ANALYSIS OF CHEMICAL REACTION SYSTEMS

This paper examines strategies for integration of the stiff ordinary differential equations that comprise the mass balances in a complex reaction scheme. A reduced set of mass balances is obtained by taking certain reactions at equilibrium and applying the method of Sorensen and Stewart (1980). The GEAR integrator is coupled with the Rand algorithm for minimization of Gibbs free energy. Advantages and disadvantages of this approach are considered, with emphasis on combustion of hexane in a tube.     

Integration of combustion reaction systems

When integrating the mass and energy balances with a stiff integrator, such as LSODE (Hindmarsh, [1]), absolute error tolerances are inefficient during the initiation of free radicals, loss of precision in evaluating the algebraic mass balances can lead to numerical instability, and integrator stall can occur when species decay to depletion with a sub-first-order kinetic model. To improve reliability and efficiency, asymptotic expansions ar patched with the combustion model. When loss of precision exceeds some heuristic measure, the state variables of the differential equations (concentrations of the basic species) are reselected in order that the largest concentrations are computed by the algebraic mass balances.     

Regional mass flux balancing for controlling gentle soil remediation operations

Extraction of heavy metals by accumulating plants is a method which is currently in development for the "gentle" remediation of contaminated agricultural soils (phytoremediation, see [2]). Areal contaminant mass flux balances are basic criteria for the design of such remediations and their control. A framework for the integration of contaminant balances relating the field scale of remediation with the regional scale of soil monitoring networks is provided by the recently developed method PROTERRA [3]. The objective of the study presented in this paper was to test the suitability of PROTERRA for planning and monitoring gentle soil remediations. For this purpose we applied the PROTERRA method to the contaminated agricultural land in and around Dornach, Switzerland, to assess copper flux balances.The calculations showed that atmospheric deposition and the application of pesticides and manure are important pathways for the inputs of copper. The copper export with a special maize cultivar accumulating heavy metals would be about three times higher than the average metal export with crops. A moderate increase of sewage sludge application would lead to a substantial increase of the copper input. Decisions to remediate the soil should take the uncertainty of mass flux balances both on field scale as well as on regional scale into account. Therefore, an important need of further development of the PROTERRA method is the integration of uncertainty analysis on both scales.     

USEFULNESS AND SIGNIFICANCE OF ENERGY AND MASS BALANCES OF A FLUIDIZED SUPERHEATED STEAM DRYER

The key characteristics of a drying method for biomass are, firstly, its ability to control temperature, steam flow and pressure drop and, secondly, its ability to stabilise the material flows, particularly the outgoing moisture content. This paper presents the usefulness and significance of using energy and mass balances to improve the measurements and control systems of a drying system of industrial size in order to fulfil the moisture content requirements for biomass compression. In order to assess the reliability and accuracy of the measurements a series of tests at four different temperature and pressure levels were conducted. By verifying the plant's energy and mass balances the accuracy of the measurements could be determined and the control system was evaluated. The test results are used to determine the energy and mass balances. The control system yields good stability for the pressure drop, the temperature and the gas flow.     

USEFULNESS AND SIGNIFICANCE OF ENERGY AND MASS BALANCES OF A FLUIDIZED SUPERHEATED STEAM DRYER

The key characteristics of a drying method for biomass are, firstly, its ability to control temperature, steam flow and pressure drop and, secondly, its ability to stabilise the material flows, particularly the outgoing moisture content. This paper presents the usefulness and significance of using energy and mass balances to improve the measurements and control systems of a drying system of industrial size in order to fulfil the moisture content requirements for biomass compression. In order to assess the reliability and accuracy of the measurements a series of tests at four different temperature and pressure levels were conducted. By verifying the plant's energy and mass balances the accuracy of the measurements could be determined and the control system was evaluated. The test results are used to determine the energy and mass balances. The control system yields good stability for the pressure drop, the temperature and the gas flow.     

A practical approach to dynamic simulation of two-phase systems

A general method is presented for the dynamic simulation of two-phase flow systems. The analysis is based on the cross section averaged form of the mass, energy and momentum conservation laws. In order to predict the bulk dynamics and to avoid numerical difficulties a quasi-steady-state assumption is used in formulating the overall mass and momentum balances. For the wall shear stress and the void fraction, empirical correlations are used. In each computational step the pressure distribution is predicted solving an ordinary boundary value problem; then, we solve the non-steady enthalpy balances. The method is applied to simulate forced convection flow-boiling phenomena in a furnace.     

Process control of a gaseous diffusion cascade for isotopic separation of uranium

Various aspects of dynamics and process control of a gaseous diffusion cascade are described. The cascade enriches uranium hexafluoride gas (HEX) in the light isotope of uranium in a countercurrent flow. The linearized equations describing the equipment models are derived. One can then write the mass balances on the high and low pressure sides of a stage and the overall heat balance of a stage. These heat and mass balances are linear difference equations on the stage number with time derivatives which are then replaced by jω factors to examine the effects of cyclic perturbations. The mass balances are first treated for a cascade section of 12 stages with temperatures assumed constant. The effect of a perturbation of pressure on one of the stages is described first for ω = 0 (that is for steady state). Then Nyquist diagrams are obtained. The effect of transport change is also studied.Then temperature is introduced, assuming pressures to be constant. The cases of a section of 12 stages and a cascade of 120 stages are examined. Again Nyquist diagrams of temperature frequency response to a perturbation on one stage are calculated. Process control of the heat exchangers is introduced. The method used to solve the difference equations may be applied to other types of perturbations and to the complete scheme of process control.     

Modeling of ethanol dehydration by diffusion distillation in consideration of the sensible heat transfer

The diffusion distillation is the evaporation and diffusion process below the boiling temperature of the mixture in a gap filled with the inert gas. It can separate the azeotropic mixture of ethanol and water. The mass transfer in a differential single column can be described by the Maxwell-Stefan equations. Differential mass balances which can extend a column model from a differential single column to an integral column and heat balances were suggested. The new model considers the sensible heat transfers and develops algorithm which enables to calculate interfacial temperature more precisely at condensing liquid film and include one more iterative loop. The results are compared with the experimental data and other models.     

Recovery of molecular weight distributions from transformed domains. Part I. Application of pgf to mass balances describing reactions involving free radicals

We present a general framework for the application of a transform technique, probability generating functions (pgf), to mass balances that describe free radical reactions, in particular synthesis or modification of polyolefins. Contributions of specific reactions to the mass balances are identified and transformed separately, so that a modular approach is possible for the construction of the pgf balance equations for different free radical processes. This simplifies the transformation step hopefully making the method useful to more people. Three examples taken from the literature are transformed using this modular method showing its ease of use. In Part II of this work, the resulting transforms are inverted to recover the complete molecular weight distribution.     

Study of model application for drying of pulp fruit in spouted bed with intermittent feeding and accumulation

In the present study, we applied and improved a model to describe the behavior of a spouted bed dryer with intermittent feeding for suspension drying, considering suspension accumulation inside the device. This model is important in macroscopic heat and mass balances, represented by a system of ordinary differential balances, implemented and resolved numerically using Fortran routines, in which the influence of process variables on drying dynamics were assessed. The results obtained in modeling and mathematical simulations were compared with experimental data, indicating that the model fits the process well, based on outlet air temperature and moisture.     

Modeling and simulation of a small-scale trickle bed reactor for sugar hydrogenation

Laboratory-scale trickle bed reactor was modeled and simulated, taking into account axial dispersion, gas–liquid, liquid–solid and internal mass transfer as well as catalyst deactivation under isothermal conditions. For catalyst particles dynamic and steady state models were developed, including both mass and heat balances. Catalyst deactivation was included in the model by using the final activity concept for the catalyst particles. A well-working numerical algorithm (method of lines) was applied for solving the reactor model with Matlab 7.1 and the results followed experimental trends very well. The steady-state reactor model was based on simultaneous solution of mass balances. The aim was to illustrate how these parabolic partial differential equations could be solved with a step-by-step calculation for a selected geometry. The final model verification was done against experimental data from the hydrogenation of arabinose to arabitol on a ruthenium catalyst.     

Ökobilanzen als Instrument der Produktbewertung

Ecological Balances as an Instrument for Product Evaluation. The predecessor of today's increasingly important ecological balances was the Limits of Growth Report published by the Club of Rome in 1972. Ecological balances cover mass and energy flows and emissions from the raw materials via intermediates all the way to the end products, as well as waste disposal. This also includes the balance of ecological activity at all stages. The components of ecological balances are goal definition, material balance, action balance, balance evaluation, and optimisation analysis. The advantages of ecological balances are their fundamental acceptance by industry and environmental protection groups, clarity and essentially objective assessment, and the possibility of application to systems, comparison of equivalent products, systems, and services and comparison of null variants. Problems encountered with ecological balances arise, for example, because of frequently inaccessible data basis and because of the system definition.     

From process simulation to general estimation

The ability to use a simulation program with the aim of making mass and energy balances in a plant, starting from just raw data and process knowledge, is an ambitious and attractive goal. We propose to address a general formulation for the estimation problem in the framework of a simultaneous modular approach. As raw data are corrected to satisfy mass and energy balances and some parameters are computed to give a unit operation performance diagnosis, the estimation consists both of data reconciliation and parameter identification. It follows that the numerical problem is a minimization of a least square objective function. Constrained minimization is performed with an infeasible path strategy which solves the optimization problem and process balance convergence at the same level, with a nonlinear programming code. The confidence intervals computation, for parameters and corrected values of measurements, is also discussed. A simple flash loop flowsheet example gives a better understanding of the theoretical aspects. A more complex flowsheet has been chosen as a second illustrative example.     

INTERFACIAL TEMPERATURE RISE AND MULTIPLICITY IN NONISOTHERMAL GAS-LIQUID CSTRs

For exothermic gas-liquid reactions.the interfacial temperature affects the gas-solubility, interfacial reaction rate, mass transfer rate and the bulk temperature of the reactor. An overall heat balance on the reaction-diffusion 'film' relates the interfacial temperature to the bulk variables (temperature, concentration), and the interfacial variables (enhancement factor, etc.). While the interfacial balance shows (apparent) multiplicity of interfacial temperature for a given bulk temperature, uniqueness results when the interfacial balances are solved together with the mass and energy balances for the reactor bulk. It is shown that the state of interface and bulk are intimately related, and thus, consideration of interfacial temperature does not increase the multiplicty of a gas-liquid CSTR. Simple a priori estimates are derived for the interfacial temperature. All of the results are found to be rather independent of kinetic details. The interfacial temperature rise is encouraged by low interfacial heat and mass transfer coefficients, by small liquid residence time in the bulk and by increased heat losses from the reactor bulk.     

Modeling and simulation of an entrained flow coal gasifier

A mathematical model has been developed to simulate the Texaco downflow entrained-bed pilot-plant gasifier using coal liquefaction residues and coal-water slurries as feedstocks. This model describes the physical and chemical processes occurring in an entrained coal gasifier. The gasification kinetics describes different complex reactions occurring in the gasifier and the hydrodynamics describes mass, momentum and energy balances for solid and gas phases. Temperature, concentration and velocity profiles along the reactor height were obtained by solving the mass, momentum and energy balances. Parameter studies were made to provide a better understanding of the reactor performance for various inlet feed conditions utilizing the model.     

Analysis of dialysis coupled with ultrafiltration through cocurrently parallel-flow rectangular membrane modules

The mass transfer for the systems of dialysis with ultrafiltration in cocurrently parallel-flow rectangular membrane modules was investigated, based on mass balances with the assumption of uniform ultrafiltration flux. Considerable improvement in separation efficiency is achievable if the effect of ultrafiltration is applied, especially for the system with low mass transfer coefficient. The enhancement in separation efficiency is significantly increased with increasing ultrafiltration flux, as well as with increasing the volumetric flow rates. Furthermore, increasing the volumetric flow rate in retentate phase is more beneficial to mass transfer than increasing in dialysate phase.     

超临界流体萃取固态物料数值模拟的研究进展

介绍了超临界流体萃取固态物料的数值模拟方法 ,对固体物料萃取的经验动力学模型、热质类比模型、质量守恒模型的原理及传质特性进行了评述     

Energetic Optimization of the Three-Stage Gas Permeation Process for the Upgrading of Biogas

The mass balances of countercurrent gas permeation modules for the separation of multicomponent gas mixtures are formulated as a boundary value problem, using the ideal gas law and isobaric isothermal stages. The balances are extended for the common three-stage gas permeation process for the upgrading of biogas. The solution is calculated with MATLAB's BVP4C boundary value solver. The process is optimized by means of the FMINCON SQP-algorithm towards lowest power consumption. Parameter variations are conducted, highlighting the impact of product and lean-gas quality setpoints, biogas composition, membrane surface and selectivity, permeate compression, and choice of compressor model on the energetic optimum.     

有最大入口浓度限制的单杂质废水处理网络设计

分布式废水处理系统集成的本质特征之一是通过最大程度减少不必要的水流混合量而降低系统的总处理量。根据这一思想,提出了一种基于启发式规则的方法设计废水处理单元有最大入口浓度限制的单杂质废水处理系统。首先依据提出的规则确定处理单元的执行顺序,并在此基础上建立初始网络结构;然后通过计算确定最终网络结构。在设计过程中,上述规则的运用和最终网络结构的确定需要与杂质负荷平衡、夹点确定等废水处理网络设计的基本概念以及入口浓度限制条件相结合。对文献实例的研究表明,结果与数学规划法的求解结果相当,但设计过程更为简单且具有明确的工程意义。     

Nonequilibrium Stage Based Modeling of a Falling Film Distillation Unit

Theoretical Foundations of Chemical Engineering - A novel nonequilibrium stage based model was developed for a falling film distillation unit. The model combines mass and energy balances in the...