Sequential Slope and Intercept Method for Estimation of Gas Absorption and Diffusion Coefficients in Binary Gas–Liquid Systems

Abstract

A novel geometric method based on a sequential slope−intercept approach is derived for estimation of concentration-dependent diffusion, gas absorption, and gas dissolution concentration in gas−liquid binary systems. The gas absorption and diffusion are modeled using an inverse free boundary problem governed by Fick's second law of diffusion and Henry's absorption law. An unknown gas−liquid interface is governed by the Stefan's type boundary condition. Implementation of the estimation method involves piecewise linear approximation of the transformed concentration data and sequential application of the estimated slopes and intercepts from this approximation. Application and validation of the developed estimation method is given for synthetic concentration profiles and for real concentration measurements for a dimethyl ether− bitumen binary system obtained using computer tomography. The developed estimation method overcomes the existing estimation methods derived from polynomial approximations that significantly underestimate or overestimate the diffusion coefficients at very low dissolved gas concentrations.

Experimental determination of gas diffusivity in liquids—A review

“…Semi‐analytical approaches that address the concentration‐dependence consider gas diffusivity to be some analytical function beforehand, and approximate the gas concentration with a known function depending on interfacial composition. [ 69,70 ] The method developed by Babak and Kantzas, [ 71 ] however, deals with the concentration‐dependence by approximating the concentration profile with a complementary error function. [ 72 ] The argument of this function is a linear expression stemming from the slope and intercept of the experimentally recorded concentration profile, using x‐ray computer tomography, near a point in a transformed spatial domain.…”