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32
Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models
 IND. ENG. CHEM. RES
, 1998
"... The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution meth ..."
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Cited by 32 (21 self)
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The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution methods are initialization dependent, and may fail by converging to trivial or nonphysical solutions or to a point that is a local but not global minimum. Thus there has been considerable recent interest in developing more reliable techniques for stability analysis. Recently we have demonstrated, using cubic equation of state models, a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. However, there is much room for improvement in the computational efficiency of the technique. In this paper we consider two means of enhancing the efficiency of the method, both based on sharpening the range of interval function evaluations. Results indicate that by using the enhanced method, computation times can be reduced by nearly an order of magnitude in some cases.
Robust phase stability analysis using interval methods
 In AIChE Symp. Ser
, 1995
"... Conventional equation solving and optimization techniques for solving the phase stability problem may fail to converge or may converge to an incorrect result. A technique for solving the problem with mathematical certainty is needed. One approach to providing such assurance can be found in the use o ..."
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Cited by 23 (22 self)
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Conventional equation solving and optimization techniques for solving the phase stability problem may fail to converge or may converge to an incorrect result. A technique for solving the problem with mathematical certainty is needed. One approach to providing such assurance can be found in the use of interval methods. An interval Newton/generalized bisection technique is applied here to solve the phase stability problem. Results for two models of liquidphase systems, using several different feed compositions, indicate that the technique used is reliable and very efficient.
Nonlinear Parameter Estimation Using Interval Analysis
, 1999
"... The reliable solution of nonlinear parameter estimation problems is an important computational problem in chemical process engineering, both in online and offline applications. Conventional solution methods may not be reliable since they do not guarantee convergence to the global optimum sought in ..."
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Cited by 17 (8 self)
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The reliable solution of nonlinear parameter estimation problems is an important computational problem in chemical process engineering, both in online and offline applications. Conventional solution methods may not be reliable since they do not guarantee convergence to the global optimum sought in the parameter estimation problem. We demonstrate here a technique, based on interval analysis, that can solve the nonlinear parameter estimation problem with complete reliability, providing a mathematical and computational guarantee that the global optimum is found. As an example, we consider the estimation of parameters in vaporliquid equilibrium (VLE) models. Twelve VLE data sets are fit to the Wilson equation. Results indicate that several sets of published parameter values correspond to local optima only, with new globally optimal parameter values found by using the interval approach. Keywords Parameter estimation, Global optimization, Interval analysis, Vaporliquid equilibrium Intro...
Reliable Computation of Reactive Azeotropes
, 2000
"... The determination of the existence and composition of reactive azeotropes is important from both theoretical and practical standpoints in the analysis of combined reaction and phase equilibrium and in the synthesis and design of reactive separation systems. We present here a new method for reliably ..."
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Cited by 17 (3 self)
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The determination of the existence and composition of reactive azeotropes is important from both theoretical and practical standpoints in the analysis of combined reaction and phase equilibrium and in the synthesis and design of reactive separation systems. We present here a new method for reliably locating, from given thermodynamic models, any and all reactive azeotropes for multicomponent mixtures. The method also verifies the nonexistence of reactive azeotropes if none are present. The method is based on interval analysis, in particular an intervalNewton/generalizedbisection algorithm that provides a mathematical and computational guarantee that all reactive azeotropes are located. The technique is general purpose and can be applied in connection with any thermodynamic models. We illustrate the technique here using several example problems. In two cases, the liquid phase is modeled as ideal; in the other cases, liquid phase nonideality is modeled using either the Wilson or NRTL equ...
Reliable phase stability analysis for excess Gibbs energy models
 CHEM. ENG. SCI
, 2000
"... Because models used to represent the Gibbs energy of mixing are typically highly nonlinear, the reliable prediction of phase stability from such models is a challenging computational problem. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear ..."
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Cited by 15 (10 self)
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Because models used to represent the Gibbs energy of mixing are typically highly nonlinear, the reliable prediction of phase stability from such models is a challenging computational problem. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. However, conventional solution methods are initialization dependent, and may fail by converging to trivial or nonphysical solutions or to a point that is a local but not global minimum. Since the correct prediction of phase stability is critical in the design and analysis of separation processes, there has been considerable recent interest in developing more reliable techniques for stability analysis. Recently we have demonstrated a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. In this paper, we demonstrate the use of this technique in connection with excess Gibbs energy models. The NRTL and UNIQUAC models are used in examples, and larger problems than previously considered are solved. We also consider two means of enhancing the efficiency of the method, both based on sharpening the range of interval function evaluations. Results indicate that by using the enhanced method, computation times can be substantially reduced, especially for the larger problems.
Reliable Computation of Homogeneous Azeotropes
 AIChE J. 1998
, 1998
"... The determination of the existence and composition of azeotropes is important both from theoretical and practical standpoints. An important test of the veracityofthermodynamic models is whether or not known azeotropes are predicted, and whether or not they are predicted accurately. Model parameters ..."
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Cited by 15 (8 self)
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The determination of the existence and composition of azeotropes is important both from theoretical and practical standpoints. An important test of the veracityofthermodynamic models is whether or not known azeotropes are predicted, and whether or not they are predicted accurately. Model parameters can be #ne tuned by comparing the model predictions can be used as starting points for experimental searches for actual azeotropes. These azeotropes often present limitations in process design whichmust be known, and their determination strictly from experiment alone can be expensive.
New Interval Methodologies for Reliable Chemical Process Modeling
 COMPUT. CHEM. ENG. 2002
, 2002
"... The use of interval methods, in particular intervalNewton/generalizedbisection techniques, provides an approach that is mathematically and computationally guaranteed to reliably solve difficult nonlinear equation solving and global optimization problems, such as those that arise in chemical proces ..."
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Cited by 10 (8 self)
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The use of interval methods, in particular intervalNewton/generalizedbisection techniques, provides an approach that is mathematically and computationally guaranteed to reliably solve difficult nonlinear equation solving and global optimization problems, such as those that arise in chemical process modeling. The most significant drawback of the currently used interval methods is the potentially high computational cost that must be paid to obtain the mathematical and computational guarantees of certainty. New methodologies are described here for improving the efficiency of the interval approach. In particular, a new hybrid preconditioning strategy, in which a simple pivoting preconditioner is used in combination with the standard inversemidpoint method, is presented, as is a new scheme for selection of the real point used in formulating the intervalNewton equation. These techniques can be implemented with relatively little computational overhead, and lead to a large reduction in the number of subintervals that must be tested during the intervalNewton procedure. Tests on a variety of problems arising in chemical process modeling have shown that the new methodologies lead to substantial reductions in computation time requirements, in many cases by multiple orders of magnitude.
LP Strategy for IntervalNewton Method in Deterministic Global Optimization
, 2004
"... A strategy is described for using linear programming (LP) to bound the solution set of the linear interval equation system that must be solved in the context of the intervalNewton method for deterministic global optimization. An implementation of this technique is described in detail, and several i ..."
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Cited by 9 (3 self)
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A strategy is described for using linear programming (LP) to bound the solution set of the linear interval equation system that must be solved in the context of the intervalNewton method for deterministic global optimization. An implementation of this technique is described in detail, and several important issues are considered. These include selection of the interval corner required by the LP strategy, and determination of rigorous bounds on the solutions of the LP problems. The impact of using a local minimizer for updating the upper bound on the global minimum in this context is also considered. The procedure based on these techniques, LISS LP, is demonstrated using several global optimization problems, with focus on problems arising in chemical engineering. Problems with a very large number of local optima can be effectively solved, as well as problems with a relatively large number of variables.
Reliable computation of phase stability and equilibrium from the SAFT equation of state
 Industrial and Engineering Chemistry Research
, 2002
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