This contribution presents an integer-linear model of a post-combustion carbon capture plant featuring discrete sizing, part load operation and dynamic behavior. In particular, the model covers a design space from 200 tCO2/h (size of Petra Nova) down to 7.5 tCO2/h, a part load operation range from 50% to 100%, and a CO2 concentration range from 7.5% to 12%. Starting with detailed, partly rate-based, models in Aspen Plus and deriving linear performance planes thereof allows to bring process model information into a linear system modeling domain for a reasonable range of design specifications. By applying this model to a low-emission energy system design optimization, its practicability and added value could be demonstrated. The simulations show that especially for systems with high non-dispatchable energy generation, the information about the carbon capture plant's dynamic behavior is essential. To fit the scope of this paper, the mathematical formulation of the model is reported in a condensed manner. However, all information required to formulate the model is provided.