanofluids in small rectangular channels of different sizes, the convection heat transfer equations applicable to graphene nanofluids of different concentrations in small rectangular channels with different channel rib ratios were fitted, based on factors such as flow Re number, graphene concentration, channel rib ratio, Pr number, and Pe number; the average relative error (MRE) was 8.2%. The mean relative error (MRE) was 8.2%. The equations can thus describe the heat transfer characteristics of graphene nanofluids in rectangular channels with different groove-to-rib ratios.

Fixed-bed column for phosphate adsorption combining experimental observation, mathematical simulation, and statistics: Classical and Bayesian

The purpose of this work is to investigate the removal of phosphate in a fixed-bed column, using a layered double hydroxide (CaMgAl-LDH) as adsorbent, applying experimental observation, mathematical simulation and statistical analysis. Also, an experimental design was carried out in order to evaluate the influence of the operational conditions applied in the column on its adsorption efficiency. At a natural pH of 7.5, three independent parameters were considered: initial phosphate concentration (15, 30, and 60 mg L-1); feed flow rate (2.5, 5, and 10 mL min−1); and solid adsorbent mass (0.2, 0.5, and 1 g). As response variables the saturation time and the concentration of saturation in the column were evaluated. For the study of the fixed-bed column performance, through its breakthrough curves, a mathematical simulation, applying Bayesian statistics, was built in order to estimate its parameters, these being: the Peclet number (Pe), the equilibrium Langmuir constant (KL) and the kinetic coefficient (KS). To illustrate the model that was used to describe the mass transport through the fixed-bed, differential partial equations were obtained by the mass balance of the column. The results obtained in this research demonstrated that the Peclet number, for all operational conditions, suggests that the dispersion and the advection forces present in the column are approximately equal to each other. Also, the Langmuir isotherm represented well the adsorption equilibrium in all operational conditions and the kinetic coefficient ranged between 4.52 and 0.81 mL mg−1 min−1, these values shows that the kinetic effect has little interference in the breakthrough curves evaluated in the present work. Then, the estimated parameters were validated by the experimental design applied. Therefore, it was shown that the technique used to estimate the parameters and the mass balance model applied in this work, to describe the adsorption process, was robust, since the model was able to predict the breakthrough curves. In this way, this approach can be used to design columns based on the desired operational conditions, as well as for scaleup studies.