An inverse solution methodology for estimating the diffusion coefficient of gases in Athabasca bitumen from pressure-decay data

An inverse solution methodology is developed for the estimation of diffusion coefficient of gases in highly viscous, oil-sands bitumens from isothermal, pressure-decay measurements. The approach involves modeling the rate of change in pressure using the diffusion equation for the liquid phase coupled with a mass balance equation for the gas phase. The inverse solution framework is utilized to arrive at two graphical techniques for estimating the diffusion coefficient. Both techniques involve the determination of the slope of a straight line resulting from plotting the experimental data in accordance with the developed model. An advantage of the proposed techniques is that the diffusion coefficient is estimated directly, i.e. without making it an adjustable parameter. The novelty of the proposed method is in its simplicity as well as its ability to isolate portions of the pressure-decay data affected by experimental fluctuations. The effect of the initial pressure on the predicted diffusion coefficient and pressure-decay profile was also investigated. The diffusion coefficients of CO₂, CH₄, C₂H₆ and N₂ in Athabasca bitumen at 50–90 °C and about 8 MPa were estimated and compared with literature values.