An inverse approach for estimating the initial distribution of volatile organic compounds in dry building material

A model for the prediction of emission of volatile organic compounds (VOCs) from dry building material was developed based on mass transfer theory. The model considers both diffusion and convective mass transfer. In addition, it does not neglect the fact that, in most cases, the initial distribution of VOCs within the material is non-uniform. Under the condition that the initial amount of VOCs contained in the building material is the same, six different types of initial VOC distributions were studied in order to show their effects on the characteristics of emission. The results show that, for short-term predictions, the effects are significant and thus cannot be neglected. Based on the fact that the initial distribution of VOCs is very difficult to directly determine, a conjugate gradient method with an adjoint problem for estimating functions was developed, which can be used to inversely estimate the initial distribution of VOCs within the material without a priori information on the functional form of the unknown function. Simulated measurements with and without measurement errors were used to validate the algorithm. This powerful method successfully recovered all of the aforementioned six different types of initial VOC distributions. A deviation between the exact and predicted initial condition near the bottom of the material was noticed, and a twin chamber method is proposed to obtain more accurate results. With accurate knowledge of the initial distribution of VOCs, source models will be able to yield more accurate predictions.