Different gas equilibrium adsorption models (or isotherms) with various theoretical frameworks have been applied to quantify adsorbed volume (V) of gas (or fluid) through pressure-volume behaviour at a constant temperature. Most often, Langmuir isotherm (representing Type I Isotherm) has been used in modelling monolayer adsorption even though it yields over-estimation at higher pressures thus contradicting the description of Type I isotherm. Here, higher pressures refer to pressures above the adsorption saturation pressure(Ps) . Hence, in this work, a new Type I adsorption isotherm involving pressure(P), adsorption saturation pressure(Ps) , maximum adsorbed volume and adsorbate-adsorbent resistance parameter was developed using kinetic approach. The developed adsorption isotherm is V=
and it shows that Vmax is attained when pressure increases to Ps , above which no further gas adsorption occurs. The developed isotherm can be used to model all cases of monolayer adsorptions of gases (or fluids) on adsorbents. The developed and Langmuir isotherms were used in modelling secondary low-pressure gas adsorption data of different adsorbents and the qualities of fit were statistically assessed. For laboratory methane adsorption on Turkey’s shale sample at 25°C, the developed isotherm yields a correlation with an R2 value of 0.997 and predicts a maximum adsorption volume of 0.0450 mmol g-1 at a Ps of 2,005 psia. However, Langmuir isotherm yields a correlation with an R2 value of 0.989 and predicts a maximum adsorption volume (Langmuir volume,VL ) of 0.0548 mmol g-1 at infinite Ps. At the higher-pressure range, the developed isotherm reveals that Langmuir isotherm is not a Type I isotherm but a "pseudo-Type I” isotherm.
Study on Shale Adsorption Equation Based on Monolayer Adsorption, Multilayer Adsorption, and Capillary Condensation