The present paper presents two process functions for the estimation of the energy demand for SO$_2$ filtering from coal flue gas streams and the gypsum production by wet flue gas desulfurization (WFGD) systems. Functions are prepared to be used as plugins on conceptual design procedures of industrial processes based on coal combustion with some sulfur content without the need of modeling the complete WFGD system. An energy penalty function (EPF) is proposed as the ratio of demanded work to operate the filtering process with respect to the input flue gas volumetric flow rate, called the work ratio. Dihydrate calcium sulfate is a value product estimated by a gypsum slurry production function (GPF) based on the ratio of gypsum production to the input flue gas volumetric flow rate. Mass, energy and species balances are solved to simulate WFGD operation based on the inlet and outlet flue gas temperature, SO$_2$ content and cleaning efficiency, and results are compared to data from coal-fired power plants, from now on called the reference model. Design of experiment (Box–Behnken method) is used to identify main parameter weighting and cross-dependencies to finally build the EPF and GPF plugin functions. Relative deviations with respect to the reference model are of 1.41% and 0.05% for EPF and GPF, respectively. Both equations can be coupled to any kind of combustion system to quantify the energy penalty related to flue gas SO$_2$ removal and to predict the corresponding amount of gypsum as a by-product and to predict optimal operational conditions.