https://doi.org/10.1016/j.gee.2016.11.003
“The molecule–molecule interaction parameters, τij, for DEEA-H2O were regressed together with the non-randomness parameters, using experimental data [20], [24]. As seen in Fig. 2, the model produces results in a good agreement with the equilibrium of the binary system. The blue solid line is the total pressure of the solution plotted against the mole fraction of DEEA in the liquid phase (bubble point curve). The orange line is the total pressure of the solution as a function of the vapour phase concentration of DEEA (dew point). The total pressure and gas phase DEEA composition were calculated as a function of the fixed molar concentrations in the liquid phase, obtaining AARD of 1.76% and 11.79%, for the bubble point and DEEA concentration in the gas phase, respectively. As seen in the Fig. 2, the model is less accurate at very low DEEA concentrations and high temperature.
Fig. 2. VLE of DEEA-H2O solutions at (from left to the right, from the top to the bottom) 50, 60, 80 and 95 °C: open points, experimental data from Hartono et al. [15]; solid lines, outputs from the Aspen model included in this work: red for the liquid phase and blue for the gas phase.
The activity coefficients are represented with AARD of 14.9% and shown in Fig. 3. As seen in Fig. 3, the activity coefficient decreases as the DEEA content increases. The regressed interaction parameters are given in Table 7.
Fig. 3. Activity coefficients of DEEA and water at (from left to right, from the top to the bottom) 50, 60, 80 and 95 °C: open points from [15]; solid lines from this work: red for the liquid phase and blue for the gas phase.
Table 7. eNRTL parameters.
| Molecular parameters: am,m′, bm,m′, em,m′ | |||||
|---|---|---|---|---|---|
| aH2O,DEEA | 4.34228 | bH2O,DEEA | −763.917 | eH2O,DEEA | 0.619047 |
| aDEEA,H2O | 313.709 | bDEEA,H2O | −152126 | eDEEA,H2O | −45.3131 |
| aH2O,CO2 | 0a | bH2O,CO2 | 0a | eH2O,CO2 | 0a |
| aCO2,H2O | 0a | bCO2,H2O | 0a | eCO2,H2O | 0a |
| aCO2,DEEA | 0a | bCO2,DEEA | 0a | eCO2,DEEA | 0a |
| Molecule/salt parameters: am,c/a, bm,c/a | |||
|---|---|---|---|
| aH2O,H3O·/OH− | 0 | bH2O,H3O+/OH− | 0a |
| aH2O,H3O+/HCO3− | 8a | bH2O,H3O+/HCO3− | 0a |
| aH2O,H3O+/CO32− | 8a | bH2O,H3O+/CO3−2 | 0a |
| aCO2,H3O+/OH− | 15a | bCO2,H3O+/OH− | 0a |
| aDEEA,H3O+/OH− | 0a | bDEEA,H3O+/OH− | 0 |
| aH2O,DEEAH+/HCO3− | −4.0053 | bH2O,DEEAH+/HCO3− | 311.364b |
| aH2O,DEEAH+/OH− | 0 | bH2O,DEEAH+/OH− | 0 |
| aH2O,DEEAH+/CO3−2 | −60 | bH2O,DEEAH+/CO3−2 | −93.261b |
| aCO2,H3O+/CO3−2 | 15a | bCO2,H3O+/CO3−2 | 0a |
| aCO2,H3O+/HCO3− | 15a | bCO2,H3O+/HCO3− | 0a |
| aCO2,DEEAH+/OH− | −0.24226 | bCO2,DEEAH+/OH− | −0.24226 |
| aCO2,DEEAH+/HCO3− | 8.384b | bCO2,DEEAH+/HCO3− | 608.436b |
| aCO2,DEEAH+/CO3−2 | −2.7114b | bCO2,DEEAH+/CO3−2 | −527.063b |
| aDEEA,H3O+/HCO3− | 3.5081b | bDEEA,H3O+/HCO3− | −602.792b |
| aDEEA,H3O+/CO3−2 | 3.1376b | bDEEA,H3O+/CO3−2 | −282.638b |
| aDEEA,DEEAH+/OH− | 0 | bDEEA,DEEAH+/OH− | 0 |
| aDEEA,DEEAH+/HCO3− | 9 | bDEEA,DEEAH+/HCO3− | −810.104 |
| aDEEA,DEEAH+/CO3−2 | 8.3565b | bDEEA,DEEAH+/CO3−2 | −767.262b |
| Salt–molecules parameters: ac/a,m, bc/a,m | |||
|---|---|---|---|
| aH3O+/HCO3−,H2O | −4a | bH3O+/HCO3−,H2O | 0a |
| aH3O+/CO32−,H2O | −4a | bH3O+/CO32−,H2O | 0a |
| aH3O+/OH−,CO2 | −8a | bH3O+/OH−,CO2 | 0a |
| aH3O+/OH−,DEEA | −0.5 | bH3O+/OH−,DEEA | 0 |
| aDEEAH+/HCO3−,H2O | 1.1823 | bDEEAH+/HCO3−,H2O | 46 |
| aDEEAH+/HCO3−,DEEA | 2.5 | bDEEAH+/HCO3−,DEEA | −126.497b |
| aDEEAH+/OH−,DEEA | 0 | bDEEAH+/OH−,DEEA | 0 |
| aH3O+/HCO3−,CO2 | −8a | bH3O+/HCO3−,CO2 | 0a |
| aH3O+/HCO3−,DEEA | −1.3105b | bH3O+/HCO3−,DEEA | 146.617b |
| aH3O+/CO32−,CO2 | −8a | bH3O+/CO32−,CO2 | 0a |
| aH3O+/CO32−,DEEA | −2.3338b | bH3O+/CO32−,DEEA | 151.66 |
| aDEEAH+/OH−,H2O | 0 | bDEEAH+/OH−,H2O | 0 |
| aDEEAH+/OH−,CO2 | −4.24226 | bDEEAH+/OH−,CO2 | −0.24226 |
| aDEEAH+/HCO3−,CO2 | −6.6385 | bDEEAH+/HCO3−,CO2 | 200.853b |
| aDEEAH+/CO32−,H2O | −4.4225b | bDEEAH+/CO32−,H2O | −162 |
| aDEEAH+/CO32−,CO2 | 1.8621b | bDEEAH+/CO32−,CO2 | −53.014b |
| aDEEAH+/CO32−,DEEA | 15.3149 | bDEEAH+/CO32−,DEEA | −969.983b |
| aH3O+/OH−,H2O | 0 | bH3O+/OH−,H2O | 0a |
- a
-
Aspen default value.
- b
-
Monteiro et al. [20].
In terms of the mixture of two pure liquids, in that case H2O and DEEA, the excess of enthalpy is the change of isothermal enthalpy per mole of solution, which is similar to the heat of mixing of the solution. This property is significant because it is related to the excess Gibbs energy (Eq. (11)), which depends on the temperature. In the case of the eNRTL model, the excess of enthalpy (Eq. (12)) is dependent on the calculated interaction parameters, energy parameters (τ) and non-randomness factors (α) as seen from Equation (12). Consequently, the excess of enthalpy will impact the calculation of the VLE [27].(11)dgexRTd(1T)=−hexR(12)−hexR=x1x2b21G21(x1(ατ21−1)−x2G21)(x1+x2G21)2+x1x2b12G12(x2(ατ12−1)−x1G12(x2+x1G12)2
The excess of enthalpy of the binary system DEEA-H2O was considered in this work and is included in Fig. 4. It was analysed and compared with data from literature [23]. As seen in the Fig. 4, the model compares well with the experimental data, obtaining an AARD of 5.63%. It follows a parabolic shape with minimum at 0.4 molar fraction of DEEA. It means that it is an exothermic system with the highest release of heat of mixing at that point.
Fig. 4. Excess of enthalpy as function of composition at 298.15 K. Line represents the result from the simulation model from this work while points are from Mathonat et al. [23].
“