Comparison of Single, Binary and Temperature-Dependent Adsorption Models Based on Error Function Analysis

Abstract

The choice of adsorption model to use when accounting for gas adsorption in shale gas reservoirs is critical especially for Gas in Place (OGIP) calculations since inaccurate predictions can affect reporting of overall gas reserves. To that end, different adsorption models would have to be compared and evaluated in order to select the model that fits experimental data accurately. In examining the effect of using different error criteria for determining parameters for shale gas adsorption models, a statistically robust error analysis has been performed based on the sum of normalised error (SNE). Most shale gas adsorption modelling are conducted without finding out the most appropriate error function to use which introduces adsorption prediction errors in calculations. Five different error analysis were used including Sum of squared error (SSE), average relative error (ARE), the sum of absolute error (SAE), Marquardt's Percent standard Deviation (MPSD), and Hybrid fractional error (HYBRID). To account for the influence of temperature in adsorption capacities, the study also compares the use of temperature dependent models, such as Exponential and Bi-Langmuir models for gas adsorption. These models can be conducted at multiple temperatures and ensure adsorption data can be obtained at any temperature beyond laboratory conditions. This is particularly useful when conducting thermal stimulation as an enhanced gas recovery in both coal/shale gas reservoirs.

A review on polymer, gas, surfactant and nanoparticle adsorption modeling in porous media

“…The Langmuir model has generally been the most implemented model for the prediction of gas adsorption in porous media (Fianu et al, 2019a). It is an equilibrium model that captures the relationship between gas pressure and the quantity of gas adsorbed at a constant temperature.…”