This study develops the one dimensional quasi-steady quenching model to be able to evaluate the nonuniform effect of the water penetration pattern by modeling the volume-averaged liquid saturation as the area fraction of penetrating water column. The model is based on the assumption that the quench front leaves the quenched region and the unquenched region behind and that the interactions between two regions are neglected. The quenched region isolated from the unquenched region by the liquid saturation is assumed to be formed by the primary heat transfer process which is controlled by CCFL condition, while the unquenched region is assumed to be cooled by steam which is generated in the quenched region. The governing equations for the primary heat transfer process are derived by introducing the quasi-steady approximation using Leibnitz``s rule for volume integration, the two coupled time-dependent equations for steam cooling in the unquenched region are also derived on the basis of some assumptions. This study includes two approaches to treat CCFL condition, "Packed Bed Concept Approach" and "Imaginary Tube Concept Approach", and considers the subcooling effect of inlet water by calculating the pool temperature for each time step. The sensitivity study is carried out in order to seek the better model and to verify the validity of the model. It is shown from the comparison of the model prediction with the experimental data and the sensitivity study that the present models can be used for predicting the heat removal rate, the quench front velocity, and the area fraction of penetrating water column as well as the steam cooled particle temperature in the unquenched region with the reasonable accuracy.