In this article a well-stirred reactor model is utilized to model the etching of silicon in low-pressure chlorine/argon plasmas. Well-stirred reactor models are increasingly common in the literature due to their low requirements of computer resources for detailed chemical kinetics calculations. The model predicts the spatially averaged species composition and etch rate in a plasma etch reactor by solving conservation equations for species, mass, and the electron energy distribution function (EEDF). The reactor is characterized by a chamber volume, surface area,surface area fraction of the wafer, mass flow, pressure, power deposition, and composition of the feed gas. In such plasma etch models, assumptions on the EEDF which are needed to determine reaction rate coefficients for electron-impact reactions, are crucial for a prediction of steady state conditions. The model presented in a recent article [P. Ahlrichs, U. Riedel, and J. Warnatz, J. Vac. Sci. Technol. A 16, 1560 (1998)] is extended to describe the etching of the wafer with a special set of reactions occurring on a certain area fraction of the total reactor surface. A modified numerical procedure to solve the species conservation equations and the EEDF is presented, which needs considerably less computation time than the approach previously taken. Systematic sensitivity studies are presented to identify the connection between input parameters, outflow composition, and etch rate of the process. Such numerical studies are an important step towards fault detection and model based process control of plasma reactors.