We present a methodology for approximating dynamic adsorption of vapor coupled with diffusion in polymeric materials. In previous publications, the dynamic adsorption was represented by ordinary differential equations (ODEs) and solved in concentration and parameter space. To accelerate the calculation, we have developed a statistical approximation method using computationally cheap surrogate models (e.g., algebraic polynomials) that replace the ODE solutions of adsorption and are coupled with the diffusion equations. Since the polynomial presentation of the adsorption term is obtained in a standard format prior to modeling coupled sorption-diffusion, the adsorption operator can be expressed as input data in the transport code. Compared to conventional operator-splitting methods, the polynomial approximation of adsorption offers better computational efficiency. The methodology is demonstrated and validated using a dynamic Langmuir adsorption model that is coupled to diffusion and absorption models and applied to a water vapor sorptiondiffusion process in polydimethylsiloxane polymers. V C 2017 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2017 Keywords: reactive transport, surrogate model, operator splitting, numerical modeling, Langmuir adsorption
IntroductionModeling vapor and gas sorption and diffusion in polymeric and nanoporous materials is of fundamental importance to a variety of industries and applications. Since Vieth and Sladek, 1 the dual-mode sorption model with equilibrium Henry's absorption and Langmuir adsorption has been used to interpret sorption-diffusion processes in polymers, [2][3][4][5] forming the basis or complimenting reactive transport modeling in polymers. [6][7][8][9][10] Recent advances in the technology for experimentally measuring vapor uptake and outgassing facilitate data collection for the understanding of the dynamic processes of diffusion coupled with triple-mode sorptions (absorption, Langmuir adsorption, and pooling). [11][12][13] Rigorous mathematical models have been developed for simulating vapor diffusion coupled with triple-mode sorption. Equilibrium and kinetic sorption processes are treated separately and modeled accordingly using suitable solution methods. Typically, the Langmuir adsorption is treated as a kinetic-reaction and modeled by solving ordinary differential equations (ODEs). Solving these ODEs is computationally expensive and time consuming, limiting the applicability of these models to only high priority calculations and forcing the majority of the field to subsist on lower-fidelity but more computationally efficient models.These computational challenges are experienced in a variety of modeling applications, especially in the field of reactive transport modeling. In addition to the kinetic-Langmuir adsorption equations, there is also a need for coupling userdefined chemical kinetic equations with diffusion. Because of the wide variety of kinetic reaction mechanisms and their respective mathematical formulations, coding kinetic reactions in...