Adsorption models have many applications in industry such as in gas separation and/purification, natural gas storage, and CO 2 capture. In this work, a simple and robust method is introduced for calculation of natural gas and biogas adsorption on activated carbon, which is not only less complex than existing models but also not limited to isothermal condition. The proposed equation collapses the experimental data at different temperatures into a single linear curve, from which the adsorbed amounts at equilibrium can be calculated for any desired pressure and temperature in the range of experimental data. Model parameters are also calculated and presented for different gas components on activated carbon, and the accuracy of the proposed model is compared with that of three most common adsorption isotherms. As a result, the proposed scaling equation approach is shown to be more accurate and robust than the Langmuir and Sips models. Also, although application of these models is limited to isothermal condition, the proposed model is temperature dependent. It is shown that the proposed model predicts the experimental data with less than 4% error in term of sum of squared errors, and with correlation factors (R 2 ) higher than 0.95, which demonstrate the applicability of the developed approach. Proposed scaling equation scheme could help adsorption-based process design and separation or purification of mainly CH 4 from natural gas and/or biogas streams with distinct CO 2 -based contents along with a decrease in necessity of experimental data to address these purposes.
KEYWORDS activated carbon, adsorption, adsorption isotherm, biogasNomenclature: A 1 , proposed model constants (g/g adsorbent/bar); A 2 , proposed model constants (g/g adsorbent); ANG, adsorbed natural gas; b, b 0 , Sips/Toth models constants (1/bar); CNG, compressed natural gas; CSS, CO 2 capture and sequestration; K L , Langmuir model constant (1/bar); LNG, liquefied natural gas; N, number of data; n, n 0 , Sips model constants; NG, natural gas; n P , proposed model constant, pressure exponent; n T , proposed model constant, pseudoreduced temperature exponent; P, pressure (bar); q eq , equilibrium adsorption per unit mass of adsorbent (g/g adsorbent); q m , Langmuir model constant, maximum uptake capacity of gas at the adsorbent surface (g/g); q s , Sips/Toth models constant (g/g); Q RT 0 , heat coefficient;R 2 , correlation factor; RMSE, root mean square error; SSE, sum of squared error of prediction; t, Toth model constant; T, temperature (K); T c , critical temperature (K); y i , original data value; b y i , modeled data value; y i , original data mean value; Y, X, proposed model variables Greek Letters: α, Sips/Toth model constant