In slagging gasifiers, the molten slag gets deposited on the gasifier wall eventually causing refractory degradation. Replacement of the gasifier refractory is not only expensive, but it also leads to significant downtime. A computational model can help understand the impacts of various operating conditions on the refractory degradation and can be utilized for developing mitigation strategies. Therefore, the focus of this work is to develop rigorous, dynamic, first-principles models integrated with comprehensive mechanistic models that can be used for estimating the extent of degradation of the gasifier wall at any location at any point of time. Traditionally while modeling the entrained-flow gasifiers, it is assumed that as the char reacts, the ash remains attached to it leading to higher mass transfer resistances. Therefore a shrinking core model is used. However, the gasifier operating temperature is much higher than the melting temperature of the ash and therefore, it is likely that molten droplets of slag will form on the char surface. Due to strong detachment forces on the surface of a reacting char particle, these droplets may separate and some of them may eventually get deposited on the wall. To capture this phenomenon, a shrinking particle model is developed where the size of the char particles keeps decreasing due to the heterogeneous reactions leading to formation of molten slag droplets. These slag droplets remain attached to the char surface till the detachment forces exceed the adhesive forces. These mechanisms are modeled by combining the continuum model of the gasifier with a discrete particle model that accounts for the size of the slag droplets attached to the char particle and the population and size of the slag droplets in the bulk. A comprehensive transport model is developed for calculating the flux of the slag droplets towards the wall. The model estimates the numbers and sizes of the slag droplets that hit the refractory wall at a particular location. In addition, a model for the slag layer is developed to calculate the thickness of the slag layer along the wall and the temperature profile across it. Finally, a model is developed to capture penetration of the molten slag inside the refractory and the resulting degradation of the wall due to tensile and compressive forces. Both the continuum and discrete particle models are developed in Aspen Custom Modeler® (ACM) environment. The gasifier dynamics are studied by simulating a number of disturbances. In addition to results from these studies, the presentation will also include results that show the effects of gasifier operating conditions on population and sizes of the slag droplets, slag layer thickness, wall temperature profile, and refractory degradation.