(553c) Efficient Numerical Schemes for the Simulation of Adsorption Processes to Cyclic Steady State

We present the implementation of accurate models and numerical solution of adsorption column dynamics. The suite of simulation tools that we have developed can be applied to a wide range of adsorption processes. In this contribution we show the implementation for the simulation of pressure swing adsorption cycles coupled with efficient numerical strategies for the calculation of Cyclic Steady State (CSS). We describe a model hierarchy which is developed from mass and energy balances in the gas and solid phases, with varying degrees of complexity in both the description of flow and mass transfer in the adsorbent particles. The resulting set of highly non-linear Partial Differential Equations (PDEs) are solved with state-of-the-art discretisation schemes, which are tailored to the character of the governing equations. PDEs with a strong hyperbolic character, i.e. mass and energy transport in the gas phase, are discretised with the Finite Volume Method (FVM) with a flux-limiting scheme; this guarantees the conservation of mass and energy as well as correct tracking of the moving fronts. The mass and heat transfer in the adsorbent materials is discretised with the orthogonal collocation on finite elements method which is a very efficient method for problems with steep, stationary gradients. The spatial discretisation of the PDEs leads to large systems of Differential Algebraic Equations (DAEs), which are solved with the state-of-the-art DAE solver SUNDIALS. Even with these sophisticated discretisation schemes, the computation times to reach CSS are long due to the non-linear system behaviour as well as the complex nature of the system. We use several strategies to reduce the computation time: i) model hierarchy, use the simplest model which accurately describes the problem; ii) model and discretisation switch: initial simulation with simpler model, e.g. LDF instead of full diffusion model, and lower resolution discretisation; iii) implementation of numerical acceleration schemes, e.g. extrapolation or Newton method, which accelerate the convergence to CSS; iv) interpolation of the starting conditions from previous simulation runs. The application to standard PSA cycles is discussed and a comparison with the commercially available Adsim simulator is presented.