Kinetic Modelling And Analysis Of A Class Of Microalgae Culture Process

Today,the production of many bulk chemicals and fine chemicals by chemical methods with high temperature,high pressure and high pollution have been gradually replaced by microbial production,which requires mild conditions for production and is environmentally friendly.Process optimization is an effective way to realize high e ciency of microbial production and reduce the cost of biological manufacturing,and it is also a necessary procedure for microbial production from laboratory to industrial production.The research of microbial process kinetics is the basis of this procedure.Mathematical models play an important role in the mechanism exploration,process prediction and simulation of microbial process,which can effectively reduce the experimental cost.Therefore,it is very important to use mathematical models to describe the dynamic changes of various variables in microbial production processes.As a photosynthetic microorganism,microalgae have abundant sources,fast growth and reproduction rate,high survival rate,low production cost,and can be easily controlled for large-scale production.Therefore,it is of great theoretical and practical significance to establish a suitable mathematical model for microalgae process.In this paper,based on the production of fucoxanthin by microalgae(Thalassiosira weissflogi ND-8),a kinetic model is established and a series of discussions and analyses are carried out on this basis.The key contributions of this work are summarized as follows.Firstly,based on the process data of the concentrations of various substances during the synthesis of fucoxanthin by microalgae under different initial conditions,the microalgae growth,substrate consumption and synthetic characteristics of the product are preliminarily analyzed.On this basis,the mathematical model is established to describe the growth of microalgae in the photobioreactor,and the particle swarmed optimization algorithm is constructed to identify the parameters of the model.Through numerical simulation of the established kinetic model,the effects of two limited substrates(nitrogen and phosphorus)on the growth and metabolism of microalgae,the synthesis of target products and the interdependencies among the substances are analyzed.It can be inferred from the results that a fold increase in the initial phosphorus concentration inhibits the growth rate of the microalgal cells,the nitrogen plays an important role in the growth of microalgal cells and the synthesis of fucoxanthin,and the accumulation of fucoxanthin from the maintenance metabolism of cells is higher that from the growth of microalgae.Secondly,due to the existence of various uncertainties and disturbances in the experiments,the measured data may be disturbed and the identified values of the kinetic parameters may deviate from their actual values.Therefore,sensitivity analysis of the kinetic parameters is carried out by two methods.The first method is disturbance sensitivity.In this method,the disturbance sensitivity index of the parameter is defined and the sensitivity index of each parameter is evaluated by changing the value of this parameters by±10%.The second method is local sensitivity.In this method,the existence and uniqueness of solutions to the system,the continuous dependence and differentiability of the solutions with respect to the initial value and the parameters are proved in terms of the theory of ordinary differential equations and the sensitivity functions of the model are characterized by a parametric sensitivity system.The trajectories of parametric sensitivity functions are then simulated by solving the parametric sensitivity system numerically.