A simulation package for the plato educational computer system

A simulation package has been developed for the PLATO educational computer system which allows the user to apply numerical and graphical solution techniques to small-scale problems. Current state-of-the-art numerical algorithms are used with the interactive graphic capabilities of a PLATO terminal to provide efficient problem solution in less than a minute of terminal time. Convenient entry, execution, modification, and output options are combined with on-line input error detection and extensive error messages. Although primarily intended for educational purposes, industrial users will also find this package very efficient for solving small-scale problems.     

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.     

The ascend-II system—a flowsheeting application of a successive quadratic programming methodology

This paper describes ASCEND-II, an interactive equation based flowsheeting system capable of doing performance, design and optimization calculations with comparable ease. The optimization capability is a new, as yet unpublished, successive quadratic programming method operating in the reduced space which is the size of the degrees of freedom for the problem. Its performance is very encouraging.We spend considerable time describing the ASCEND-II system details because we believe the concepts underlying it make the system a powerful aid for design. It allows one to evolve toward the solution to a problem by allowing one to add and delete model complexity, interactively alter which variables are to be calculated and which fixed, single step through the convergence of a model, move easily from design to optimization and back, use any variable as an objective to be maximized or minimized, and to place an upper or lower bound on any variable desired.     

Large scale nonlinear programming

Our ability to solve large nonlinear programs has increased significantly in the last several years. New algorithms have been developed, existing ones have been refined, some good software has been developed, and there has been some computational experience and practical applications. This paper summarizes some of this activity, focusing on Successive Linear Programming (SLP), Successive Quadratic Programming (SQP), and Generalized Reduced Gradient (GRG) algorithims.     

A pilot-scale distillation facility for digital computer control research

A new pilot-scale multicomponent distillation facility and associated computer control system are described. The control system design utilizes a hierarchical structure, with a microcomputer for direct digital control of secondary process variables and a general-purpose, real-time computer for high-level control of the primary variables. The facility is used for advanced process control research and real-time system instruction. Some typical results incorporating a new multivariable predictive control algorithm are presented.     

Applications of mixed-integer linear programming in process synthesis

It is shown that important problems arising in process synthesis can be tackled effectively using mixed-integer linear programming techniques. Two examples are considered: the synthesis of chemical complexes that maximize its present value for a given number of periods where prices and demands fluctuate; and the synthesis of stream generation systems that minimize the total annual cost. Numerical results are presented for both cases.     

GRIP: A problem-oriented language

GRIP (GeneRal Interactive Processor) is a problem-oriented language which establishes a powerful and convenient communication linkage between engineer and computer. GRIP is implemented in a set of programs which provide its capabilities for command translation, on-line programming and small database management. The GRIP application program, written using the grammer of the language, provides access to one or more task specific programs and to utility resources such as numerical methods and interactive graphics packages. This paper describes the structure and function of GRIP applications which support chemical engineering education and research activities.     

An approach to large-scale nonlinear programming

Due to changing matrix elements, many of the computational benefits embodied in sparse matrix theory and implemented in commercial LP codes for maintaining a sparse matrix inverse updates are lost for NLP. This paper reports on the results of investigating the use of structural decomposition in large, sparse NLP problems using the GRG algorithm. The approach is to partition the basis matrix into block lower triangular (BLT) form. At each step of the GRG algorithm, all operations are based upon the smaller diagonal subsets of variables.This approach led to the development of an algorithm to dynamically order a square matrix into block, lower triangular form after a column replacement. The method is fast, showing computational time reductions of up to a factor of 10 over performing the ordering on the complete occurrence matrix, while requiring a minimal amount of computer memory. Only one subset of the occurrence matrix followed by only the condensed occurrence matrix is required in computer memory to order the modified matrix. The algorithm is applicable to any numerical method which requires structural modification of a matrix by changing the structure of one column.An experimental GRG computer code, called GRGLSS, was developed for testing the technique. Examples demonstrate significantly faster computation speeds in the feasibility phase of the GRG algorithm.     

Application of mixed-integer linear programming in multiterm expansion planning under multiobjectives

A procedure to expand plant capacities over a time horizon is presented under multiobjectives. A stepwise interactive approach has been proposed to formulate a problem that is small but complete enough to provide a best-compromise solution for decision-making. The approach relies on the relaxation of flexible constraints and the sensitivity analysis of linear programming. It yields the significant feature of identifying the expansion increments associated with specific objectives or with structural infeasibility. The resulting multiobjective mixed-integer linear programming problem was solved advantageously by an interactive goal programming algorithm. An illustrative example is provided to clarify the procedure and show its computational effectiveness.     

Exxon experience with large scale linear and nonlinear programming applications

Exxon has been a large user of linear programming since its introduction. Exxon's primary large scale math programming system has evolved to also include facilities for sucessive linear programming and mixed integer programming. Some of Exxon's other math programming tools for quadratic programming and succesive quadratic programming are also described in this paper. Results of a recent study conducted to compare the performance of Exxon's succesive linear programming and successive quadratic programming techniques with the reduced gradient technology employed in other programs are presented.     

On the formulation of optimal water allocation problem by linear programming

A problem of maximizing the efficiency of water use in industry is considered as a problem of optimizing water allocation in a total system which consists of water using and treating sub-systems. A problem formulation presented here is directed toward the iterative use of the linear programming based on characteristics specific to water allocation problems.     

Development of transport equations for multiphase system—I: General Development for two phase system

The spatial averaging theorem is used to develop transport equations for the average concentration of a solute being distributed between two phases by convection, diffusion, and interfacial transport. Closure schemes are formulated for the spatial deviations in concentration by developing transport equations for these deviations. This formalism allows a priori predictions of the transport parameters. What results is a two-equation model, one equation for the average interstitial solute concentration in each phase. From a moment analysis of the resulting averaged equations, one can predict model behavior for long times in pulsed systems. It is found that the pulse velocities in each phase become equal and constant, and that the two equati model described here reduces to a single dispersion equation for sufficiently long times.     

Simulation of batch crystallization

The closed mathematical model of a well-mixed batch crystallizer has been presented. This model takes into consideration crystals growth rate fluctuations producing an increased spread of crystal sizes. The numerical methods for solving partial integro-differential system of this model equations are proposed for the cases of when growth rate is expressible as product of supersaturation and size functions.Simultaneous population and mass balance equations have been calculated together with power law kinetics of nucleation and growth to determine crystal-size distribution functions (CSD), variation coefficients (CV), produced crystal sizes and numbers. The case of size-dependent crystal growth determined by sequential processes of diffusion and surface reaction is also investigated.The computer results are presented in the dimensionless form as functions on both diffusion and fluctuation Peclet numbers and dimensionless cooling rate. In particular, it has been established that the CV of weight CSD increases approximately twice due to fluctuations and becomes close to 40%; the CV also increases owing to the decrease of cooling rate and approaches 28%. Some formulae are suggested for predicting the kinetics of crystallization (or precipitation) and determining the kinetic parameters of crystals growth and nucleation.     

Approximation programming of chemical processes—1: Optimization of flowtran® models

A FLOWTRAN® modelled ammonia synthesis loop has been optimized by Quadratic Approximation Programming (QAP),—a method based on successive quadratic approximation to the plant objective and constraint functions. The algorithm is easily adapted to FLOWTRAN and functions efficiently. In two examples, the total computing time for optimization is only about 65 times that for a single simulation. this is a significant improvement over earlier studies.     

A study of the development of a mexican petrochemical industry using mixed-integer programming

A large interactive system such as the petrochemical industry requires a model that can account for the different interactions among units, providing at the same time a suitable mathematical representation of the variables of interest. In this work, a model for the development of a Mexican petrochemical industry is presented. The system is formulated as a Mixed-Integer Programming model, where installing a process is compared on an economic basis to importing its corresponding product. This formulation lets the model take economies-of-scale into account which are shown to be a very decisive factor in the selection of chemical processes, since a simple linear model does not seem to provide an adequate tool for the planning and development of a Mexican petrochemical industry. A heuristic approach using multiple linear programs is also discussed.     

An improved algorithm for diagnosis of system failures in the chemical process

The detailed techniques for improving the efficiency of a fault-diagnosis algorithm can be based on the signed directed graph. This graph represents the structure of the system, and the pattern on the graph represents a state of the system. The usefulness of the improved algorithm is demonstrated using a model of a chemical process comprising a reactor, a heat exchanger and a distillation tower.     

Development of an expert system for physical property predictions

In this article we describe the steps followed to develop a prototype expert system called CONPHYDE (CONsultant for PHYsical property DEcisions). Using the framework of the existing expert system PROSPECTOR, CONPHYDE is designed to aid an engineer in the selection of an appropriate vapor-liquid equilibrium method when performing various process calculations. We also present the structure of the inference networks in CONPHYDE which capture the intent of the 37 heuristic rules that from the knowledge base on which the current version is based. An example session with CONPHYDE demonstrates its ability to ask questions in an “intelligent” sequence and provide “expert” advice based on them. The session also illustrates CONPHYDE's (i.e. PROSPECTOR's) ability to explain on request why it is asking certain questions and why it is offering the advice it is.     

Effectiveness factor and selectivity estimation for a parallel reaction system

The case of double parallel reaction scheme taking place in a porous catalytic pellet is analyzed. Effectiveness factor expressions for both reactions are derived after matching asymptotic solutions strictly valid for small and large values of the Thiele moduli.It is assumed that the kinetics of both reactions follow a general irreversible power law model, that isothermal conditions prevail and that external mApproximate results in terms of effectiveness factors compare fairly well with exact results obtained by numerical integration of the differential equa     

Simulation of an extraction column

An efficient program for the simulation of an extraction column is described. Many alternate numerical methods were tested. The final version of the program uses Newton's method combined with a search along the damping factor, and Gauss Elimination with limited normalization for the inversion of the Jacobian. The Jacobian is stored as a vector. The program is compared with published programs and is efficient and reliable.     

Simulation of air-cooled heat exchangers

An algorithm is presented for the simulation of air-cooled finned tubes heat exchangers with topological configuration which preclude the use of method based on overall coefficients and mean temperatures differences. It is a generalization of the step by step method arising when the transfer area of each tube is divided into a finite number of elements. The heat transfer rate equations and the energy balances corresponding to all the elements of all tubes constitute a system of linear equations which is solved iteratively.