A Multi-objective Variational Based Approach To The Intensification And Simulation Of Chemical Process

Numerical methods have become an important tool for addressing scientific research and engineering problems.The numerical methods have been widely used not only in the chemical process simulation but also in the intensification of the processes.However,chemical processes are so complex that it is usually difficult to develop sufficient number model equations to represent the problem in a way of closed equation system.To intensify a process,a criterion needs to be set up to appreciate if the process is good or not in optimizing all the free vriables.In this paper,a multi-objective variational principle has been proposed.And this principle has been applied in the chemical process intensification and process simulation.Multi-objective variational principle is a method developed from the extremum principle of entropy generation in non-equilibrium thermodynamics.Different from the extremum principle of entropy generation,the multi-objective variational principle employs multi-objective function not the total entropy generation.All the objective functions are parts of the entropy generation due to heat transfer,mass transfer,chemical reaction and viscous dissipation.Consider the extreme trend of each part of the entropy generation during the process intensification and simulation,and construct the objective function of functional form base on the extreme trend.The governing equations of the process are the constraints.Use the variational method to solve the extremum of functional with constraints.Finally,the results of process intensification and simulation can be calculated.At first,the multi-objective variational principle is applied to the process intensification.During the convective mass transfer process,the entropy generation due to mass transfer and viscous dissipation are chosen as the objective functions.Through the multi-objective variational principle,the optimal flow distribution and body force field can be solved.In the Pareto optimal solution theory,the optimal results can be considered as the thermodynamics limitation of the mass transfer intensification.The multi-objective variational principle need to solve a negative diffusion equation.In this paper,the converged problem of the negative diffusion equation can be solved by the Ritz method.The Ritz method can also provide a new idea for the construction of the real body force.And then the multi-objective variational principle is applied to the process simulation.The extreme trend of the heat transfer entropy generation and viscous dissipation in Rayleigh-Bénard convection are analyzed.For the complex transport process which the conservation equations are difficult to find out,the multi-objective variational principle is used to close the equations.This work gives new method for the application of non-equilibrium thermodynamics.Finally,this paper goes beyond the frame of Navier-Stokes equation,and applies the extremum principle to the modeling of diffusivity for binary system in liquid mixture.The entropy generation is used as the objective function which derived from the Maxwell-Stefan diffusion equation.And the Maxwell-Stefan diffusion coefficients can be calculated.In this paper,excess molar internal energy is found from the partition function,and employed to correct error due to linear mixing rule.The local surface area fraction is used to replace the total mole fraction,which can reduce the error.And the new model is applied to predict the diffusivity for five binary systems.The average relative deviation is the best compared with other predict model.The multi-objective variational principle proposed in this paper can be expected to have a wide application and good prospect.And this principle can be expanded to many aspects of chemical engineering process.