Cost estimation of biogas upgrading by PSA for small scale applications

(1)

POLITECNICO DI MILANO

School of Industrial and Information Engineering

Master of Science in Chemical Engineering

Department of Chemistry, Materials and Chemical Engineering

“Giulio Natta”

COST ESTIMATION OF BIOGAS UPGRADING BY PSA FOR

SMALL SCALE APPLIACATIONS

Supervisors:

Prof. Flavio Manenti

(Politecnico di Milano)

Dr. Carlos Grande

(SINTEF)

M.Sc. Thesis of:

Boguslaw Ziemniak

898735

Academic year

2018 - 2019

(2)

(3)

Project developed in:

Process Technology department SINTEF Industry

(4)

(5)

v

Acknowledgements

First and foremost, I am very thankful to Carlos Grande for the acceptance and for the opportunity of doing the thesis in SINTEF as well as for the time, guidelines and encouragement throughout all my stay in Norway.

I would like to thank Professor Flavio Manenti for accepting me as his master student, for being the supervisor of this work at Politecnico di Milano and for his support. I would like to express my gratitude to all the institutes being involved in the project: Wroclaw University of Technology, Politecnico di Milano and SINTEF. These years of doing the Master of Science degree gave me invaluable experience and knowledge which enabled me to start professional career.

My grateful thanks are also extended to all my friends and people who stayed with me and made all this time enjoyable. Special thanks are given to Grzegorz, Maciej, Matias, Joris, Gianluca and Piertobia.

Finally, I would like to thank all my family who always believed in me and backed up my choices.

This work was partly founded by the Innovation Fund Denmark (IFD) under File No. 5157-00008B, HiGradeGas (www.higradegas.eu).

(6)

(7)

vii

Abstract

Pushed by the undeniable changes in Earth climate, the interest of the policymakers and the industrial world has been shifting towards an increased protection of the environment and sustainable development. For this reason, the generation of energy from renewable sources plays an increasingly important role when it comes to energy supply.

Biogas and its further upgrading to biomethane is an already used technique for substitution of fossil fuels, namely natural gas. One of the most important advantages of the biogas is its decentralized production which allows application of the process in almost every place of the world.

Pressure Swing Adsorption (PSA) is a well-known technology for gas separation and has been one of the most popular choices for the biomethane purification. However, the high investment costs of PSA technology lead to the conclusion that the process is feasible for large and intermediate scales, inhibiting its growth to small-scale applications.

In order to conquer small-scale farm-based markets, further developments of the PSA technology have to be done. The main focus is to make the process more effective and attractive, especially in terms of financial considerations. For this reason, it is important to understand the structure of the cost of biogas upgrading plants.

The cost estimation model, which constitute the main deliverable of this thesis, allows not only to have a better view of the cost of PSA plants for biogas upgrading but also to understand what change of the PSA design will have a real effect in bringing the cost down.

The results show that, when downscaling the process, the specific investment cost increases significantly causing troubles in implementing the technology for small biogas capacities. Furthermore, the major part of the total investment cost is influenced by the total installed cost of pressure vessels. Additionally, the influence of the adsorbent cost is decreasing for smaller plants.

The conclusions entail the need for new developments with respect to the PSA cycle configuration as well as new adsorbent materials approaching a decrease of the overall size of the plant and a reduction in the total number of columns.

(8)

(9)

ix

5.1.2. Isothermal, constant pressure and velocity, lumped resistance, with axial dispersion ... 44 5.2. Breakthrough curve ... 45 5.3. PSA simulation ... 50 5.4. Cost estimation ... 55 5.4.1. Assumptions ... 55 5.4.2. CAPEX ... 57 5.4.3. OPEX... 60 6. Conclusions ... 62 References ... 65 Appendix A ... 67

(11)

(12)

xii

List of Figures

Figure 1. Water scrubbing flowsheet. ... 5

Figure 2. Organic solvent scrubbing flowsheet. ... 6

Figure 3. Amine scrubbing flowsheet. ... 7

Figure 4. Four-column PSA flowsheet. ... 9

Figure 5. Membrane separation flowsheet. ... 10

Figure 6. Evolution of upgrading technologies in the XXI century. ... 12

Figure 7. Upgrading technologies in 2017. ... 12

Figure 8. Global energy consumption, CO2 concentration and total population over time. ... 15

Figure 9. Renewable electricity production in the world in 2017. ... 15

Figure 10. Renewable electricity capacity by technology. ... 16

Figure 11. Worldwide biogas installed capacity over time. ... 16

Figure 12. Total number of biogas upgrading plants in 2017. ... 17

Figure 13. Inter- and intraparticle porosities. ... 21

Figure 14. The Gas-Solid Mass Transfer. ... 22

Figure 15. Screw compressor cost. ... 35

Figure 16. Vacuum pump cost. ... 36

Figure 17. Carbon dioxide breakthrough for different mass transfer coefficients [1/s]. ... 44

Figure 18. Simulated carbon dioxide breakthrough curves for different axial dispersion coefficients [m2_{/s]. ... 45}

Figure 19. Aspen Adsorption isotherm parameters. ... 46

Figure 20. Isotherm of carbon dioxide. Experimental Data and Reference model are taken from (19). ... 47

Figure 21. Isotherm of methane. Experimental Data and Reference model are taken from (19). ... 47

Figure 22. Virial plot for carbon dioxide. Experimental Data and Reference model are taken from (19). ... 48

Figure 23. Virial plot for methane. Experimental Data and Reference model are taken from (19). ... 48

Figure 24. Breakthrough curve at 10bar. Experimental Data and Reference model are taken from (7). ... 49

(13)

xiii Figure 25. Temperature profile at 10bar. Experimental Data and Reference model are

taken from (7). ... 50

Figure 26. The Aspen Adsorption PSA layout. ... 51

Figure 27. The PSA cycle. ... 52

Figure 28. The valves operations. ... 52

Figure 29. Loading profiles at the end of the feed step. ... 53

Figure 30. Loading profiles at the end of each step of the cycle after steady state is reached. ... 53

Figure 31. Temperature profiles at the end of each step of the cycle after steady state is reached. ... 53

Figure 32. Pressure history over one cycle. ... 54

Figure 33. Outlet flowrates during one cycle. ... 54

Figure 34. The PSA simulation results. ... 55

Figure 35. Total Investment Cost for small-scale biogas upgrading plants. ... 57

Figure 36. Specific investment cost for small-scale biogas upgrading plants. ... 58

Figure 37. CAPEX breakdown structure for the 500 Nm3_{/h capacity biogas upgrading} plant. ... 59

Figure 38. Total Cost Of Production for small-scale biogas upgrading plants. ... 60

Figure 39. Specific Production Cost for small-scale biogas upgrading plants. ... 60

Figure 40. OPEX breakdown structure for the 500 Nm3_{/h capacity biogas upgrading} plant. ... 61

(14)

(15)

xv

List of Tables

Table 1. Typical raw biogas composition depending on different production sources.2 Table 2. Summary of some technical specification of different biogas upgrading

technologies. ... 11

Table 3. Units of isotherm parameters for different isotherm models ... 28

Table 4. Installation factors. ... 33

Table 5. Lang factors. ... 36

Table 6. Bed properties. ... 42

Table 7. Process conditions. ... 42

Table 8. Isotherm parameters. ... 42

Table 9. The isotherm parameters. ... 46

Table 10. Column and adsorbent properties. ... 49

Table 11. PSA working conditions. ... 51

Table 12. Raw biogas specification. ... 55

Table 13. PSA unit assumptions. ... 56

Table 14. Adsorber parameters. ... 56

Table 15. OPEX assumptions. ... 56

Table 16. The results obtained from the cost estimation model. ... 61

Table 17. Vessel sizing results for 500Nm3_{/h. ... 67}

Table 18. Single vessel costing results for 500Nm3_{/h. ... 67}

Table 19. Compressor sizing results for 500Nm3_{/h. ... 68}

Table 20. Compressor costing results for 500Nm3_{/h. ... 68}

Table 21. Vacuum pump costing results for 500Nm3_{/h. ... 69}

Table 22. ISBL components for 500Nm3_{/h. ... 69}

Table 23. CAPEX for 500Nm3_{/h. ... 69}

(16)

(17)

1

1. Introduction

1.1. Biogas overview

Biogas is a versatile renewable energy source and it is a subject of research for many of scientists nowadays. The growth in this field is also reflected in terms of publications: the number of articles in 1985 with biogas as a topic was 26 (1). In 2018, this number increased to 2560. It is a new topic comparing to well-known conventional energy sources, but its development is very rapid. One of reasons for such an interest is the policies for mitigation of climate change and the fact that people around the world, especially citizens of developed countries, are more and more aware of environment’s degradation caused by anthropogenic gas emissions. The global energy demand increases every year and one of the major challenges for people to face in this century, will be to provide energy in a more sustainable and environmentally friendly way. The economy based on “take, make and dispose” rule is no longer accurate and the goal of these days is to reduce both the material input as well as the waste output. Another important global problem is the growth of population. This entails intensification of animals and plants production in order to satisfy needs of increasing number of people. The animals production sector is responsible for 18% of the overall greenhouse gas emissions and for 37% of the anthropogenic methane which has a global warming potential 23 times higher than the one of CO2 (2). This results in a policy tending to

reduce negative impact of our civilization on the environment which in consequence yield in both some domestic law regulations as well as international agreements. One of the examples, the Paris agreement, was signed in 2016 and ratified by 185 countries. This agreement focuses on keeping the global temperature rise below 2℃ in this century (3). To comply with new law regulations, companies need to keep improving existing industrial activities which is often financially supported by governmental programmes. These are incentives also for searching new possibilities and solutions that could replace the unsustainable ones. Biogas is one of them. Biogas is a gaseous product obtained during from biomass fermentation. Its composition strongly depends on the material feedstock, as well as on the production technology itself. Biogas can be produced in sewage treatment plants, landfills, sites with industrial processing and in digestion plants for agricultural organic waste (4). There are various biomass sources that can be used in order to obtain biogas. It utilizes organic waste streams from the overall society. The largest available feedstock are animal manure and slurries from the production of cattle, pigs, poultry, fish or fur but also can be represented by energy crops (2). In contrast with conventional energy sources, like oil, gas and coal, the biogas input materials are widespread and easily accessible. Moreover, the conventional energy resources can be still found in some politically unstable regions and for this reason the globally decentralized biogas production can guarantee better energy security.

(18)

2 Raw biogas contains mostly methane (40-75%) and carbon dioxide (15-60%). Other compounds are considered as contaminants that must be treated before processing the biogas as they can be harmful for the equipment. These are (among others) water (5-10%), hydrogen sulphide (0.005-2%), ammonia (<1%), oxygen (0.1%), carbon monoxide (<0.6%) and siloxanes. Moreover, in order to comply with pipeline-grade biomethane specifications, water and nitrogen must be removed as well (5). Example compositions of landfill gas and biogas are shown in Table 1 (6). The raw biogas does not qualify to be transported or used as a fuel. It can only be employed as a power and heat source in areas close to the generation unit (7). In order have a possibility to use a full range of applications, biogas has to be purified and upgraded to biomethane.

Compound Unit Landfill gas Anaerobic Digester

gas

Methane mol% 30-60 50-80

Carbon dioxide mol% 15-40 15-50

Nitrogen mol% 0-50 0-5 Oxygen mol% 0-10 0-1 Hydrogen sulphide mg/m3 _0-1000 _100-10000 Ammonia mg/m3 _0-5 _0-100 Total chlorine mg/m3 _0-800 _0-100 Total fluorine mg/m3 _0-800 _0-100 Siloxanes mg/m3 _0-50

Table 1. Typical raw biogas composition depending on different production sources.

1.2. Biogas purification

Biogas purification involves all the operations necessary to remove impurities i.e. compounds that can have a negative impact on the final product. All contaminants are listed below with the short description of their origin, harmful activities and methods applied to separate them from the biomethane.

1.2.1. Water

Water is always present during the anaerobic digestion process and thus raw biogas is saturated with the vapor and its total amount depends on the temperature. Water, when being in contact with H2S, NH3 and CO2, can form acids which cause corrosion

in some elements of the plant. Another issue related to water is its condensation in a high pressure environment. Moreover, in order to meet the specification for gas transportation through the pipeline, water has to be removed below some established limits which is 100mg/m3_{(4). The removal of water is one of the first steps of the biogas}

cleaning process. There are several techniques that can be applied and they are based on both physical and chemical separation.

(19)

3 a) Cooling or compression

Water can be removed from the biogas by changing its saturation which depends on temperature and pressure. Thus, lowering the temperature and increasing the pressure lead to water condensation. There are several techniques and equipment based on physical separation including demisters, cyclones or moisture traps.

b) Adsorption

Adsorption can also be used in order to remove water. Typical adsorbents for that purpose are silica, zeolites, activated carbon, aluminium oxide or magnesium oxide. The system usually is composed by two columns to achieve continuous operation – one column is working in an adsorption mode whereas the other one is being regenerated.

c) Absorption

Absorption can be applied for removing water when glycol solutions are used. Typical solutions are MEG – ethylene glycol, DEG – diethylene glycol and TEG – triethylene glycol whereby the latter one is the most commonly used. After the absorption, glycol solutions are being regenerated in high temperature and used again.

1.2.2. Hydrogen sulphide

Hydrogen sulphide is produced by some bacteria present in the digester that reduce sulphates into H2S. The reaction is competing with methane formation as they both

use the same substrates. The negative impact of hydrogen sulphide is related mainly to the corrosion. Depending on the adsorbent used in the PSA unit, it can be irreversibly adsorbed inside the material. Other problems are due to the emission of pollutions during the combustion process and the toxic features of hydrogen sulphide that can cause serious health problems. Thus, it is being removed in early stages of the biogas production process. Removal of H2S can be done during or after the

digestion by using biological, physical or chemical methods. a) Biological methods

Biological methods are based on hydrogen sulphide oxidation into elemental sulphur. The reaction is catalysed by Thiobacillus bacteria present inside the digester or downstream on the biological filter. As oxygen is needed for the reaction to happen so it has to be supplied to the system. It can be done by injection an air straight into the digester however in this case nitrogen is being added as well which is difficult to separate from methane and it usually leaves the process lowering the biomethane quality. Therefore, this method is used only when biomethane is injected to the gas grid with low heating value or when injection of pure oxygen is applied.

b) Physical methods

Hydrogen sulphide can be removed by using absorption and adsorption processes. Absorption can be done with water or organic solvents. Well known method is cleaning by sodium hydroxide scrubbing. Also chemical absorption can be applied with water

(20)

4 solutions of NaOH, FeCl2 or Fe(OH)3. Adsorption process includes using doted

activated carbon as an adsorbent and it is the most commonly used desulphurization method today. Hydrogen sulphide can also be removed in the PSA unit but it is more advantageous to do it upstream the upgrading process.

c) Chemical methods

Chemical methods are based on addition of iron ions into the digester. Commonly used compounds are FeCl2, FeCl3 and FeSO4. Their presence in the system result in

formation of iron sulphide and its precipitation inside the digester. However, hydrogen sulphide can be removed also downstream the digester by using materials coated with iron oxide like steel wool or wood chips. In this case, the column is regenerated by heating or applying oxygen and reused until the material is saturated with sulphur.

1.2.3. Siloxanes

Siloxanes can be found in the raw biogas if they were present in the feedstock entering the digester where their evaporation can occur. The amount of siloxanes in the biogas depends on the temperature inside the digester as well as on the molecular weight of particular compounds. The removal of siloxanes is in particular necessary for landfill gas. The presence of siloxanes can lead to further siloxane oxide formation inside engines during the combustion process.

Siloxanes can be removed from the biogas by using absorption or adsorption processes. When using absorption following liquids are usually applied: organic solvents, strong acids and strong bases. For the purpose of adsorption method, silica gel or activated carbon can be used as adsorbents. Another processes that can be applied are cryogenic and membrane separations.

1.2.4. Halogenated hydrocarbons

These are hydrocarbons containing chlorine, bromine and fluorine. They are mostly found in the landfill gas and can be dangerous to the plant due to the corrosion and formation of acids, for example hydrochloric acid, when the biogas is combusted.

1.2.5. Oxygen/Air

Usually neither oxygen nor nitrogen are present in the biogas as long as the air is not added to the process on purpose for example to reduce hydrogen sulphide content. The presence of nitrogen can be a sign of potential air leakages in the system. As a consequence, flammable methane and oxygen mixtures can be formed.

Oxygen and nitrogen can be separated from the biogas by applying adsorption with activated carbon or molecular sieves. Other techniques include membranes or separation during desulphurization and upgrading processes.

1.2.6. Ammonia

Ammonia can be present in the raw biogas as a result of hydrolysis of materials which contain proteins. Its high level can cause inhibition of production of methane inside the digester. Ammonia can be removed from the biogas during the drying process as it dissolves in water or it can be separated with CO2 in some biogas upgrading units.

(21)

5 1.3. Biogas upgrading

The goal of biogas upgrading process, no matter which technology is used, is to increase the calorific value of the gas by removing carbon dioxide from it. This process can be combined with some biogas cleaning methods to simultaneously remove CO2

and other impurities. However, in this section only main technologies for carbon dioxide separation will be discussed and compared.

1.3.1. Physical absorption with water

Physical absorption is based on the difference in solubility of compounds that are going to be separated. The solubility of carbon dioxide in water is approximately 25 times higher than methane which makes separation possible (8). Physical separation does not involve chemical reaction but uses Van der Waal forces. Using water as a working liquid allows simultaneous removal of H2S and NH3 and therefore separate

cleaning sections in the upstream are not necessary however it entails treatment of the off-gas. The scheme of a typical water scrubbing process is shown in Figure 1 (6).

Figure 1. Water scrubbing flowsheet.

The water scrubbing system is composed by three main equipment: scrubber, flash tank and stripper. The biogas enters the scrubber column after passing multiple stages compression with intermediate cooling. Water scrubbing operates within low temperature and high pressure to favour absorption. Typical ranges are 4-8bar and up to 40℃. The liquid phase goes from the top to the bottom whereas the gas phase travels in counter-current direction. Usually random packing is used inside the absorption column to increase the specific surface of gas-liquid contact. The top product contains mostly CH4 saturated with water and therefore it has to be sent to the

drying section. The bottom stream is an aqueous solution of absorbed gases mostly CO2 and H2S but it also contains some amount of CH4. Therefore to reduce a methane

(22)

6 flash tank. The desorbed gas is returned and mixed with the untreated input stream. Next, water from the flash tank enters the desorption column (stripper) where absorbed gases are being stripped by air. Regenerated in this way, water can be reused in the absorption column. The top stream can be sent to a further treatment due to some methane contamination. The total methane loss is about 0.5-2% which results in the final efficiency of the system about 98-99.5%. The specific water demand is about 2.1-3.3 litres per day per m3_{of biogas. The water demand can be decreased}

by cooling down the recirculating water or by increasing the pressure inside the absorption column.

1.3.2. Physical absorption with organic solvents

The configuration of this process is very similar to that one of the water scrubbing method. The main difference is the working fluid which are organic compounds instead of water. The carbon dioxide solubility in the organic solvent is about 5 times higher than in water. The most commonly used process nowadays is so-called Genosorb process which uses a mixture of dimethyl ethers of polyethylene glycol. Other organic compounds can be applied as well including methanol, N-methyl-pyrrolidone (NMP) or polyethylene glycol ethers (PEG). The example of the organic solvent scrubbing flowsheet is shown in Figure 2 (6).

Figure 2. Organic solvent scrubbing flowsheet.

One of the advantages of the usage of organic solvents with respect to water is a higher absorption rate and consequently lower circulation liquid demand which result in smaller equipment and less pumping costs. Another thing is that due to non-corrosive features of organic solvents the equipment does not necessarily have to be made up of stainless steel (8). By using organic solvents it is possible to

(23)

7 simultaneously remove CO2, H2S and H2O. Operating pressure of the absorption

column is in the range of 6-7bar and the temperature 10-20℃. Similarly as in the water scrubbing method, the bottom stream from the column is being sent to the flash tank and some part of the gaseous stream is being recirculated to minimize methane slip. Then, the bottom stream from the flash tank enters the desorption column which operates under 1bar of pressure in higher temperature of about 40-80℃ and is using air as a stripping medium. The heat supply can be combined with a cooling section after the raw gas is being compressed to avoid usage of external heating sources. The efficiency of that system allows to obtain 96-99% of methane recovery.

1.3.3. Chemical absorption

Chemical absorption is a method that uses organic solvents which can be chemically bounded with CO2 and sometimes also with H2S. Most commonly used chemicals are

alkanolamine solutions such as monoethanolamine (MEA), diethanolamine (DEA) and methyldiethanolamine (MDEA). Because of a possible simultaneous removal of hydrogen sulphide with carbon dioxide, the desulphurization process is not necessary but it is usually applied anyway in order to reduce the energy load needed for the regeneration step. Moreover, the presence of oxygen should be avoided in the system due to its unwanted reactions with amine solutions. Figure 3 shows the flowsheet of chemical absorption method (6).

Figure 3. Amine scrubbing flowsheet.

As mentioned above the desulphurization unit is not necessary but in case when it is not used in the upstream the off-gas treatment has to be applied. The operating

(24)

8 pressure inside the absorption column does not have to be high as in the case of physical separation and thus it is about the atmospheric one. The temperature of the liquid phase is about 20-45℃. However, the reaction between CO2 and amine solution

is exothermic, it causes a temperature increase. As a result, the liquid phase can reach around 45-65℃. From the thermodynamic point of view, low temperature favours the absorption process as the CO2 solubility increases in colder solutions. From a kinetic

point of view though higher temperature means faster chemical reaction. In contrast to the physical absorption methods, the bottom stream leaving the absorption column does not have to go to the flash tank, so it enters directly the desorption column. The regeneration is conducted by supplying heat as the temperature range of 106-160℃ inside the stripper is required. Usually steam is applied as a stripping medium. Chemical absorption is characterized by high efficiency which gives around 99.9% methane recovery.

1.3.4. Pressure Swing Adsorption (PSA)

PSA is based on the adsorption phenomenon. In biogas upgrading by using adsorption processes, the CO2 is selectively trapped by the adsorbent material whereas purified

methane is being received as a product. There are several different materials that can be applied for the purpose of methane separation. They can be divided into two categories: equilibrium-based materials and kinetic adsorbents.

Equilibrium-based adsorbents have a higher selectivity toward carbon dioxide. The examples of such materials are commonly used activated carbon and zeolites which have much higher capacity of carbon dioxide comparing with the one of methane. Kinetic adsorbents base on the small size of the pores which make a diffusion of one molecule much slower than the diffusion of another compound. Therefore, the equilibrium adsorption of bigger molecule is being obtained after longer time with respect to the smaller molecule. Carbon Molecular Sieve (CMS) is an example of the kinetic adsorbent material which allows much faster adsorption of CO2 due to the size

limitations to diffuse through pores for CH4. CMS was used also as the adsorbent

material in the simulation discussed in the next chapters of this work.

Depending on the material used other compounds like H2O, H2S, NH3 can be

adsorbed as well but some of them, like H2S, are trapped irreversibly. Adsorption is

an unsteady process, therefore to make it resemble a continuous technology, at least 2 beds have to be used simultaneously. Figure 4 shows the example of PSA flowsheet (6).

(25)

9

Figure 4. Four-column PSA flowsheet.

The raw biogas, after being pre-cleaned by removing hydrogen sulphide and water, enters the PSA columns working at high pressure around 4-10bar. Selective adsorption of CO2 occurs and a CH4-rich gas is obtained as a product. When the bed

is saturated (when the adsorbent cannot trap more carbon dioxide and it starts to appear in the product stream), the feed inlet is switched into another column whereas the saturated column goes into regeneration. The adsorption process is more favourable under high pressure and low temperature. The regeneration can be done by releasing the pressure to atmospheric pressure (PSA), by lowering the pressure to sub-atmospheric pressure using a vacuum pump (VPSA) or by increasing the temperature (TSA). Moreover, different cycles can be applied which use additional steps in order to increase the purity of methane or to decrease the methane slip and the energy consumption. Currently the methane recovery obtained by PSA process is in the range of 97.5-98.5%.

1.3.5. Membrane separation

Membrane separation is based on the difference in permeability through membrane material. Compounds with high permeability goes through the membrane and compose the permeate stream, whereas molecules with low permeability does not pass through and leave the unit as a retentate. In the case of biogas upgrading systems, the material chosen for membrane separation should be characterized by high permeability of impurities with respect to methane. Nowadays some membranes can reach CO2/CH4 selectivity in the range of 50-70. The example flowsheet of the

(26)

10

Figure 5. Membrane separation flowsheet.

Before biogas enters into the membrane modules, it has to be compressed and dried. Desulphurization step can be placed before or after the compression stage. Although methane has got much lower permeability than carbon dioxide it still passes through the membrane in some small amounts. Therefore, several stages can be applied to reduce the methane slip. However, the compressor duty increases with every additional stage, making the overall electric energy consumption rise. In case when there is too much methane in the off-gas, a further treatment step can be used. As a result, 85-99% of the methane recovery can be achieved depending on the energy consumption and material used.

1.3.6. Cryogenic separation

Cryogenic method takes the advantage of different temperatures in which methane, carbon dioxide and other components liquefy. Therefore, cryogenic separation is based on cooling and compressing the biogas. There are different approaches used to obtain the final biomethane. One of them includes four steps. First is compression to 10bar and cooling down to -25℃. In this conditions water, hydrogen sulphide and siloxanes can be removed. Second step is cooling the stream down to -55℃ when CO2 is removed by liquefaction. Third step is to cool the stream further down to -85℃

when CO2 solidification occurs. The last step is depressurization of the gaseous

phase. Methane recovery done by cryogenic separation method can be expected at the level above 97% being the rest mostly nitrogen.

1.3.7. Comparison

The comparison of a technical specification of all the above-mentioned upgrading methods is shown in the Table 2 (6).

(27)

11 PSA Water scrubbing Organic solvents scrubbing Amine scrubbing Membrane separation Cryogenic separation Electricity demand [kWh/m3_BG] 0.16-0.35 0.20-0.30 0.23-0.33 0.06-0.17 0.18-0.35 0.18-0.25 Heat demand [kWh/m3_BG] 0 0 0.10-0.15 0.4-0.8 0 0 Operating temperature [℃] 5-35 5-10 40-80 106-160 Ambient (-50)-(-59) Operating pressure [bar] 1-10 4-10 4-8 0.05-4 7-20 10-25 Methane loss [%] 1.5-10 0.5-2 1-4 ⁓0.1 1-15 0.1-2 Methane recovery [%] 90-98.5 98-99.5 96-99 ⁓99-9 85-99 98-99.9 Off-gas treatment recommended

Yes Yes Yes No Yes Yes

Precision

desulphurization required

Yes No No Yes

Recom-mended

Yes

Water demand No Yes No Yes No No

Chemical substances demand

No No Yes Yes No No

Table 2. Summary of some technical specification of different biogas upgrading technologies.

All the methods are characterized by a high efficiency, allowing biomethane production that meets the requirements for natural gas grid injection or use as a vehicle fuel. However, higher methane purity entails either a rise of the energy consumption and thus higher operating costs or decrease of methane recovery. From an investment costs point of view, there is a significant dependency of CAPEX on the capacity which is called the economy of scale (8). It means that specific capital costs go down when the plant’s capacity is higher.

However, the selection of a proper upgrading technology should not be done by choosing the cheapest way, but it is rather a case-sensitive choice

The selection of a proper upgrading technology is a case-sensitive choice which makes the final decision being not easy to make (9). The right method is chosen depending on several factors and circumstances including consideration of different final destinations of biomethane, regulations and requirements which have to be met to utilise it as well as the experience of staff. Therefore it is not possible to point out one best technology. This is proven by the number of industrial applications already existing and applied in the world.

(28)

12 At the beginning of 21st_{century the industry was dominated by two technologies}

namely PSA and water scrubbing (8). Nowadays the market situation has been changed and it is more balanced by other methods, mainly amine scrubbing and membrane separation. Figure 6 shows the applications breakdown (10).

Figure 6. Evolution of upgrading technologies in the XXI century.

The share of the applications by different technologies in 2017 is shown in the Figure 7 (10).

Figure 7. Upgrading technologies in 2017. 0 20 40 60 80 100 120 140 160 180 <2001 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2014 2015 2016 2017 N u m b er o f p lan ts

Water Scrubber Chemical Scrubber Membrane

PSA Organic physical scrubber Other

Cryogenic upgrading Water Scrubber, 162 Membrane, 133 Chemical Scrubber, 94 PSA, 77

Organic physical scrubber, 19

(29)

13 1.4. Biogas applications

Biogas is a versatile energy source. However, the direct use of raw biogas itself is limited to its usage as a fuel only in heat and power generation plants that are located close to the biogas production site. Its composition does not allow it to be transported due to corrosion issues and low concentration of methane. The only way to transport and use biogas in locations not defined by its production site, is to upgrade it into biomethane. Also, to use it as vehicular fuel, even if close to the production site, biogas should be upgraded. The number of biogas upgrading plants has been increasing significantly in the recent years. However they still represent a small fraction of the total biogas factories (which will be shown in the next subpoint of this chapter).

The production of renewable electricity in the European Union has reached 927TWh in 2015 and is on the trajectory to obtain 1210TWh in 2020. The renewable electricity consumption in 2015 reached almost 29% of the total European consumption whereas the production is at the level of 40% at the same time.

As well as the electricity, the contribution of renewable sources in the heating sector is characterized by the growth in the recent years and is expected to reach 21% in 2020. However, the input of biogas to all the renewable sources is quite small and in 2015 it was at the level of 3.7%. It is worth mentioning that in terms of countries both electricity and heating sectors are dominated by Germany with 50% of the total in both categories (11)

1.4.1. Biomethane

Biomethane is obtained after conducting cleaning and upgrading processes which result in a higher concentration of methane with respect to the raw biogas. This allow it to be stored and distributed using already existing infrastructure for the natural gas (2). For this reason, the biomethane must comply with the pipeline quality and meet specifications established by each country. EN 16726 is the European standard for the natural gas grid injection and fuelling which determines the requirements that must be met before the application of biomethane including relative density, sulphur content, carbon dioxide, oxygen and siloxanes limits as well as water dew point (12). Thus, there are new ways of biomethane utilisation comparing to the raw biogas. Biomethane can be injected into the natural gas grid and used as an input into heat and power generation plants or used as a feedstock in the chemical industry. Obviously before the gas can be utilised it has to comply with specifications related to its final application which can different among countries. However, biomethane cannot compete with the natural gas in terms of the price as the output of the product of the biogas upgrading is much more expensive than its conventional equivalent. Therefore, main economic drivers for the biomethane production are governmental subsidies and grants.

The other application of biomethane is placed in the transportation sector as it can be used in existing combustion engines. It can replace the natural gas in CNG (Compressed Natural Gas) and LNG (Liquified Natural Gas) fuels. The usage of biomethane as a vehicles fuel reached 160 million m3_{in 2015 (11). This market is}

(30)

14 dominated by Sweden with a contribution of 113 million m3_{, followed by Germany,}

Norway and Iceland. Natural gas engines are characterized by low NOx, CO2 and

particles emissions which make them environmentally friendly. 1.4.2. Carbon dioxide

Climate changes, global warming and increasing concentration of carbon dioxide in the atmosphere cause higher and higher interest in possibilities of CO2 utilisation. One

of methods that gained much attention is the Carbon Capture and Storage (CCS) (9). It consists of three steps which include capturing the carbon dioxide, its transportation and storage underground. Captured gas can be used in Enhanced Oil Recovery (EOR) technology when it is being injected into the oil well to obtain crude oil which cannot be extracted in any conventional way. Other opportunities for the carbon dioxide utilisation are the food industry and algal biomass production. However, in all possible CO2 applications the gas has to be primarily treated to obtain high purity

which increases the total production cost. 1.4.3. Digestate

It is worth mentioning that also the digestate can be used in an efficient way. The slurry obtained during the biogas production is rich in nutrients and contains important phosphorus and potassium. Therefore, it can be applied as a high-quality compost, soil improver or it can be used as a substitute for mineral fertilisers. In that method the nutrient cycle is closed and the digestate is utilised in a most sustainable way. However, before that, it is important to conduct heat treatment in order to reduce pathogens population (13). Another possible way that is commonly used in practice to utilise the digestate is to recycle it to the anaerobic digester (6).

1.5. Biogas market

As mentioned in the introduction part, one of the major motivations for the interest in biogas technologies and renewable energy sources in general is an environmental care. It is related to the constant population growth and the energy demand rise. Current total population in the world is around 7500 million people and according to statistics it has doubled in the last 50 years (14). The level of CO2 in the atmosphere

is nowadays the highest in the history (15). Thus, one of the goals for the 21st_century

is to reduce global warming effect by lowering emissions to the atmosphere (3). The relations between global energy consumption, CO2 concentration in the atmosphere

(31)

15

Figure 8. Global energy consumption, CO2 concentration and total population over time.

According to (16) the electricity produced from renewable sources represents 25% of the overall electricity production in 2017. The Figure 9 shows the breakdown of the electricity production in 2017 by countries and the percentage of energy coming from renewable sources.

Figure 9. Renewable electricity production in the world in 2017.

0 1000 2000 3000 4000 5000 6000 7000 8000 0 200 400 600 800 1000 1200 1400 1600 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 [Milli o n s o f Peop le ] [T o n n es Oil E q u iv alent 10 5] [p p m ]

(32)

16 The country with the highest contribution of renewable energy sources in the electricity production is Norway with 97.9% followed by Colombia (86.8%) and New Zealand (81.4%).

It is worth mentioning that the power production coming from the biogas is still very small with respect to other resources. Figure 10 shows the input to the total renewable electricity capacity by different origins.

Figure 10. Renewable electricity capacity by technology.

In 2017 the contribution of biogas was about 1% (17). However, the worldwide installed capacity of biogas is characterized by a continued growth. Its breakdown with contributions of different regions is shown in Figure 11 (17).

Figure 11. Worldwide biogas installed capacity over time.

0 500 000 1 000 000 1 500 000 2 000 000 2 500 000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Ele ctricity Cap acity [MW] Marine Liquid biofuels Geothermal Biogas Bioenergy Solar Wind Hydropower 0 2 000 4 000 6 000 8 000 10 000 12 000 14 000 16 000 18 000 In sta lle d Cap acity [ MW] Central America Africa Middle East Oceania Eurasia South America Asia North America Europe

(33)

17 The biggest development over the years was done by European countries which result in 71% of the total capacity installed in 2017. The total number of biogas plants in Europe in 2016 was 17662 only part of them correspond to upgrading biogas to biomethane (18). However, very rapid growth can be observed in the biomethane production. In 2011 the production was equal to 752GWh but in 2016 it was 17264GWh which is almost 23 times higher in 5 years. Total number of upgrading biogas plants in 2017 was 600 according to (10). Figure 12 shows the total number of plants by countries in 2017.

Figure 12. Total number of biogas upgrading plants in 2017.

The worldwide leader with the highest number of biogas upgrading plants is Germany followed by United Kingdom and Sweden.

200 96 65 50 47 ₃₉ 24 13 12 11 10 9 ₆ ₅ ₄ ₃ ₂ ₁ ₁ ₁ ₁ 0 50 100 150 200 250

(34)

18

2. Objectives

There are three objectives within this work.

The first objective is to understand the PSA technology and its design phase. This is done by the simulation of the process in an appropriate software, in this case it is Aspen Adsorption, and by comparing the results obtained in this work with the results of another work which uses different software.

However, before the simulation can be conducted, the derivation and discussion of the mathematical model used by the software was be done. The understanding of the PSA unit is based on the description of isotherms of adsorption of the biogas components, the gas diffusion through the pores of the adsorbent and also the thermal effects of adsorption and desorption. Simulation of the breakthrough curves with the analysis of the temperature profiles and in the end simulation of the PSA cycle are standard methodologies to approach the PSA design.

All of this was done to have a better understanding of the process which is necessary for a proper design of the plant.

The second objective of this work is to create a cost estimation model. The model will be based on the basic assumptions regarding the PSA unit and the biogas feed specification. The approach will enable sizing and costing of each of the elements of the biogas upgrading plant by PSA process in the small-scale applications.

The next step will be to collect all the necessary data and parameters for the estimation of the yearly operational costs. These include prices of the raw materials and utilities, wages of the workers as well as number of workers and number of the working hours in the year.

After that, the model was verified with the data obtained from the real industrial cases both in terms of the CAPEX and OPEX.

The third objective of this work is to use the model to characterize the influence of the components of the PSA plant on the Total Capital Investment (TCI). This will allow researchers and industrial developers to have a better understanding of the cost breakdown structure and will help scientists to focus their attention on the most important aspects of the plant regarding the cost.

The structure of the next chapters is following: • Chapter 3

It includes the derivation of the mathematical model which describes the PSA process and enables its simulation in the Aspen Adsorption software. The model is based on unsteady mass, momentum and energy balances for all different phases of the system including both gas and solid. Also, the methods for calculation of the adsorption equilibrium will be presented and discussed here.

(35)

19 • Chapter 4

In Chapter 4 the cost estimation model is presented. The model is based on calculations of CAPEX and OPEX.

CAPEX includes the cost of the hardware which is all the equipment called ISBL here, the cost of all the structural changes for implementing a new plant on a site called OSBL, the cost of the design, supervision and management of the project named E&D and in the end the contingency which covers all the unexpected expenses due to the changes of the material prices or scope of the project.

OPEX is composed of three elements which are annual capital cost, variable and fixed cost of production. The annual capital cost is the money that has to be spent to pay off the plant after some years refer as the lifetime of the plant. The variable costs of production include all raw materials, utilities and consumables and can be generalized to all the expenses which are proportional to the production capacity. The fixed costs of production include mainly human labour, administration, taxes and insurance and they have to be paid no matter the plant is running or no.

• Chapter 5

This chapter shows the results obtained during the thesis work and it is divided into two parts. The first one regards the simulation of the process in the Aspen Adsorption software and the second one refers to the results obtained by implementing the cost estimation model:

PSA simulation

This part is devoted to the simulation of the process in the Aspen Adsorption software. First the verification of the software is done by comparing it with the hand calculations for the simple adsorption case. Next, the isotherm parameters are derived and the breakthrough curve for carbon dioxide is obtained. The output from the software is compared with the results obtained from the paper (19).

Finally, the simulation of the PSA cycle is shown. The simulation is supported by the description of the cycle and the operation of PSA valves. The results given by the software are shown and analysed.

Cost estimation

This part refers to the cost estimation model which can be applied for the small-scale biogas upgrading plants. The model was implemented in order to get both CAPEX and OPEX depending on the inlet raw biogas flowrate. Necessary assumptions are shown and explained at the beginning of this part. Next, the output of the model is shown and discussed.

• Chapter 6

This chapter includes the final summary and conclusions coming from this work accompanied by the discussion of the results, their verification and suggestions for the future usage of the thesis deliverables.

(36)

20

3. PSA mathematical model

Pressure Swing Adsorption process is a comprehensive method used for the separation of gases. It is based on the adsorption phenomenon occurring on the solid surface of the porous of the adsorption material. The adsorbent is placed inside the column in which the gaseous mixture is fed from the bottom whereas the product is received from the top. While the PSA column is during the regeneration step, counter current flow of the gas phase is observed. It means that the purge stream enters the column from the top whereas the off-gas leaves the column from the bottom part. For this reason, several columns are coupled together to provide the continuous operation. The PSA column can be described as a packed bed reactor with a plug flow of the gas phase. In order to fully analyse the adsorption process, an appropriate set of mass, momentum and energy balances has to be written and coupled with equations accounting for an adsorption isotherm and a mass transfer between the gas phase and the solid. In this chapter, all of the balances are described, both with assumptions made for simplifying the model and for the numerical methods used to solve the system.

3.1. Assumptions

All the assumptions made for the sake of simplicity are listed below:

• The gas phase is described by the Peng-Robinson equation of state

• The system is fully mixed in the radial direction i.e. mass, velocity and temperature gradients are negligible in radial direction

• Mass transfer is characterized by lumped overall resistance • Constant cross section area

• Uniform void fraction in the column • No chemical reaction occurs

• No internal heat exchanger

3.2. Mass balance

The mass balance is composed of 4 terms as shown below:

Gas Phase Accumulation = Convection + Axial Dispersion + Gas-Solid Mass Transfer

(37)

21 The component mass balance equation for the gas phase is given by:

𝜀𝐵 𝜕𝑐_𝑘 𝜕𝑡 = − 𝜕(𝑣_𝑔𝑐_𝑘) 𝜕𝑧 + 𝜀𝐵𝐸𝑧𝑘 𝜕2𝑐_𝑘 𝜕𝑧2 − 𝐽𝑘

where 𝜀_𝐵 is the bed void fraction, 𝑐_𝑘 is the molar concentration of component k, 𝑡 is time, 𝑣_𝑔 is the gas phase superficial velocity, 𝑧 is the axial coordinate, 𝐸_𝑧𝑘 is the axial dispersion coefficient of component k and 𝐽𝑘 is the gas-solid mass transfer term of

component k.

The mass transfer term between the gas phase and the solid is given by: 𝐽_𝑘 = −𝜌_𝑠𝜕𝑤𝑘

𝜕𝑡

where 𝜌_𝑠 is the adsorbent bulk density and 𝑤_𝑘 is the loading of component k.

The adsorbent bulk density is related to the particle density 𝜌_𝑝 and can be expressed by:

𝜌_𝑠 = (1 − 𝜀_𝐵)𝜌𝑝

Therefore, the mass balance equation can be rewritten as: 𝜀_𝐵𝜕𝑐𝑘 𝜕𝑡 = − 𝜕(𝑣_𝑔𝑐_𝑘) 𝜕𝑧 + 𝜀𝐵𝐸𝑧𝑘 𝜕2𝑐𝑘 𝜕𝑧2 + 𝜌𝑠 𝜕𝑤𝑘 𝜕𝑡

The bed void fraction 𝜀𝐵 is composed of inter- and intraparticle void fractions:

𝜀_𝐵 = 𝜀_𝑖 + (1 − 𝜀_𝑖)𝜀_𝑝

where 𝜀_𝑖 is the interparticle void fraction and 𝜀_𝑝 is the intraparticle void fraction.

The model of the adsorption bed both with the inter- and intraparticle porosity is shown in the Figure 13 (20):

(38)

22 3.3. Mass transfer

The mass transfer between the gas phase and the solid can be represented in several different ways according to the assumptions done on the system. Typical approach is to consider first a mass transfer from the bulk gas phase to the macropores and then from the macropores to the micropores of the porous solid material. This model is shown in the Figure 14 (20):

Figure 14. The Gas-Solid Mass Transfer.

However, it is also a common method to use, so-called Lumped Resistance method which combines micro- and macropore resistances under one coefficient which simplifies overall system. Both of the approaches are described in the following points 3.3.1 and 3.3.2 of this work.

It is also worth mentioning that the mass transfer driving force description can be based on either solid or fluid film model assumption. For the solid assumption the mass transfer is driven by the solid phase loading whereas for the fluid assumption it is described by the gas phase concentration.

3.3.1. Micro- and Macropore Resistances

This method considers two concentration gradients observed in the macro- and micropores of the adsorbent material. The first one occurs within the pores of the solid whereas the second one is in the solid directly. For this reason, two separate mass balances for both macro- and micropores are required. They are given by following equations: • Macropores Macropore Accumulation = Bulk-Macropore Mass Transfer + Micropore mass transfer Fluid: (1 − 𝜀𝑖) 𝜀𝑝 𝜕𝑐𝑚𝑠𝑘 𝜕𝑡 = 𝐾𝑚𝑎𝑐(𝑐𝑏𝑘− 𝑐𝑚𝑠𝑘) − (1 − 𝜀𝑝)𝜌𝑠 𝜕𝑤𝑘 𝜕𝑡

(39)

23 Solid: (1 − 𝜀𝑖) 𝜀𝑝 𝜕𝑐_𝑚𝑠𝑘 𝜕𝑡 = (1 − 𝜀𝑝)𝜌𝑠𝐾𝑚𝑎𝑐(𝑤𝑏𝑘 ∗_{− 𝑤} 𝑚𝑠𝑘∗) − (1 − 𝜀𝑝)𝜌𝑠 𝜕𝑤_𝑘 𝜕𝑡

where 𝐾_𝑚𝑎𝑐 is the macropore mass transfer coefficient and it is characterized by: 𝐾_𝑚𝑎𝑐 = 15𝐷𝑒𝑓𝑝

𝑟_𝑝2

where 𝐷𝑒𝑓𝑝 is an effective macropore diffusion coefficient and 𝑟𝑝 is the particle radius.

• Micropores Micropore Accumulation = Macropore-Micropore Mass Transfer Fluid: (1 − 𝜀_𝑝)𝜌_𝑠𝜕𝑤𝑘 𝜕𝑡 = 𝐾𝑚𝑖𝑐(𝑐𝑚𝑠𝑘− 𝑐𝑘 ∗₎ Solid: (1 − 𝜀_𝑝)𝜌_𝑠𝜕𝑤𝑘 𝜕𝑡 = (1 − 𝜀𝑝)𝜌𝑠𝐾𝑚𝑎𝑐(𝑤𝑚𝑠𝑘 ∗_{− 𝑤} 𝑘)

where 𝐾_𝑚𝑖𝑐 is the micropore mass transfer coefficient and it is characterized by: 𝐾𝑚𝑖𝑐 = 15

𝐷𝑒𝑓𝑐

𝑟𝑐2

where 𝐷𝑒𝑓𝑐 is an effective micropore diffusion coefficient and 𝑟𝑐 is the microparticle

radius.

3.3.2. Lumped Resistance

The Lumped Resistance model substitutes all the resistances with a single overall coefficient. The mass transfer driving force can be either a linear or a quadratic function of the gas phase concentration or solid phase loading.

Macropore Accumulation = Bulk-Macropore Mass Transfer + Micropore mass transfer Solid: 𝜌_𝑠𝜕𝑤𝑘 𝜕𝑡 = 𝑀𝑇𝐶𝑠𝑘(𝑤𝑘 ∗_{− 𝑤} 𝑘)

(40)

24 Fluid:

𝜕𝑤_𝑘

𝜕𝑡 = 𝑀𝑇𝐶𝑔𝑘(𝑐𝑘− 𝑐𝑘

∗₎

where 𝑀𝑇𝐶𝑠_𝑘 is the solid film mass transfer coefficient of component k, 𝑀𝑇𝐶𝑔_𝑘 is the gas film mass transfer coefficient of component k.

3.4. Momentum balance

The momentum balance characterizes the relationship between gas phase velocity and pressure drop. The typical expressions used for the momentum balance description are the Karman-Kozeny equation for laminar flow, Burke-Plammer equation for turbulent flow and the Ergun equation which is a combination of both equations mentioned above.

The Ergun equation is given by: 𝜕𝑃 𝜕𝑧 = − [ 1.5 ∙ 10−3_{(1 − 𝜀} 𝑖)2 (2𝑟_𝑝Ψ)2𝜀_𝑖3 𝜇𝑣𝑔 + 1.75 ∙ 10 −5_𝑀𝜌 𝑔 (1 − 𝜀𝑖) 2𝑟_𝑝Ψ𝜀_𝑖3𝑣𝑔2]

where is 𝑃 the pressure, 𝑟_𝑝 is the particle radius, Ψ is the particle shape factor, 𝜇 is the dynamic viscosity, 𝑀 is the molecular weight and 𝜌𝑔 is the gas phase molar density.

3.5. Energy balance

The system is composed of 3 phases: gas, solid and the column wall, therefore different energy balances should be considered for each of them separately.

3.5.1. Gas phase

Due to the assumption of no chemical reaction, the equation describing the gas phase includes 6 terms as shown below:

Gas Phase Accumulation = Convection + Gas Phase Axial Thermal Conduction + Compression + Gas-Solid Heat Transfer + Gas and Internal Wall Heat Exchange The overall energy balance for the gas phase is given by:

𝜀_𝑖𝐶_𝑣𝑔𝜌_𝑔𝜕𝑇𝑔 𝜕𝑡 = −𝐶𝑣𝑔𝑣𝑔𝜌𝑔 𝜕𝑇_𝑔 𝜕𝑧 + 𝑘𝑔𝑧𝜀𝑖 𝜕2𝑇_𝑔 𝜕𝑧2 − 𝑃 𝜕𝑣_𝑔 𝜕𝑧 − 𝐻𝑇𝐶𝛼𝑝(𝑇𝑔 − 𝑇𝑠) − 4𝐻_𝑤 𝐷_𝐵 (𝑇𝑔 − 𝑇𝑤) where 𝐶_𝑣𝑔 is the specific gas phase heat capacity at constant volume, 𝑇_𝑔 is the gas phase temperature, 𝑘_𝑔𝑧 is the effective axial gas phase thermal conductivity, 𝐻𝑇𝐶 is the gas-solid heat transfer coefficient, 𝛼_𝑝 is the specific particle surface per unit volume

(41)

25 bed, 𝑇_𝑠 is the solid phase temperature, 𝐻_𝑤 is the gas-wall heat transfer coefficient, 𝐷_𝐵 is the bed diameter and 𝑇_𝑤 is the wall temperature.

𝛼𝑝 is described by:

𝛼_𝑝 = (1 − 𝜀_𝑖) 3 𝑟_𝑝 3.5.2. Solid phase

The equation for the solid phase contains 5 terms:

Solid Phase Accumulation = Solid Phase Axial Thermal Conductivity + Heat of Adsorbed Phase + Heat of Adsorption + Gas-Solid Heat Transfer The overall energy balance for the solid phase is given by:

𝜌_𝑠𝐶_𝑝𝑠𝜕𝑇𝑠 𝜕𝑡 = 𝑘𝑠𝑧 𝜕2𝑇𝑠 𝜕𝑧2 − 𝜌𝑠∑(𝐶𝑝𝑎𝑘𝑤𝑘) 𝑘 𝜕𝑇𝑠 𝜕𝑡 − 𝜌𝑠∑ (Δ𝐻𝑘 𝜕𝑤𝑘 𝜕𝑡 ) 𝑘 + 𝐻𝑇𝐶𝛼_𝑝(𝑇_𝑔 − 𝑇_𝑠)

where 𝐶𝑝𝑠 is the specific heat capacity of adsorbent, 𝑘𝑠𝑧 is the effective axial solid

phase thermal conductivity, 𝐶_𝑝𝑎𝑘 is the specific heat capacity of adsorbed phase and Δ𝐻_𝑘 is the heat of adsorption of component k.

3.5.3. Column wall

The equation describing the column wall is composed of 4 terms:

Wall Heat Content = Axial Thermal Conductivity along Wall + Heat Exchange between Gas and Wall + Heat Exchange between Wall and

Environment The overall energy balance for the wall:

𝜌_𝑤𝑐_𝑝𝑤𝜕𝑇𝑤 𝜕𝑡 = 𝑘𝑤 𝜕2𝑇𝑤 𝜕𝑧2 + 𝐻𝑤 4𝐷𝐵 (𝐷𝐵+ 𝑊𝑇)2− 𝐷𝐵2 (𝑇_𝑔− 𝑇_𝑤) − 𝐻_𝑎𝑚𝑏 4(𝐷𝐵+ 𝑊𝑇) 2 (𝐷𝐵+ 𝑊𝑇)2− 𝐷𝐵2 (𝑇_𝑤 − 𝑇_𝑎𝑚𝑏)

where 𝜌𝑤 is the wall density, 𝑐𝑝𝑤 is the specific heat capacity of column wall, 𝑘𝑤 is the

is the thermal conductivity of column wall, 𝐻_𝑤 is the gas-wall heat transfer coefficient, 𝑊_𝑇 is the width of column wall and 𝐻_𝑎𝑚𝑏 is the wall-ambient heat transfer coefficient.

(42)

26 3.6. Adsorption isotherm

The adsorption isotherm model describes the adsorbed amount of components on the solid surface at thermodynamic equilibrium. The model can be either partial pressure or concentration based. There are a lot of choices for the isotherm model in Aspen Adsorption that can be applied both for pure components as well as for mixtures. One of typically applied models is Langmuir Model which describes adsorption of a single molecule layer with negligible interactions between adsorbed species. The equations used by Langmuir Model are given below:

• For single components: Langmuir 1 𝑤𝑘 = 𝐼𝑃₁𝑃_𝑘 1 + 𝐼𝑃2𝑃𝑘 or 𝑤𝑘= 𝐼𝑃₁𝑐_𝑘 1 + 𝐼𝑃2𝑐𝑘

where 𝐼𝑃1 and 𝐼𝑃2 are isotherm parameters, 𝑃𝑘 is the partial pressure of component k

and 𝑐_𝑘 is the molar concentration of component k. It is worth mentioning that in this model, the isotherm parameters does not depend on the temperature.

The units of isotherm parameters for models discussed in this section are shown in the table at the end of this point.

Langmuir 2 𝑤𝑘 = 𝐼𝑃₁∙ 𝑒𝐼𝑃2⁄𝑇𝑠_{∙ 𝑃} 𝑘 1 + 𝐼𝑃₃∙ 𝑒𝐼𝑃4⁄𝑇𝑠∙ 𝑃 𝑘 or 𝑤_𝑘 = 𝐼𝑃1∙ 𝑒 𝐼𝑃2⁄𝑇𝑠 _{∙ 𝑐} 𝑘 1 + 𝐼𝑃3∙ 𝑒𝐼𝑃4⁄𝑇𝑠 ∙ 𝑐𝑘

where 𝐼𝑃1, 𝐼𝑃2, 𝐼𝑃3 and 𝐼𝑃4 are isotherm parameters. As opposite to Langmuir 1 model,

Langmuir 2 does account for the temperature dependency of isotherm parameters. Langmuir 3 𝑤_𝑘 =(𝐼𝑃1− 𝐼𝑃2∙ 𝑇𝑠) ∙ 𝐼𝑃3∙ 𝑒 𝐼𝑃4⁄𝑇𝑠_{∙ 𝑃} 𝑘 1 + 𝐼𝑃3∙ 𝑒𝐼𝑃4⁄𝑇𝑠∙ 𝑃𝑘 or 𝑤_𝑘= (𝐼𝑃1− 𝐼𝑃2∙ 𝑇𝑠) ∙ 𝐼𝑃3∙ 𝑒 𝐼𝑃4⁄𝑇𝑠_{∙ 𝑐} 𝑘 1 + 𝐼𝑃₃∙ 𝑒𝐼𝑃4⁄𝑇𝑠 ∙ 𝑐 𝑘

(43)

27 Langmuir 3 takes into account also the temperature dependence of the maximum loading represented by (𝐼𝑃₁− 𝐼𝑃₂∙ 𝑇_𝑠). • For mixtures: Extended Langmuir 1 𝑤_𝑘 = 𝐼𝑃1𝑘𝑃𝑘 1 + ∑ (𝐼𝑃_𝑘 _2𝑘𝑃_𝑘) or 𝑤_𝑘= 𝐼𝑃1𝑘𝑐𝑘 1 + ∑ (𝐼𝑃_𝑘 _2𝑘𝑐_𝑘) Extended Langmuir 2 𝑤_𝑘= 𝐼𝑃1𝑘∙ 𝑒 𝐼𝑃2𝑘⁄𝑇𝑠_{∙ 𝑃} 𝑘 1 + ∑ (𝐼𝑃𝑘 3𝑘∙ 𝑒𝐼𝑃4𝑘⁄𝑇𝑠∙ 𝑃𝑘) or 𝑤𝑘 = 𝐼𝑃_1𝑘∙ 𝑒𝐼𝑃2𝑘⁄𝑇𝑠 _{∙ 𝑐} 𝑘 1 + ∑ (𝐼𝑃_3𝑘∙ 𝑒𝐼𝑃4𝑘⁄𝑇𝑠∙ 𝑐 𝑘) 𝑘 Extended Langmuir 3 𝑤_𝑘 =(𝐼𝑃1𝑘− 𝐼𝑃2𝑘∙ 𝑇𝑠) ∙ 𝐼𝑃3𝑘∙ 𝑒 𝐼𝑃4𝑘⁄𝑇𝑠 _{∙ 𝑃} 𝑘 1 + ∑ (𝐼𝑃𝑘 3𝑘∙ 𝑒𝐼𝑃4𝑘⁄𝑇𝑠∙ 𝑃𝑘) or 𝑤𝑘 = (𝐼𝑃_1𝑘− 𝐼𝑃_2𝑘 ∙ 𝑇_𝑠) ∙ 𝐼𝑃_3𝑘 ∙ 𝑒𝐼𝑃4𝑘⁄𝑇𝑠_{∙ 𝑐} 𝑘 1 + ∑ (𝐼𝑃_3𝑘∙ 𝑒𝐼𝑃4𝑘⁄𝑇𝑠∙ 𝑐 𝑘) 𝑘

Extended Langmuir model is the extension of the classical Langmuir approach which considers interactions between different molecular species. The actual parameters accounting for the presence of other components are calculated by Aspen

Adsorption form the parameters for the single component model. Parameters and they corresponding units are shown in the table below:

(44)

28

Model Parameter Unit (pressure) Unit (concentration)

Langmuir 1 𝐼𝑃₁ [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑔] 𝐼𝑃2 [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] Langmuir 2 𝐼𝑃₁ [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑔] 𝐼𝑃2 [𝐾] [𝐾] 𝐼𝑃₃ [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] 𝐼𝑃₄ [𝐾] [𝐾] Langmuir 3 𝐼𝑃₁ [𝑘𝑚𝑜𝑙 𝑘𝑔 ] [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ] 𝐼𝑃2 [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝐾] [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝐾] 𝐼𝑃₃ [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] 𝐼𝑃₄ [𝐾] [𝐾] Extended Langmuir 1 𝐼𝑃1 [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑔] 𝐼𝑃₂ [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] Extended Langmuir 2 𝐼𝑃1 [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑔] 𝐼𝑃₂ [𝐾] [𝐾] 𝐼𝑃₃ [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] 𝐼𝑃4 [𝐾] [𝐾] Extended Langmuir 3 𝐼𝑃1 [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ] [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ] 𝐼𝑃₂ [𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝐾] [ 𝑘𝑚𝑜𝑙 𝑘𝑔 ∙ 𝐾] 𝐼𝑃3 [ 1 𝑏𝑎𝑟] [ 𝑚3 𝑘𝑚𝑜𝑙] 𝐼𝑃₄ [𝐾] [𝐾]

Table 3. Units of isotherm parameters for different isotherm models

3.7. Numerical methods

In order to describe the adsorption process, it is necessary to solve a set of partial differential and algebraic equations. The approximations of first- and second order derivatives are distributed over a fixed and uniform grid consisting of specified number of nodes. The variables sets are determined for each node and the differential and

(45)

29 algebraic equations are solved simultaneously since they are coupled. The choice of an appropriate numerical method depends on the process to simulate, level of accuracy, stability and required simulation time as well. The three best methods mentioned by Aspen Adsorption software are first-order Upwind Differencing Scheme 1 (UDS1), third-order Quadratic Upwind Differencing Scheme (QDS) and third-order Mixed Differencing Scheme (MDS).

UDS1 is a method set by default in Aspen Adsorption and it is characterized by a good trade-off between accuracy and simulation time. Better accuracy can be obtained by setting higher number of nodes however this results in higher simulation time. The method is based on a first-order Taylor expansion.

First order (convection) term is defined as: 𝜕Γ_𝑖

𝜕𝑧 =

Γ_𝑖− Γ_𝑖−1 Δ𝑧 Second order (dispersion) term:

𝜕2_Γ 𝑖

𝜕𝑧2 =

Γ_𝑖+1− 2Γ_𝑖+ Γ_𝑖−1 Δ𝑧2