The obtained data in the isotherms ([q.sub.eq] and [C.sub.eq]) were adjusted to Langmuir
and Freundlich models.
Equation 2 denotes Langmuir
isotherm, where "qe" denotes the amount of adsorbate adsorbed at the equilibrium (mg/Kg), "Qmax" the maximum adsorption capacity of the adsorbent (mg/Kg).
A high value of Kd indicates a high adsorption  The experimental data were fitted into the two most widely used isotherm models (Freundlich and Langmuir
); these two models were linearized appropriately .
The regression provides an empirical basis for estimatingthe Langmuir
maximum CH4 adsorption capacity from TOC content in a shale reservoir.A similar correlation between gas sorption capacity and TOC content at 30[degrees]C and 6 MPa pressure has been observed in previous studies (Chalmers and Bustin, 2007a,b; Ross and Bustin, 2007, 2009; Zhang et al., 2012; Msarah and Alsier, 2018).
isotherm model, which is based on the assumption that the maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, with no lateral interaction between adsorbed molecules, is given by the following equation:
Adsorption equilibrium information is the most important part of the adsorption process, when [partial derivative]V/[[partial derivative].sub.t] = 0; (13) can be recovered as the equivalent Langmuir
isothermal adsorption equilibrium equation
 examined the formation of various PVDF Langmuir
This model is considered more general than Langmuir
because in its derivation homogenous surface and constant sorption potential are not assumed .
The data of the adsorption process for the organic acids and three phenolic compounds were analyzed using the Langmuir
isotherm linear model according to the following equation :
and Freundlich isotherms were used for the analysis of adsorption equilibrium data.
isotherm: [C.sub.e]/[q.sub.e] = [C.sub.e]/[q.sub.m] + 1/[K.sub.L][q.sub.m] (3)
Several researchers obtained excellent fit of phosphate sorption data with the two-site Langmuir
model  and metal sorption, that is, Lanthanide on smectite clays [37, 38].