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The extraction of natural gas from the earth has been shown to be governed bydifferential equations concerning flow through a porous material. Recently,models such as fractional differential equations have been developed to modelthis phenomenon. One key issue with these models is estimating the fraction ofthe differential equation. Traditional methods such as maximum likelihood,least squares and even method of moments are not available to estimate thisparameter as traditional calculus methods do not apply. We develop a Bayesianapproach to estimate the fraction of the order of the differential equationthat models transport in unconventional hydrocarbon reservoirs. In this paper,we use this approach to adequately quantify the uncertainties associated withthe error and predictions. A simulation study is presented as well to assessthe utility of the modeling approach.

A Bayesian Estimation for the Fractional Order of the Differential Equation that Models Transport in Unconventional Hydrocarbon Reservoirs