The limiting residence time distribution of continuous recycle systems

The limiting residence time distribution (RTD) of continuous recycle systems as the recycle ratio approaches infinity is considered. It is shown that the RTD converges to the exponential distribution whenever the system does not consist of a “dead volume” at the limit. This limiting behavior is independent of the system configuration and flow patterns. Issues concerning the proper modeling approach and the mathematical formulation of the condition that the system has no “dead volume” are discussed in detail. Some examples illustrating the importance of selecting the proper modeling approach are also provided.     

Limiting forms of the residence time distribution for recycle system.

The widely held supposition that the residence time distribution of a recycle system always approaches that of an ideal mixer in the limit of high recyNecessary and sufficient conditions for a limit to exist and for this limit to be exponential are derived.     

Optimized design of a reverse osmosis system with a recycle

Small scale brackish water desalination units are used in remote areas and their sustenance depend on the twin factors of consistency of product water quality and availability of raw water resources. A mathematical model has been developed based on the input parameters of feed salinity, basic membrane characteristics, feed temperature, desired product quality and quantity to predict the operating recycle ratio at constant operating parameters. This ensures the consistent quality of product water at the same time minimizing the raw water consumption. The algorithm used include calculation of recovery, determination of membrane configuration and operating pressure within the guidelines of manufacturer's specified hydrodynamic parameters. The model has a range with respect to reference value of design. The model can estimate the feed quality variation +10% to −70% and feed temperature variation ±5EC based on the design reference value.     

Application of a recycle dialysis system in a reversed micellar reactor

A recycle dialysis stirred cell has been successfully used for integrating the reaction and product recovery of the lipase-catalyzed hydrolysis of olive oil in bis (2-ethylhexyl) sodium sulfosuccinate (AOT)-iso-octane reversed micelles. The resistance of membrane to reversed micelles was monitored by the water content and found to be 95.9% rejection after 24 h and 93.4% rejection after 48 h. The resistance of the membrane to free surfactants, by monitoring the UV absorption, was found to be 98.5% rejection after 10 h and 97.3% rejection after 24 h. Mathematical formulations involving the enzymatic reaction coupled with mass transfer were developed for predicting the performance of a membrane reactor. Theoretical predictions in terms of time course of oleic acid concentrations were found to be in agreement with the experimental results.     

氯丙烯回收系统的改造

分析了氯丙烯回收系统改造前后的工艺情况。系统经改造后,在节能降耗方面取得了较好的效益,同时保证了装置的稳定生产。     

Optimization of a reaction and heat exchange system with recycle

Data obtained from an operating plant involving a gas phase reaction and heat exchange system has been correlated using a multiple regression program. The results of the regression analysis have been incorporated in a mathematical model of the plant which can determine the steady state optimum conditions for the major process variables. This approach to optimization has been successfully employed on an existing vinyl chloride plant where significant gains in production have been obtained, and a more thorough understanding of process variables has been acquired.     

具有回收丙烯氮气双功能的膜技术在聚丙烯尾气回收系统中的应用

本文对小本体聚丙烯装置原尾气回收系统存在的问题进行了分析,通过具有回收丙烯及N2双功能膜分离技术与压缩/冷凝液化回收技术的组合,回收聚丙烯装置尾气中的丙烯及N2,效果显著。     

The application of a multistage-bed model for residence-time analysis in chemical-looping combustion of solid fuel

The behavior of a 10 kW chemical-looping combustor for solid fuels, normally operated in continuous mode, has been studied by addition of fuel batches. From analysis of gas leaving the air reactor, it was possible to determine the residence time and residence-time distribution of particles in the fuel reactor. Knowing the solids inventory in the fuel reactor, the circulation mass flow could be directly correlated to measured operational data, i.e. pressure drop, temperature and gas flow in air reactor riser. Using results for carbon-capture efficiency and residence-time distribution, a model was developed which could determine a mass-based reaction-rate constant for char conversion. The reaction-rate constant of a Mexican petroleum coke at both 950 and 970 °C was calculated to 8.2 and 28.8 wt%/min, respectively. The reaction-rate constant of a South African coal at 950 °C was calculated to 26.1 wt%/min. This reaction-rate constant could also be determined independently from the conversion rates of char during the batch tests. The results showed a good agreement between the two approaches, indicating that the model well describes the behavior of the unit. From the determination of the circulation mass flow, and comparison with previous testing with different circulation, it was also possible to estimate the limit for which the ilmenite was unable to supply sufficient oxygen to achieve good conversion. This limit was compared to theoretical limits for ilmenite as well as the limit set by a heat balance. It was concluded that the latter will be the one setting the limit.     

Conditions for the existence of families of steady states in a recycle system comprising a perfectly mixed reactor and a separating unit

A recycle system comprising a perfectly mixed reactor and a separating unit is considered. A regime when unreacted starting reagents and intermediates (separated from their final reaction products) fully recirculate into the reactor are considered. Conditions for the existence of various families of steady states in the reactor are found.     

外部环流反应精馏塔的分散控制方案设计

对于具有最不利相对挥发度排序（即反应物为最轻和最重组分，生成物为中间组分）的四元反应分离物系而言，在反应精馏塔的顶部和底部之间引入外部环流能够提高系统的反应分离效率，从而大幅度地降低系统的能量消耗和固定投资成本。以理想四元可逆放热反应的分离为例，研究了外部环流反应精馏塔的分散控制方案的设计问题。结果表明外部环流的引入提高了系统的反应速率，使得外部环流反应精馏塔的闭环控制效果更好（与传统反应精馏塔相比），对干扰的处理能力更强。另外，由于外部环流反应精馏塔比常规反应精馏塔有更多的操作变量（即外部环流流量），利用该变量对出料浓度进行控制，可以进一步提高系统的闭环控制效果。     

Mathematical modelling and simulation of a recycle dialysis membrane reactor in a reversed micellar system

A mathematical framework was developed for the evaluation of a recycle dialysis membrane reactor (RDMR). The lipase-catalyzed hydrolysis of olive oil in an AOT-iso-octane reversed micellar system was employed as a model. Three specific operational strategies have been considered, namely batch, fed-batch, and fed-batch-bleed. Simulation shows the conversion of substrate to be strongly dependent on efficient use of the substrate, since the permeability coefficients of both substrate and product are quite similar. Sensitivity analyses were performed to assess the influences of various parameters (membrane area, substrate feed rate, solvent bleed rate and permeability) on the performance of the reactor in different modes of operation. The analyses presented are useful to assist the optimization of the operational strategy used for the RDMR system.     

On the form of the strain energy function for a family of SBR materials

A strain energy function of the Valanis-Landel type, W = w(λ₁) + w(λ₂) + w(λ₃), is shown to be applicable to styrene–butadiene rubber (SBR) materials having varying crosslink densities ν_e. A previously obtained functional form of the strain energy derivative w′(λ), normalized by dividing by ν_e, is confirmed by one of the validity check plots in which a single curve represents the whole body of large-deformation test results for all degrees of biaxiality and crosslink density.