Molten compositions in the CaO-K2O-SiO2 system relevant to woody biomass ash slags were simulated with molecular dynamics to extract structural characteristics. Multivariate analysis elucidated correlations of these structural characteristics with viscosity measurements. The simulations show SiO4/silicate tetrahedral units (STUB) diffusing slowly and forming flexible networks via oxygen bridges. The degree of STU polymerization varies linearly with the (K2O + CaO)/SiO2 ratio. Ca depolymerises stronger than K, but K diffuses quicker. Depolymerization and diffusion cause network disruptions and agitations that promote collective atomic mobility of the system. This imposes structural characteristics in the slag that correlate with viscosity. The inter-STU Si-O-Si angle narrows with decreasing viscosity, while the Si-O bond length of these bridges increases. Attributes related to atomic mobility, such as the variations in the Si-O-Si angle and the distance of nearest Si-Si pairs, also correlate with viscosity. The discussion provides insight into the connection between structural characteristics and viscosity.