Analysis of the Shrinkage Effect on Mass Transfer During Convective Drying of Sawdust/Sludge Mixtures

Convective drying of wastewater sludges and sawdust/sludge mixtures was studied. The first part of this work was an experimental study performed in a cross-flow convective dryer using 500 g of wet material extruded through a disk with circular dies of 12 mm. The results showed that the sawdust addition has a positive impact on the drying process from a mass ratio of 2/8, on a dry basis, with observed drying rates higher than the original sludge. The second part of this work consisted of developing a drying model in order to identify the internal diffusion coefficient and convective mass transfer coefficient from the experimental data. A comparison was made between fitted drying curves, well represented by the Newton’s model, and the analytical solutions of the diffusion equation applied to a finite cylinder. Variations of dimensional characteristics such as the volume and exchange surface of the sample bed were obtained by X-ray tomography. This technique allowed confirm that shrinkage, which is an important phenomenon occurring during sludge and sawdust/mixture drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by mixing and sawdust addition. The internal diffusion coefficient changed from 7.77×10-9 m2/s for the original sludge to 7.01×10-9 m2/s for the mixed sludge and then increased to 8.35×10-9 m2/s for the mixture of a mass ratio of 4/6. The convective mass transfer coefficient changed from 9.70×10-8 m/s for the original sludge to 8.67×10-8 m/s for the mixed sludge and then increased to 12.09×10-8 m/s for the mixture of a mass ratio of 4/6. These results confirmed that sawdust addition was beneficial to the sludge drying process as the mass transfer efficiency between the air and material increased. Reinforcing the texture of sludge by adding sawdust can increase the drying rate and decrease the drying time, and then the heat energy supply will be reduced significantly. The study also showed that neglecting shrinkage phenomenon resulted in an overestimation for the internal diffusion coefficient for the convective drying of sludges and sawdust/sludge mixtures

Spousal and Survivor Benefits in Option Value Models of Retirement: An Application to Belgium

We study retirement incentives with augmented option value model à la Stock and Wise (1990). We propose methodological extensions to better reflect the respective incentives faced by singles and couples. Our results show that a more comprehensive modelling of couples' incentives leads to very different patterns of retirement incentives – particularly for women. We apply the new indicators to data from the Survey of Health, Ageing and retirement in Europe (SHARE) in Belgium and find two key results. First, contrary to several previous studies, we obtain a positive signed income effects. Second, we find very different retirement incentives for men and women, with little flexibility in the retirement decision for men and substantially more flexibility for women as a function of financial incentives and household composition