Process Simulations in PCC

Process simulations of amine-based PCC are performed based on two approaches of equilibrium-based and rate-based models for the absorption of CO² into aqueous alkanolamine mixtures. In the equilibrium-based approach, the relation between vapour and liquid is considered to be at thermodynamical equilibrium with each other. In the rate-based approach, mass and heat transfer phenomena are adopted to treat the separation process.

2.5.1 Murphree Efficiency Based Simulations

The ideal scenario of complete thermodynamic equilibrium between vapour and liquid streams is not feasible in a real separation process. Accordingly, stage or tray efficiency is introduced to deal with the non-ideality of the process. Tray efficiency is described in several ways [179]. The point efficiency is defined as the ratio of change of composition at a point to the change of composition that would occur on a theoretical stage. Instead of a single point, Murphree efficiency is defined for the entire tray as given in Eq (95).

𝐸_𝑀 = ^{(𝑦𝑛−𝑦𝑛−1)}

(𝑦_𝑛^∗−𝑦_𝑛−1) (95)

The overall column efficiency 𝐸_𝑜 is given as 𝐸_𝑜 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑑𝑒𝑎𝑙 𝑠𝑡𝑎𝑔𝑒𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑎𝑙 𝑠𝑡𝑎𝑔𝑒𝑠 (96) And these two efficiencies can be related as

𝐸_𝑜 = ^{𝑙𝑛[1+𝐸𝑀(}

𝑚𝑉 𝐿 −1)]

𝑙𝑛(^𝑚𝑉

𝐿 ) (97)

For a packed column, Murphree efficiency of a tray is applicable for a packing section with a certain height.

2.5.2 Rate-Based Simulations

Rate-based modelling of an absorption process is a non-equilibrium approach in which a continuous mass and heat transfer is considered through the vapour-liquid interface.

The methodology for the rate-based approach is to perform material balance, energy balance with appropriate equilibrium models and mass and energy transfer models. The equilibrium models can be used to calculate the concentration of the species in the reaction system.

___

44

2.5.3 Equilibrium Models for Amine + H

O + CO

Systems

Vapour–liquid equilibria of CO² in aqueous amine solution undergoes both phase and chemical equilibria [180]. Kent and Eisenberg [181] proposed an equilibrium model based on the Henry’s law constant (𝐻_𝐶𝑂2) and equilibrium constants for reactions involving amine, water and CO². The Kent-Eisenberg model is simple as it assumes the activity coefficients and fugacity coefficients to be unity (ideal liquid and gas phase). Li and Mather [182] correlated solubility of CO² in a mixed alkanolamine mixture using the Clegg-Pitzer equation that comprises an extended Debye-Huckel term [183].

Debye-Huckel theory [184] describes the deviation of electrolyte solution from an ideal solution by introducing a method to calculate the activity coefficient 𝛾_𝑖 of an ion in a dilute solution [128]. Chen, et al. [185] developed an electrolyte local composition model by combining the extended form of the Debye-Huckel equation proposed by Pitzer [186]

and the non-random two liquid (NRTL) model [128, 187]. The extended Debye-Huckel equation was adopted to represent the contribution of long-range ion-ion interactions, while all kinds of contributions from the short-range interactions are represented by the local composition concept. Accordingly, the Pitzer-Debye-Huckel expression and the local composition expression are added to define an excess Gibbs energy expression for electrolyte solutions.

𝐺𝑒𝑥∗,𝐸𝑙−𝑁𝑅𝑇𝐿

𝑅𝑇 =^{𝐺𝑒𝑥∗,𝑝𝑑ℎ}

𝑅𝑇 +^{𝐺𝑒𝑥∗,𝑙𝑐}

𝑅𝑇 (98)

Similarly,

𝑙𝑛𝛾_𝑖 = 𝑙𝑛𝛾_𝑖^𝑝𝑑ℎ + 𝑙𝑛𝛾_𝑖^𝑙𝑐 (99)

A model of vapour-liquid equilibria (VLE) for an acid gas-alkanolamine was proposed by Austgen, et al. [188] based on the Electrolyte-NRTL model of Chen, et al. [185]. In this model, parameters were fitted for MEA + H²O + CO² system VLE data to obtain adjustable parameters and binary energy interaction parameters of the model.

2.5.4 Aspen HYSYS and Aspen Plus Simulation Environments

Aspen Plus and Aspen HYSYS are process simulators equipped with many methods to calculate material and energy balance of the process. It also facilitates the environment for different approaches e.g. equilibrium-based and rate-based approaches for absorption column simulations. For the calculation of VLE, Aspen HYSYS is availab le with Kent-Eisenberg [181] and Li-Mather [189] models, while in Aspen Plus, Chen-Austgen model [188] can be used. In the latest version of Aspen HYSYS, an amine package is recommended to replace the Kent-Eisenberg or Li-Mather models.

2.5.5 Physical Property Methods

For the physical properties, the measured density and viscosity of MEA + H²O + CO² by Weiland, et al. [80] or Hartono, et al. [81] can be regressed to estimate relevant model

___

45 parameters. In Aspen Plus, the Clarke model called VAQCLK for liquid molar volume is available with regressed model parameters. This model determines the liquid molar volume of aqueous electrolyte solutions using Amagat’s law as shown in Eq (100) and the relationship between partial molar volume of an electrolyte and its mole fraction in the solvent as illustrated in Eq (101) [190].

𝑉𝑚𝑙 = ∑ 𝑥𝑖 𝑖𝑉𝑖 (100)

Where 𝑉_𝑚^𝑙, 𝑥_𝑖 and 𝑉_𝑖 are molar volume of the mixture, mole fraction and the molar volume of the components respectively.

𝑉_𝑐𝑎= 𝑉_𝑐𝑎^∞+ 𝐴_𝑐𝑎 ^{√𝑥𝑐𝑎}

1+√𝑥𝑐𝑎 (101)

Where 𝑉𝑐𝑎is the partial molar volume of electrolytes, 𝑥𝑐𝑎is the apparent electrolyte mole fraction and 𝑉_𝑐𝑎^∞, 𝐴_𝑐𝑎 are regression parameters.

In Aspen Plus, the option code 1 signifies the quadratic mixing rule for solvent in which the interaction parameter VLQKIJ for MEA and H²O can be regressed against density data of MEA + H²O from Kapadi, et al. [69] and Han, et al. [77]. For the main electrolyte (MEAH⁺, HCO^3-), (MEAH⁺, MEACOO^-) and (MEAH⁺, CO^32-), the Clarke model parameters 𝑉_𝑐𝑎^∞ named as VLCLK/1 can also be regressed against experimental MEA + H²O + CO² density data. Aspen Plus provides the Jones-Dole electrolyte correction model, referred as MUL2JONS to model the liquid viscosities in a MEA + H²O + CO² mixture. There, the model calculates the correction to the liquid mixture viscosity of a solvent mixture due to the presence of electrolytes. The Jones-Dole electrolyte correction model is described as follows [190],

𝜂 = 𝜂_{𝑠𝑜𝑙𝑣}(1 + ∑ Δ𝜂_{𝑐𝑎 𝑐𝑎}) (102) Where 𝜂, 𝜂_{𝑠𝑜𝑙𝑣} and Δ𝜂_𝑐𝑎 are the viscosity of the liquid mixture, viscosity of the liquid mixture calculated by the Andrade/DIPPR model and contribution to the viscosity correction due to apparent electrolyte ca from cation c and anion a respectively.

The measured viscosity data of MEA + H²O mixtures can be adopted to determine the interaction parameters MUKIJ and MULIJ between MEA and H²O in the Aspen liquid mixture model. And, the Jones-Dole model parameters in Δ𝜂_𝑐𝑎, IONMUB, for MEAH⁺ and MEACOO^- are possible to regress against MEA + H²O + CO² viscosity data [191].

In principle, it is possible to integrate specific correlations in simulation programs like Aspen HYSYS and Aspen Plus. However, this requires use of complex tools to obtain.

In the future, integration of new correlations including specific parameters may be more convenient.

___

46

___

47