In-line physical desorption unit—Part 2: Optimisation analysis

Accepted Manuscript Title: In-line Physical Desorption Unit – Part 2: Optimisation Analysis Author: Z.H. Ban K.K. Lau A.M. Shariff PII: DOI: Reference:

S0263-8762(16)30370-7 http://dx.doi.org/doi:10.1016/j.cherd.2016.10.032 CHERD 2455

To appear in: Received date: Revised date: Accepted date:

5-1-2016 10-10-2016 18-10-2016

Please cite this article as: Ban, Z.H., Lau, K.K., Shariff, A.M., In-line Physical Desorption Unit – Part 2: Optimisation Analysis.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2016.10.032 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

In-line Physical Desorption Unit – Part 2: Optimisation Analysis

Z.H. Bana, K.K. Lau*,b, A.M. Shariffb

a

School of Engineering, Xiamen University Malaysia, Bandar Sunsuria, 43900 Sepang, Selangor, Malaysia.

b

Chemical Engineering Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia.

* E-mail: [email protected], Tel: +605-3687589 Fax: +605-3656176

1

Highlights 

Three objective functions were identified for the optimisation of desorption unit



The behaviour of seven design parameters were analysed via design of experiment



Three optimised design based on three operating conditions have been identified



High velocity fluid profile has been generated at the outlet of desorption unit



Desorption efficiency of optimised nozzle was superior than the conventional nozzle

2

Abstract This paper is the second part of our study on a novel in-line physical desorption unit. In the first part, the conceptual design and desorption modelling were discussed. In this paper, the work was extended to the optimisation and numerical analysis on the optimised desorption unit design. Similar to first part of our study, the desorption phenomenon was modelled via Computational Fluid Dynamics (CFD) approach. The desorption performance for seven different design parameters were studied and analysed via design of experiment (DOE) method. The objective functions were analysed and the suggested optimised design parameters were determined. Thereafter, the detailed hydrodynamics and mass transfer profile in the suggested optimised designs were simulated and studied. The performances of the optimised designs were found better than conventional nozzle. The solvent velocity at the outlet was found to be relatively high, which was ideal to be utilised together with compact gas liquid separator. The proposed in-line physical desorption unit has potential to be employed in various process conditions including remote and offshore conditions.

Keywords: In-line desorption, Computational Fluid Dynamics (CFD), Population Balance Model (PBM), physical solvent, optimisation

3

1.0 Introduction As mentioned in first part of our study, it is crucial to enhance the physical solvent regeneration process in order to improve natural gas sweetening process. The natural gas sweetening process favour physical absorption method over chemical absorption method due to lower CO2 solubility in chemical solvent at high pressure. The study on physical absorption of acid gas remains limited up to date. Siefert et al. (2016) have synthesised two new hydrophobic physical solvents (PEG-Siloxane-1 and allylpyridinium bis(trifluoromethylsulfonyl) imide [aPy][Tf2N])for CO2 capture from precombustion syngas stream. The properties of these solvents were imported into AspenPlus and detailed techno-economic analysis was conducted. Their results showed that the cost competitiveness of PEG-Siloxane-1 and Selexol were similar, while the cost for CO2 capture by using [aPy][Tf2N] could be lower than Selexol. In addition, they also postulated that the reason for the higher CO2 solubility for the two new solvent as compared to Selexol is because water absorption into Selexol has consumed the free volume where the CO2 gas can be accumulated. Dave et al. (2016) have studied the process design for CO2 absorption from syngas using physical solvent DMEPEG via rate based simulation method. They have optimised the configuration of packed tower and solvent circulation rate, and subsequently minimize the equipment size and utility consumption. Process integration and technoeconomic assessment could also be accomplished with the detailed sizing and rating of process equipment and solvent circulation. However, the desorption calculations were not included in their work. Biard et al. (2016) have developed a simple and timesaving experimental procedure to study the mass transfer in physical absorption. The developed experimental method allowed determination of partition and mass-transfer coefficients. Heldebrant et al. (2016) have invented a new system and process for CO2 capture using 4

organic solvent. CO2 gas was captured chemically by the organic solvent at elevated pressure and formed zwitterionic salt, which would release the CO2 gas when the pressure was reduced. The organics solvent was regenerated after the pressure reduction. Guo et al. (2012) have developed a simplified process simulation for Selexol process. The power requirements and separation processes were taken into consideration. The optimum operating conditions could be determined via the simplified process simulation. A mathematical model has been developed by Boributh et al. (2011) to investigate the physical absorption of CO2 by water by using hollow fibre membrane contactor. Membrane pore size distribution and properties, and operating conditions were included in the model. Naim and Ismail (2013) have studied the effect of fibre packing density on the performance of physical CO2 absorption in hollow fibre membrane contactor. They have concluded that increasing packing density would cause reduction in CO2 absorption flux but increase in overall mass transfer coefficient. Most of the available study for physical solvent was focusing on absorption and techno-economic assessment. The study on desorption is limited and the available mathematical models are not suitable to describe non-equilibrium desorption phenomenon. The lack of study on desorption makes the improvements in terms of desorption unit to be difficult. The main objectives of this whole project were to model non-equilibrium desorption phenomenon, design and optimise a compact physical desorption unit.

A detailed

introduction to solvent regeneration process and motivation to carry out the study is discussed in detail in the first part of our study (DOI: http://dx.doi.org/10.1016/j.cherd.2016.08.029). In the first part of our study, a new conceptual design of physical solvent regeneration unit was proposed. The foundation of the conceptual design has been discussed in detail. This proposed design is aimed to replace the conventional desorber, which is typically used for physical solvent regeneration process. The desorption phenomenon was studied and modelled via Computational Fluid Dynamics (CFD) modelling approach. 5

In second part of our study, a detailed analysis to study the behaviour of several design parameters has been carried out by using design of experiment (DOE) method. The optimisation of the design would be carried out based on the DOE analysis, which is presented in current work. The detailed hydrodynamics and desorption profile in the computational domain will also be discussed here. Lastly, the performance of the optimised design is compared with a conventional nozzle.

2.0 An introduction to the conceptual design and analysis It is necessary to introduce and summarise the concept and analysis obtained in the first part of our study work (refer to supplementary document), for the ease of understanding the work presented in this paper. In short, first part of our study presented the concept foundation to design an in-line physical desorption unit and analysed the effect of different design parameters. The motivation for the work was to remove CO2 from natural gas stream via physical solvent absorption process and the main focus was to enhance the solvent regeneration process. The working principles for the in-line physical desorption unit has utilised the fact that low local pressure can increase desorption rate. The new unit shall be able to create low or negative pressure region so that the desorption process can be enhanced, while maintaining the pressure in pipeline without using additional pumps. There were several design considerations that were required to be taken into consideration, including effort to maintain the pressure in pipeline before entering the unit, increase solvent flow rate and improve desorption efficiency. As a start, three main sections of the unit, namely pressure maintaining, pressure reducing and desorption enhancing sections, were proposed. In current work, seven design parameters were introduced to modify the unit design so that the design can be optimised as shown in Figure 1. The range of study for each design parameters and their own

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different roles to fulfil the design considerations are summarised in Table 1. It is essential to understand the behaviour of each design parameters as different combination of these design parameters settings would result in different desorption phenomenon.

Figure 1: General proposed conceptual design of the novel in-line physical desorption unit

Table 1: Range of design parameters and their functions No. Design parameters A

CO2 saturation pressure and

Range 10 – 30 bar

pressure inlet B

Number of blocks at I, i

C

Number of blocks at II, j

Function To study the effect of different CO2 saturation pressure and pressure inlet

1–3

To reduce the solvent flowing velocity To create different channel height in

0–2 section II D

Number of blocks at III, k

To enhance desorption via low pressure 1–3 region

E

Channel height, H to Inlet 0.5 – 1.0

To reduce the solvent flow rate

diameter, D ratio (H/ID) F

Outlet diameter, OD to Inlet

To allocate enough space for desorbed 2–4

diameter, ID ratio (OD/ID) G

Angle of blocks at C, r

gas 45° – 135°

To further enhance pressure reduction

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3.0 Methodology 3.1 Optimisation Approach The multi-objective optimisation of design parameters was determined based on the analysis from DOE model. In current work, detailed simulations to study the behaviours of various design parameters on the objective functions were carried out via Design of Experiment (DOE) method. An estimation for the objective functions could be made through the outcome of the DOE method. Box-Behnken experimental design was employed in current work as it is an efficient design for modelling of quantitative factors (Schmidt et al., 1994). This design has been widely used for analysing experimental data and optimisation in various works. For example, Li et al. (2013) have optimised the extraction method of insecticidal Cry1Ac from soil by using Box-Behnken experimental design. The same experimental design was used by Xie et al. (2015) to optimise the process parameters of high pressure machine decocting process. There were three objective functions being identified, namely pressure maintenance factor (OP1), solvent flow rate relative to inlet pressure (OP2) and desorption efficiency (OP3). The three objective functions were important to be optimised; pressure maintenance can prevent the risk of sudden explosion in the pipeline before undergoes desorption; higher solvent flow rate relative to inlet pressure could ensure the processing speed would be optimised; high desorption efficiency would enhance the desorption process. The three objective functions were quantified in current work and known as OP1, OP2 and OP3. The first objective function, OP1, which was known as pressure maintenance factor, was defined as, (1)

where

= Inlet pressure 8

= Pressure in channel of section I The second objective function, OP2, which was the solvent flow rate relative to inlet pressure, was defined as, (2)

⁄

where F = Solvent flow rate

The third objective function, OP3, which was known as desorption efficiency, was defined as, (3) where

= Mass fraction of dissolved CO2 in water solution at inlet = Mass fraction of dissolved CO2 in water solution at outlet

The desorption efficiency is higher at greater pressure reduction and supersaturation ratio while the pressure in CO2 rich solvent must be maintained before undergoes desorption process to prevent sudden explosion. One of the challenges to develop a solvent regeneration method is to maintain the pressure in CO2 rich solvent without using a pump. The ideal condition for this method is to have high flow rate and desorption efficiency. The design of the proposed method was optimised against pressure maintenance factor, desorption efficiency and solvent flow rate by changing the dimension of the invention.

In this context, the design parameters were optimised under three different CO2 saturation pressure, including 10, 20 and 30 bar. The case for solvent entering the low pressure solvent regeneration process with 10 bar pressure and CO2 saturated at 10 bar, was referred as P10. Similarly, the cases with pressure of 20 and 30 bar were referred as P20 and P30 (refer to Part 1 for detail explanation). 9

3.2 Computational Details The computational domains in current work were defined based on the requirements from DOE analysis. The optimised condition and values for various design parameters could be determined via the analysis within the range of study. The values for design parameters were optimised against the three cases (P10, P20 and P30) and determined via the DOE model. Three optimised designs were obtained from the analysis with different design parameter values. The similar mathematical modelling approach as discussed in our first part of our study (DOI: http://dx.doi.org/10.1016/j.cherd.2016.08.029) was employed in current work. The desorption phenomenon was modelled via integration of Computational Fluid Dynamics – Population Balance Model (CFD – PBM) with bubble nucleation and growth model approach after a thorough evaluation on the modelling tools including rate-based model, Rachford-Rice model, cavitation model, bubble formation model and Computational Fluid Dynamics – Population Balance Model (CFD – PBM) model as presented in the first part of our study. As the dissolved gas was desorbed from the solution, the amount of dissolved gas would decrease. The volume of gas bubbles occupied in the domain was also modelled via this method. Table 2 summarised the boundary conditions and settings for the validated numerical simulation employed in first part of our study. All the simulations in current work were carried out based in the similar settings and boundary conditions

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Table 2: Boundary conditions and settings for the numerical simulation Property

Boundary Conditions and Settings

Materials

Water and CO2

Dimensionality

2D

Solution method

Coupled pressure-based solver

Solution formulation

Implicit

Time dependence

Steady state

Turbulence model

Realised k-ε model

Pressure inlet

Pressure = 10, 20 and 30 bar for three cases

Pressure outlet

Pressure = 0

Population balance model

Quadrature method of moments (QMOM)

Three sets of simulation based on the similar condition for P10, P20 and P30 were computed for conventional nozzle computational domain as shown in Figure 2. These simulations were conducted to compare their performance with the optimised designs suggested by the DOE model as shown in Figure 16.

Inlet

Outlet (7 mm)

Throat (5 mm)

(7mm) 650 mm Figure 2: Computational domain for conventional nozzle

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4.0 Results and discussion 4.1 Parametric Study Design of Experiment (DOE) is a powerful method to correlate the behaviour of the seven design parameters against the three objective functions (refer to Table 1).

4.1.1 Objective function 1 – OP1 (Pressure Maintenance Factor - Dimensionless) From the simulation data obtained as part of the design of experiment, a mathematical model was suggested to predict the pressure maintenance factor as defined in Equation (1) based on the different design parameters. The most suitable type of model used as suggested was quadratic model. The R-squared and predicted R-squared values obtained via quadratic model were found to be 0.9978 and 0.9848 respectively. Figure 3 shows the residual against predicted plot for objective function – OP1. From the figure, the data points are scattered randomly without a specific shape and the model did not depend specifically on any design parameters.

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Figure 3: Residual against predicted plot for objective function – OP1 Figure 4 shows the predicted against actual plot for objective function – OP1. From the figure, the actual data lies very closely with the prediction line, indicating that the pressure maintenance factor can be predicted at high confidence level.

Figure 4: Predicted against actual plot for objective function – OP1 Figure 5 shows the perturbation plot for objective function – OP1. From the figure, the changes in two design parameters (B and E), which are number of blocks, i, at section I and the ratio of channel height at middle of section I to inlet diameter (H/ID), will greatly affect the pressure maintenance factor. As the number of blocks i increase, the pressure maintenance factor was found to be higher. The blockage has successfully slow down the liquid flow velocity that passed through it. The pressure maintenance factor would decrease with the increase of ratio of channel height, H, to inlet diameter, ID. The liquid would flow at higher flow rate with larger channel height, H, diameter and this has caused higher pressure drop at the inlet according to energy balance equation when no pump was used to increase the pressure.

13

Figure 5: Perturbation plot for objective function – OP1 Figure 6 shows the 3D contour plot of design parameters B and E against optimization parameter – OP1. This 3D graph relates the interaction between the two design parameters B and E with the optimization parameter, which was the pressure maintenance factor. From the figure, the lowest point is found at the position of B = 1.0 and E = 1.0. This is the design settings where the liquid at the pressure maintaining section would experience the highest pressure drop. The pressure maintenance factor increased gradually with the decrease of design parameter E and increase of design parameter B. The highest point was found at position B = 3.0 and E = 0.5. This was the design settings with the least of pressure drop. The pressure maintenance factor can be predicted via the quadratic model suggested as shown in Equation (4).

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Figure 6: 3D contour plot of design parameters B and E against objective function - OP1

(

)

(4)

4.1.2 Objective function 2 – OP2 (Solvent Flow Rate Relative to Inlet Pressure – kg/Pa·s) The mathematical model to predict the solvent flow rate relative to inlet pressure as defined in Equation (2) based on different design parameters was suggested with the analysis of simulated data. The type of model suggested was a quadratic model, with R-squared value

15

of 0.9962 and predicted R-squared value of 0.9734. The high predicted R-squared value has suggested that the model can predict the solvent flow rate relative to inlet pressure at high level of confidence. Figure 7 shows the residual against predicted plot for objective function – OP2. The residuals were scattered randomly and no specific shape formed from the data points.

Figure 7: Residual against predicted plot for objective function – OP2 Figure 8 shows the predicted against actual plot for objective function – OP2. From the figure, the actual data points fall closely with the predicted line. This has further confirmed that the model is capable to predict the solvent flow rate relative to inlet pressure precisely.

16

Figure 8: Predicted against actual plot for objective function – OP2 Figure 9 shows the perturbation plot for objective function – OP2. From the figure, the changes in design parameters A, B and E have significant effects on the objective function – OP2. The increase of design parameter B, which was the number of block i in section I, would cause a decrease in objective function – OP2. The decrease of solvent flow rate with the increase of design parameter B because more blockages i, have caused the solvent to flow at lower speed. The design parameter E, which was the H/ID ratio, has different effect on the objective function – OP2. As the channel height, H, increased, the solvent flow rate would increase accordingly. This was because the increase in channel height, H would allow more solvent to pass through at a specific time. Therefore, the solvent flow rate would increase. The increase of design parameter A would decrease the objective function – OP2. This has shown that although the increase of inlet pressure would typically cause the increase in solvent flow rate, the magnitude of increase was not significant as compared to the increase of inlet pressure. The objective function – OP2 would decrease instead of increase with the increase of design parameter A.

17

Figure 9: Perturbation plot for objective function – OP2 Figure 10 shows the 3D contour plot of different design parameters against objective function – OP2. Figure 10 (a) shows the interaction between design parameter A and B against the objective function – OP2. The objective function – OP2 was highest when the design parameter A (inlet pressure) was at 10.0 and design parameter B at 1.0 while it was lowest when design parameter A was at 30.0 and design parameter B was at 3.00. The correlation graph was a slightly exponentially curved 3D graph. The objective function – OP2 could be predicted with the 3D graph as both the design parameter A and B has almost the same effect on it.

18

(a)

(b)

19

(c) Figure 10: 3D contour plot of different design parameters against objective function – OP2 (a) A and B (b) A and E, and (c) B and E

Figure 10 (b) shows the interaction between design parameter A and E against the objective function – OP2. The objective function – OP2 was at its highest point at A = 10.0 and E = 1.0 while its lowest point was at A = 20.0 and E = 0.5. From the figure, the effect of design parameter A on the objective function – OP2 was relatively small as compared to design parameter E. An interesting phenomenon was found where the lowest objective functions was not at design parameter A = 30.0 but at 20.0. Figure 10 (c) shows the interaction between design parameter B and E against the objective function – OP2. From the figure, the highest objective function – OP2 could be obtain at the point B = 1.0 and E = 1.0. The lowest objective function – OP2 was found to be at position B = 3.0 and E = 0.5. The solvent flow rate could be increased with lower number of block i and larger channel height, H.

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The analysis on the different design parameters on the objective function – OP2 has suggested a correlation as shown in Equation (5). (

)

(5)

4.1.3 Objective function 3 – OP3 (Desorption Efficiency - Dimensionless) There are two mathematical models suggested by the design of experiment method for objective function – OP3 (refer to Equation (3)), including linear and quadratic. The Rsquared for linear model was recorded as 0.7334 and predicted R-squared as 0.6472 while the R-squared value for quadratic model was found to be 0.9116 and predicted R-squared value as 0.4871. The linear model was chosen for this project as it has higher predicted R-squared value as compared to quadratic model. The predicted R-square value of 0.6472 for the regression model implies that it is capable to predict the OP3 value in a reasonable range (Gu et al., 2015). The predicted R-squared value for OP3 was slightly lower than objective functions OP1 and OP2 because of its dependency on many factors in the mathematical modelling and simulation. The CO2 mass transfer was determined by many factors including bubble nucleation rate, bubble nuclei number density and bubble growth rate. A slight changes in the parameters in the long series of mathematical models that used to predict these factors would result a significant difference in the values for the factors, which would cause the desorption rate and efficiency (OP3) to change. 21

Figure 11 shows the residual against predicted plot for objective function – OP3. From the figure, the data points in the plot are scattered randomly. The mathematical model was considered to be good enough to predict the objective function – OP3.

Figure 11: Residual against predicted plot for objective function – OP3 Figure 12 shows the predicted against actual plot for objective function – OP3. From the figure, the actual data points were scattered around the prediction line. These actual data points were slightly far away from the prediction line as compared to the prediction for objective functions OP1 and OP2.

22

Figure 12: Predicted against actual plot for objective function – OP3 Figure 13 shows the perturbation plot for objective function – OP3. From the figure, almost all design parameters have significant effect on the objective function – OP3, except for design parameter D and G. Design parameters D and G are number of blocks at III, k and its angle, respectively. The objective function – OP3 would decrease with the increase of design parameters A, B, C and E while it would be increased with the increase of design parameter F.

23

Figure 13: Perturbation plot for objective function – OP3 Figure 14 shows one factor plot for objective function – OP3 with design parameters A, B, C, D, E, F and G respectively. Figure 14 (a) shows the interaction between the design parameter A and objective function – OP3. The objective function – OP3 was found to decrease with the increase of design parameter A. The amount of dissolved gas in solvent would increase with design parameter A. Since the amount of dissolved CO2 introduced into the system was higher for higher design parameter A, the insufficient increase of desorption rate would typically reduce the desorption efficiency.

(a)

24

(b)

(c)

25

(d)

(e)

26

(f)

(g) Figure 14: One factor plot for objective function – OP3 with design parameters A, B, C, D, E, F and G respectively

27

Figure 14 (b) shows the interaction between the design parameter B and objective function – OP3. From the figure, the objective function – OP3 decreases with the increase of design parameter B. This probably because higher number of blockages i would reduce the solvent flow rate and subsequently reduce the momentum. The negative pressure formation at blockages k would reduce accordingly. This has resulted in a lower bubble nucleation rate that would reduce the mass transfer of dissolved CO2. Figure 14 (c) shows the interaction between the design parameter C with the objective function – OP3. The objective function – OP3 has decreased with the increase of design parameter C. The increase of design parameter C has reduced the diameter of channel at the throat. This has caused loss of momentum for the solvent and subsequently reduce the desorption rate. Figure 14 (e) shows the interaction between the design parameter E and objective function – OP3. The figure shows that the objective function – OP3 would decrease as the design parameter E increased. As the design parameter E increased, the throat diameter at section II would increase. Solvent would be flowed at higher flow rate, which indicated that larger amount of CO2 was introduced into the system. Higher desorption rate was required to increase the desorption efficiency. Due to the limited design parameters range, the system could not increase the desorption rate sufficiently and the objective function – OP3 would decrease. The underlying reason for the decrease of objective function – OP3 with parameter A was similar. Figure 14 (f) shows the interaction between the design parameter F and objective function – OP3. From the figure, the objective function – OP3 increases with design parameter F. The higher value of design parameter F indicated that more space was allocated in desorption enhancing section (III). The desorption process will form a large volume of gas due to the large density difference. The large volume of gas would occupy the space in

28

section III and caused the solvent to flow at lower speed. Similarly, this would reduce the bubble nucleation rate and subsequently the desorption rate. Figure 14 (d) and (g) shows the interaction between the design parameter D and G with the objective function – OP3 respectively. The effect of changes in this two design parameters on objective function – OP3 were found to be less significant. It is important to note that, the analysis has shown that the changes in design parameters D and G has similar effect on OP3, but each of them has their own different weightage on the OP3. The objective function – OP3 increased slightly with the angle and number of blockages k. A regression model was suggested based on the detail analysis as shown in Equation (6). (

) (6)

4.2 Optimisation Analysis Desorption process is desired to be carried out at higher solvent flow rate and higher desorption efficiency. Higher solvent flow rate is usually suffered high pressure loss in CO2 rich solvent before entering into desorption column if no additional pumps were used. An optimised design where the flow rate, desorption efficiency and pressure loss is crucial for the invention of desorption method. A total of 62 simulation were attempted to study the performance of desorption phenomenon in the developed desorption method with different dimensions. The BoxBehnken method was employed as the response surface methodology to optimise the design. These factors were inter-related to each other and resulted in different responses. For example, a design with larger H/D ratio may induce higher solvent flow rate but more number of block i in section I may have reverse effect. A detailed study on the behaviour of the

29

hydrodynamics and desorption efficiency under different dimensions of the initial conceptual design was required for the optimisation purpose. In current work, the optimisation of the design dimensions was computed against pressure maintenance factor, relative solvent flow rate, and desorption efficiency. Different combinations of the dimensions and configurations would result in different value of pressure maintenance factor, relative solvent flow rate and desorption efficiency. The three objective functions were unlikely to be at the optimum points concurrently as one may limits the others. For example, higher relative solvent flow rate would probably induce higher pressure drop, which was not in favour in this case. Therefore, a balance between these three parameters with desorption efficiency as priority, has to be considered for the optimisation. In current work, three different optimum designs were obtained according to three different pre-saturation pressure of CO2 in water, including 10, 20, and 30 bar. The three simulation cases were referred as P10, P20 and P30 in this context, with pressure inlet set to be same as the CO2 pre-saturation pressure at 10, 20 and 30 bar. Since the amount of CO2 in water and the pressure inlet for each simulation case were not be the same, the hydrodynamics and desorption phenomenon were expected to be different. Therefore, different cases would result in different optimum design. Table 3 shows the range for the three objective functions that have been obtained through the simulation results within the design settings as shown in Table 1. The interaction between the dimensions settings were computed via the response surface methodology. This approach has enabled the determination for the optimum dimensions settings. The optimum responses for the three studied cases for desorption of CO2 in water at P10, P20 and P30, were determined. These optimisation studies were carried out by using the DOE model to estimate the objective function values.

30

Table 3: Range of objective functions obtained from the simulated result for P10, P20 and P30 cases Parameter

Value

Objective function 1, OP1 (pressure maintenance factor) (dimensionless)

0.905 - 0.989

Objective function 2, OP2 (solvent flowrate relative to inlet pressure) 1.076 - 3.824 (kg/Pa·s) Objective function 3, OP3 (desorption efficiency) (dimensionless)

0.286 - 0.946

Figure 15 shows the graph of the three objective functions for cases P10, P20 and P30 with their respective overall optimised dimensions settings. From Figure 15, the OP1 values for the three cases were able to be sustained at above 0.96. The relatively low pressure drop was insufficient to initiate bubble nucleation at the inlet as predicted from the simulations. Solvent flow rate relative to inlet pressure was found to be reducing when the water was presaturated with CO2 at higher pressure. This phenomenon was probably because the inlet pressure increased larger as compared with solvent flow rate. Desorption efficiency was modelled at 0.946 for both case for P10 and P20 bar cases while it was predicted to be 0.907

Pressure maintenance factor, OP1 (dimensionless)

for P30 bar case. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 P10

P20 Simulation case

P30

(a)

31

Solvent flowrate relative to inlet pressure, OP2 (kg/Pa·s)

2.5 2 1.5 1 0.5 0 P10

P20 Simulation case

P30

(b)

Desorption efficiency, OP3 (dimensionless)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 P10

P20 Simulation case

P30

(c) Figure 15: Graph of the objective functions with respect to overall performance (a) OP1 (b) OP2 (c) OP3

32

4.3Optimised Design Analysis Three optimum design and dimensions were selected based on the response surface analysis as discussed in Section 4.2 for P10, P20 and P30 cases. These designs were selected according to overall optimisation consideration, where the three objective functions including OP1, OP2 and OP3 were considered. The geometry of the three optimised designs is presented in Figure 16. The suggested values of various design parameters via DOE model for conditions P10, P20 and P30 are shown in Table 4.

(a)

(b)

(c) Figure 16: Geometry of optimised designs (a) P10 (b) P20 (c) P30 (unit in mm)

33

Table 4: Settings for design parameters according to conditions P10, P20 and P30 Design Parameters

P10

P20

P30

B

1

1

1

C

1

1

1

D

1

2

3

E

0.56

0.59

0.54

F

4

4

4

G

81°

126°

127°

Detailed analysis of hydrodynamics and desorption phenomenon (bubbling process) via CFD simulations were further discussed in this section. In general, effective physical desorption (solvent regeneration) will favour for low pressure condition as the dissolved gas solubility in solvent will be lower in most of the common cases. Low pressure will also induce higher bubble nucleation and growth rate, which will aid in increase of desorption rate. The pressure, velocity, bubble nucleation and growth rate, desorption rate, dissolved gas concentration in solvent, and volume fraction of the gas and liquid phase in the computational domain were analysed in depth for the description of bubbling desorption process.

4.3.1 Pressure Pressure profile played an important role in determining bubble nucleation and growth rate, which subsequently promote desorption rate. Low pressure, or even vacuum pressure was preferred in enhancing desorption rate. The pressure of the feed stream, where the CO2 saturated solution must be maintained at high pressure to avoid sudden explosion similar to boiling liquid expanding vapour explosion (BLEVE). For the BLEVE case, the pressurised liquid has experienced either sudden pressure reduction or heating above boiling point, and caused the liquid to boil. The liquid will change into gas which takes up more space in vented container or build up pressure in sealed container. The similar concept was 34

applied in the CO2 saturated solution, whereby the dissolved gas would escape from the solution and form gas when the pressure of the system was reduced. The pressure reduction has caused the solution to become supersaturated solution. The dissolved gas concentration in the solution must be reduced in order for the system to return back to equilibrium state. The gas formation would in turn increase the system pressure as the pipeline was a sealed container and the gas could not be released elsewhere. This is one of the main challenges in designing desorption system. Figure 17 shows the contour plot of pressure profile in the three optimised design for the P10, P20 and P30 cases. Figure 17 (a) shows the pressure profile for the P10 case. The pressure contour is divided into four main regions. The pressure at region L1 was successfully maintained at around 10 bar, which have met the requirement to maintain the pressure in the incoming pipeline to avoid explosion. The pressure was maintained by the pressure maintenance block in region L2 and the empty channel in region L3. Since the Classical Nucleation theory (CNT) has suggested that a sufficient amount of energy (provided by pressure drop) is required to initiate bubble nucleation, the slight pressure drop in the L1 region was found to be in non-nucleating condition (Lubetkin, 1995). The solution would pass through region L2 with a pressure maintaining block. The solution in this region has experienced the pressure drop from 10 bar to near atmospheric pressure. The solution would enter three empty channels and exit in an expanded area at near atmospheric pressure in region L3. The pressure in L3 was sustained around atmospheric pressure with the blocking element. The pressure of the solution has dropped to sub-atmospheric level in region L4 (after blocking element). The pressure drop was due to the constriction formed by the blocking element, which was similar to the venturi effect. This phenomenon was in accordance to energy balance equations where an increase of velocity of the incompressible fluid has to be compensated by decrease in pressure. The sub-atmospheric condition is

35

important to regenerate the solvent as it was capable to further enhance the desorption process.

(a)

(b)

36

(c) Figure 17: Contour plot of pressure profile in computational domain, Pa (a) P10 (b) P20 (c) P30 The pressure profile has suggested that the liquid flow was in a flashing or outgassing flow condition, where the pressure of the liquid was not recovered. This type of liquid flow was the desired flow type as compared to choked flow and cavitation. The damage caused by flashing flow was relatively mild as compared to cavitation damage (Riveland, 1985). The damage caused by flashing flow could be usually tolerated by the use of erosion resistant materials. The sub picture in Figure 17 (a) shows the pressure profile in the computational domain for sub-atmospheric region. The L4 region was found below the atmospheric pressure and pressure was found to drop to almost –15 kPa below atmospheric pressure at L5. This phenomenon occurred probably because of the strong collision of the solvent with the wall. The pressure has gradually recovered towards the exit and reached atmospheric pressure. Figure 17 (b) shows the contour plot of pressure profile for simulation of case P20. The pressure at L6 was successfully maintained near to 20 bar, and experienced pressure drop along the pathway to near atmospheric pressure at L10. Pressure at L10 was found slightly above atmospheric pressure but not sub-atmospheric as recorded in case P10. This was 37

probably due to the large amount of CO2 gas being released from the solvent trapped in the confined space and created pressure build-up before it reached the exit. There were a total of four regions (L9 – 1 to L9 – 4) were predicted to be in sub-atmospheric region. The pressure profile for the simulation case P30 was found to be similar to the P10 and P20 cases. The pressure at L11 was sustained at near 30 bar, which was sufficient to prevent the onset of bubble nucleation. Similarly, the pressure was reduced significantly at L12 from 30 bar to about 5 bar. The pressure has dropped to almost 35 kPa after L14 blocking elements and increased to about 50 kPa at L15-1. The large amount of CO2 released gas was believed to cause the increase in pressure. In P30 case, the sub-atmospheric region was found at region L14. The pressure in L15 decreased gradually to atmospheric pressure towards the outlet.

4.3.2 Velocity The pressure head would be converted into velocity head based on the energy balance equation. Therefore, the region with low pressure was expected to be associated with high velocity. Figure 18 shows the velocity profile of liquid solution phase in the computational domains for the three cases of P10, P20 and P30 by using their own optimised design. Figure 18 (a) shows the velocity profile for the P10 case. The computational domain was divided into six regions. The liquid solution velocity at V1 was relatively low at around 8 m/s as compared to liquid solution velocity at other regions, which was predicted to be more than 30 m/s. The relatively low liquid solution velocity was predicted at V1 was because of the high pressure maintenance at this region. The velocity profile at V2 has experienced big changes, which was in accordance to the high pressure drop. The liquid solution flowed into the empty channel and exited into an expansion region in V3 with high velocity.

38

(a)

(b)

39

(c) Figure 18: Contour plot of velocity in the computational domain, m/s (a) P10 (b) P20 (c) P30 The liquid solution hit with the blocking element in region V4 with pressure drop at region V4 and generated high radial velocity at about 27 m/s at region V4-1 and V4-2. The liquid solution has flowed at relatively high speed at about 33 m/s in region V5 after hitting the wall of the block. The pressure was found to be at sub-atmospheric condition at regions V4-1 and V4-2, which agreed well with the energy balance equation. The liquid solution flow velocity in V5 was predicted to be about 2 to 3 times higher than V1. The high velocity liquid solution flow was maintained at velocity of about 20 m/s in region V6. The high velocity flow was partly induced by large gas volume that was formed after the desorption process. This is similar to the flashing flow where high velocity of liquid solution flow is found after the solution was flashed. The high velocity of the liquid solution flow in V6 has provided a good condition to separate the gas and liquid solution via mechanical separator such as cyclone. The separator will utilise the high velocity of the solution to create high centrifugal or swirling force to separate gas and liquid solution (schook and van Asperen, 2005). Thus, the high kinetic energy of the system would not be wasted.

40

Figure 18 (b) shows the contour plot of velocity profile of liquid phase for P20 case. The liquid solution flow velocity was found to be relatively slow at about 10 m/s in region V7 and increased to about 40 m/s in region V8. The liquid solution velocity was maintained at about 40 m/s in region V9 and hit the blocking elements in region V10. High radial velocity at about 40 m/s was recorded for the liquid solution at region V10-1 and V10-2. This has created small negative pressure region as found in regions L9-1, L9-2, L9-3 and L9-4 as discussed in Section 4.3.1. The liquid solution that passed through the small passage between the blocking elements has experienced a slight increase of velocity to 45 m/s. The liquid solution continued to flow at about 40 m/s in region V11 towards the exit. Figure 18 (c) shows the contour plot of velocity profile for P30 case. The velocity of the liquid solution flow was found to be relatively slower at about 15 m/s in region V12 as compared to other region. The velocity of the liquid solution has increased to about 40 m/s in region V13 with the pressure drop from 30 bar to almost 2 bar. Similarly, the liquid solution flowed at high velocity in region V14 and hit the blocking elements at V 15. The blocking elements have induced high radial velocity up to 48 m/s at region V15. High pressure drop was found in the region V15, with creation of high negative pressure at region L14 as discussed in Section 4.3.1. The liquid solution velocity in region V16 has changed from high (

) to low (

) and increased to almost 68 m/s near to the outlet. This

phenomenon was probably due to the high amount of released CO2 gas trapped in the confined space that caused the liquid solution velocity to be lower and create higher pressure region (Mayinger, 1988). The high velocity flow is one of the essential cost savings elements for gas-liquid separation via mechanical separators such as cyclone.

4.3.3 Nucleation Rate

41

The desorption phenomenon of the dissolved gas is greatly depended on the bubble nucleation rate. Bubble nucleation is a process of a bubble nuclei formation. The mechanism for bubble nucleation of vapour and dissolved gas are different. According to Kwak and Oh (2004), bubble nuclei can be formed from different proportion of vapour and dissolved gas. They have suggested that the statistical mean of all possible bubble nucleation rates is more meaning to represent the actual bubble nucleation rate. The bubble nucleation rate is depended on several factors including the number of molecules of dissolved gas in the solution and the pressure difference between the saturation pressure and instantaneous pressure. Sufficient pressure drop is required to initiate the onset of bubble nucleation. Figure 19 (a – c) shows the contour plot of bubble nucleation rate in the computational domain for cases of P10, P20 and P30 respectively. From Figure 19 (a), the contour plot shows that there is no bubble nucleation event in the region N1 for P10 case. This phenomenon was due to the high pressure maintenance, where the pressure reduction was insufficient to initiate bubble nucleation event. The bubble nucleation rate in region N2 was recorded at almost 1.3 × 1010 nuclei/m3·s, indicating that the bubble nucleation have started to form in this region. The onset of bubble nucleation event was because of the pressure drop with the availability of dissolved CO2 in the solution in region N2. The significant bubble nucleation events were found at region N3 and N4. The highest bubble nucleation rate found in region N3 was about 1 × 1019 nuclei/m3·s while it was found to be around 3.5 × 1020 nuclei/m3·s in region N4. The bubble nucleation events in P10 case was mainly determined by the bubble nucleation at region N3 and N4.

42

(a)

(b)

(c) 43

Figure 19: Contour plot of bubble nucleation rate in computational domain, nuclei/m3·s(a) P10 (b) P20 (c) P30 Figure 19 (b) shows the contour plot of bubble nucleation rate profile for P20 case. There was no bubble nucleation events found in region N5. The bubble nucleation rate was predicted to be about 1 × 1011 nuclei/m3·s in the small passages in region N6. The bubble nucleation rate has decreased to about 8 × 1010 nuclei/m3·s after exit the small passages. The reduction of bubble nucleation rate was probably due to the decrease in the amount of dissolved CO2 in liquid solution, which was caused by the desorption process. The blocking elements in region N7 has successfully reduced the pressure and further enhanced the bubble nucleation rate, especially at N7-1 and N7-2. A relatively small bubble nucleation at a rate of about 2 × 1010 nuclei/m3·s was found in region N8 due to the existence of dissolved CO2 that remained in the solution. The region after N8 has insignificant bubble nucleation as the amount of dissolved CO2 has decreased to a relatively low level. Figure 19 (c) shows the contour plot of bubble nucleation rate for the P30 case. The bubble nucleation in region N9 was found almost negligible. The bubble nucleation rate in region N10 was predicted to be around 3.5 × 1010 nuclei/m3·s and the bubble nucleation in this region was predicted to be highest among the three cases due to the highest amount of dissolved gas existed in the solution. Besides, the higher pressure drop has also contributed to initiate higher bubble nucleation rate. The highest bubble nucleation in P30 case was recorded to be 1.82 × 1022 nuclei/m3 at location N11. The high negative pressure found at location L14 was the main reason to form the high bubble nucleation rate (Lubetkin, 2003). This could greatly enhance the number of bubble nuclei formed in the domain. The region after N12 was predicted to be negligible.

4.3.4 Growth Rate

44

Bubble growth rate has played an important role to determine the desorption rate. The bubble growth rate is an indicator to describe the growth of the bubble nuclei. The bubble growth is depended mainly on the supersaturation ratio. The supersaturation ratio is in turn determined by the amount of excess dissolved gas molecules remained in the solution after experienced pressure reduction. The dissolved gas molecules become excess when the pressure is reduced, as the solubility of the dissolved gas will be reduced accordingly. The dissolved CO2 will form gas bubbles to escape from the solution so that the system will return back into equilibrium condition. The desorption rate will be increased accordingly with the increase of bubble growth rate. Figure 20 shows the bubble growth rate in the computational domain for cases of P10, P20 and P30. The profile of bubble growth rate was strongly depended on the pressure profile. Figure 20 (a) shows the bubble growth rate contour plot for the P10 case. There was no bubble growth feasible to occur in the region G1 as the pressure was high enough to maintain non-supersaturated condition. The bubble growth started at the region G2, where the region has experienced pressure drop and the solution became supersaturated solution. The average bubble growth rate in region G2 was about 2.8 mm/s. The bubble growth rate was recorded at about 6.5 mm/s at location G3, which corresponded to the highest negative pressure location. Region G4 have negligible bubble growth rate because the supersaturation level has reduced.

(a)

45

(b)

(c) Figure 20: Contour plot of bubble growth rate in the computational domain, m/s (a) P10 (b) P20 (c) P30 Figure 20 (b) shows the contour plot of bubble growth profile for the P20 case. The bubble growth at region G5 was negligible as the pressure has maintained the solution to be near to equilibrium state. The bubble growth started in region G6 with the growth rate of about 15 mm/s in the small passages. The bubble growth rate reduced gradually to about 6 mm/s before hitting the blocking elements at G7. Since the pressure in this region was almost the same, the reduction in bubble growth rate was probably due to the decreased 46

amount of dissolved CO2 in solution resulted from the desorption process. The highest bubble growth rate was recorded at about 20 mm/s at the location N7-1 and N7-2 (corresponded to the location with highest negative pressure and bubble nucleation rate). The bubble growth rate at region G8 was found to increase to almost 15 mm/s. This phenomenon occurred probably due to the higher pressure drop caused by venturi effect as the supersaturation level will be increased (Jones et al., 1999). The bubble growth rate was found to be gradually reduced in region G9, where the amount of dissolved CO2 in solution has reduced accordingly. Figure 20 (c) shows the contour plot of bubble growth rate for P30 case. From the figure, the bubble growth rate in region G10 is found to be almost negligible as the pressure at this region was sufficiently high to maintain the solution to be in near equilibrium state and did not enter supersaturation condition. The solution became supersaturated solution in the G11 region and bubble growth could be observed in this region. The bubble growth rate was recorded as around 30 mm/s at the beginning part of the small passages, and reduced gradually until about 15 mm/s at the exit of the small passages. The bubble growth rate has remained the same at about 15 mm/s after exiting the small passages. The highest bubble growth rate was found 42 mm/s at the G12 region. The amount of dissolved CO2 in the solution has been greatly reduced, and led to the decrease of bubble growth rate in the G13 region. Since the bubble growth was still could be found near to the exit, the solution was expected still remained in the supersaturated condition.

4.3.5 Desorption Rate The excess amount of dissolved CO2 will escape from the solution and form gas bubbles. These dissolved CO2 molecules will diffuse into the bubble and reduce the amount of excess dissolved CO2 molecules in the solution. The desorption rate is governed by both

47

bubble nucleation rate and growth rate. The modelling of bubble nucleation rate and growth rate in current work has enabled the possibility of determination of desorption rate in molecular level. The desorption phenomenon in various different design of desorption unit operation can be modelled. Figure 21 shows the desorption rate in the computational domain for cases of P10, P20 and P30. Figure 21 (a) shows the desorption rate profile for P10 case. From the figure, the MT1 region is found to have no mass transfer event occurrence, in accordance with the findings that no bubble nucleation and growth were predicted in the same region. The desorption rate predicted in region MT2 was insignificant due to relatively low bubble nucleation and growth rate. The desorption rate was found to be about 800 kg/m3·s in the small passages in region MT3. The pressure drop in this region has caused relatively high bubble nucleation rate and growth rate. Therefore, high amount of bubble nuclei formed would grow at high rate, which generated high desorption rate. The desorption rate at region MT4 was predicted to decrease from 800 kg/m3·s to 100 kg/m3·s. The reduction in desorption rate was mostly due to the decrease in the amount of dissolved CO2 in the solution along the region MT4. The highest desorption rate in this case was found in the regions MT5 and MT6. The mass transfer at MT5 and MT6 has greatly enhanced the desorption of dissolved CO2 from the solution. Figure 21 (b) shows the desorption rate profile for P20 case. The mass transfer in region MT7 was found to be negligible as there was no bubble nucleation or growth found in this region. The desorption was initiated in the small passages in region MT8, which was similar to the P10 case, where the high desorption rate was found in between the gas-liquid interface. Relatively high desorption rate was found in the region MT9-1 and decreased towards the blocking elements in region MT10 due to the reduction in amount of dissolved gas. The solution hit the blocking elements and greatly enhanced the desorption rate in region

48

MT10. An interesting phenomenon was observed as the highest bubble nucleation and growth rate was found to be at region MT10-1 and MT10-4 but the desorption rate was lower than MT10-2 and MT10-3. This phenomenon was formed probably due to the high amount of bubble nuclei formation in region MT8 and MT9 and these bubble nuclei has flowed into region MT10-2 and MT10-3 instead of MT10-1 and MT10-4.

(a)

49

(b)

(c) Figure 21: Contour plot of desorption rate in the computational domain, kg/m3·s(a) P10 (b) P20 (c) P30 Figure 21 (c) shows the contour plot of desorption rate for P30 case. Similarly, the region MT12 was found to have insignificant mass transfer event. The mass transfer started 50

in region MT13. The desorption rate was maintained to be almost the same in region MT14, probably due to the high amount of dissolved CO2 in the solution. The blocking elements in region MT15 have successfully enhanced the desorption rate. The highest desorption rate was found at MT15-2 and decreased along the pathway towards the exit in region MT16.

4.3.6 Gas Phase Volume Fraction Since the dissolved gas molecules in the solution will form gas bubbles during desorption process, the gas phase volume fraction will be increased. The dissolved gas molecules are dissolved in the solution and the liquid phase is predominant in this region. As the desorption process occurs, gas bubbles will form and thus the gas phase become significant. The volume of gas is many times larger than liquid solution and thus it will occupy significant space as compared to liquid solution. This will result in an abrupt change in gas phase. Therefore, the space for desorption has to be sufficiently enough for the gas phase expansion to avoid explosion. Besides, insufficient of space will also cause pressure build up that will limit the desorption process. Figure 22 (a), (b) and (c) show the gas phase volume fraction profile for P10, P20 and P30 cases respectively. The three profiles were almost identical to each other. In general, the regions near to the inlet (GP1, GP7 and GP12) did not consist of significant gas phase volume fraction as desorption process was not initiated. The gas phase has occupied a significant space near to the wall of the small passages in GP3, GP8 and GP13. The solution exited the small passages as observed in GP4, GP9 and GP14. Since the mass transfer occurred along the gas-liquid interface, the volume fraction of gas phase in these regions was approaching to be unity, except for the pathway for the solution flowing. The solution hit the blocking elements in regions GP5, GP10 and GP15, and generated high desorption rate regions. The volume fraction of liquid phase has been reduced accordingly. From Figure 22

51

(a), the gas phase volume fraction in region GP6 is found to be almost the same. This was different for the P20 and P30 cases, where the gas phase volume fraction was increasing towards the exit in regions GP11 and GP16 respectively. The reason that cause this phenomenon was due to the incomplete desorption process to fully desorb the excess dissolved CO2 from the solution for P20 and P30 case. Therefore, the mass transfer from dissolved CO2 into CO2 gas would continue until the system has returned to equilibrium state.

(a)

(b)

(c) Figure 22: Contour plot of gas phase volume fraction in the computational domain (a) P10 (b) P20 (c) P30 52

4.3.7 Mole Fraction of Dissolved Gas in Solution The ultimate goal for the desorption system is to reduce the amount of dissolved CO2 in the solution. The excess dissolved gas that escapes from the solution to form bubbles and reduce the amount of dissolved gas molecules and mole fraction in solution. Mole fraction of dissolved gas in solution can be reduced with higher desorption rate. Figure 23 shows the contour plot of mole fraction of dissolved CO2 in solution for P10, P20 and P30 cases. From Figure 23 (a), the mole fraction of dissolved CO2 in region M1 is found to be at around 0.0064, which is its saturated state at 10 bar condition. The mole faction of CO2 has experienced reduction in region M2 due to the mass transfer from dissolved CO2 in solution into CO2 gas bubbles. The mole fraction of dissolved CO2 in solution remain almost the same at about 0.005 in region M3. The insignificant mole fraction reduction in region M3 was due to the low desorption rate in this region. The mole fraction of dissolved CO2 in the solution has reduced quickly in region M4 to about 0.004 with the high mass transfer in region MT5 as shown in Figure 23 (a). The mole fraction of dissolved CO2 has reduced to 0.00044 at the end of region M5, which was about the solubility of CO2 in solution at atmospheric pressure.

(a)

53

(b)

(c) Figure 23: Contour plot of mole fraction of dissolved CO2 in solution in the computational domain (a) P10 (b) P20 (c) P30 Figure 23 (b) shows the contour plot of mole fraction of dissolved CO2 in solution for P20 case. The mole fraction of CO2 dissolved in water solution at 20 bar is 0.01075. Since there was no mass transfer occurred in region M6, the mole fraction of dissolved CO2 remained at the same amount. As the solution entered region M7, there was mass transfer observed but the changes in CO2 mole fraction was insignificant. The CO2 mole fraction experienced significant reduction in the region M8 as the mass transfer rate was relatively high. The CO2 mole fraction in the solution was about 0.008 before hitting the blocking elements in region M9. The relatively high desorption rate found in region M9 has caused the mole fraction of CO2 to drop further. Since the solution remained to be supersaturated solution in region M10, the desorption process continued until the exit. The mole fraction of CO2 in the solution at the end of region M10 was found to be about 0.0013. Since the dissolved CO2 has not been fully desorbed from the solution, a slightly longer desorption

54

region of M10 was required to accomplish the regeneration process. The CO2 mole fraction was reduced from 0.01075 to 0.0010 in the computational domain. The relatively big reduction of CO2 mole fraction has indicated that large amount of dissolved CO2 has been desorbed. Figure 23 (c) shows the contour plot of CO2 mole fraction in the computational domain for P30 case. In general, the profile is similar to the P10 and P20 cases. The CO2 mole fraction in water solution at 30 bar is 0.01406 and this amount of dissolved CO2 was also found in the region M11. The insignificant mass transfer event predicted in this region has resulted in the same amount of dissolved CO2 found in region M11. The solution entered region M12 where it has experienced significant pressure drop and initiated mass transfer in this region. The change in CO2 mole fraction was negligible. The CO2 mole fraction in region M13 has also found to be relatively high at around 0.013. It could be noticed that the CO2 mole fraction was increasing towards the centre of the solution. This was in accordance to the mass transfer profile, where the mass transfer event was predicted to be at the gasliquid interface region. The CO2 mole fraction was greatly reduced in the region M14, in between the blocking elements. Relatively high desorption rate has been predicted in this region. Similar to P20 case, the CO2 mole fraction was reducing as the solution travelled towards the exit. In this case, the average CO2 mole fraction in the solution at the exit was recorded as 0.003. The residual of excess dissolved CO2 in the solution was found to be higher than the P20 case, and thus the desorption length required was longer than P20 case. The CO2 mole fraction has successfully to be reduced from 0.01406 to about 0.0031 in this case.

4.4 Comparison with a Conventional Nozzle

55

This section compares the optimised in-line physical desorption units (Figure 16) with conventional nozzle (Figure 2). They were compared against the three objective functions including pressure maintenance factor (OP1), solvent flow rate relative to inlet pressure (OP2) and desorption efficiency (OP3). The CFD simulation results were compared here instead of using the estimated values from DOE model. Figure 24 shows the graph of objective function OP1 for conventional nozzle and optimised design at three conditions, including P10, P20 and P30. From the figure, the optimised designs were proven to be better than conventional nozzle in terms of pressure maintenance factor. In general, the OP1 for the three cases for optimised design were found to be more than 0.96. The OP1 values for conventional nozzle were recorded to be in the range of 0.82 to 0.85. The efforts to maintain the pipeline pressure, such as introduction of blocks at section I, before undergoes desorption process were considered to be effective. The difference in terms of OP1 between conventional nozzle and optimised design for P10, P20

Pressure maintenance factor, OP1

and P30 were 15.4%, 17.1% and 13.8% respectively. 1 0.95 0.9 0.85 0.8 0.75 0.7

P10

P20 Simulation case

Conventional nozzle

P30

Optimised design

Figure 24: Graph of objective function OP1 for conventional nozzle and optimised design at three conditions - P10, P20 and P30

56

Figure 25 shows the graph of objective function OP2 for conventional nozzle and optimised design at three conditions, including P10, P20 and P30. In terms of OP2, conventional nozzle has outperformed as compared to the suggested optimised design. The OP2 values for conventional nozzle were more than twice the OP2 values obtained for the suggested optimised design. The higher OP2 values obtained for conventional nozzle were probably due to the lack of pressure maintaining elements such as blocks, i, in section I. Therefore, the solvent was free to flow directly towards the outlet. The difference in term of OP2 between conventional nozzle and optimised design for P10, P20 and P30 were found to

Solvent flowrate relative to inlet pressure, OP2 (kg/s·Pa)

be about 50%.

6 5 4 3 2 1 0

P10

P20 Simulation case

Conventional nozzle

P30

Optimised design

Figure 25: Graph of objective function OP2 for conventional nozzle and optimised design at three conditions - P10, P20 and P30 Figure 26 shows the graph of objective function OP3 for conventional nozzle and optimised design at three conditions including P10, P20 and P30. From the figure, the desorption efficiency for optimised design is found to be significantly higher than a conventional nozzle. The desorption efficiencies for conventional nozzle were recorded around 0.5 for the three cases while they were found for optimised design to be 0.93, 0.88 57

and 0.77 for P10, P20 and P30 case respectively. The difference in term of OP3 between conventional nozzle and optimised design for P10, P20 and P30 were calculated as 76.6%, 66.6% and 75.2%, respectively. This is an important parameter that will determine the equipment sizing. As the parameter values were relatively high for optimised design, the

Desorption efficiency, OP3

equipment sizing was expected to be smaller as compared to a conventional nozzle.

1 0.8 0.6 0.4 0.2 0 P10

P20 Simulation case

Conventional nozzle

P30

Optimised design

Figure 26: Graph of objective function OP3 for conventional nozzle and optimised design at three conditions - P10, P20 and P30

5.0 Conclusion The overall optimisation which considered the three objective functions was employed in current work. Three optimised design have been identified for the three cases (P10, P20 and P30) via the optimisation analysis. The effort to enhance the design has been proven capable to increase pressure maintenance factor and desorption efficiency. From the hydrodynamics and mass transfer profiles in the optimised designs, the desorption phenomenon was greatly depended on the pressure profile. As a result from the desorption, the mole fraction of dissolved CO2 in the solution has reduced from 0.0064 to 0.00044 for 58

P10 case, 0.01075 to 0.0013 for P20 case and from 0.01406 to 0.0031 for P30 case. In the comparison of the optimised design with a conventional nozzle, the optimised designs have outperformed in terms of pressure maintenance factor (higher by 15.4% for P10, 17.1% for P20 and 13.8% for P30) and desorption efficiency (higher by 76.6% for P10, 66.6% for P20 and 75.2% for P30 case), but conventional nozzle has a better solvent flow rate (higher by 50% for P10, P20 and P30). Besides, the high fluid flow velocity at the exit (about 20m/s for P10, 40 m/s for P20 and 68 m/s for P30) has provided an ideal condition to be utilised together with compact gas liquid separator.

Acknowledgement This work was supported by UTP Research Centre for CO2 Capture (RCCO2C).

59

Nomenclature I

Pressure maintaining section

II

Pressure reducing section

III

Desorption enhancing section

H

Channel height

i,j,k

Number of blocks in computational domain shown in Figure 1

ID

Inlet diameter

OD

Outlet diameter

OP1

Objective function 1 (Pressure maintenance factor)

OP2

Objective function 2 (Solvent flow rate relative to inlet pressure, kg/Pa·s)

OP3

Objective function 3 (Desorption efficiency)

r

Block angle

60

References Ban, Z.H., Lau, K.K., Shariff, A.M., 2015. Prediction of the bubble nucleation rate in a quasistable cavitating nozzle using 2D computational fluid dynamics and enhanced classical nucleation theory. Engineering Applications of Computational Fluid Mechanics 9, 247-258. Ban, Z.H., Lau, K.K., Shariff, A.M., 2016. CFD modelling of most probable bubble nucleation rate from binary mixture with estimation of components’ mole fraction in critical cluster. Continuum Mechanics and Thermodynamics 28, 655-668. Biard, P.-F., Coudon, A., Couvert, A., Giraudet, S., 2016. A simple and timesaving method for the mass-transfer assessment of solvents used in physical absorption. Chemical Engineering Journal 290, 302-311. Boributh, S., Assabumrungrat, S., Laosiripojana, N., Jiraratananon, R., 2011. A modeling study on the effects of membrane characteristics and operating parameters on physical absorption of CO2 by hollow fiber membrane contactor. Journal of Membrane Science 380, 21-33. Dave, A., Dave, M., Huang, Y., Rezvani, S., Hewitt, N., 2016. Process design for CO2 absorption from syngas using physical solvent DMEPEG. International Journal of Greenhouse Gas Control 49, 436-448. Gu, B., Linehan, B., Tseng, Y.-C., 2015. Optimization of the Büchi B-90 spray drying process using central composite design for preparation of solid dispersions. International Journal of Pharmaceutics 491, 208-217.

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Guo, W., Feng, F., Song, G., Xiao, J., Shen, L., 2012. Simulation and energy performance assessment of CO2 removal from crude synthetic natural gas via physical absorption process. Journal of Natural Gas Chemistry 21, 633-638. Heldebrant, D.J., Koech, P.K., Linehan, J.C., Rainbolt, J.E., Bearden, M.D., Zheng, F., 2016. System and process for capture of acid gasses at elevated pressure from gaseous process streams, in: Patent, U.S. (Ed.). Battelle Memorial Institute, pp. 1-13. Jones, S.F., Evans, G.M., Galvin, K.P., 1999. The cycle of bubble production from a gas cavity in a supersaturated solution. Advances in Colloid and Interface Science 80, 5184. Kwak, H.-Y., Oh, S.-D., 2004. Gas-vapor bubble nucleation-a unified approach. Journal of Colloid and Interface Science 278, 436-446. Li, Y.-L., Fang, Z.-X., You, J., 2013. Application of Box-Behnken Experimental Design to Optimize the Extraction of Insecticidal Cry1Ac from Soil. Journal of Agricultural and Food Chemistry 61, 1464-1470. Lubetkin, S.D., 1995. The fundamentals of bubble evolution. Chemical Society Reviews 24, 243-250. Lubetkin, S.D., 2003. Why Is It Much Easier To Nucleate Gas Bubbles than Theory Predicts? Langmuir 19, 2575-2587. Mayinger, F., 1988. Two-phase flow phenomena with depressurization—consequences for the design and layout of safety and pressure relief valves. Chemical Engineering and Processing: Process Intensification 23, 1-11. Naim, R., Ismail, A.F., 2013. Effect of fiber packing density on physical CO2 absorption performance in gas–liquid membrane contactor. Separation and Purification Technology 115, 152-157.

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Riveland, M., 1985. Fundamentals of Valve Sizing for Liquids. Fisher Controls International, Inc., Iowa, US. Schmidt, S.R., Launsby, R.G., Kiemele, M.J., 1994. Understanding Industrial Designed Experiments. Air Academy Press, Colorado Springs, Colorado. schook, r., van Asperen, V., 2005. Compact separation by means of inline technology, SPE Middle East Oil and Gas Show and Conference. Society of Petroleum Engineers, Kingdom of Bahrain. Siefert, N.S., Agarwal, S., Shi, F., Shi, W., Roth, E.A., Hopkinson, D., Kusuma, V.A., Thompson, R.L., Luebke, D.R., Nulwala, H.B., 2016. Hydrophobic physical solvents for pre-combustion CO2 capture: Experiments, computational simulations, and techno-economic analysis. International Journal of Greenhouse Gas Control 49, 364371. Xie, R.-F., Shi, Z.-N., Li, Z.-C., Chen, P.-P., Li, Y.-M., Zhou, X., 2015. Optimization of high pressure machine decocting process for Dachengqi Tang using HPLC fingerprints combined with the Box–Behnken experimental design. Journal of Pharmaceutical Analysis 5, 110-119.

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