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2 Theoretical background 12 The adsorption equilibrium is commonly represented in the two-dimensional form, either (1) at constant temperature (adsorption isotherm), (2) at constant partial pressure (adsorption isobar), or (3) at constant amount adsorbed/adsorbent loading (adsorption isostere); as shown in Fig. 2.1-1. Considering the fundamental point of view on the adsorption phenomenon, it is feasible to derive models for a quantitative representation of thermodynamic equilibrium state. For instance, the classical Langmuir isotherm model results from the kinetic approach, and the Volmer model from the Gibbs thermodynamic equation [34]. In practice, however, models based on the fundamental theories do not always represent the data well, mostly due to inadequate assumptions. Therefore, empirical approaches are well-established in describing equilibrium data. Fig. 2.1-1 Two-dimensional representation of adsorption equilibrium In this work, the equation of Sips adsorption isotherm is applied to describe the behaviour of a single component at thermodynamic equilibrium, and the adsorption isostere is exploited to calculate the isosteric adsorption enthalpy. Moreover, the Ideal Adsorbed Solution Theory (IAST) was applied in order to evaluate the multi-component adsorption equilibria. 2.1.1 Sips isotherm The Sips model for characterising the adsorption isotherm originates in the combination of Langmuir and Freundlich equations. It was introduced to describe adsorption of gases and vapors on heterogeneous surfaces below the capillary condensation region [34]; or in cases where Langmuir and Freundlich isotherms fail, e.g. the representation of water adsorption on zeolites which exhibits an S-shape isotherm [54], characterisation of adsorption in the liquid phase [55] including the pH-dependent adsorption [56], or biosorption of heavy metals ions [57]. The Sips single-component adsorption isotherm is calculated according to Eq. 2.1.1-1 [34]. w* =w* (T) k sk 1/n (T) (b (T)p ) k k k (Eq. 2.1.1-1) 1/n (T) 1+(b (T)p ) k kk where: pk is the partial pressure of component k, wsk* is the saturation equilibrium loading of component k, T is the temperature, bk is the adsorption affinity of component k, and nk is a dimensionless parameter that qualitatively characterises the heterogeneity of the adsorbate- adsorbent system. When nk equals unity, the isotherm model reduces to the classical LangmuirPDF Image | Modelling and Simulation of Twin-Bed Pressure Swing Adsorption Plants
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