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An inverse technique to determine volatile organic compounds diffusion and partition coefficients in dry building material

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Abstract

A mass transfer theory based model describing volatile organic compounds (VOCs) diffusion in dry building material was presented. Effects of some key parameters on the model output were theoretically studied. An inverse method was developed to estimate the diffusion coefficient (D) and partition coefficient (K) of VOC/material combination by utilizing dynamic chamber emission data. The present inverse parameter estimation problem was solved with Levenberg–Marquardt method of minimization of the ordinary least-squares norm. Sensitivity analysis showed the feasibility of simultaneous estimation of D and K. The present inverse method was first validated by a theoretical case. Measurements with different error levels were used to show their effects on the accuracy of the estimates. Results indicate that the present inverse method can be used to accurately estimate both D and K with the additional information of measured VOC concentration in chamber. Then experimental data of styrene/carpet combination obtained from standard field and laboratory emission cell emission test were used to determine D and K using the validated inverse method. Reliable results were obtained.

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Abbreviations

C a :

Concentration in chamber/FLEC air (kg/m3)

C :

Concentration in the material (kg/m3)

C 0 :

Initial concentration (kg/m3)

C as :

Concentration in the chamber/FLEC air at the air/material interface (kg/m3)

D :

Diffusion coefficient (m2/s)

K :

Partition coefficient

h m :

Mean convective mass transfer coefficients (m/s)

b :

Thickness of material slab (m)

N :

Air exchange rate (s−1)

L :

Loading ratio (m2/m3)

Re:

Reynolds number

Sc:

Schmidt number

Sh:

Sherwood number

u m :

Mean air velocity of the air over the material (m/s)

x :

Coordinate (m)

t :

Time (s)

J :

Sensitivity matrix

J P :

Relative sensitivity matrix

P :

Vector of unknown parameters

σ:

Standard deviation of the measurements

ν:

Kinematic viscosity of air (m2/s)

μ:

Damping parameter

ɛ:

Tolerance

a:

Air-phase

T:

Transpose

k :

Iteration number

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Acknowledgements

This research was funded by the PolyU 2000/01 grant for large equipment, and by the RGC CERG PolyU 5023/02E grant.

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Authors and Affiliations

  1. Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China

    F. Li & J. L. Niu

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  1. F. Li
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  2. J. L. Niu
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Correspondence to F. Li.

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Li, F., Niu, J.L. An inverse technique to determine volatile organic compounds diffusion and partition coefficients in dry building material. Heat Mass Transfer 41, 834–842 (2005). https://doi.org/10.1007/s00231-004-0614-5

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