Computation of optimal feed rates and operation intervals for tubular reactors

Birk, J.; Liepelt, Michael; Schittkowski, Klaus; Vogel, Frank

doi:10.1016/s0959-1524(98)00053-5

Cited by 14 publications

(8 citation statements)

References 10 publications

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“…Distributed systems often arise in chemical engineering, see for example the acetylene reactor discussed by Birk et al [5] in more detail.…”

Section: Distributed Systems (Acetyl T Acetyl Z)mentioning

confidence: 99%

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Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

Schittkowski

2007

GAMM-Mitteilungen

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In this paper we discuss a couple of situations, where algebraic equations are to be attached to a system of one-dimensional partial differential equations. Besides of models leading directly to algebraic equations because of the underlying practical background, for example in case of stationary equations, there are many others where the specific mathematical structure requires a certain reformulation leading to time-independent equations. To be able to apply our approach to a large class of real-life problems, we have to take into account flux formulations, constraints, switching points, different integration areas with transition conditions, and coupled ordinary differential algebraic equations (DAEs), for example. The system of partial differential algebraic equations (PDAEs) is discretized by the method of lines leading to a large system of differential algebraic equations which can be solved by any available implicit integration method. Standard difference formulas are applied to discretize first and second partial derivatives, and upwind formulae are used for transport equations. Proceeding from given experimental data, i.e., observation times and measurements, the minimum least squares distance of measured data from a fitting criterion is computed, which depends on the solution of the system of PDAEs. Parameters to be identified can be part of the differential equations, initial, transition, or boundary conditions, coupled DAEs, constraints, fitting criterion, etc. Also the switching points can become optimization variables. The resulting least squares problem is solved by an adapted sequential quadratic programming (SQP) algorithm which retains typical features of a classical Gauss-Newton method by retaining robustness and fast convergence speed of SQP methods. The mathematical structure of the identification problems is outlined in detail, and we present a number of case studies to illustrate the different model classes which can be treated by our approach.

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“…Distributed systems often arise in chemical engineering, see for example the acetylene reactor discussed by Birk et al [5] in more detail.…”

Section: Distributed Systems (Acetyl T Acetyl Z)mentioning

confidence: 99%

“…[34]. Another application from chemical engineering, the simulation model for an acetylene reactor, is given in form of a distributed system and consists of one temperature and nine reaction equations, all of first order, see Birk et al [5].…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

Schittkowski

2007

GAMM-Mitteilungen

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“…By an appropriate regularization of the objective function, strict convexity of f k ( y ) is guaranteed, see Zillober [50]. As shown there, the search direction (yk -xk, vk -u k ) is a descent direction for the augmented Lagrangian merit function (4,5), see also (6). The approximation scheme (10) can be applied only to inequality constraints.…”

Section: Sequential Convex Programmingmentioning

confidence: 99%

“…In both cases, we know initial values either in the form of time-dependent feed control functions or a constant tube diameter. Alternative approaches to compute optimal reactor feed rates are discussed in Birk et al [4], and Liepelt and Schittkowski [20]. We consider a chemical reactor producing acetylene (C2H2), reacting methane (CH4) in natural gas with oxygen.…”

Section: Case Study: Optimal Control Of An Acetylene Reactormentioning

confidence: 99%

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Nonlinear Programming: Algorithms, Software, and Applications

Schittkowski

Zillober

2005

IFIP International Federation for Information Processing

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A b s t r a c tWe introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The methods are outlined in a uniform way and the results of some comparative performance tests are listed. We especially show the suitability of sequential convex programming methods to solve some classes of very large scale nonlinear programs, where implicitly defined systems of equations seem to support the usage of inverse approximations. The areas of interest are structural mechanical optimization, i.e., topology optimization, and optimal control of partial differential equations after a full discretization. In addition, a few industrial applications and case studies are shown to illustrate practical situations under which the codes implemented by the authors are in use.

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SQP versus SCP Methods for Nonlinear Programming

Schittkowski

Zillober

Applied Optimization

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Computation of optimal feed rates and operation intervals for tubular reactors

Cited by 14 publications

References 10 publications

Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

Nonlinear Programming: Algorithms, Software, and Applications

SQP versus SCP Methods for Nonlinear Programming

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