Estimation of the transfer function, time moments, and model parameters of a flow process

Zee, G.A. van; Schinkel, W. M. M.; Bosgra, О.H.

doi:10.1002/aic.690330227

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…1 In general, in a transient process, adsorption of a species will lower its concentration in the fluid phase and result in the PoA concentration being smaller than the PoS concentration. 2,3 Desorption, on the other hand, has the opposite effect and will result in the measured value at the PoA being higher than the concentration at the PoS.…”

Section: Introductionmentioning

confidence: 99%

“…The effect of the sampling line on the analysis of sample properties is basically due to the fluid transport effects (dispersion and residence time) in the line as well as the adsorption and desorption of fluid constituents on the surfaces of the sampling line parts that come into contact with the fluid . In general, in a transient process, adsorption of a species will lower its concentration in the fluid phase and result in the PoA concentration being smaller than the PoS concentration. , Desorption, on the other hand, has the opposite effect and will result in the measured value at the PoA being higher than the concentration at the PoS. − These errors and alteration of composition by the sampling line are not present during steady-state operations when all components come to equilibrium with the sampled fluid.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Sampling Line Characteristics on the Dynamic Monitoring of Fluid Concentrations

Juneja

Yao

Shadman

2009

Ind. Eng. Chem. Res.

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A novel approach is developed and demonstrated to characterize the sampling line effects during dynamic monitoring of fluid concentrations. The "sampling line" in this study refers to all components between the point of fluid sampling and the point of analyzer sensor. In general, sampling lines introduce errors in measurements by altering the sample properties due to the fluid transport in the line as well as the adsorption and desorption of fluid constituents on the surfaces of the sampling components that come into contact with the sample fluid. A methodology based on a sampling line simulator is developed for taking these effects into account and correcting the measurements. The model is validated by direct experimental measurements using several different analyzers under various conditions. The sampling line simulator can be used to analyze the effect of various sampling configurations and operating conditions; this would be helpful in the design of sampling lines and their location. An algorithm is proposed that can be used to convert concentration values measured and reported by the analyzer to the concentration values at the point of sampling that are the actual and desired values.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Sampling Line Characteristics on the Dynamic Monitoring of Fluid Concentrations

Juneja

Yao

Shadman

2009

Ind. Eng. Chem. Res.

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“…As applied to tracer testing, x ( t ) and y ( t ) may represent the responses of two sensors located in a flow process using the configuration shown in Figure 1 of Van Zee et al (1987). Also, x ( t ) could be the response of the combined tracer injection-sampling system when the test section of a flow process is removed, whiley(t) would be the response obtained when the test section is inserted in place (cf., Mills and Dudukovik, 1981;Wakao et al, 1980).…”

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confidence: 99%

Deconvolution of noisy tracer response data by a linear filtering method

Mills

Duduković

1988

AIChE Journal

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Deconvolution is used in a variety of areas to extract the impulse response e ( t ) of a linear system from experimental measurements of the system output y ( t ) and input excitation function x ( t ) . Some specific examples where deconvolution is important include: analysis of fluorescence decay data (Jakeman et al., 1978a); evaluation of transport functionals in the human circulatory system (Jakeman et al., 1978b;Jordinson et al., 1976); determination of transport properties of the phloem in plants (Minchin, 1978); interpretation of hydrological response data (Young, 1978); refinement and reconstruction of absorption spectra (Blass and Halsey, 1981); process control (Young et al., 1973); and impulse response estimation from chemical reactor tracer response data (Wen and Fan, 1975). A knowledge of the impulse response e ( t ) is a necessary first step for these and other related applications where model discrimination and parameter estimation are key objectives.For linear systems, the impulse response e ( t ) is related to the system input excitation function x ( t ) and system output y ( t ) by the convolution integral Random noise and measurement errors that are present in the experimental response data are represented by the unknown noise function n(t). As applied to tracer testing, x ( t ) and y ( t ) may represent the responses of two sensors located in a flow process using the configuration shown in Figure 1 of Van Zee et al. (1987). Also, x ( t ) could be the response of the combined tracer injection-sampling system when the test section of a flow process is removed, whiley(t) would be the response obtained when the test section is inserted in place (cf., Mills and Dudukovik, 1981;Wakao et al., 1980).The common approach for obtaining the impulse response from Eq. 1 is to use Fourier transforms. Applications of this method to Eq. 1 yields the following estimate of the Fourier transformed impulse response where j = and w denotes the frequency. Applying inverse Fourier transformation to Eq. 2, or so-called inverse filtering (Blass and Halsey, 1981), yields the following estimate of the time-domain impulse response where F-' denotes the inverse Fourier transform operator Expressions for the Fourier transform and its inverse operator are given in standard texts (cf., Churchill, 1972). In practice, evaluation of the Fourier transform and the inverse Fourier transform is often performed by numerical quadrature (Davis and Rabinowitz, 1975).When random noise and measurement errors in the data are sufficiently small, the quotient Y ( j w ) / X ( j w ) is well-behaved so that a reliable estimate of the time-domain impulse response 3(t) can be obtained. However, for many experimental systems, the errors in B ( j o ) defined by N ( j w ) / X ( j w ) either rapidly increase with increasing values of the frequency w, or randomly, vary in such a way that the estimate 2 ( t ) is obscured by noise. One objective of this paper is to briefly illustrate this observation using actual data collected in our laboratory from tric...

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A study of two-dimensional dispersion in unconsolidated porous media

1990

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An experimental and numerical investigation into the magnitude of longitudinal and transverse dispersion in a two-dimensional flow field over a particle Peclet number range of 50-8500 is reported. Numerical modelling using a Galerkin finite element method is used to test various models, notably those of Fried and combarnous and Koch and Brady. Dispersion at low Peclet numbers (<200) is found to be described adequately by either model, which at large Peclet, the degree of dispersion is significantly underestimated. An improved dispersion model for Peclet numbers greater than 200 is proposed. The transverse dispersion term and the choice of inlet boundary condition are found to have a negligible effect on the shape of the breakthrough curve.

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Estimation of the transfer function, time moments, and model parameters of a flow process

Cited by 4 publications

References 13 publications

Effect of Sampling Line Characteristics on the Dynamic Monitoring of Fluid Concentrations

Effect of Sampling Line Characteristics on the Dynamic Monitoring of Fluid Concentrations

Deconvolution of noisy tracer response data by a linear filtering method

A study of two-dimensional dispersion in unconsolidated porous media

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