Mathematical modelling of lignin pyrolysis

Seven lignins from different sources were pyrolysed (i) isothermally in vacuum over the temperature range 300–1300 °C and (ii) at a constant heating rate of 30 °C min^?1 and a pressure of 0.1 MPa over the temperature range 150–900 °C. The mass fraction of each product—char, tar and gas species—and the elemental composition of the char and the tar were determined for the flash pyrolysis experiments. The evolution rates of the gas species and the tar versus the dynamic temperature of pyrolysis were determined for the constant heating rate pyrolysis experiments. Although the amount of each product species varied from lignin to lignin, the evolution rates were insensitive to the lignin source and the extraction process. To model the data, modifications were made to a recently developed model of coal pyrolysis. The model proved to be successful in simulating both the data from vacuum flash pyrolysis and constant heating rate pyrolysis of Iotech lignin.     

Mathematical modelling of an industrial furnace for high‐temperature heat treatment of wood

There are various high‐temperature treatment methods for wood. In the “Bois Perdure” process, the thermal treatment of wood is carried out in a furnace by contacting it with hot combustion gases over 200°C without the addition of any chemicals in order to improve its dimensional stability and durability. The treatment eliminates free and bound water in the wood and modifies its molecular structure. In this study, a mathematical model describing the industrial furnace has been developed. The overall model consists of a 3‐D unsteady‐state sub‐model which solves for the flow, heat, and mass transfer in the gas coupled with a 1‐D unsteady‐state sub‐model which calculates the heat and mass transfer in the wood. The 3‐D gas sub‐model was developed using the commercial CFD code CFX. The 1‐D wood sub‐model is based on the solution of simultaneous heat and mass transfer equations (Luikov equations) using the implicit finite difference formulation. The model predicts the temperature and moisture distributions in the wood as well as the flow, heat, and moisture profiles in the gas. The model results are compared with the data obtained from the industrial furnace, and a good agreement was found between them.     

Mathematical modelling of landfill degradation

This paper presents a mathematical model for the primary and secondary stages of biodegradation within domestic landfills. Quantitative relations are proposed to describe the rates of mass conversion between the major landfill chemicals and the effects of gas evolution. Particular attention is given to the methanogenic stage with the associated bacterial population being modelled explicitly. The processes are phrased in terms of a system of coupled differential equations, and examples of their numerical solution are given for cases in which spatial dependency is neglected. The main inadequacies of this model and the need for more appropriate data are indicated.     

Mathematical modelling of the MCFC cathode

Different models for the NiO cathode have been compared with respect to their abilities to predict polarization curves and the influence of the amount of electrolyte on the electrode performance. It has been shown that the agglomerate model for the MCFC cathode gives more reasonable results when the exterior agglomerate surface area is specifically taken into account. In the cathode only the outermost layer of nickel oxide particles in the agglomerate is utilized for the electrochemical reaction. The pseudohomogeneous approach is questionable for these agglomerates since the individual particles constituting the agglomerate are of the same size as the reaction zone thickness. A thin-film model with a roughness factor for the electrode surface appears to be as good a model as the agglomerate model. A model based on a chain of spherical agglomerates and the partially drowned agglomerate model are physically more realistic models than the homogeneous agglomerate model for the prediction of the influence of electrolyte fill on the electrochemical performance.     

Mathematical modelling of a reverse flow reactor with catalytic surface dynamics

This paper studies a system of partial differential equations modelling the behaviour of a reverse flow reactor. For the parameters appropriate for the oxidation of ammonia on a Pt/Al₂O₃ catalyst in a typical laboratory set-up, the reactor may be split into regions where approximate formulas that determine its behaviour are deduced. Numerical calculations are presented and can be used to compare with the analytical formulas. The physical insight gained from the asymptotic analysis suggests a new switching strategy which is the subject of numerical experiments. The switching strategy is found to be efficient at minimising the ammonia exiting the reactor after reversal.     

Optimal mixing to improve the performance of batch and continuous fermentations with recombinant Escherichia coli

Fermentations with genetically altered bacteria tend to lose plasmids as the fermentation progresses. Methods such as two‐stage cultivation, cell recycle and the addition of antibiotics are commonly used to enhance plasmid stability. Here we examine a different method, the regulation of mixing in the bioreactor. In particular, large bioreactors are considered where uniform mixing is difficult to achieve and the probability of plasmid loss varies with the specific growth rate. For both batch and continuous cultivations of Escherichia coli C600 gal K containing the plasmid pBR Eco gap, it is seen through a model that both modes of operation exhibit high plasmid stability and cell growth when the broth is incompletely mixed, and mixing near and away from the point of inoculation are unequal. Thus, the natural incomplete mixing in large bioreactors may be utilized to improve plasmid stability. A practical method to implement this idea is suggested. Copyright © 2005 Society of Chemical Industry     

Dynamic modelling of an industrial R2R FCC unit

The aim of this study is to obtain a model that can simulate the performance of an industrial fluid catalytic cracking (FCC) unit in steady and dynamic state, and which will subsequently be used in studies of control and real time optimisation. In this paper, a dynamic model for a R2R type FCC unit is presented. The model includes the riser, the stripper/disengager, the regeneration system and the catalyst transport lines. Mass, energy and pressure balances are performed for each of these sections.Simulation results for steady state are presented and compared qualitatively to those obtained from previous FCC models. The dynamic behaviour of the system is explored through two perturbations in open loop, one on the fresh feed flow rate and one on the air flow rate to the first regenerator. The results illustrate the consistency of the model and are in agreement with what has been observed in studies available in the open literature.     

Mathematical modelling of temperature induced moisture migration in bulk powders

This paper reviews the importance of temperature gradient induced moisture diffusion in powder beds. Redistribution of moisture by this mechanism is important for a wide variety of products, especially those which are crystalline in nature. Moisture transfer in these products can result in very high local water activity and lead to microbial spoilage and caking problems. A conceptual model was developed for heat and moisture transfer due to the application of thermal gradients across a one-dimensional powder bed. The validity of the key assumptions in the model formulation were demonstrated and a mathematical model was derived and solved numerically. The model was validated against experimental data collected using crystalline lactose powders as a working example.     

青霉素发酵过程的模型仿真与补料优化

补料分批式青霉素发酵的机理模型已得到深入研究,但是模型往往难以用于补料的优化和批次内的控制。为了对模型进行优化控制,针对Birol等提出的青霉素发酵非结构动力学模型,合理调整了温度和pH变化的影响,得到了青霉素发酵过程的简化机理模型。反应基质的补料是青霉素优化控制的关键,选择对补料速率进行优化来提高青霉素的产量。由于机理模型具有非线性和约束条件,采用序贯二次规划算法来进行求解,其中将补料轨线进行分段处理提高了优化效率。优化计算结果表明改进的补料过程可以提高青霉素的浓度和产量。     

A review of just-in-time learning-based soft sensor in industrial process

Data-driven soft sensing approaches have been a hot research field for decades and are increasingly used in industrial processes due to their advantages of easy implementation and high efficiency. However, nonlinear and time-varying problems widely exist in practical industrial processes. Just-in-time learning (JITL) was proposed to solve these problems and has attracted great attention in practical applications. To present a comprehensive review of JITL-based soft sensor studies and provide detailed technical guidance for new researchers, this paper introduces the recent research on JITL-based soft sensor modelling methods in the industrial process from three aspects: similarity criterion, sample subset, and local model, which include the whole process of establishing a JITL-based soft sensor. Moreover, the future research and innovation directions of JITL-based soft sensors in industrial processes are also prospected.     

Linking science and industrial catalysis

Several aspects of the current needs for new industrial catalytic processes are discussed in the present article with emphasis on ammonia synthesis, natural gas conversion, power generation and environmental processes. Recent developments in surface science, in situ methods and microkinetic modelling have resulted in new strategies for catalysis research and the scale-up of industrial processes.     

Mathematical modelling of protein diffusion in microcapsules: A comparison with experimental results

The objective of this study was to develop a general diffusion model for describing mass transport phenomena and membrane diffusivities in alginate—polylysine (PLL) microcapsules. Good agreement between calculated and experimental protein concentration profiles was obtained based on a microcapsule model, consisting of a capsule membrane containing a partially impermeable alginate gel core with a decreasing gel pore size towards the centre of the capsule. The apparent size of the impermeable gel core and the capsule membrane permeability were directly dependent on the size of the diffusing protein and the alginate-PLL reaction time. The presence of this impermeable core may hinder the commercial and clinical use of these microcapsules in cell culture engineering and cell transplantation by affecting cell viability.     

Supercritical carbon dioxide extraction of astaxanthin from Paracoccus NBRC 101723: Mathematical modelling study

Astaxanthin (AX) is a secondary metabolite that accumulates inside the cell during Paracoccus fermentation. The fermentation biomass was extracted using supercritical carbon dioxide (SC-CO₂). The solubility parameter of AX, CO₂ and entrainer solvents was calculated and validated with experimental results. The pressure and particle size of the biomass had a significant effect on the extraction of AX. A maximum recovery of 963.33 μg/g of AX was obtained after SC-CO₂ extraction at 40ºC, 350 bar and a run time of 60 min with ethanol (20% v/w) as an entrainer. Further, the experimental data has been modelled using non-linear regression analysis method.     

Mathematical modelling of a solid particle motion in a re‐circulatory fluidised bed unit

Two fundamental properties of the particles are their velocity and consequent displacement versus time history during the granulation process. Knowledge of the particle velocity might supply much information about the sub‐processes. In this paper, an analytical model of a solid particle motion in an internal re‐circulatory fluidised bed unit is developed and validated against experimentally obtained data. The model predictions show good correspondence with the experimental results for the spherical particles. For the case of non‐spherical granules, the agreement between the model and the experiments is not equally convincing but still adequate.     

Synthesis of poly(alkylene succinate) biodegradable polyesters I. Mathematical modelling of the esterification reaction

Synthesis of three biodegradable aliphatic polyesters, namely poly(ethylene succinate), poly(propylene succinate) and poly(butylene succinate) is presented using the appropriate diols and succinic acid in the presence of tetrabutoxytitanium as catalyst. A theoretical mathematical model for the esterification reaction, based on the functional group approach, is developed and applied successfully in the simulation of all experimental data. Values for the kinetic rate constants are proposed for different catalyst molar ratios and comonomer chemical structure. It was found that the presence of the metal catalyst used leads to a poor activity of self-catalyzed acid and the main kinetic rate constant of the esterification reaction correlates well with the square root of the catalyst concentration. Different glycols do not influence much the number average degree of polymerization (NADP) values of the oligomers produced, even thought they slightly affect esterification rates in the order BG>PG>EG. In contrast, these values are affected by the amount of catalyst, with larger catalyst molar ratio giving polymer with bigger average molecular weight. These results were verified from measurements of the final polyester average molecular weight obtained at different polycondensation temperatures. Finally, from theoretical simulation results it was found that although higher initial ratios of glycol to succinic acid are useful to increase the esterification rate, they lower the NADP of the oligomers formed at a fixed conversion of acid end groups.     

Mathematical modelling of polyphenol extraction by aqueous two-phase system in continuously operated macro- and micro-extractors

An aqueous two-phase system (ATPS) in combination with macro- and micro-extractors was used for polyphenol extraction from a model solution (gallic acid) and three real samples (red and white wine, and orange juice). The objective of the present study was to apply a mathematical model that successfully describes and predicts performances of macro- and micro-extractors. The micro-extractor system was selected as the most suitable for the polyphenol extraction because the same extraction efficiency was obtained for two levels of magnitude shorter residence time compared to the macro-extractor. Based on good agreement between model predictions and experimental results, the obtained simulations could be used for further process optimization and improvement.     

The inverse emulsion polymerization of acrylamide with pentaerythritolmyristate as emulsifier. 2. Mathematical modelling

A mathematical model of the inverse emulsion polymerization of aqueous acrylamide solutions in isooctane as dispersing media with the chemically pure emulsifier pentaerythritolmonomyristate and an oil-soluble azo initiator has been developed. A Monte Carlo method was used successfully to calculate the kinetics, molar mass averages and average particle sizes. The computation time of the method was reduced by calculating the chain length of the polymer molecules via the life-time of the radicals. It is shown that a few assumptions based on the mirror image of an ideal conventional emulsion polymerization with Smith–Ewart case 2 kinetics are sufficient to comprehensively describe the experimental findings. © 1998 SCI.     

基于KTA-LSSVM的青霉素发酵过程预测建模

为解决青霉素发酵过程预测建模中存在的输入变量选择问题,提出了基于核目标度量（kernel target alignment,KTA）和最小二乘支持向量机（least squares support vector machines,LSSVM）的青霉素发酵过程预测模型。首先,在分析影响青霉素产物浓度相关因素的基础上选取输入变量,采用KTA对输入变量进行尺度缩放,然后,利用Pensim仿真平台数据,采用混沌粒子群算法对LSSVM的参数寻优,建立青霉素发酵过程的KTA-LSSVM预测模型。青霉素浓度预测的KTA-LSSVM模型均方根误差为0.0179,LSSVM模型的均方根误差为0.0276,实验结果表明,本文提出的模型预测精度高,推广性能好。