Dusty Gas Model Research Articles

Multi-objective optimization of aniline and hydrogen production in a directly coupled membrane reactor

A numerical study of aniline production by hydrogenation of nitrobenzene (NBH) and hydrogen production by steam methane reforming (SMR) in a directly coupled membrane reactor is developed. This membrane reactor was proposed aiming to decarbonize heating in SMR and to favor the recovery of all products. Aniline recovery is improved in this reactor as water, a byproduct in NBH, is consumed in SMR. The simulation is performed using a heterogeneous-one dimensional model (Dusty gas model) and results are compared against the homogeneous model. The operating conditions of the reactor were selected using a multi-objective optimization method, genetic algorithms. The aims of the optimization were: methane conversion maximization, minimum membrane area, minimum reactor size, hydrogen yield maximization, nitrobenzene conversion maximization and the maximization of hydrogen recovery. This process was able to achieve complete conversion of methane and nitrobenzene. The hydrogen yield achieved can be as high as the maximum (∼4). 35% of this hydrogen was used as a reactant for aniline production. 99% of the unreacted hydrogen was recovered and purified. As the steam flow was minimized, aniline was obtained with a molar composition (70%), 2.1 times higher than that obtained in a conventional process for aniline production (33%). CO 2 was obtained with a purity of 97%, hence, CO 2 carbon capture and storage techniques were also favored. In addition, the energy requirements of heating of feedstock, reaction and recovery system of this novel process was 2.7 times lower than that of conventional processes carried out independently. • Operating conditions were selected through a multi objective optimization. • Energy requirements were reduced 2.7 times. • The recovery of the final products (aniline, hydrogen, and CO2) was favored. • Complete conversion of reactants was achieved. • A hydrogen efficiency of 99% was achieved.

Coupled Transport Effects in Solid Oxide Fuel Cell Modeling.

With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick’s law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring -characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At K and A/m2, 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials.

Numerical validation of the dusty-gas model for binary diffusion in low aspect ratio capillaries

The dusty-gas model is an empirical formulation commonly used to describe gas flows in porous media. While experiments have validated the model for pores with high aspect ratios, a validation for near-unity aspect ratios is lacking. We used direct simulation Monte Carlo to evaluate the accuracy of the dusty-gas model for binary diffusion in low aspect ratio capillaries. Our results suggest that the dusty-gas model deviates from the Monte Carlo simulations by less than 3% for aspect ratios ≥ 1, thus supporting its suitability as a phenomenological model for transport in nanoporous structures in various applications such as heat transfer, catalysis, and water purification.

A Numerical Study of Hydrogen Production via High-temperature and Low-temperature Water-Gas Shift Reactors’ System: The Multi-Scale Modeling Approach and Simulation

The primary purpose of this study is to develop an advanced, and comprehensive multi-scale mathematical models of a packed bed reactors (PBRs) carrying out high and low temperature water-gas-shift reactions (WGSRs) for the hydrogen production. In industrial hydrogen generation applications, the water-gas-shift reactors are considered at high (called HTSR) and low (called LTSR) temperature stages with a cooling process between them. Therefore, detailed and advanced numerical studies on the HTSR and the LTSR in series are carried out to assess the overall performance of hydrogen production system. After completing a single-pellet, non-isothermal, steady-state simulation, we couple our model with a non-isothermal (adiabatic), steady-state packed-bed reactor model to form a hybrid multi-scale reactor model. The velocity, temperature and species’ concentration profiles along both the reactor length and the pellet radius are captured by using rigorously defined momentum, energy, and species transport models, accounting for the physical mechanisms involved in the system such as convection, conduction, and reaction-diffusion. The model’s equations are simultaneously solved for each domain: bulk gas domain and catalyst-pellet domain. The rigorous Maxwell-Stefan Model is applied on the reactor scale to account mass diffusion fluxes. On the other hand, Dusty Gas Model is considered to describe mass diffusion fluxes for the single pellet scale. Studies that include a broad range of the operating conditions and design parameters are carried out in this paper, in order to investigate the upper and lower limit conditions’ effects on the results.

Investigation of shock and a dust cloud interaction in Eulerian framework using a newly developed OpenFOAM solver

The current study documents the development of a new multiphase solver for the simulation of dilute dusty gas flows in the OpenFOAM suite. Even though various solvers for simulation of multiphase flows are developed in OpenFOAM, the lack of a density-based Riemann solver (which is the desirable model for the description of the interaction of shock waves with a dispersed particulate phase) is evident. As the code is developed in this open-source framework more users with broader backgrounds can use, assess and extend the code to include new features for studying new complex phenomena that are present in multiphase gas-solid flows. Moreover, the conventional dusty gas model is modified in such a way that the eigenvalue degeneracy is circumvented. The idea is that rather than devising new flux functions or modifying all the previously well-established numerical flux functions to be applicable to the pressureless Euler equation, to modify the equation model in a way that fluxes can be applied to our system. The simulation results for problems in one, two, and three-dimensional space indicate that the developed solver is a promising tool in the study of these types of flows. Furthermore, the computationally demanding problem of shock-bubble interaction in three-dimensional space is investigated with a twist. Here the bubble is replaced with a spherical dust cloud for the first time and with the help of high-performance computing facilities, justifications on topology deformation of the cloud in interaction with dust particles of different diameters and loadings are discussed in detail.

Mathematical approaches to modelling the mass transfer process in solid oxide fuel cell anode

In the recent literature, the influence of lean fuel, type of fuel, velocity profile and the flow direction on the performance operation of solid oxide cells (SOCs) is commonly investigated. SOCs generate electricity when they operate in fuel cell mode (SOFC – Solid Oxide Fuel Cell) or produce hydrogen in electrolysis mode (SOEC – Solid Oxide Electrolyzer Cell). They consist of several layers, including two porous electrodes separated by a gas-tight electrolyte. Typical anode porosity (fuel electrode in SOFC mode) varies from 20% to 50% (after sintering). The porosity value may limit the mass transport and the overall performance of SOC. This work investigates computationally and experimentally, the existing challenge such as diffusion mechanism in porous medium using the example of SOC electrode. A set of mass transport models (Fick's laws, modified Fick's law, Maxwell-Stefan Model, Dusty Gas Model) are described and discussed, highlighting their similarities, differences, advantages, and disadvantages as well as restrictions in usage. Finally, a detailed computational fluid dynamics (CFD) model of the diffusive transport in porous electrode was elaborated and validated. An experimental campaign was conducted using anode supported SOC, fabricated at the Institute of Power Engineering in Poland. Simulations were performed of the mass transport of pure hydrogen and pure water vapor or carbon dioxide (substitute of real product of electrochemical reaction in SOC for validation purposes) through porous anode. Tests were conducted in the wide flow range 10 [ml/min] up to 200 [ml/min] for both gases. The results demonstrate that hydrogen mole fractions reached similar values (0.5–0.6) at both outlets only for the maximum residence time or high porosity of anode. This implies that residence time and gas diffusion can be controlled by a combination of operating and microstructural parameters and can be estimated by numerical simulation using computational fluid dynamics. The main motivation and outcome of this work were to reduce the cost and time required for the optimization of the mass transport process through SOC's porous electrode.

Theoretical Investigation of Vapor Transport Mechanism Using Tubular Membrane Distillation Module.

This paper’s primary objective is to examine the vapor delivery mechanism through a tubular membrane distillation (MD) module. Experiments were conducted utilizing a hydrophobic tubular membrane module with a pore size of 0.2 µm. To establish the mass transport mechanism of water vapor, tests were carried out first with pure water as a feed. The permeate flow was then determined using NaCl aqueous feed solutions. Distilled water flux at diverse feed temperatures, feed flow rates, and feed salt concentrations was investigated. The permeate flux improved linearly with rising temperature and flow rate of the feed, however, it declined with feed concentration. Increasing temperature from 40 to 70 °C increased the permeate flux by a factor of 2.2, while increasing the feed flow rate from 60 to 120 L/h increased the permeate flux by a factor ranging from 0.7 to 1.1 depending on feed temperature. Using the Dusty gas model (DGM) the mass transport of water vapor is estimated in the membrane pores. The results showed that the water vapor delivery is controlled by way of the Knudsen molecular diffusion transition mechanism and its version changed into one capable of predicting the permeate fluxes. The mass transfer coefficient calculated and located using the Knudsen molecular transition version agreed properly with the corresponding experimental value. The delivery resistances were affected by working parameters, along with feed temperature, flow rate, and concentration. The mass transfer resistance of the membrane became the predominant controlling step to the MD process.

Three-Dimensional Membrane Imaging with X-ray Ptychography: Determination of Membrane Transport Properties for Membrane Distillation

Membrane distillation (MD) is a desalination technique that uses a membrane to thermally separate potable water from sea or brackish water. The mass transport processes through the membrane are commonly described by the dusty gas model. These processes are modeled assuming uniform, ideally cylindrical capillaries and are adjusted for the membrane geometry by including porosity and tortuosity. The tortuosity is usually set to 2 or is used as an adjusting parameter to fit theoretical models to experimentally measured data. In this work, ptychographic X-ray computed tomography is employed to map the three-dimensional (3D) structure of three commercial state-of-the-art PTFE membranes in MD. The porosity, tortuosity and permeability (viscous flow coefficient) of the samples are computed using the lattice Boltzmann method. The intrinsic permeability is compared to the dusty gas model and an apparent permeability is proposed which is corrected for Knudsen slip effects at the membrane structure.Article Highlights3D structure of membranes for distillation measured at full height at an unprecedented detail using X-ray ptychography for the first time.Comparison of the dusty gas model to 3D direct numerical simulation: permeability and Knudsen effects.Membrane characterization and calculation of the hydraulic tortuosity factor from 3D flow field simulations.

Effective transport parameters of porous media from 2D microstructure images

Transport in porous media is central in chemical engineering. Effective transport properties are required for evaluating and improving many processes and applications. A widely used model to describe transport in porous media is the Dusty-gas model. This model accounts for permeation, Knudsen-diffusion and binary diffusion. The model parameters are commonly determined from experiments, for instance, performed in a Wicke-Kallenbach cell. The parameters derived in this way are spatially averaged effective parameters.In this contribution, we present an approach to calculate transport parameters of the Dusty-Gas model from a cross-sectional image of the porous material, which often reduces experimental effort. The approach is also applicable to virtually designed materials for which structural information is available from simulations, but no physical sample has yet been synthesized.The method applied here is asymptotic homogenization, which allows lumping structural information on the micro-scale into effective transport properties. In a previous contribution, we successfully demonstrated the calculation of effective permeability for a porous hollow fiber from image data. Here we extend the work to Knudsen diffusion and binary diffusion.To validate our results, we compare model predictions for Knudsen-diffusion with experimental data from measurements in a Wicke-Kallenbach cell and predictions of the effective binary diffusion coefficient by comparison to literature data for a sphere packing.

Influence of Microstructure on Electrochemical Performance of Plasma Sprayed Ni‐YSZ Anodes for SOFCs

AbstractThe influence of anode microstructural parameters on the electrochemical performance of plasma sprayed solid oxide fuel cells with metal supports has been investigated. Electrochemical impedance spectroscopy (EIS) was used to correlate the measured polarization resistances associated with both the three‐phase boundary length density and gas diffusivity of porous nickel/yttria‐stabilized zirconia (YSZ) anodes. Each anode was deposited in atmospheric conditions using solution precursor plasma spraying (SPPS), dry‐powder plasma spraying (DPPS), or suspension plasma spraying (SPS). The high‐frequency (> 1 kHz) part of the impedance spectrum was found to correlate with the three‐phase boundary length per unit volume of each anode. The low‐frequency part of the impedance spectrum was found to correlate with diffusive transport of gases through the porous anode. Gas transport measurements in the context of the dusty gas model were used to extract microstructure‐dependent parameters that provided a quantitative comparison among the distinct microstructures obtained using the three plasma spray methods. These results were compared to measurements using Darcy's law, which yielded similar trends and provided an efficient method to more rapidly compare gas transport rates in porous electrodes having different structures.

Upward Transport of Trichloroethylene Vapour in a Dry Soil Column

Experimental and modelling studies were performed to assess the predictability of gas phase transport models based on the Fickian-type diffusion expression and dusty-gas model (DGM) equations for the upward transport of trichloroethylene (TCE) vapour at low vapour source densities in a dry soil column. The TCE vapour concentrations measured upstream in the column were only 6% and 15.7% of the TCE saturated vapour concentration (i.e., TCE vapour densities of 0.031 and 0.08 g/L, respectively) when TCE liquid existed in the upstream cavity as a vapour source. A good fit between the model-predicted profile of the downstream TCE vapour concentration and the observed data can only be attained by using a tortuosity value that is 0.2–0.3 times of that computed by the Millington and Quirk’s (1961) empirical equation. This result revealed that diffusion dominates over advection for the aforementioned transport conditions. Furthermore, the differences between the concentration evolution profiles away from the source predicted by the Fickian and DGM-based models present a reverse trend depending on whether the downstream boundary is covered (impermeable) or uncovered (opened to the air). The results revealed that the predicted upward transport of dense vapour at low source densities with a covered downstream boundary predicted by the two models differed considerably. • Trichloroethylene (TCE) vapour was <20% saturated in the experimental soil column containing the TCE liquid. • The fitted effective molecular diffusion coefficient was less than the estimated coefficient by the usual method. • A Fickian-type diffusion model may under- or over-predict vapour concentrations for upward transport of dense vapour.

Experimental and modeling study of CO2 separation by modified Pebax 1657 TFC membranes

Ionic liquid modified Pebax 1657 thin-film composite (TFC) membranes were synthesized on different porous supports for improved separation of CO2 from CH4 and N2. XRD, SEM, FTIR, TGA, DFT, and BJH tests were utilized for the characterization of TFC membranes and supports. The incorporation of 1,3-Di-n-butyl-2-methylimidazolium chloride ionic liquid into the Pebax 1657 solution led to better compatibility between selective layer and support. The results of gas permeation tests showed an enhanced CO2/CH4 and CO2/N2 selectivity for most of the ionic liquid modified TFC membranes. To derive a predictive model for the permeability of gases in TFC membranes, correction factors (β) for fractional free volumes of TFC membranes were linearly correlated against correction factors (α) for porosity and tortuosity of the substrate in the dusty gas model using CO2 experimental permeance data at 20, 60, 100 and 140 °C. The resulting modified model showed remarkable effectiveness in the prediction of permeability of CH4 and N2 in the TFC membrane at investigated temperatures. The comparison of model predictive performance with previous models showed the supremacy of the new model in terms of average absolute relative errors (AARE) and the standard deviation of relative errors (σ).

Thermophysical model for icy cometary dust particles

Context. Cometary dust particles are subjected to various forces after being lifted off the nucleus. These forces define the dynamics of dust, trajectories, alignment, and fragmentation, which, in turn, have a significant effect on the particle distribution in the coma. Aims. We develop a numerical thermophysical model that is applicable to icy cometary dust to study the forces attributed to the sublimation of ice. Methods. We extended the recently introduced synoptic model for ice-free dust particles to ice-containing dust. We introduced an additional source term to the energy balance equation accounting for the heat of sublimation and condensation. We use the direct simulation Monte Carlo approach with the dusty gas model to solve the mass balance equation and the energy balance equation simultaneously. Results. The numerical tests show that the proposed method can be applied for dust particles covering the size range from tens of microns to centimetres with a moderate computational cost. We predict that for an assumed ice volume fraction of 0.05, particles with a radius, r ≫ 1 mm, at 1.35 AU, may disintegrate into mm-sized fragments due to internal pressure build-up. Particles with r &lt; 1 cm lose their ice content within minutes. Hence, we expect that only particles with r &gt; 1 cm may demonstrate sustained sublimation and the resulting outgassing forces.

Methane transport in a soil column: experimental and modeling investigation

This study explored two diffusion approaches, Fick’s law and the dusty gas model (DGM), to assess their differences on modeling methane transport in porous systems. Laboratory experiments were also conducted for methane transport through a nitrogen gas-dry soil column from different source densities. Gas pressures and methane densities at transient state were measured along the column for two transport configurations (horizontal and vertically upward) and compared with the predictions obtained from the DGM- and Fickian-based models. The retardation factor is the only parameter used in the model calibration. The results showed that the methane density profiles predicted by these models fairly matched the measured data and are quite consistent for vertically upward transport of methane. However, the predictions were over the measured ones for horizontal transport of methane. We suspected it is due to incomplete mixing of gas mixture in the inlet chamber since high pressure variations were observed in the horizontal transport experiments. Further, we found that the methane density profile predicted by the Fickian-based model is lagged behind the DGM result for at most 15% of difference in methane density for horizontal transport of methane from a pure methane source.horizontal transport experiments. Further, we found that the methane density profile predicted by the Fickian-based model lagged behind the DGM result for at most 15% of difference in methane density for horizontal transport of methane from a pure methane source.

Multicomponent landfill gas transport in soil cover: column tests and numerical modelling

A soil column test was carried out to investigate the mechanism of multicomponent landfill gas transport in loess. Four gas components, namely methane (CH4), carbon dioxide (CO2), oxygen (O2) and nitrogen (N2), were considered. Based on the dusty-gas model and mass balance equation, a one-dimensional transient model for multicomponent gas transport in landfill layered cover soils was then developed. Methane oxidation in the soil is also considered in the model. The numerical model was solved by the finite-element method-based program Comsol Multiphysics v5.1. The numerical results agree well with those observed from the soil column tests. The parameter analysis shows that ordinary diffusion plays an important role in the transport of multicomponent gases. For methane and carbon dioxide, ordinary diffusion contributes to 97% of the total transport flux in the shallow zone. The effect of ordinary diffusion decreases with the increase in the depth. Advection contributes to 37% of the flux at the bottom of the cover soil. The effect of Knudsen diffusion is relatively weak, which only contributes 0.5–12% to the total flux. This is due to the relatively high gas permeability of the soil. The contribution of advection is comparable to that of diffusion when the gas permeability increases up to 3 × 10−13 m2. The maximum methane oxidation rate is found to increase by a factor of 1.8, when influent flux increases from 1 × 10−5 to 1 × 10−4 (mol/m2)/s. The numerical solution can be used for the analysis of multicomponent landfill gas transport in the soils and the design of landfill cover systems with respect to gas pollution control.

Numerical Simulation of Methane and Propane Reforming Over a Porous Rh/Al2O3 Catalyst in Stagnation-Flows: Impact of Internal and External Mass Transfer Limitations on Species Profiles

Hydrogen production by catalytic partial oxidation and steam reforming of methane and propane towards synthesis gas are numerically investigated in stagnation-flow over a disc coated with a porous Rh/Al2O3 layer. A one-dimensional flow field is coupled with three models for internal diffusion and with a 62-step surface reaction mechanism. Numerical simulations are conducted with the recently developed computer code DETCHEMSTAG. Dusty-Gas model, a reaction-diffusion model and a simple effectiveness factor model, are alternatively used in simulations to study the internal mass transfer inside the 100 µm thick washcoat layer. Numerically predicted species profiles in the external boundary layer agree well with the recently published experimental data. All three models for internal diffusion exhibit strong species concentration gradients in the catalyst layer. In partial oxidation conditions, a thin total oxidation zone occurs close to the gas-washcoat interface, followed by a zone of steam and dry reforming of methane. Increasing the reactor pressure and decreasing the inlet flow velocity increases/decreases the external/internal mass transfer limitations. The comparison of reaction-diffusion and Dusty-Gas model results reveal the insignificance of convective flow on species transport inside the washcoat. Simulations, which additionally solve a heat transport equation, do not show any temperature gradients inside the washcoat.

Effect of catalyst shape and multicomponent diffusion flux models on intraparticle transport-kinetic interactions in the gas-phase Fischer-Tropsch synthesis

Intraparticle Fischer-Tropsch (FT) transport-kinetics interactions for various Fe-based catalyst particle shapes (sphere, solid cylinder, hollow cylinder, 4-hole cylinder, modified 4-hole cylinder, and 7-hole cylinder) under typical gas-phase FT process conditions (T = 493–533 K, P = 25–30 bar, and H2/CO = 2) are investigated using different multicomponent diffusion flux models. A Fe-based microkinetic gas-phase FT model is used to describe the intrinsic reaction rates for all reactants and products. The Soave-Redlich-Kwong (SRK) EOS is used to describe the vapor-liquid equilibrium associated with the FT product distribution. The effect of process conditions and catalyst shape on the effectiveness factor, particle volume-averaged key component concentrations, liquid-to-vapor (L/V) ratios and diesel range concentration profiles, along with methane-based diesel selectivities, are presented. It is found that the solid cylinder has the highest volume-average diesel concentration (ca. 4.4 mol/m3 at T = 493 K and P = 25 bar) when compared to the other shapes. The hollow cylinder and 7-hole cylinder shapes have the lowest intraparticle liquid-to-vapor (L/V) ratio (ca. 0.004 at T = 493 K and P = 25 bar) and the highest effectiveness factor (η) of 0.35. Temperature-based diffusivity correlations do not consider the change in effective diffusivities of the species in the FT reaction network. The simulations show that the inclusion of Knudsen diffusion through the Wilke-Bosanquet and Dusty-Gas Models resulted in an intraparticle FT product distribution that closely approximate literature results.

Effect of the support layer morphological structure on the performance of forward osmosis hollow fiber membranes

A thin-film polyamide layer was synthesized on three different hollow-fiber support layers, each of which possess different morphological structures (i.e., sponge-like structures (SM-1), finger-like macrovoid close to the outer surface (SM-2), and middle-partitioned finger-like structures (SM-3)). In this work, we found that forward osmosis (FO) performance of thin-film composite (TFC) membranes could be significantly affected by their sub-layer morphology. During FO tests, SM-1 showed the highest water permeability of 0.742 LMH/bar followed by SM-3 and SM-2. In addition, SM-1 exhibited the lowest solute permeability of 0.039 LMH, followed by SM-2 and SM-3. To more systematically evaluate the effect of the support layer structures on the performance of TFC FO membranes, the structural parameters (S) of the membranes were estimated using the dusty gas model (DGM) prior to interfacial polymerization on the support layers. The S values of the support layers obtained from the DGM method are in accord with the FO membrane performance. Although the conventional S parameter determination method showed relatively similar values with the DGM method, the overall trend corresponds, confirming that the smaller S value is related to a smaller internal concentration polarization decrease. Moreover, this study clearly demonstrates that the support layer needs to be considered alongside the active layer of TFC FO membranes, and that a sponge-like support layer can be a better option for high-performance FO TFC membranes.

Computational study of sweeping gas membrane distillation process – Flux performance and polarization characteristics

Computational fluid dynamics simulations were conducted in a three-dimensional sweeping gas membrane distillation (SGMD) desalination module. The module flux performance and polarization characteristics were investigated for a wide range of flow rates spanning the laminar and turbulent flow regime in the feed and permeate channel. The membrane was treated as a functional surface with zero thickness, and the membrane permeability was determined by a combination of Knudsen and molecular diffusion using the Dusty Gas model. The mathematical model and numerical method was validated against existing experimental work. It was shown that low membrane thickness, high porosity, and low tortuosity yield high vapor flux. It was demonstrated that high vapor flux can be achieved in a SGMD module by increasing the permeate flow rate to avoid temperature and moisture polarization in the permeate channel. By increasing the feed flow rate, the flux also increased, and temperature and concentration polarization decreased. It was shown that the SGMD process, as effective as other MD processes, could be used as an alternative method for water desalination. The model developed here can be utilized for design and optimization of full-scale SGMD modules.

Analytical Expression for Concentration Overpotential of Anode-Supported Solid Oxide Fuel Cell Based on the Dusty Gas Model

Abstract The Dusty Gas model (DGM), despite being arguably the most accurate representation of gas diffusion in electrodes, is not readily adopted in the literature as it entails relatively expensive numerical integration of differential equations for concentration polarization calculations. To address this issue, this article demonstrates an analytical procedure to solve the DGM equations in a fuel cell electrode setting. In the process, it highlights the differences with previous attempts in the literature and improves upon the shortcomings. This paper specifically provides explicit expressions of concentration overpotentials of anode-supported solid oxide fuel cells (SOFCs) for binary and ternary gas systems via the analytical solution of DGM equations in one dimension without considering the viscous effects. The model predictions match very well with the experimental data available in the open literature. This paper also provides a semi-analytical framework for higher-order multicomponent systems. Finally, the effect of the pore-size distribution in the porous electrode on the concentration polarization is thoroughly explored.