Kinetic modeling of solid-catalyzed deep oxidation of pollutants in water is crucial to the design and scale-up of wastewater wet oxidation treatment. Due to their simplicity, the overall kinetics using power-law rates are often unable to capture the important features in such oxidation systems. However, detailed mechanistic approaches aimed at establishing complex reaction networks where several species and intermediates need to be identified become quickly cumbersome and costly. Lumped kinetic approaches offer a balanced trade-off between sophistication and simplicity. A versatile "three-lump" triangular kinetic model was proposed for the description of solid-catalyzed wet oxidation of various pollutants in wastewater effluents. The model is an offshoot of the well-known "generalized lumped kinetic model" introduced for homogeneous wet oxidation. This model was extended, using the Langmuir-Hinshelwood-Hougen-Watson framework, to describe the evolution of heterogeneous catalytic wet oxidation reactions. The model, in the form of a set of three implicit nonlinear differential equations, was validated using literature data obtained under a variety of experimental conditions, such as subcritical or supercritical water conditions, batch and continuous reactors, a multitude of organic loads in the form of carbon-, nitrogen-, and oxygen-bearing compounds, and using different kinetic variables such as TOC and COD. In all cases, this strategy led to calculated parameters that met the thermodynamic, kinetic, and statistical criteria. The uncertainty and confidence joint regions were estimated using bootstrap "Monte Carlo" techniques.