Construction from the Ideal Cycle to the Actual Cycle

• The absorption and the desorption are set to an isothermal process.
• During the pre-heating and cooling process, the CO₂ loading remains unchanged, that is, no CO₂ desorption occurs.
• The absorption and the desorption process are in a gas–liquid equilibrium state.
• All kinds of heat loss in the cycle are not considered.
• The solution does not react with other types of gases in the flue gas except CO₂, and the flue gas is assumed to be an ideal gas.

Based on the above assumptions, the ideal four-step chemical amine-based cycle was established as follows:

Step 1(a–b): The process is an isothermal absorption process, CO₂ is absorbed, and the absorption process can be regarded as slowly reaching the equilibrium state, point b, along the gas–liquid isothermal equilibrium line. The determination of the state point, b, is determined by the concentration of CO₂ in the flue gas, that is, by the carbon source. For example, the flue gas pressure is set at an atmospheric pressure of 101 kPa and the CO₂ concentration is 10%, then the state point b corresponds to a CO₂ partial pressure of 10.1 kPa, which is according to Dalton’s partial pressure law.

Step 2(b–c): The process is a pre-heating process in which the rich solvent is heated up by the heater, and no CO₂ desorption occurs, that is, CO₂ loading remains unchanged.

Step 3(c–d): The desorption process, in which a large amount of water vapor is generated by the reboiler in the process, resulting in a decrease in the partial pressure of CO₂, and the CO₂ in the liquid phase is desorbed along with the isothermal equilibrium line.

Step 4(d–a): The cooling process, in which the lean solvent is cooled by the condenser, returning to the state point a, and starting a new cycle.

As shown in Figure 3, the ideal cycle implies the reaction time is infinitely long and the performance of the absorbent is too ideal. At the same time, it indicates the ideal energy efficiency that the actual cycle can never reach, which is also not easy to compare with other models. Therefore, combined with the actual performance of the MEA solution and other practical constraints, the lean and rich solvent loading were set to 0.2 mol/mol and 0.50 mol/mol, respectively. Within the constraints of the carbon source and carbon sink, this ensures the state points 2 and 4, the driving force, R_abs and R_des, and a condition parameter will be used to describe the how close the actual partial pressure is with the equilibrium partial pressure in the absorption and desorption process, which are defined as Equation (5) and Equation (6):

where R_abs and R_des are the partial pressure ratios for absorption and desorption; P′1 and P′3 are the equilibrium CO₂ partial pressure of lean and rich solvent; and P₁ and P₃ are the CO₂ partial pressure of the inlet of the absorber and the inlet of the desorber.

Then, a new four-step chemical amine-based cycle, 1-2-3-4-1, a close match with the actual cycle, is formed.