A simplified solution technique for carbon adsorption model

Roy, Dipak; Wang, Guang-Te; Adrian, Donald Dean

doi:10.1016/0043-1354(93)90067-r

Cited by 46 publications

(31 citation statements)

References 5 publications

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“…There are several methods for solving the HSDM; herein (Roy et al 1993) approach was used. These authors used the orthogonal collocation method to discretize the partial differential equations of the HSDM to ordinary differential equations with initial conditions, and then applied Laplace transforms to convert the linear ordinary differential equations to algebraic equations (Roy et al 1993).…”

Section: Hsdmmentioning

confidence: 99%

How do the HSDM and Boyd’s model compare for estimating intraparticle diffusion coefficients in adsorption processes

et al. 2014

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Adsorption kinetics is a key-issue for a successful activated carbon selection and design of the treatment system. Crucial predictive aspects are the determination of the diffusion coefficients and the establishment of the controlling adsorption step. Several kinetic models have been developed and two of the most frequently used, the homogeneous surface diffusion model (HSDM) and the Boyd's model, were applied to microcystins, and particularly MC-LR adsorption. Different initial MC-LR concentrations and carbons (particle diameter, porosity), yielding diverse Biot numbers (Bi), were tested. The model outcomes were compared, namely the Boyd's effective intraparticle diffusion coefficient (D i ) with the HSDM surface diffusion coefficient (D s ), as well as the Bi and Boyd's criteria to establish the controlling adsorption step, which constitute a novel approach. Very good HSDM fittings were achieved with a constant diffusion model (D s independent of MC-LR surface concentration). D i was similar to D s whenever Boyd plots intercepted the origin. The Biot limit above which it may be considered that intraparticle diffusion is the rate limiting step depended on the carbon. A lower limit was observed for smaller carbons.

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Section: Hsdmmentioning

confidence: 99%

How do the HSDM and Boyd’s model compare for estimating intraparticle diffusion coefficients in adsorption processes

et al. 2014

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“…According to Roy et al (1993), for Bi<<1, film diffusion dominates the mass transfer, while for Bi>>100, internal surface diffusion controls the mass transfer rate. A Biot number between 1 and 100 indicates that the process is limited by both mass transfer mechanisms.…”

Section: Adsorption Kineticsmentioning

confidence: 99%

“…In a mixed system, the transport rate is usually limited by film diffusion and internal surface diffusion. For such systems, the homogeneous surface diffusion model (HSDM) can be used to describe the adsorption process (Weber and Chakravorty 1994;Roy et al 1993;Traegner and Suidan 1989;Najm 1996). Table 1 shows basics equations and initial and boundary conditions involved in HSDM theory for closed batch adsorption.…”

Section: Adsorption Kineticsmentioning

confidence: 99%

“…Table 1 shows basics equations and initial and boundary conditions involved in HSDM theory for closed batch adsorption. Roy et al (1993) developed a simplified solution for the HSDM using the orthogonal collocation techniques (using three orthogonal collocation points) and Laplace transformation, which can reduce the equations in Table 1 into five non-linear algebraic equations. For a linear isotherm relationship, the HSDM solution can be simplified to the following set of equation for cases with and without film diffusion:…”

Section: Adsorption Kineticsmentioning

confidence: 99%

“…Morris and Weber (1964;1969) presented a considerable amount of data on the adsorption of phenol, sodium salts of sulfonated organics, and pesticides. The kinetics of adsorption of organics on activated carbon have also been extensively studied by a number of investigators (Weber and Chakravorty 1974;Traegner and Suidan 1989;Roy et al 1993;Najm 1996;Knappe et al 1998). Research has also been undertaken showing that the combination of MF/UF with coagulation or carbon adsorption could be very effective for organic removal in tertiary wastewater or drinking water treatment.…”

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confidence: 99%

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Assessment of Trace Estrogenic Contaminants Removal by Coagulant Addition, Powdered Activated Carbon Adsorption and Powdered Activated Carbon/Microfiltration Processes

et al. 2004

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Abstract:Increasing attention is being paid to health and environmental risk as a result of the presence of trace steroid estrogens in the effluent discharged from municipal sewage treatment plants. This paper focuses on assessment of removal of these trace compounds using 3 H-labelled estrone as the model compound. Jar tests over a range of ferric chloride dosage and pH conditions showed that coagulation was ineffective in removal of estrone from secondary effluent. The experiments showed that the combination of PAC and microfiltration could be effective for removal of trace estrone from water. The rate and extent of estrone removal by PAC are functions of PAC dosage and retention time of PAC in the system. Mathematical analysis of the results using a homogeneous surface diffusion model (HSMD) indicates that the adsorption of estrone on PAC can be limited by film diffusion and internal surface diffusion. The surface and film mass transfer coefficients were determined to be 9.72 x 10 -10 cm 2 /min and 1.963 cm/min, respectively, under the conditions used.

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Adsorption diffusion behaviour of 4,6‐DMDBT from diesel fuel

Zheng

Huang

et al. 2016

Can J Chem Eng

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The equilibrium and kinetics of adsorption desulphurization of model diesel fuel under different operating conditions were investigated. The homogeneous surface diffusion model (HSDM) and pore diffusion model (PDM) taking into account external resistance and intraparticle resistance were employed to represent the adsorption kinetics of 4,6‐dimethyldibenzothiophene (4,6‐DMDBT). The equilibrium isotherm analysis revealed that the equilibrium can be represented well by the Freundlich model. The proposed HSDM model and PDM model can successfully describe the adsorption of 4,6‐DMDBT for different operating conditions studied. The adsorbate was absorbed rapidly initially because the adsorption rate at the beginning was dominated only by external diffusion. The Biot numbers proved that the predominant rate‐controlling step was intraparticle diffusion. Simultaneously, the adsorption rate was mainly controlled by surface diffusion at lower initial bulk phase concentration and less adsorbent dosage, while pore diffusion played a significant role at higher initial bulk phase concentration and more adsorbent dosage. The temperature had little effect on the diffusion of 4,6‐DMDBT from diesel fuel. The estimated values of pore diffusion coefficient and surface diffusion coefficient were 1.55 × 10−12 m2/s and 5.855 × 10−14 m2/s, respectively. They were independent of adsorbent dosage, initial 4,6‐DMDBT concentration, and temperature, which can provide guidance for fixed‐bed adsorption columns design and process operation.

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A simplified solution technique for carbon adsorption model

Cited by 46 publications

References 5 publications

How do the HSDM and Boyd’s model compare for estimating intraparticle diffusion coefficients in adsorption processes

How do the HSDM and Boyd’s model compare for estimating intraparticle diffusion coefficients in adsorption processes

Assessment of Trace Estrogenic Contaminants Removal by Coagulant Addition, Powdered Activated Carbon Adsorption and Powdered Activated Carbon/Microfiltration Processes

Adsorption diffusion behaviour of 4,6‐DMDBT from diesel fuel

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