Constrained positive limit cycles in linear periodic processes

A test is suggested for processes described by linear ordinary differential equations with periodic coefficients that will ascertain asymptotic convergence of the solution to a physically meaningful limit cycle. This test can be useful as a check on mathematical models of periodic processes before spending efforts on a computational exploration of the solutions. It may also be used to generate a control policy that forces the solution into a desired region of space. Three chemical engineering sample applications are presented concerning a periodic chemical reactor, a parametric pump and the control of a solar evaporation pond.     

A comprehensive approach to chemical engineering computational problems

A general programme for the solution of large sparse systems of non-linear equations is presented that allows to afford in a general way most computational problems in chemical engineering.Equipments and plants can, in fact, be represented as networks of “unit cells” to which material and energy balance equations are applied in finite form.The lay-out of the network and the assessment of the equations is a matter of the engineer's judgment and depends upon the aims of the computation and the complexity and importance of the phenomena involved.The solution of the equations then becomes a straightforward procedure that may be committed to the computer.Examples of application to a variety of chemical equipments and to process computation are given.     

Methodische Entwicklung verfahrenstechnischer Prozesse

Methodological development of chemical engineering processes . The development of complex systems is especially dependent upon methodologically structured procedures to provide a clear-cut framework for the application of specialist knowledge and creativity and to develop and exploit the field of possible solutions in order to single out a powerful solution. The method of choice should always be systems engineering. It provides, in relatively abtract and interpretable manner, principles, methods, and proven aids in the form of a system concept, a systems engineering plan of procedure, and project management. A brief introduction to the system concept is followed by application of the systems engineering procedural model to process development. Safety engineering and data acquisition are then considered in detail. Heuristic models are also considered in relation to data acquisition. Expert systems are recommended for setting up collections of information. The article closes with a survey of computer-aided process development.     

Automatic generation of the symptom tree model for process fault diagnosis

The Symptom Tree Model (STM) has been studied extensively as a model for fault diagnosis in chemical processes and has been applied to real processes. In this study, a program to build a model, AUSST (Automatic Synthesis of the Symptom Tree model), which generates the STM automatically is developed. The input information supplied to AUSST includes the process topology and the unit model library. The unit model library is represented in the form of mini-fault trees which can be constructed systematically through qualitative abstraction from the mathematical model or the operation data and experienced operators. AUSST has worked well, the generated symptom trees describe the paths of fault propagation sufficiently and contain all the possible primal faults. AUSST helps to assure the accuracy of the STM as well as managing the STM consistently. It is expected that AUSST reduces the engineering efforts required to develop a fault diagnostic system for a new process.     

Computer modelling and numerical analysis of hydrodynamics and heat transfer in non-porous catalytic reactor for the decomposition of ammonia

Chemical reactors exhibit very complex behaviours such as multiple steady states, oscillations, etc. resulting from complex linkage between the transport processes and the non-linear chemical reaction kinetics. Ammonia is a potential hydrogen source for a number of fuel cell applications for small scale power generation useful for portable equipments. In the present work, we analyse the fluid dynamics and heat transfer in catalytic microreactor systems for the decomposition of ammonia over a monolayer Ni non-porous catalyst. The overall model for this convective-diffusive-reactive system consists of a flow model, a mass transport model, an energy conservation model and a reaction kinetics model for ammonia decomposition. The flow model is described by the Stokes equation for a creeping flow regime. The mass transport and energy conservation models are based on convective-diffusion equations. The rate of ammonia decomposition can be measured as a function of the catalyst activity and ammonia concentration. A standard Galerkin finite element technique has been applied for the solution of the flow equations. A slightly perturbed form of the mass continuity equation is used to satisfy the Ladyzhenskaya-Babuška-Brezzi stability criterion. For the solution of convection-diffusion equations, a streamline inconsistent upwind finite element scheme has been chosen to avoid any spurious oscillations. C⁰-continuous 9-noded Lagrangian biquadratic isoparametric finite elements are used for the approximation of the field variables. A second-order Taylor-Galerkin time-stepping scheme has been chosen for the temporal discretisation of the flow equations whilst an implicit theta method has been used for convection-diffusion equations. The results are presented in the form of velocity vectors and concentration, temperature contours and are examined for stability, convergence and theoretical consistency.     

Numerische Methoden zur Simulation verfahrenstechnischer Prozesse

Numerical Methods for Simulation of Chemical Engineering Processes. Essential fundamentals and the current state of the art in simulating the dynamic and the steady state behaviour of chemical engineering processes are discussed. It is shown that discretization of the spatial derivatives in the balance equations leads to a system of so-called DAE (differential algebraic equations), consisting of ordinary differential equations in time and algebraic equations. The paper discusses necessary steps to solve the DAE and mentions approved standard software for these steps as well as for the solution of the DAE as a whole.     

Multicomponent Fuzzy Model for Evaluating the Energy Efficiency of Chemical and Power Engineering Processes of Drying of the Multilayer Mass of Phosphorite Pellets

A multicomponent fuzzy model was proposed for evaluating the energy efficiency of the chemical and power engineering processes of the drying of a dynamic multilayer mass of phosphorite pellets in a complex multistage chemical and power engineering system (roasting conveyor machine). The developed model includes a set of fuzzy component models for analyzing the chemical and power engineering processes of pellet drying corresponding to the results of the decomposition of these processes, a set of neuro-fuzzy production models for evaluating the energy efficiency of the individual stages of the chemical and power engineering processes of pellet drying, and a neuro-fuzzy production model of generalized evaluation of the energy efficiency of the chemical and power engineering process of pellet drying. The use of the proposed model makes it possible to evaluate the energy efficiency of both the individual stages and, in general, the chemical and power engineering process of phosphorite pellet drying under conditions of uncertainty of their thermophysical characteristics and the processes themselves; to perform online structural adjustment and parametric adaptation of the model when the mode and chemical and power engineering process of pellet drying are changed; to perform online evaluation of the energy efficiency of the chemical and power engineering process of pellet drying; and to provide quality improvement and speed of decision making on optimization of the chemical and power engineering process of pellet drying to increase the energy efficiency of these processes.     

Sequential experimental design procedures for precise parameter estimation in ordinary differential equations

In this paper, it is shown how an experimental program for precise parameter estimation can be designed sequentially for the case that the mathematical model is given in the form of a set of ordinary differential equations. Two strategies are proposed. The first aims at minimizing the volume of the joint confidence region associated with the parameter estimates. The second attempts to alter as much as possible the shape towards a spherical region, by shortening the length of the longest principal axis of the confidence region to the maximum extent. The application of both criteria is illustrated by means of examples, representative for real problems in chemical reaction engineering. The techniques are easily applicable with our present day computing facilities. Qualitative indications are derived concerning the question when the use of an experimental design will result in an appreciable gain in significance for the parameter estimates.     

A Theoretical Model for the Formation of Functional Micro- and Nano-Particles from Combustion of Emulsion Droplets

In this paper a theoretical model is developed to simulate the process of vaporization and burning of emulsion droplets of a fuel and the evolution and formation of micro- and nano-particles. This process is usually known as the Emulsion Combustion Method (ECM). In the ECM, a proper salt solution is mixed with a fuel to form an emulsion of micro-solution droplets. The emulsion is then sprayed into micron-sized emulsion droplets; spray droplets burn in a spray flame to form final micro- or nano-particles. A mathematical model for the entire process from the droplet interior to the gas phase processes is proposed. Model equations are solved numerically. It is found that particle characteristics are dependent on the operating and processing conditions, such as the initial size and concentration of the suspended micro solution droplets in emulsion droplets and the fuel type and fraction of the emulsion droplets. Although a quantitative evaluation of the model performance is not yet possible due to the lack of sufficient experimental data, the developed model may be used to design an ECM process to produce particles with tailored properties. The main novelty of the model is that in an ECM process it can predict whether mono-dispersed single particles will be formed or agglomerated larger particles.     

Multi-dimensional design process management by extended product modeling for concurrent process engineering

Conventional product and process models have focused on static features. That means product models are mainly based on structural decomposition of products, and process models are also often described by activity decomposition such as work breakdown structure. From the view of design process management, it is difficult to describe dynamic features of design processes appropriately through conventional methodologies. In this paper, a multidimensional approach for design process management was explored to manifest characteristics of design processes for chemical plant design. Parallelized design process for concurrent process engineering should be managed by twodimensional design activity flows. The process management makes it possible to guide progress of design processes in a helix structure by horizontal and vertical activity control simultaneously. They stand for teleological and causal relation between design activities, respectively. That can be achieved based on an extended product model, which represents various design perspectives explicitly from a conventional design activity model. The extended product model is composed of product data, design activities, and activity drivers. Dynamic features of the extended product model are expressed by an activity chain model. These concepts will support the realization of concurrent process engineering for chemical plant design in the sense that they provide design process management strategies.     

Wellenausbreitung in verfahrenstechnischen Prozessen

Wave propagation phenomena in chemical engineering processes. A phenomenological analysis of the dynamics of a number of different distributed parameter systems in chemical engineering reveals a surprisingly simple dynamic behaviour despite the complexity of the underlying nonlinear process models. Spatial structures or waves are propagating along a spatial coordinate during transients. The dynamics of most of the processes under consideration can be described with sufficient accuracy by three different model structures. These models serve as a basis for a theoretical system analysis. The investigation of characteristic properties of the propagating waves and the mechanisms responsible for wave formation are of central significance. Finally, it is shown how the extended knowledge about the processes may be applied for the solution of problems of technical interest.     

伴有平衡反应的分离过程的数学模拟(Ⅰ)板式反应精馏塔的模拟计算

本文提出了相平衡和化学平衡同时存在的多相复杂可逆反应的反应精馏计算方法。模型方程由物料衡算方程,化学平衡方程,相平衡方程,归一方程,焓衡算方程组成。模型分三层迭代求解。该算法可适用于非理想系统、反应动力学未知的快速可逆反应过程。并且对不同操作条件下的计算均能稳定收敛,可以进行操作条件的调优。应用该算法模拟计算未达到平衡的反应过程,可以预测各板上的最大转化率和各板组成。     

Moderne Methoden der Meß- und Regelungstechnik und ihre Bedeutung für die Automatisierung verfahrenstechnischer Prozesse

Modern methods of measurement and control engineering and their significance for the automation of chemical engineering processes . This article demonstrates that modern system-theoretical methods open up new approaches in the solution of difficult measurement and control problems. These methods are frequently based on the assumption that a certain a priori knowledge of the process behaviour is available, which can be formulated as a mathematical process model. Model-supported measuring procedures are of particular significance and are discussed at length. These methods greatly enhance the information value of measured values, with regard to both extent and reliability. It is shown how the problem of early recognition of dangerous reaction states in reactors in the case of exothermic reaction can be overcome. In order to minimize the computational effort, methods of model reduction are considered.     

The continuum mechanical theory of multicomponent diffusion in fluid mixtures

The continuum mechanical approach for deriving the generalized equations of multicomponent diffusion in fluids is described here in detail, which is based on application of the principle of linear momentum balance to a species in a mixture, resulting in the complete set of diffusion driving forces. When combined with the usual constitutive equations including the continuum friction treatment of diffusion, the result is a very complete and clear exposition of multicomponent diffusion that unifies previous work and includes all of the various possible driving forces as well as the generalized Maxwell–Stefan form of the constitutive equations, with reciprocal diffusion coefficients resulting from Newton’s third law applied to individual molecular encounters. This intuitively appealing and rigorous approach, first proposed over 50 years ago, has been virtually ignored in the chemical engineering literature, although it has a considerable following in the mechanical engineering literature, where the focus, naturally, has been physical properties of multiphase fluid and solid mixtures. The described approach has the advantages of transparency over the conventional approach of non-equilibrium thermodynamics and of simplicity over those based on statistical mechanical or kinetic theory of gases or liquids. We provide the general derivation along with some new results in order to call attention of chemical engineers to this comprehensive, attractive, and accessible theory of multicomponent diffusion in fluids.     

Free radical polymerization engineering—I: A new method for modeling free radical homogeneous polymerization reactions

This paper deals with a new appraisal of free radical polymerization modeling. Classical properties of the distribution of polymerization degrees and methods for studying them thanks to the z-transform are recalled. When simple mechanisms are involved, the kinetics may be represented by a “detailed analytic” model relying on macromolecule balances. This is no longer possible when complex processes are occurring, e.g. transfer to polymer, β-scission, terminal double bond propagation… In order to deal with these more complex cases, a “tendency model” is proposed, relying on balances of quantities such as free radicals, macromolecules and the moments of the distribution of polymerization degrees. The quality of the polymer is described by chemical characters such as double bonds, long and short branching points, terminal double bonds… for which kinetic equations are established. Equations are given for calculating the moments of free radicals and those of instantaneously produced macromolecules via various processes. The simplicity and the usefulness of the method are illustrated by several examples and a comparison is made, when possible, with the detailed approach. Finally, equations are given, making it possible to calculate the quality of polymer produced in any kind of reactor and for different states of segregation.     

Development of transport equations for multiphase systems—II: Application to one-dimensional axi-symmetric flows of two phases

In the previous paper, we considered the problem of transport of a solute between two moving fluid phases, and developed a formalism that would allow a priori estimates of the transport parameters in the equations for the average solute concentration in each phase. In this work, the formalism is applied to the case of one-dimensional axi-symmetric flow of the two phases. The predictions of the model are compared to the exact solution of the governing differential equations for pulsed systems. The agreement between the computed average concentrations from the model and the point equations is excellent for all values of the physical parameters. An analysis of the model equations using the method of moments leads to equations for the mean pulse positions, velocities and rates of spread for long times.     

Steady-state multiplicity and bifurcation analysis via the newton polyhedron approach

A method based on the Newton polyhedron determines bifurcation of solution branches for simultaneous algebraic equations. This method has broad applicability in multiple steady-state analysis in chemical engineering. Reduction of the steady-state equations to a single nonlinear equation is not required. The method provides in nondegenerate cases the normal form of the algebraic equations—the leading nonlinear terms which alone determine steady-state multiplicity. Bifurcation conditions are developed for isothermal reaction between two adsorbed species in a catalytic CSTR and for two and three parallel reactions of arbitrary order in a nonisothermal CSTR.     

The effect of changes in initial reactant composition on solid-gas equilibria resulting from constant-volume,adiabatic processes

A method is given for the computation of the chemical equilibria attained by adiabatic chemical reactions in similar systems, all with the same volume and mass, as a result of changes in the initial reactant compositions. Changes in equilibrium composition and temperature are directly related to changes in the initial elemental abundances, in the form of a set of simultaneous equations. Since it is not necessary to perform complete calculations for each solution required, the solution of these equations constitutes a saving in computation. The method can be applied to solid-gas systems. The systems must be ideal or they have to obey an empirical equation of state, wherein covolume is a function of volume only.     

Phase equilibrium studying for the supercritical fluid extraction process using carbon dioxide solvent with 1.35 mole ratio of octane to ethanol mixture

Supercritical fluid extraction is a clean environmental chemical engineering process that has been given an interest to many researchers worldwide. The assessment of the feasibility of the extraction process utilizing a near critical solvent would be speeded up if it is possible to predict solubility data. Solubility data were measured for carbon dioxide with a mole ratio 1.35 of octane to ethanol using a phase equilibrium loading re-circulating high-pressure type apparatus at pressures up to 100 bar and at temperature 75 °C. The experimental data were then compared with calculated theoretical data which is calculated form the regular solution equations. A thermodynamic procedure is employed to each phase by applying activity coefficient expressions related to interaction parameters which are dependent on the pressure.