Increasing Sorption Isotherms Accuracy: Weibull Modelling and Linear Regression

Abstract

Relying on an adequate mathematical approach, two different mathematical procedures can be applied to the huge database produced during gas sorption isotherm experiments in order to obtain accurate data to be used in the industrial practice. To treat data determined from gas sorption isotherms without a careful mathematical support will produce inaccurate results, because all the determinations will be dependent on human decision. The minimum error reported since the first stage of a sorption isotherm determination, which corresponds to volume calibrations of reference and sample cells performed through the use of helium, will produce enormous inaccuracies on sorption isotherm behavior. These inaccurate behaviors may sometimes invalidate any Coalbed Methane recovery and CO2 injection programs. The study consisted on investigating gas sorption isotherm accuracies determined during the first part of the sorption process, which is mainly conducted by monitoring the pressure decline with time, in the reference and the sample cells (when both cells are not in contact), until the stabilization stage is achieved. Three samples from two different coals were selected in order to study their gas sorption behavior, in terms of a clear mathematical approach, when submitted to three different gas compositions, viz. 99.999% methane (CH4); 99.999% carbon dioxide (CO2); and a gas mixture containing 74.99% CH4 + 19.99% CO2 + 5.02% nitrogen (N2). Sorption experiments allow to conclude that the three samples present the same mathematical response during the first part of the sorption process. However, all gas sorption data (adsorption and desorption) collected from reference cell have a better fitting to a Modified Weibull Model, and all gas sorption data (adsorption and desorption) collected from sample cell respond in a trustworthy way to a Linear Regression Model. Confidence bands and prediction intervals (or bands) were also computed.