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A new Gaussian adsorption isotherm model: test data is methane-5A zeolite

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Abstract

An adsorption isotherm model is deduced based on the Gaussian cumulative frequency distribution principles. This isotherm has three parameters: q max, the 50% adsorbate loading pressure P 50, and the standard deviation σ. The isotherm development hinges on establishing P 50 and σ. These are deduced from a log plot of the isotherm pressure P versus the inverse Gaussian cumulative frequency distribution plot. The slope of this plot is σ and the y-intercept is P 50. The temperature dependency of P 50 is deduced from a plot of log P 50 versus 1/T: this is actually the isosteric plot at 50% loading with slope equal to the heat of adsorption at 50% loading.

The model is tested using the literature methane data for 5A zeolite. Twenty-four isotherms from six different studies are fitted with the model using a q max of 9 g/100 gZ applicable to methane 5A isotherms in the temperature range of the study, as reported in the literature. The standard deviation σ is observed to be 0.98±0.088. The isostere of P 50 indicates a heat of adsorption between 4.62–4.97 kcals/mole consistent with literature values. All 24 isotherms reduce to one characteristic curve when θ is plotted against (P/P 50)1/σ. The θ values approaching zero (<0.05) are shown to be consistent with reported Henry constant data using the heat of adsorption value calculated at 50% loading as is expected for homogeneous adsorption.

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Abbreviations

a :

Constant in (10) and (16)

k :

Boltzmann’s constant

K :

Langmuir equilibrium parameter, kPa−1

K H :

Henry’s constant, g/100 gZ/kPa

P :

Pressure, kPa

P C :

Critical pressure, kPa

P LM :

Log mean pressure for the entire isotherm, kPa

P 50 :

Pressure at 50% loading, same value as P LM, kPa

P r :

Reduced pressure, dimensionless

P r,50 :

Reduced pressure at 50% loading, dimensionless

R :

Gas constant

q :

Zeolite loading, g/100 gZ

q max :

Maximum zeolite loading, g/100 gZ

T :

Temperature, K

T CAR :

Critical adsorbate reduced temperature

T r :

Reduced temperature

Z :

Standard normal probability distribution variable

u :

Multisite Langmuir parameter

θ :

Loading (= q/q max)

σ :

Standard deviation for the isotherm

−ΔH 0 :

Heat of adsorption at 0% loading, kcals/mole

−ΔH 50 :

Heat of adsorption at 50% loading, kcals/mole

Φ:

Cumulative distribution function.

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Authors and Affiliations

  1. Department of Chemical Engineering, American University of Sharjah, PO Box 26666, University City, Sharjah, United Arab Emirates

    Dana Abouelnasr & Kevin F. Loughlin

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  1. Dana Abouelnasr
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  2. Kevin F. Loughlin
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Correspondence to Kevin F. Loughlin.

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Abouelnasr, D., Loughlin, K.F. A new Gaussian adsorption isotherm model: test data is methane-5A zeolite. Adsorption 16, 93–101 (2010). https://doi.org/10.1007/s10450-010-9217-2

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