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.