Multi-scale Modeling And Simulation Of Adsorption Kinetics In Particles,Batch Tanks And Fixed Beds

Adsorption separation technology is a conventional chemical unit operation process,which can be used for purification of products,as well as environmental treatment of gas or liquid waste.It is highly necessary to develop simple and practical mathematical models capable of predicting the adsorption kinetics because experimental measurements of such kinetics under different conditions are always expensive and time consuming.This thesis aims to build unified adsorption kinetic models at different scales such that they can be used for the development adsorbent materials and process design.To this end,we developed three types of adsorption kinetics models corresponding to the particle,betch adsorption tank and fixed bed scales,respectively.The three kinetics models were verified by comparing the simulation results with the data reported in the literature.The results show that the model can be used not only to predict the performances of particle,batch tank and fixed bed adsorption,but also to identify mass transfer rate limiting steps,while less computational cost is needed.First,at the particle scale,in order to simulate the non-cyclic and cyclic transient diffusion and adsorption in particles,the particle diffusion equation is combined with the linear system theory,and the Pade summation of the Taylor series of the transfer function of the adsorption system is used to derive the approximate values of the constant coefficient.Through the rational fraction approximation based on the Pade approximation,the rational fraction simplification of the transfer function is realized.The convolution theorem is used to obtain the time function of the concentration of adsorbate in the particles during non-cyclic adsorption and cyclic adsorption.The new model established in this paper is used to simulate the adsorption behaviors of particles,and the results show that the new model can well simulate the changes of adsorbate concentration in particles with time during non-cyclic and cyclic operations.Compared with the numerical solution of the diffusion equation and Nakao et al.’s LDF model during cyclic adsorption,the calculated results of the new model are in better agreement with the numerical solution data.Compared with the poor performance of the LDF method in the initial time after startup,the new model can simulate the adsorption performance of the initial stage of the cycle very well.Finally,the new model is used to explore the adsorption kinetics of the particles.Secondly,at the batch tank scale,a kinetic model capable of identifying mass transfer limiting steps was established.Through the simplification and dimensionless analysis of the transfer function of the adsorption system when there is no external film diffusion resistance and when there is external film diffusion resistance,respectively,the partial differential of the fluid phase conservation equation and the uptake rate equations and the phase coupling equation at the interface are realized.Solving the set of equations,the function of intermittent tank adsorption capacity and time when there is no external film diffusion resistance and when there is external film diffusion resistance are obtained respectively.Three adsorption systems are simulated with the new model established in this paper.The results show that the new model can well identify the mass transfer control steps and can optimize the intermittent adsorption system.Lastly,at the fixed bed scale,in order to simulate the breakthrough behavior of the fixed bed,models for predicting the breakthrough curve of the fixed bed when there is no external film diffusion resistance and when there is an external film diffusion resistance are established.Comparing the new model with Rosen’s complex and accurate model under the same conditions,it is found that the new model can simulate the penetration behavior of a fixed bed very well under various conditions,and is also better than the model established by Liaw based on the parabolic hypothesis,compared with other models.The model has less computational complexity.Finally,the adsorption performance of the fixed bed of the new model is used to simulate,and the results show that the new model has the function of identifying the mass transfer control steps during the the fixed bed adsorption.