1 *K*-value model

Define a new variable for the *K* value of the reference component, *Kb,j*, and the reference component b is an imaginary component. *Kb,j* was calculated by the following formula, where <sup>ω</sup>*i,j* is a weighting factor.

$$\mathcal{K}\_{b,j} = \exp(\sum\_{i} \omega\_{i,j} \ln \mathcal{K}\_{i,j})\_\prime \tag{15}$$

$$\omega\_{i,j} = \frac{y\_{i,j} \left[ \partial \ln \mathcal{K}\_{i,j} / \partial (1/T) \right]}{\sum y\_{i,j} \left[ \partial \ln \mathcal{K}\_{i,j} / \partial (1/T) \right]}. \tag{16}$$

The relationship between *Kb,j* and the stage temperature *Tj* is related using Equation (17), *T\** is the reference temperature.

$$
\ln K\_{b,j} = A\_j + B\_j \left(\frac{1}{T} - \frac{1}{T^\*}\right). \tag{17}
$$

The value of the parameter *Bj* can be obtained by the differential calculation of *1*/*T* by the *Kb*, and the temperatures *Tj*−*<sup>1</sup>* and *Tj*+*<sup>1</sup>* of the two adjacent stages are selected as *T*1 and *T*2.

$$B\_{j} = \frac{\partial \ln \mathbb{K}\_{b}}{\partial (1/T)} = \frac{\ln \left( \mathbb{K}\_{b,T1}/\mathbb{K}\_{b,T2} \right)}{(1/T\_{1} - 1/T\_{2})},\tag{18}$$

$$A\_{\dot{j}} = \ln K\_{b,\dot{j}} - B\_{\dot{j}} \left( \frac{1}{T} - \frac{1}{T^\*} \right). \tag{19}$$

2 Enthalpy model

The calculation of the enthalpy difference is the main time-consuming part of the entire enthalpy calculation, so the calculation of the enthalpy difference was simplified in the approximate enthalpy model, and a simple linear function was used to fit the calculation of the enthalpy difference.

$$
\Delta H\_{\circ} = c\_{\circ} - d\_{\circ}(T\_{\circ} - T^{\star})\_{\circ} \tag{20}
$$

$$
\Delta h\_{\dot{j}} = e\_{\dot{j}} - f\_{\dot{j}} (T\_{\dot{j}} - T^\*). \tag{21}
$$
