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Chapter 1: Rate-Base Simulations of Absorption Processes; Fata Morgana or Panacea?

Chapter 3: Thermodynamic Approach of CO₂ Capture, Combination of Experimental Study and Modeling

Chapter 4: Employing Simulation Software for Optimized Carbon Capture Process

Chapter 6: Calorimetry in Aqueous Solutions of Demixing Amines for Processes in CO₂ Capture

Chapter 7: Speciation in Liquid-Liquid Phase-Separating Solutions of Aqueous Amines for Carbon Capture Applications by Raman Spectroscopy

Chapter 8: A Simple Model for the Calculation of Electrolyte Mixture Viscosities

Chapter 9: Phase Equilibria Investigations of Acid Gas Hydrates: Experiments and Modelling

Chapter 10: Thermophysical Properties, Hydrate and Phase Behaviour Modelling in Acid Gas-Rich Systems

Chapter 11: “Self-Preservation” of Methane Hydrate in Pure Water and (Water +Diesel Oil + Surfactant) Dispersed Systems

Chapter 14: Vapor-Liquid Equilibria Predictions of Carbon Dioxide + Hydrogen Sulfide Mixtures Using the CPA, SRK, PR, SAFT, and PC-SAFT Equations of State

Chapter 16: Review and Testing of Radial Simulations of Plume Expansion and Confirmation of Acid Gas Containment Associated with Acid Gas Injection in an Underpressured Clastic Carbonate Reservoir

Chapter 17: Three-Dimensional Reservoir Simulation of Acid Gas Injection in Complex Geology – Process and Practice

17.2 Step by Step Approach to a Reservoir Simulation Study for Acid Gas Injection

Chapter 18: Production Forecasting of Fractured Wells in Shale Gas Reservoirs with Discontinuous Micro-Fractures

Chapter 19: Study on the Multi-Scale Nonlinear Seepage Flow Theory of Shale Gas Reservoir

Chapter 21: Study on the Microscopic Residual Oil of CO₂ Flooding for Extra-High Water-Cut Reservois

21.3 Experimental Microscopic Residual Oil Distribution of CO₂ Flooding for Extra High Water Cut Reservoirs

21.4 Displacement Characteristics of CO₂ Flooding and Improve Oil Recovery Method for Post CO₂ Flooding

Chapter 22: Monitoring of Carbon Dioxide Geological Utilization and Storage in China: A Review

Chapter 23: Separation of Methane from Biogas by Absorption-Adsorption Hybrid Method

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Published simultaneously in Canada.

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The fifth in the series of Symposia on the injection of gases for disposal and enhanced recovery was held in Banff, Canada, in May 2015. This volume contains select papers that were presented at the Symposium. In addition, some papers were backups and they too are included here.

The keynote presentation, and Chapter 1 in this book, was on the modelling of processes for removing CO₂ from gas streams. This is followed by several chapters on acid gas removal technology, including data and correlation. This includes several interesting papers on hydrates.

The final chapters discuss the reservoir aspects of gas injection. Included in these sections are papers on acid gas injection and CO₂ for enhanced oil recovery.

Chapter 1

Rate-Base Simulations of Absorption Processes; Fata Morgana or Panacea?

Abstract

The design and simulation of separation processes have been traditionally handled using the concept of ideal stages and efficiencies. The growing importance of chemically based separation processes, such as the use of alkanolamines for gas processing and now carbon capture underline the importance of proper modeling of coupled mass transfer and chemical kinetics in multiphase systems.

In the present study it will be demonstrated by means of various (real-life) cases that rate-based simulation can be a beautiful tool to improve on the process performance and develop new insights in gas-liquid processes accompanied by complex chemical reactions. But also in this rate-based approach the user should fully understand the mechanisms behind the phenomena occurring. Otherwise, this approach can lead to erroneous results.

1.1 Introduction

The design of absorption processes based on complex aqueous chemical reactions such as CO₂-capture, selective H₂S-removal as well as rate limited physical separations like LNG pre-treatment are neither simple nor straightforward. Reaction kinetics, mass transfer rates and thermodynamics are coupled and their effects must be taken into account simultaneously. The development of sound simulation models is dependent on algorithms, which take into account the aforementioned phenomena in a rigorous and consistent manner.

How the mass transfer parameters collectively affect the results, is an important part of the training required by a process engineer to become proficient in using this type of technology.

In this paper a high pressure CO₂ capture case is simulated with a rate based simulator. The impact of the several mass transfer parameters on the absorption performance is presented and it is shown that knowledge of these parameters is required to obtain reliable and correct results from the simulator.

1.2 Procede Process Simulator (PPS)

The simulations described in this paper have been carried out with the Procede Process Simulator. Procede Process Simulations developed a new flowsheeting tool, Procede Process Simulator (PPS), specifically designed for steady-state simulations of acid gas treating processes [1]. The process models include all features relevant for the design, optimization, and analysis of acid gas treating processes, like selective H₂S removal, post combustion CO₂ capture or CO₂ removal with a physical solvent. The simulator consists of a user-friendly graphical user interface and a powerful numerical solver that handles the rigorous simultaneous solution of thermodynamics, kinetics and mass transfer equations (this combination usually called a “rate-based” model). PPS also supports the main unit operations relevant for gas treating plants like absorbers, strippers, flash drums, heaters, pumps, compressors, mixers and splitters as well, as novel unit operations designed to make the process engineer’s work more productive such as automatic ways to calculate water and solvent makeup. PPS has been extensively validated and used for several carbon capture projects [2–4]. A thorough and systematic comparison between the equilibrium based and rate based modeling approaches using the absorption of CO₂ from flue gas produced by a coal-fired power plant into an aqueous MEA solution as a benchmark was presented in [5].

The Procede Process Simulator includes an extensive, carefully evaluated database of thermodynamic model parameters, binary interaction parameters, kinetics constants, chemical equilibrium constants, diffusivities and other required physical properties. The physical property model parameters were optimized to accurately predict the vapour-liquid equilibria (VLE), thermodynamic and physical properties, and the kinetically enhanced mass transfer behavior of acid gases in amine-based capturing processes. Several models for hydrodynamics and mass transfer such as the Higbie penetration model [6] are available.

The thermodynamic model combines consistent liquid activity coefficient models derived from a Gibbs excess function with the necessary modifications to handle ions in aqueous solutions with a cubic equation of state for the gas phase. For the convenient prediction of column performance, the program also includes an extensive database of various tray types as well as a large collection of both random and structured packing data. Several mass transfer (k_G, k_L and a) and hydrodynamic models were implemented that benefit from accurate physical property models for density, viscosity, surface tension, diffusivity and thermal conductivity specifically selected and validated for acid gas treating applications.

This attention to detail allowed for the construction of a simulator able to describe complete acid gas treating processes, including complex processes with multiple (mixed or hybrid) solvent loops. This simulator provides significant understanding of the performance of potential new solvents, current operations and an environment to better understand current operations.

1.3 Mass Transfer Fundamentals

Most important part of the Procede Process Simulator is the mass transfer module. In this module the mass transfer from gas phase to liquid phase and vice versa is calculated.

In the example described below gaseous component A (=CO₂) is transported to the liquid phase (B), were the reaction takes place.

The reaction rate can be calculated from the reaction rate constant k_1,1 and the concentration A and B in the liquid phase:

A commonly used fundamental mass transfer model to describe this absorption process quantitatively is the stagnant film model. In this stagnant film model the fluid (in this case both gas and liquid phase) are divided in two different zones: a stagnant film of thickness δ (gas and liquid) near the interface and a well-mixed bulk (gas and liquid) behind it, in which no concentration gradients occur. A schematic representation of the absorption process according the stagnant film model is presented in Figure 1.1.

Figure 1.1 Driving force for a gas – liquid process according to the film model.

In Figure 1.1 the parameters (according the film model) for the driving force in a countercurrent gas-liquid system with and without chemical reaction are shown:

Gas and liquid resistances are determined by the diffusion coefficients and the film thickness in both phases. In the film model it is assumed that equilibrium exists at the gas-liquid interface. For an acid gas – solvent system, where a chemical reaction takes place in the liquid, mass transfer in the liquid may be enhanced by the chemical reaction as can be seen in Figure 1.1.

Depending on the values of the stated variables in the reaction rate equations, several limiting conditions can be identified. If one assumes a negligible gas phase resistance (high k_G; in most CO₂ capture absorption processes k_G is not limiting) the following absorption rate for component A (=CO₂) can be developed:

where: r_A = absorption rate of component A [mol. s⁻¹.m⁻³ reactor]
            m_A = physical solubility of component A in the solvent, -
            k_L = liquid side mass transfer coefficient, m.s⁻¹
            a = effective gas-liquid area, m².m⁻³ reactor
            E = chemical enhancement factor, -
            C_A,G = concentration of component A in gas phase, mol.m⁻³

E is the enhancement factor, which is the ratio of the flux with reaction and the flux without reaction at identical driving forces. For non-reactive systems the enhancement factor is by definition equal to one. To calculate the CO₂ flux, the chemical enhancement should be determined and for this calculation the definition of the Hatta number (Ha) is introduced. The dimensionless number Hatta number compares the maximum chemical conversion in the mass transfer film to the maximum diffusion flux through the film. For the example described above, the Hatta number is defined as follows:

where: k_1,1 = the reaction rate constant;
            C_B = concentration of reactant (=B) in the liquid phase;
            D_A = diffusion coefficient of component A in the solvent;
            k_L = liquid side mass transfer coefficient.

Dependent of the value of the Hatta number the several reaction regimes can be identified. For CO₂ capture at low pressure in general the pseudo first order regime can be identified (Ha >> 2) and in this case the Enhancement factor (E) is equal to the Hatta number. In this case the absorption rate can be calculated as follows:

So when thermodynamic (m), kinetic (k_1,1) and mass transfer information (a) and physical properties (D) are available the absorption rate of CO₂ into the liquid phase can be determined. Under these conditions, the mass transfer of CO₂ is independent of the liquid side mass transfer coefficient k_L.

In this case the reaction between CO₂ and the solvent takes place at the gas liquid interface and in the bulk of the liquid no CO₂ is present anymore; i.e. it is converted to ionic species completely.

In PPS the Higbie penetration model is used to calculate the mass transfer instead of the above described film model. In contrast to the above described film model the Higbie Penetration Model can be used for a wide range of conditions, the entire range of Hatta numbers, (semi-) batch reactors, multiple complex reactions and equilibrium reactions, components with different diffusion coefficients and also for systems with more than one gas phase component. However, the principles as discussed above are identical.

For rate based modelling of absorbers and regenerators the contactor is discretized into a series of mass transfer units as shown in Figure 1.2. In counter-current operation the input of each transfer unit is the liquid from above and the vapour from below the unit. The output is the liquid to the unit below and the vapour to the unit above. The resulting number of transfer units (NTU) and the physical appearance (e.g. sieve trays, random packing, etc.) of these units are completely different depending on the way the model is constructed. Nevertheless the model is completely general in the sense that it captures all the essential phenomena happening in reality – thermodynamic driving forces, effective areas and rates for mass transfer, chemical kinetics and limited residence time.

In rate based modelling the gas and liquid phases are separated by an interface, the gas and liquid phases have different temperatures and the mass and heat transfer rates between the two phases are determined by the driving force between the two phases, the contact area, and the mass and heat transfer coefficients. The amount of mass transfer area is determined by the desired quality of the separation. The mole fractions of the gas (y) and liquid (x) phase are calculated by integration of the differential mass balance equations (1) and (2) across the height of the column (h).

where L is the total mole flow of the liquid phase and G is the total mole flow of the gas phase, i is the component index. V is the total volume of the segment. The effective interfacial area for mass transfer (a_e) depends on the packing type or other mass transfer area present in the contactor such as the specific area for mass transfer used to model tray columns or bubble interfacial area present in a bubble tower. The mass flux (J) in moles /(area * time) is calculated based on the driving force. If the driving force is defined as the concentration difference between the gas and liquid phase the flux is expressed as in Eqn 1.8.

where m is the distribution coefficient based on the ratio of liquid and gas concentrations. If the integration of this set of equations is done numerically the height of one transfer unit depends on the numerical discretization used for integration. In the case of a packed column, with negligible axial dispersion, the NTU is set at a value that results in plug flow. In case of trays, with the assumption that at each tray the liquid and gas phase are ideally mixed, the NTU can be set equal to the number of trays. This results in less plug flow due to axial dispersion. It should be noticed that in this way the axial dispersion is described by ideally mixed contactors in series.

In case of chemical absorption and the driving force is concentration based, the overall mass transfer coefficient k_ov is a function of the mass transfer coefficient of the gas phase (k_G) and liquid phase (k_L), the distribution coefficient based on concentrations (m). E is the enhancement factor as discussed before.

Details related to the construction of empirically determined mass transfer parameters are important since the interactions between their different governing equations and equation parameters are not always intuitive. For example, in physical separation processes only the product of mass transfer coefficient and specific interfacial area for the gas and liquid mass transfer is required (k_Ga_e and k_La_e), because this product determines the absorption rate. For chemically reactive, mass transfer limited separation processes the individual values of mass transfer coefficients and specific mass transfer areas (k_G, k_L, a_e) are required for the gas and liquid phases. A significant amount of experimental studies related to predict these mass transfer parameters in absorption columns have been carried out. From these studies several empirical or semi-empirical correlations are derived by regression of the correlations with the experimental (pilot) data or correlations are derived from theoretical hydraulic models. In general overall or volumetric mass transfer coefficients are determined from these experiments; however, a distinction between mass transfer coefficient (k_L and k_G) and effective interfacial area (a_e) is basically not possible.

1.4 CO₂ Capture Case

A high pressure (60 bar) CO₂ capture plant was simulated based on real plant data and the process flow scheme of the simulated plant is presented below:

In Figure 1.3 a flow scheme of a standard CO₂ capture plant is presented containing an absorber and desorber, flash vessel and various heat exchangers and solvent circulation pumps. The CO₂ is removed with an activated MDEA solution, i.e. a commonly used solvent containing MDEA and piperazine. The absorber is equipped with 20 valve trays. Geometric details of the valves, like weir height and tray spacing have been incorporated in the simulation. The in-house developed correlations have been used to calculate the various mass transfer parameters (k_G, k_L and a_e). The gas stream is a hydrocarbon stream containing mainly methane and 3.0 vol. % CO₂. With the default simulation the following mass transfer parameters were calculated using the default correlations implemented in the simulator:

Note that the mass transfer parameters are calculated for every tray, so the above presented data are average values over the whole column.

With these settings a CO₂ capture of 75 % was calculated with the simulator. In reality a slightly higher (few percent) capture was measured and by the execution of a sensitivity study with the three mass transfer parameters, it was studied how this capture can be influenced. As described above the physical and chemical properties of the solvent-gas mixture are rigorous implemented into PPS and the most “difficult” parameters to predict are the mass transfer parameters k_G, k_L and a.

In Figure 1.4 the influence of the effective interfacial area (a_e) on the calculated CO₂ outlet concentration is presented. The area has been varied between values of 10% and 500 % of the original number dervied from the default correlation (= 38 m².m⁻³).

Figure 1.4 Influence of effective interfacial area on the calculated CO₂ outlet concentration.

From Figure 1.4 it can be concluded that the CO₂ capture rate is very dependent on the value of the effective interfacial area. Especially, a reduction of area does have a drastic effect on the overall CO₂ capture. The reason for this large effect is that the CO₂ capture is more or less linear dependent on the CO₂ absorption in the liquid phase, so lowering the area will result in lower absorption. When the effective area calculated with the default correlation was increased with 22% to 46 m².m⁻³, the CO₂ concentration predicted by the simulator was inline with the capture measured in the field.

An increment in area does result in increased CO₂ capture, however, the effect is less pronounced as for reduced effective area. Especially at very high effective areas (> 100 m².m⁻³), a further increase in area does not result in the same increase in CO₂ capture. The reason for this lower impact of area on the capture is, that at these high capture rates, the driving force for mass transfer, i.e. the concentration difference between gas and (corrected) liquid phase is decreasing with increasing CO₂ capture. In Figure 1.5 the gas phase concentration and (corrected) liquid phase concentration is presented as function of tray number for the default case (a_e = 38 m².m⁻³). The corrected liquid concentration is the gas phase concentration which is in equilibrium with the liquid phase. The difference between these two lines is the driving force for mass transfer.

Figure 1.5 Gas phase concentration (green triangles) and (corrected) liquid concentration of CO₂ (blue dots) as function of tray number for the interfacial area of 38 m².m⁻³.

From Figure 1.5 it be seen that the gas phase concentration is reduced from around 3 mol% (in the top) to around 0.7 mol% in the bottom of the absorber. It can also be concluded that the driving force is lower in the middle of the column. This can be explained when the temperature profile in the column is studied in more detail. In Figure 1.6 this liquid temperature in the absorber is presented for three different interfacial areas and it can be seen that in the middle of the column the temperature is increased to more than 80 °C (for a_e = 38 m².m⁻³). At this high temperature the equilibrium partial pressure CO₂ is much higher than at lower temperature, i.e. the capacity of the solvent for CO₂ capture is decreased. Due to this reduced driving force, the CO₂ mass transfer from gas to liquid phase will be reduced.

Figure 1.6 Temperature profile in the absorber for three different effective areas (a_e = 7.6, 38 and 190 m².m⁻³; default value multiplied by factor of 0.2, 1 and 5).

When the effective area is decreased with a factor 5 to 7.6 m².m⁻³ a significant lower CO₂ capture is established (refer to Figure 1.4). When the area is increased with a factor 5 to 190 m².m⁻³, the CO₂ capture is increased, however, the increment is significant lower than expected. The reason for this limited increment can be explained when the driving force between gas and liquid phase is studied for this simulation (Figure 1.7).

Figure 1.7 Gasphase concentration (green triangles) and (corrected) liquid concentration of CO₂ (blue dots) as function of tray number for the interfacial area of 190 m².m⁻³ (factor = 5).

From Figure 1.7 it can be concluded that almost no driving force for mass transfer is available in approximately 50 % of the column, i.e. between tray 8 and 15. Due to the high CO₂ capture the temperature is increased in the absorber (Figure 1.6) to approximately 85 °C and at this high temperature no absorption can take place anymore, due to the high equilibrium CO₂ pressure. From this figure it can be concluded that the addition of more trays (or more interfacial area) will not result in more CO₂ capture. The overall CO₂ capture can be increased by applying inter stage cooling in the middle of the column or increase the solvent circulation rate.

In Figure 1.8 the influence of the liquid side mass transfer coefficient on the calculated CO₂ outlet concentration is presented graphically.

Figure 1.8 Influence of liquid side mass transfer coefficient on the calculated CO₂ outlet concentration.

From Figure 1.8 it can be concluded that both for low and for high values of the liquid side mass transfer coefficient, the impact on the CO₂ capture is much lower than for the interfacial area. The reason for this relatively low influence is that the reaction does take place in the pseudo first order regime. As discussed in the former chapter, when the reaction is fast compared to mass transfer, the absorption rate is not influenced by the value of the liquid side mass transfer coefficient. In Figure 1.9 the calculated chemical enhancement in the absorber is calculated for three different values for the liquid side mass transfer coefficient (k_L = 5.2.10⁻⁵, 2.6.10⁻⁴ and 1.3.10⁻³ m.s⁻¹, i.e. the default value is multiplied with respectively a factor 0.2, 1 and 5).

Figure 1.9 Chemical enhancement for three different liquid side mass transfer coefficients (default value multiplied by factor of 0.2, 1 and 5).

From this Figure 1.9 can be seen that for most of the conditions the enhancement >> 1 and for this conditions the absorption rate is not dependent on k_L. For the lower values of k_L in the bottom of the column, the chemical enhancement is approaching the value 1 and in this case, the CO₂ capture becomes dependent on the value of k_L.

In Figure 1.10 the temperature profile in the column is presented for the three different k_L values. From this figure it can be concluded that this parameter has a low impact on the temperature in the absorber.

Figure 1.10 Temperature profile in the absorber for three different liquid side mass transfer coefficients (default value multiplied by factor of 0.2, 1 and 5).

In Figure 1.11 the influence of the gas side mass transfer coefficient (k_G) on the calculated CO₂ outlet concentration is presented graphically.

Figure 1.11 Influence of gas side mass transfer coefficient on the calculated CO₂ outlet concentration.

From Figure 1.11 it can be concluded that the value of the gas side mass transfer coefficient is not limiting the overall CO₂ capture in the range presented in Figure 1.11. The reason for this is that the mass transfer is limited by the resistance in the liquid phase as discussed in the former chapter.

In Figure 1.12 the temperature in the absorber is presented graphically for three different values of k_G (k_G = 5.2.10⁻⁴, 2.6.10⁻³ and 1.3.10⁻² m.s⁻¹, i.e. the default value is multiplied with respectively a factor 0.2, 1 and 5.

Figure 1.12 Temperature profile in the absorber for three different gas side mass transfer coefficients (default value multiplied by factor of 0.2, 1 and 5).

Form Figure 1.12 it can be seen that the value of k_G has a huge impact on the temperature profile in the absorber. The CO₂ capture for the three different cases is more or less the same, so the different temperature profiles cannot be caused by the increased CO₂ capture and related exothermic reaction. The reason for this different temperature profiles is that not only the k_G for CO₂ is changed, but also the k_G for the other components present in the solvent, i.e. water. The value of the k_G for water has a large impact on the evaporation of water in the column. The higher the k_G value, the more mass transfer of water can take place and this has a large impact on the temperature profile in the absorber.

The default CO₂ absorption case as simulated in PPS has been compared with a field test and it appeared that the calculated CO₂ capture was 1.8% lower than the field case. To match the CO₂ capture calculated by the model with the capture measured in the field, the calculated effective area in the model was increased with 22% (case 1). As discussed before, it is more efficient for this case to fit the effective area than the other mass transfer parameters. With this (slightly) adjusted effective area correlation, three other field cases were calculated (case 2–4) and the comparison between model and field data are presented in Figure 1.13.

From this figure it can be concluded that the predicted CO₂ capture rate by the simulator is rather in line with the field data for all cases.

1.5 Conclusions and Recommendations

In this paper the impact on the various mass transfer parameters (a_e, k_G, and k_L) on the mass transfer parameters is studied with a rate based simulator and compared with a field case. From the simulations described in this work it can be concluded that knowledge of the individual mass transfer parameters is essential to describe the CO₂ capture process correctly. The performance of the CO₂ capture can be tuned with the individual mass transfer parameters, however, the impact on the overall performance is different for every parameter. If the wrong mass transfer parameter is tuned, extrapolation to other process conditions may lead to erroneous simulation results. In this paper a CO₂ capture process is described. In case a H₂S capture process is discussed, the results will be completely different, due to the very fast reaction rate between H₂S and amines. In case H₂S and CO₂ are both present in the gas phase the complexity increases significantly and rate based simulation is the only way to make a reliable design. From the simulations described in this paper may be concluded, that rate based simulation is a very powerful tool to describe the complex gas treating processes, however, a sound knowledge of the underlying fundamentals, i.e. the mass transfer parameters, is essential.

References

1. E.P. van Elk, A.R.J. Arendsen, G.F. Versteeg, “A new flowsheeting tool for flue gas treating”, Energy Procedia 1, 1481–1488, 2009.

2. E.S. Hamborg, P.W.J. Derks, E.P. van Elk, G.F. Versteeg, “Carbon dioxide removal by alkanolamines in aqueous organic solvents. A method for enhancing the desorption process”, Energy Procedia 4, 187–194, 2011.

3. J.C. Meerman, E.S. Hamborg, T. van Keulen, A. Ramírez, W.C. Turkenburg, A.P.C. Faaij, “Techno-economic assessment of CO₂ capture at steam methane reforming units using commercially available technology”, Int. J. Greenh. Gas Con. 9, 160–171, 2012.

4. A.R.J. Arendsen, E. van Elk, P. Huttenhuis, G. Versteeg, F. Vitse, “Validation of a post combustion CO₂ capture pilot using aqueous amines with a rate base simulator”, SOGAT, 6th International CO₂ Forum Proceedings, Abu Dhabi, UAE, 2012.

5. A.R.J. Arendsen, G.F. Versteeg, J. van der Lee, R. Cota, M.A. Satyro, “Comparison of the design of CO₂-capture processes using equilibrium and rate based models”, The Fourth International Acid Gas Injection Symposium, Calgary, 2013.

6. G.F. Versteeg, J.A.M. Kuipers, F.P.H. van Beckum, W.P.M. van Swaaij, “Mass transfer with complex chemical reactions. I. Single reversible reaction”, Chem. Eng. Sci. 44, 2295–2310, 1989.

Chapter 2

Modelling in Acid Gas Removal Processes

Department of Chemical & Materials Engineering, University of Alberta, Edmonton, AB, Canada

Abstract

One aspect of gas processing is the removal of the acid gases, H₂S and CO₂, from the gas stream. The process often involves the use of a solvent, which reacts with the acid gases. Hence the vapour-liquid equilibria are combined with chemical reaction. To design gas treating processes requires experimental data. However, the number of variables is so large that the necessary data at the conditions of interest are rarely available. Therefore models have been proposed so that the information needed can be obtained. The models that have been proposed, and their salient features, will be described.

2.1 Introduction

The acid gases (H₂S and CO₂) occur in many industrial settings. Natural gases often contain acid gases and gas processing involves their removal, together with that of water and higher hydrocarbons. Power is generated by plants fired with coal or natural gas, which produce large amounts of carbon dioxide. Carbon capture from the flue gas and subsequent sequestration could reduce anthropogenic carbon dioxide emissions. This has led to increased interest in the subject of removal of CO₂ from gas streams.

H₂S and CO₂ are called acid gases because they form a weak acid on dissolution in water (pKa = 6.36 for CO₂ and pKa = 6.99 for H₂S at 25 °C). It was recognized that the weak acid could be neutralized by a base. However, the use of a strong base, like NaOH, results in a precipitate which requires disposal. With a weak base the resulting compound is relatively unstable and can decompose by heating. Alkanolamines were first proposed for this purpose by Bottoms [1]. For over 80 years aqueous solutions of alkanolamines have been used for CO₂ and H₂S removal, originally from natural gas. Kohl and Nielsen [2] and Astarita et al. [3] have described the process and the history of gas processing. Alkanolamines are organic compounds with an amine group to provide basicity and an alcohol group so that the compound is soluble in water. Typical alkanolamines are:

Figure 2.1 Alkanolamines: Left Monoethanolamine (MEA); Right Methyldiethanolamine (MDEA).

Monoethanolamine is a primary amine with two replaceable hydrogens. Methyldiethanolamine is a tertiary amine with no replaceable hydrogens. This has an influence on the modelling. There are many other alkanolamines, but these are the ones most commonly used. An excellent review by Rayer et al. [4] presents a listing of experimental data, experimental methods and models used for many of the alkanolamines used for CO₂ removal.

The gas enters the absorber where it is contacted counter-currently by the solution. Reaction occurs and the rich solution leaves the bottom of the absorber while the purified gas leaves the top. The absorption is exothermic and so the rich solution leaves at a higher temperature than when it entered. If MEA is used, 82 kJ/mol of CO₂ is released and if the solution entered at 40 °C, it leaves at a higher temperature. For a cyclic process, it is necessary to reverse the reaction. The rich solution is sent to the regenerator where it is contacted with steam produced in the reboiler. The temperature at the bottom of the regenerator is about 120 °C, which drives the CO₂ out of solution. The 82 kJ/mol of CO₂ must be supplied to reverse the reaction. In addition energy must be supplied to raise the temperature of the rich solution to the boiling point and to provide steam to serve as the stripping vapour.

2.2 Vapour-Liquid Equilibria

The representation of the vapour-liquid equilibria for acid gas-alkanolamine solutions is different from that used for non-electrolyte solutions. The partial pressure, the mole fraction in the vapour times the total pressure, is plotted on the ordinate and the mole ratio in the liquid is plotted on the abscissa. The reason for this representation is that about 90 mole per cent of the aqueous solution is water, so that using the mole fraction of acid gas in the liquid phase would restrict the data to a small corner of the y-x diagram typically used to represent vapour-liquid equilibria. By using mole ratios, the scale ranges from 0 to about 1. The typical concentration of the alkanolamines in the aqueous solution ranges from 3 to 5 molar. Extensive data have been measured for the solubility of CO₂ and H₂S in alkanolamine solutions over the years. There are many alkanolamines and the variables are the temperature, concentration of the alkanolamine and the partial pressure of CO₂. An example of the data available for 5 M MEA is given in Figure 2.3. These data extend over 7 orders of magnitude of partial pressure and hence are normally presented on a logarithmic scale. In this case the abscissa is also on a logarithmic scale.

Data for CO₂ in an MDEA solution over a very wide range of conditions are shown in Figure 2.4. The data at 40 °C are typical of absorption conditions. The data at 120 °C are typical of regeneration conditions.

2.3 Modelling

The physical and chemical equilibria that occur in the removal of CO₂ by an alkanolamine solution are shown in Figure 2.5. The liquid phase contains a number of molecular and ionic species of weak electrolytes. The first rigourous method for weak electrolyte solutions was that of Edwards et al. [7].

When a gas containing H₂S and CO₂ is contacted by an aqueous alkanolamine solution, the following seven linearly independent reactions take place in the liquid phase:

1. Protonation of the amine

(2.1) equation

2. Formation of carbamate

(2.2) equation

3. First dissociation of carbon dioxide

(2.3) equation

4. Second dissociation of carbon dioxide

(2.4) equation

5. First dissociation of hydrogen sulphide

(2.5) equation

6. Second dissociation of hydrogen sulphide

(2.6) equation

7. Ionization of water

(2.7) equation

All models start with this basis. Tertiary amines, which lack a hydrogen atom, do not form carbamates. There are three classes of models: empirical models, activity coefficient models and equation of state models.

2.3.1 Empirical Models

The first vapour-liquid equilibrium models for weak electrolyte solutions, like acid gas-alkanolamine solutions, did not incorporate activity coefficients. Van Krevelen et al. [8] used “apparent” equilibrium constants. In their expressions for chemical equilibrium they used concentrations and then these “apparent” equilibrium constants were fit with experimental data as a function of ionic strength. A similar approach was used by Danckwerts & McNeil [9]. Kent & Eisenberg [10] used the same approach for the solubility of CO₂ and H₂S in monoethanolamine and diethanolamine solutions, but they did not consider any dependence on ionic strength. They assumed an ideal solution in the liquid phase and an ideal gas in the vapour phase. Using published data, they fit the chemical equilibrium constant for the protonation of the amine and the formation of carbamate to the data extant at the time. Of course, these simple models cannot provide the correct speciation in the solution. This information is important for the correct interpretation of kinetic experiments. Posey et al. [11] neglected the formation of carbamate to obtain a simple model. It is applicable to MDEA solutions, but cannot be used for primary and secondary amines. Dicko et al. [12] have found that the model is incapable of representing their new experimental data. Recently, Gabrielsen et al. [13] have presented a simplified model for CO₂ solubility in alkanolamine solutions. Their model describes the partial pressure of CO₂ in the relatively narrow range of conditions encountered in the capture of CO₂ from flue gases in coal-fired power stations and results in one explicit equation that has to be solved.

2.3.2 Activity Coefficient Models

A model for the activity coefficients of all the species in the liquid phase is needed. Henry’s law is used to relate the concentration of the acid gas in the vapour phase to that of the molecular acid gas in the liquid phase. The material balance equations and the requirement of electroneutrality complete the set of non-linear equations to be solved. The first activity coefficient model was that of Atwood et al. [14] who presented activity coefficients for MEA, DEA and TEA and their bisulphides. The activity coefficients were given as a function of ionic strength. Later, Klyamer & Kolesnikova [15]. assumed that the activity coefficients of the different ions were equal and independent of temperature. As well, the activity of the water was set equal to its molarity. This model was extended to mixtures of carbon dioxide and hydrogen sulphide by Klyamer et al. [16]. Deshmukh & Mather [17] used the extended Debye-Hückel equation of Guggenheim [18] for the activity coefficients:

The first term is the Debye-Hückel limiting law and represents the electrostatic forces; the second term takes into account short-range van der Waals forces. A is related to the dielectric constant of the solvent, b_k is a constant, z is the charge on an ion, I is the ionic strength, m is the molality, and ß_kj are interaction parameters. They were obtained by fitting to the experimental data.

Many activity coefficient models have been proposed and a summary of many of them has been presented by Anderko et al. [19].

Two different approaches have been considered in representing the activity coefficients. One method assumes that both water and the alkanolamine(s) are solvents. The other method assumes that only water is the solvent.

2.3.3 Two (and more) Solvent Models

Austgen et al. [20, 21] used the Pitzer extension of the Debye-Hückel equation for the long-range ion interactions and the Non-Random Two-Liquid (NRTL) model for the short-range interactions. As well, a Born term was needed to account for differences in the reference states. In this model not only water but also the alkanolamine were considered as solvents. The reference state for ionic species is the infinitely dilute state in water. The Born expression accounts for the change in the Gibbs energy associated with moving an ionic species from a mixed-solvent infinitely dilute state to an aqueous infinitely dilute state.

Fifteen molecule-molecule and molecule-ion pair parameters for the NRTL equation (all temperature dependent) were obtained by fitting experimental data. In later work the model was extended to mixtures of amines. Recently, this model has been applied to MDEA solutions by Zhang and Chen [22, 23]. It is the best available model at present.

Buenrostro-González et al. [24] used a similar model but included the use of the Smith & Missen nonstoichiometric algorithm for determination of the true compositions in the liquid. Liu et al. [25] modified the Austgen model to provide a better representation of the regeneration process. Barreau et al. [26] also used a similar model but included new experimental data in the determination of the parameters. The reason the parameters differ and the results differ is that different data sets were used to determine the parameters. Lee [27] used an activity coefficient model combined with the UNIFAC group contribution method for the activity coefficients of the neutral species. The advantage of this approach is that the model is applicable to different amines without determination of new parameters.

Li and Mather [28] used the Clegg-Pitzer equations for the short-range interaction plus the Debye-Hückel term for the long-range interaction. The resulting equation was applied to mixtures of alkanolamines.

Another model, which used the Debye-Hückel term for the long-range interaction together with the UNIQUAC model for the short-range interaction, was proposed by Sander et al. [29].