Interactive solution to multiple criteria problems in chemical process design: An approach by pairwise comparison

A process design problem is considered as a multiobjective problem that is characterized by conflicting objectives such as economics, operability, and so on. A method developed for solving multiobjective problems in man-machine interactive mode has been extensively applied to the basic process design of chemical process systems. AS an illustrative example, an optimal design of a simple, yet practical, chemical process system has been taken up to show the practical usefulness of the present method.     

An interactive process flowsheeting and simulation system based on relational data structures

An interactive graphical interface has been developed for a modular-sequential steady-state chemical process simulation program. The interface software, called AGPSS (A Graphical Process Simulation System), consists of FORTRAN-IV routines for creating new equipment unit schematics, for drawing a process flowsheet, for accepting process equipment and stream parameters, for performing automatic analysis for recycle nets, for supervising execution of the steady-state material and energy balancing simulator, and for displaying results. The program is designed to operate from refresh terminals functioning as remote time-sharing devices on the University of Michigan's Amdahl 470V/6 computing system. The Integrated Graphics (IG) software package is used for all interactive graphical operations.

All data, including both picture and process information, are organized in a relational data structure containing a total of thirteen relations. The general algorithms for addition, retrieval, and deletion of data in the relational structure require just six set-theoretic operators, which are encoded as FORTRAN utility routines. These data structures and the associated set operators assisted materially in simplifying the design, programming, and testing of the interactive graphical interface.     

Some characteristics of chemical crystallization in water purification process

Technological scheme for water purification using coprecipitation was analysed. Crystallization of BaCO₃ under the conditions of rapid mixing of reagent solution was investigated with special emphasis on: size distribution of crystals and aggregates by states in time, intensities of nucleation and growth of crystals, mean frequency of molecule binding to the surface during growth, etc. This analysis and results show that the above characteristics must be taken into account in optimization of the technological scheme.     

An improved biased difference scheme for the solution of hyperbolic equations by the method of lines

An upstream biased differencing scheme is presented for the solution of hyperbolic partial differential equations by the method of lines. The parameters in the difference formula are functions of the grid spacing and can give accuracy between first and second order. Testing has indicated that an order of 1.5 leads to a reasonable balance between stability and accuracy for typical problems. The mmethod is successfully demonstrated on hyperbolic equations which do not have shock discontinuities and is shown to be an effective means of solving coupled sets of hyperbolic and parabolic equations.     

Sparse matrix methods for equation-based chemical process flowsheeting—I: Reordering phase

Four new sparse matrix reordering algorithms, varying in degree of sophistication, are described. These and five other algorithms, including the P4 and hierarchical partitioning algorithms, are compared on the basis of reordering time and performance. Two of the new techniques offer overall improvement on randomly generated matrix structures, while another performs extremely well on flowsheeting matrices.     

Sparse Matrix Methods for equation-based chemical process flowshweeting—II: Numerical Phase

Five new general-purpose sparse matrix codes are described, two based on routine Gaussian elimination, and three on improvements of other algorithms we have described elsewhere. These, as well as two currently available and well regarded codes, MA28 and NSPIV, are compared on the basis of their perfomance with respect to solution time and storage requirements. One of the new codes performs especially well on randomly structured problems, while this code, as well as the other new codes, prove more capable than either MA28 or NSPIV on flowsheeting problems.     

PEFLOQ: An algorithm for the bifurcational analysis of periodic solutions of autonomous systems

The paper describes a numerical algorithm, and its computer implementation PEFLOQ, for the bifurcational analysis of both stable and unstable periodic solutions of autonomous systems of ordinary differential equations dependent on a real parameter. The problem is posed as a boundary-value eigenproblem on the unit time interval, then solved iteratively by the Newton-Fox method (Fox & Langer [9], Kubicek & Hlavacek [10], Keller [11]) for the unknown period, and a point on the solution. An automatically determined shifting fixed-component-index device (Chua & Lin [12]) is employed to fix its phase. Related variational matrix equations (Keller [11]) are integrated simultaneously with the primary set and used in the iterative corrections. One of these matrices (the monodromy matrix) yields the Floquet multipliers or stability modes of the limit cycles. Continuation is effected by alternatively considering the problem at each parameter value as requiring the solution of a system of algebraic equations. A Euclidean arc-length continuation procedure with adaptive step-sizing (Kubicek [13]) is incorporated into PEFLOQ and enables such a continuation, including computations past turning points.     

The use of a computer algebra system in the analysis of chemical engineering problems

Computer algebra systems are powerful processors designed to treat formal mathematical expressions. Routine features include many operations that occur frequently in the analysis of engineering problems, and provide the analyst with a powerful and reliable tool for manipulating algebraic, differential and integral equations. The power and general utility of one particular computer algebra system is first demonstrated on two elementary examples—the first involving the solution of an ordinary differential equation by weighted residual techniques, and the second, a perturbation solution of Duffing's equation. Ideas stemming from these examples are then applied to a current research problem involving the determination of the amplitude and frequency of self-sustained density wave oscillations in a once-through evaporator. All examples show the power of this system in handling large amounts of tedious algebra with relative ease, thus eliminating the potential for manual error.     

An improved group method for hydrocarbon-hydrocarbon systems arising from a comparative study of asog and unifac

A comparison of the formalism of ASOG, in the version of Kojima and Tochigi, and of UNIFAC shows the total formal equivalence of both empirical group methods for calculating activity coefficients in mixtures. The most advantageous features of each method are taken into account in the formulation of an improved method for hydrocarbon-hydrocarbon systems. Parameters for CH₂/ArCH, CH₂/CyCH, CH₂CH, ArCH/CyCH, ArCH/CH and CyCH/CH are evaluated from total pressure- liquid composition and heats of mixing data using the SIGMA procedure. The results obtained with the three empirical group methods are compared with experimental data. The ability to predict activity coefficients at infinite dilution is discussed.     

An improved mercury porosimetry apparatus — some magnetic tape applications

An improved mercury porosimetry apparatus is described. A commercially available Carlo Erba porosimeter Type 200 was made 10 times more sensitive and connected with a Philips PM 4410 minicomputer for ease of data handling and calculation.The correction for compressibility of the dilatometer was examined. The compressibility coefficient of mercury and its dependence on pressure was taken from literature data. The compressibilities of the glass dilatometer were calculated from porosimetry data.The compressibilities of a number of polymers were measured. The dependence of the compressibility of these polymers on pressure was also determined.Some pigment powders and magnetic tape samples were analyzed by mercury porosimetry with correction for compressibility.     

Period doubling and complex dynamics in an isothermal chemical reaction system

Stability and bifurcation theory have been used to organize a computational study of the dynamics of a three-variable isothermal reaction system with quadratic kinetics. This system exhibits a cascade of period-doubling bifurcations over decreasing intervals of parameter changes. This simple example illustrates a wide variety of complicated dynamics and shows that the qualitative dynamic features of isothermal reaction systems may be extremely sensitive to parameter values.     

Computer-aided reaction system synthesis based on structured process energy-exergy-flow diagram

A computerized thermodynamics-oriented procedure for reaction system synthesis is proposed. First, hierarchy structure of chemical reactions is discussed and the reaction system is categorized into three types; (1) combination with a heat source or sink, (2) combination with a reaction donor, and (3) decomposition of target reaction into subtargets. Then, the algorithm to find subtarget reactions and/or donor reactions is presented.     

An efficient tearing algorithm based on minimum sum of weights

A simple but efficient tearing algorithm for decomposition of chemical process flowsheets is described. It does not involve the use of signal flow diagrams or manipulation of any matrices. All the streams are assigned definite weights and the cut-set of tear streams is found by minimizing the sum of weights. The algorithm is equally efficient when arbitrary weights are assigned.     

A model-based scheme for the on-line optimization of a liquid extraction process

The on-line optimization of a liquid extraction process using a model-based scheme is described. Four steady-state process models are first investigated for their ability to predict the process performance; these models are subsequently used in the optimization study. The optimization scheme incorporates a simple model-updating technique and is based on an efficient method for constrained optimization which has been developed as part of this study. Rapid convergence to the true process optimum occurs, provided the predictions of the direction of change of the objective function are locally correct. In a few cases, however, poor model predictions result in failure to converge, or give convergence to a point other than the true optimum.     

Designing heat exchanger networks for existing chemical plants

New targets for the heat exchanger network synthesis problem, which account for both heating and power needs, are defined. Especially useful when updating existing facilities, the proposed targets stand for both the maximum heat flow to be recovered and the types and number of heating utilities to be allocated if all plant energy requirements are to be satisfied at the lowest fuel cost. The new goals are computed by solving a small-scale nonlinear programming problem introduced in this paper. Accounting for them, a heat exchanger network involving a low number of units is synthesized using the transportation formulation¹. The results clearly show the economic disadvantages of recycling process heat beyond a certain limiting value, unless bottlenecks in the current steam-power system, precluding further fuel savings, are removed.     

Thermal radiation controlled ignition/extinction phenomena in a system of separated catalyst layers with exothermal chemical reaction

In analogy to fixed beds ignition/extinction phenomena were observed in an exothermic and adiabatic chemical tubular reactor containing ten separated layers of catalyst particles. Obviously the thermal feed back by radiative exchange caused the system to perform like a quasihomogeneous medium. The application of the two phase homogeneous model equations revealed that the predicted ignition temperatures, which agreed well with those measured in a packed bed, were on the average 10 K lower than those measured in the multilayer system. This result is attributed to the missing contact points which in packed beds are privileged areas for the progress of ignition.     

A numerical study of the Jacobson-Oksman algorithm

The Jacobson-Oksman algorithm is a method for finding the unconstrained minimum of homogeneous functions. The optimal solution is obtained by solving a set of (n + 2) linear equation by a method based on Householder updating. The method has some very attractive features including robustness and rapid convergence, and it does not require accurate one dimensional searches. However, to date, little if any use has been recorded in the literature.We have studied the properties of the algorithm and also compared the method with the Fletcher-Reeves and Davidon-Fletcher-Powell methods. We have found the Jacobson-Oksman method to be superior to the former and comparable to the latter on general nonlinear functions. Therefore we recommend the Jacobson-Oksman algorithm as a competitive alternative to the celebrated class of quasi-Newton methods for unconstrained minimization.     

Rectification of process measurement data in the presence of gross errors

A systematic strategy is developed for the location of the source and the rectification of gross, biased measurement errors in a chemical process. The proposed strategy proceeds in three levels: (a) A structural analysis of the balance equations identifies subsets of balances with measurements which are suspected to possess gross errors. (b) A sequential analysis of the balance equations with suspect measurements further reduces the size of the problem. Statistical criteria are used in this step. (c) Finally, a sequential analysis of the suspect measurements appearing in the reduced set of balances leads to the identification of the source of the gross errors.The proposed strategy: (i) reduces the size of the data reconciliation problem significantly, even for large-scale chemical processes, (ii) is computationally simple and (iii) it conforms with the general process of variable monitoring in a chemical plant.Numerical examples are presented to clarify the elements of the procedure involved and demonstrate their value and effectiveness in dealing with realistic situations.     

An analysis of chemical reactor stability and control—XVI: The stochastic stirred pot

A continuous stirred tank reactor subject to random fluctuations in flow rate and inlet temperature was simulated on a hybrid computer. The stochastic response of the reactor about unique stable deterministic steady states was studied as a function of the damping coefficient and response time of the deterministic system and the power spectrum of the stochastic input. It was found that the stochastic response could be classified into categories similar to those used for forced periodic systems according to the relationship between the deterministic system response time and the 90% cut-off frequency of the stachastic input. The nature of the stochastic response is predictable for relatively low frequency inputs but unexpected results may occur at intermediate frequencies. The magnitude of reactor state fluctuations was seen to be dependent on the deterministic damping coefficient. The distribution of reactor states was studied as a function of input process variance and it was found that the distribution can become bimodal even when the associated deterministic steady state is unique.The concept of stochastic stability is discussed and several practical stochastic stability definitions are proposed. The stochastic stability of the random systems was seen to be well described by the stochastic regions of operation predicted by the input process power spectrum and the deterministic system response time. The input variance levels necessary to produce stochastic instability can be estimated in the Quasi Steady region of operation. It was found that exposure of an autonomous limit cycle about a unique unstable deterministic steady state to high frequency random inputs may lead to effective stabilization.