An application of metamodels for process optimization

Gomes, Marcos V.C.; Dávid, I.; Bogle, Leonard; Odloak, Darci; Biscaia, Evaristo C.

doi:10.1016/s1570-7946(06)80251-8

Cited by 3 publications

(5 citation statements)

References 10 publications

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“…45,59 It is an excellent way of interpolation compared with other meta-modelling techniques such as polynomial, regression splines, radial basis functions and artificial neural network. 1,31,32,33,44,60,61,62,63 Let be a set of training data points (also known as "design sites" in kriging) for developing the kriging model, each of which is a vector of input variables with dimension (…”

Section: The Kriging Meta-modelmentioning

confidence: 99%

“…which is a general type of kriging called universal kriging 33,34,45,54,64 for all the training data points. In this work, only the zero-th order polynomial is used which is termed "ordinary kriging" in the literature.…”

Section: The Kriging Meta-modelmentioning

confidence: 99%

“…which is a general type of kriging called universal kriging 33,34,45,54,64 . Here ( ) contains a set of regression functions of the input variables as determined by the modeller, and is the corresponding regression coefficients to be estimated.…”

Section: The Kriging Meta-modelmentioning

confidence: 99%

“…31,32 Later, the use of meta-models for real time optimisation was proposed by Gomes et al with the consideration of a typical alkylation process. 33 Furthermore, Gomes et al applied the same methodology to a crude distillation unit and solvents units. 34 More recently, Hoque developed CFD based multiple linear and neural network meta-models for bio-aerosol transport in indoor environments.…”

Section: Introductionmentioning

confidence: 99%

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Kriging meta‐model assisted calibration of computational fluid dynamics models

et al. 2016

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Computational fluid dynamics (CFD) is a simulation technique widely used in chemical and process engineering applications. However, computation has become a bottleneck when calibration of CFD models with experimental data (also known as model parameter estimation) is needed. In this research, the kriging meta-modelling approach (also termed Gaussian process) was coupled with expected improvement (EI) to address this challenge. A new EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chi-square distribution and hence existing normal distribution-based EI measures are not applicable. The new EI measure is to suggest the CFD model parameter to simulate with, hence minimising SSE and improving match between simulation and experiments. The usefulness of the developed method was demonstrated through a case study of a single-phase flow in both a straight-type and a convergent-divergent-type annular jet pump, where a single model parameter was calibrated with experimental data.Keywords: Calibration, computational fluid dynamics, expected improvement, Gaussian process, parameter estimation Correspondence concerning this article should be addressed to Tao Chen at t.chen@surrey.ac.uk. 2 IntroductionComputational fluid dynamics (CFD) simulations are usually large complex computer programs representing real life fluid systems. The complexity of such simulations can make them quite a herculean task to solve, with the run time associated with the simulation being of great concern. Such simulation run time could be for hours or days.1,2 In addition, large scale or complex systems usually place a great demand on computer memory. 3 Computation is especially a problem when the CFD simulation is required to run for a large number of times, for example when sensitivity analysis is carried out 1,4 , or the models are used within a certain optimisation problem. 4,5 Of particular interest in this research project is calibration of CFD models (also known as model parameter estimation), which can be cast into an optimisation problem.CFD model calibration can be defined as the process of adjusting numerical or physical parameters in the CFD model which, on obtaining the optimal values 6 , helps to improve agreement with experimental data. 7,8,9 The parameters in this context are typically turbulence model coefficients or turbulence model choice. The default values given by CFD software providers for turbulence parameters may apply only in standard circumstances. In this paper, calibration is formulated as an optimisation problem to minimise the mismatch between simulated and experimental outputs (responses). The calibration process may need tens to hundreds of simulation runs to evaluate the objective function, the sum of squared errors (where the errors quantify the differences between the simulated and the experimental outputs) over the region of interest, a requirement that is often infeasible for CFD.These difficulties faced by CFD simulations have led to the application of meta-modelling, whi...

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Section: The Kriging Meta-modelmentioning

confidence: 99%

Section: The Kriging Meta-modelmentioning

confidence: 99%

Section: The Kriging Meta-modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kriging meta‐model assisted calibration of computational fluid dynamics models

et al. 2016

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“…Derived metamodels can then be incorporated into reactor flow models, avoiding the necessity to solve catalyst pellet and reactor balance equations simultaneously. The development and use of metamodels constitutes an important tool that can be used for catalyst development and evaluation , and for process optimization, avoiding the necessity of solving very complex equations derived from phenomenological modeling.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Modeling of Methane Reformers. 1. A Metamodel for the Effectiveness Factor of a Catalyst Pellet with Complex Geometry

Alberton

Schwaab

Fontes

et al. 2009

Ind. Eng. Chem. Res.

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In this work, effectiveness factors for methane steam reforming reactions were obtained by solving mass and heat balance equations inside catalytic pellets for different reaction conditions and catalytic pellet geometries with the help of CFD (computational fluid dynamic) techniques. CFD computations were performed for real particle geometries and real kinetic rate expressions as described in the technical literature. A linear correlation was found between the effectiveness factor and the area/volume ratio, which characterizes the methane steam reforming as a diffusion-controlled process. The slopes of the straight lines depend of the external reaction conditions, thermal conductivity, and effective diffusivity. On the basis of the CFD results, empirical metamodels were built to represent effectiveness factors for methane steam reforming reactions at different reaction conditions. The metamodels can be easily inserted into a reactor model for simulation of the full industrial process.

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Meta‐Model‐Based Calibration and Sensitivity Studies of Computational Fluid Dynamics Simulation of Jet Pumps

Kajero

Thorpe

Yao³

et al. 2017

Chem Eng & Technol

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Calibration and sensitivity studies in the computational fluid dynamics (CFD) simulation of process equipment such as the annular jet pump are suitable for design, analysis, and optimization. The application of CFD for such purposes is computationally intensive. Hence, an alternative approach with kriging-based meta-models was utilized. Calibration via the adjustment of two turbulent model parameters, C m and C 2e , and likewise two parameters in the simulation correlation for C m was considered, while sensitivity studies were based on C m as input. The meta-model-based calibration aids exploration of different parameter combinations. Computational time was also reduced with kriging-assisted sensitivity studies which investigated the effect of different C m values on pressure distribution.

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An application of metamodels for process optimization

Cited by 3 publications

References 10 publications

Kriging meta‐model assisted calibration of computational fluid dynamics models

Kriging meta‐model assisted calibration of computational fluid dynamics models

Hybrid Modeling of Methane Reformers. 1. A Metamodel for the Effectiveness Factor of a Catalyst Pellet with Complex Geometry

Meta‐Model‐Based Calibration and Sensitivity Studies of Computational Fluid Dynamics Simulation of Jet Pumps

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