Fully implicit moving boundary model with liquid phase perfect mixing for CO 2 diffusion into n-decane DAMELYS ZABALA 1 , AURA L. LÓPEZ DE RAMOS 2 1 CIMEC, Escuela de Ingeniería Mecánica, 2 Departamento de Termodinámica y Fenómenos de Transferencia 1 Universidad de Carabobo, 2 Universidad Simón Bolívar 1 Av. Universidad, Edf. Facultad de Ingeniería, Bárbula, Estado Carabobo, 2 Apartado Postal 89.000, Caracas VENEZUELA 1 dzabala@ uc.edu.ve, 2 alopez@ usb.ve Abstract: - Carbon dioxide diffusion into n-decane inside cylindrical and square glass capillary tubes has been modeled [1,2], with two different models for each tube and the convective model for the square tube depended on the results of the cylindrical one. For those models, the liquid phase density was always considered constant and its value was adjusted from the experimental data of gas-liquid interface position. This approach was done using the diffusivities obtained by correlations which modify the infinite dilution diffusion coefficient using a thermodynamical factor. Now, the liquid phase density is considered variable on time with perfect mixing inside the phase and an effective diffusivity can be determined. This effective diffusivity involves the molecular and convective contributions to the global mass transfer. Both interface displacements (inside cilyndrical and square tubes) can be modeled using the same model without dependency between their results. The terms inside the finite difference matrix for the liquid phase are not constant, because they depend on the solute concentration and on the liquid density then an iterative calculation for the matrix coefficients must be done in each timestep. A partially implicit model considers this iterative calculation keeping the liquid density value for the previous time (j). A fully implicit model considers this iterative calculation keeping the liquid density value for the present time (j+1). It was showed that the model results, adjusted to the experimental interface position values, predicted effective diffusivities which are variable on time. The simulation time (76 min) for the fully implict numerical model is higher than the simulation time (62 min) for the partially implicit numerical model. It was found that the type of numerical solution scheme affects the results (up to 5% deviation) for the square capillary model but it doesn´t change the cilindrical capillary model results. Key-Words: - Capillary tube, Free boundary, Mass transfer, Numerical Modeling, Diffusion 1 Introduction Numerical modeling is an useful tool for representing heat and mass transfer processes. In many cases, numerical solution of a differential equation is used together with an experiment in order to determine fluid properties. For example, to obtain mass diffusivities by experimental methods usually involves mathematical simplification, like constant phase density and no convective effects [3-5]. Estimation of mass diffusivities is always a major concern for mass transfer processes, because correlations are not applicable in all the systems or process conditions. On the other hand, fluid displacement inside polygonal capillary tubes or cells has been studied trying to understand fluid-solid interactions in porous media [6-13]. The corners of capillary tubes promote fluid movement by a liquid filament which rises along the crevice and this behavior avoided that displacement experiments in polygonal capillary tubes could be used to determine molecular diffusivity because a simplified mass transfer model deviates considerably from the experimental behavior. In this work, experiments with carbon dioxide diffusing into liquid n-decane were done, with both fluids contained in square and cylindrical glass capillary tubes. Experimental gas- liquid interface positions at the center of the tube were observed and it was found that the interface moves faster inside the square capillary tube. A moving boundary mass transfer model of this miscible displacement is necessary, to determine the contribution of the corner presence to an improved mass transfer process like the miscible CO 2 injection in hydrocarbons. Such contribution is determined by adjustment of an effective diffusivity which counts for molecular and convective mass transfer. 2 Problem Formulation 2.1 Mathematical Model WSEAS TRANSACTIONS on MATHEMATICS DAMELYS ZABALA ,AURA L. LÓPEZ DE RAMOS ISSN: 1109-2769 539 Issue 8, Volume 7, August 2008