Multi-dimensional shrinkage models developed by phase field method for gasification of carbonaceous feedstock in packed-bed solar reactor

•The multi-dimensional irregular shrinkage models for packed-bed solar reactors are developed.•The developed shrinkage models are constructed innovatively by phase field method.•The collapsing behaviors of feedstock in the packed-bed gasification reactor are simulated.•The current work can be used for the optimization of large-scale packed-bed solar reactors. New numerical models are developed for describing the multi-dimensional shrinkage behavior of the packed bed in solar driven gasification reactors. These shrinkage models account for the feedstock consumption and collapse of the packed bed. The phase field functions are coupled in the governing equations to control the evolution of collapsing front, phase conversion and the multi-phase heat transfer. The governing equations are solved by finite element techniques. The developed models are applied to compare the predicted and measured performances of a 5-kW reactor driven by a 2600-sun concentrated solar radiation. The packed bed collapse is a non-negligible phenomenon, which can significantly influence the accuracy of the model numerical predictions for carbonaceous feedstock gasification in packed-bed solar reactor.