Langmuir sorption isotherm is characterised by Maximum Sorption Capacity associated with the mono layer of sorption.
Is there a feasibility that there could actually be more sorption sites than that could be accommodated by the most widely used Langmuir sorption isotherm model - associated with a CBM reservoir?
Will there be any under estimation on the volume of the desorbed methane gas by using the Langmuir model?
Yes absolutely. It underestimates. I advise you Ono-Kondo model to calculate the density of adsorbed gas so you can calculate absolute adsorption.
Langmuir gives you excess sorption, so the benefit of sorption over non-sorption. CBM reservoir engineers use the density of the sorbed phase to estimate absolute sorption and this again to calculate the desorbable gas from coal. The sorbed phase density is typically used as a constant but it is known to depend on P, T and coal type, maybe maturity. So also this is just an estimation and does not reflect reservoir conditions. I guess this unknown will be part of any uncertainty analysis when developing a coalbed reservoir
Yes, but not by much.
Firstly, if you do accurate sorption measurements using methane over a wide range of pressures, you find slight but consistent deviations from the Langmuir model.
Secondly, for materials with low permeability there is a tendency to assume equilibrium conditions before true equilibration is reached. Patience is necessary!
As has been pointed out, the sorbed phase density does vary with temperature as does the maximum sorption capacity (which for a given porous material varies as 1/T for gases that are well above their critical temperature).
dear Suresh Kumar Govindarajan ,
Langmuir is the simplest expression for this. Other well known adsorption models are the Freundlich, Sips, and Toth. A polynomial function is also an option, but then the fitting parameters will have not any relevance with the adsorption characteristics of your interest, like Henry constant or max capacity. There is also the dual site (and also a more elaborate multi - site) langmuir model in which the overall adsorption curve is partitioned in two (or more) cooperative langmuirs, (like a linear interpolation). All these models will not provide any additional (hidden) adsorption volume for your samples.
Usually that value (if I understood it correctly) gives you the excess adsorption. To assess the overall mass (volume) you need to include the additional term accounting for the methane in gas state (i.e considering the gaseous density). That gives you the total adsorption/desorption.
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