- SUMMARY
Due to fossil fuels limited availability along with its environmental concerns, the production of biodiesel, a renewable source of energy, has increased exponentially in the last few years. This growth in biodiesel has also facilitated an excess production of glycerol which is generated as a byproduct during the formation of biodiesel. Because of a limited glycerol market in the world, there are concerns regarding utilization of glycerol. One option, steam reforming of glycerol to produce hydrogen has been considered as a promising idea to utilize this excess resource. Glycerol steam reforming (GSR) occurs in the presence of catalyst and literature suggests that nickel (Ni)-based catalysts are the most applicable. However, limited studies have been carried out to investigate reaction kinetics for Ni-based GSR. In this paper, reaction kinetics for GSR using a Ni-based catalyst has been investigated. First, a set of detailed reactions have been developed through literature review. Based on the detailed reaction mechanism proposed, a global reaction rate is calculated. Furthermore, a catalyst model is derived for one-dimensional [1-D], dynamically incompressible flow. The model is used to simulate glycerol conversion rate at various temperatures. The obtained result of maximum glycerol conversion rate at temperatures above 770 kelvin supports the experimental works. The global reaction rate along with the 1-D catalyst model has closely approximated the reaction rate of GSR with minimum computational cost which makes this procedure convenient for future applications.
1. Introduction
The ever-increasing demand for energy and problems related to emissions due to the use of fossil fuels has facilitated the search for alternative and renewable sources of energy. In this respect, biodiesel is being gradually accepted as a replacement for diesel fuel since it is renewable and (theoretically) carbon dioxide neutral (Fig 1) [1]. Biodiesel is produced by an alkali-catalyzed transesterification reaction between biomass-derived triglyceride and methanol (Fig 2). During this reaction, glycerol is produced as a byproduct at about 10% of the amount of biodiesel by mass.
1.1 Problem Statement
The production of biodiesel has increased exponentially in the last decade (Fig 3) [2]. As a result, the generation of glycerol too has grown tremendously. Currently, glycerol is over-supplied to world markets due to its limited commercial exploitation which in turn has provoked an expected fall in glycerol price (Fig 4). Hence, it may even become a waste problem to dispose of [3, 4]. As a result, it is essential to find effective and economical ways for conversion of glycerol to useful products. One of the many promising methods to use glycerol is the production of hydrogen using reformation process.
Figure 1: Carbon dioxide (CO2) emission cycle between fossil fuel and biodiesel fuels [1]
Figure 2: Schematic transesterification process [2]
Hydrogen has wide applications for chemical and petroleum industries and is also considered a clean energy. At present 95% of the world’s hydrogen is mainly produced from steam reforming of natural gas, but this process does not reduce the greenhouse gas and does not promote sustainable development of global economy [5]. Therefore, the production of hydrogen from renewable source must be further studied. Among many renewable feedstock, glycerol is promising because of its relatively high hydrogen content, and nontoxicity along with being easy to store and handle [6]. However, only 13% of total glycerol produced in 2015 A.D. was used in energy sector [6]. To increase the use of glycerol in hydrogen production, efficient and practical methods must be implemented.
Figure 3: Biodiesel Production from 2000 to 2012 [2]
The best method to produce hydrogen using glycerol has been evaluated by analyzing various literatures. According to the papers, steam reforming of glycerol (GSR) is more applicable in comparison to other methods, which will be discussed later. Steam reforming reaction occurs in the presence of catalyst. So, the selection of appropriate catalyst is critical in enhancing the reaction activity. Papers state that Cobalt (Co), Iridium (Ir), Nickel (Ni), Palladium (Pd), Platinum (Pt), Rhodium (Rh), and Ruthenium (Ru) based catalyst are often used in GSR. Most papers suggest that Ni-based catalyst are more practical among other catalysts. The advantages of Ni-based catalysts over other catalysts are explained in the next chapter. GSR is often carried out in packed-bed reactors where the catalysts are held by supports. According to the papers, SiO2, CeO2, MgO, and Al2O3 are used as supports for GSR, among which Al2O3 is most preferred. Analysis of the papers suggest that GSR reaction in the presence of Ni/Al2O3 catalyst can be considered one of the most practical option to produce hydrogen using glycerol.
Figure 4: Cost trend of glycerol over last few years [2]
1.2 Scope of Efforts
The objective of this work included:
1. Selection of appropriate catalyst for GSR reaction to make this method more practical. Because the reaction is important in utilization of excess glycerol in the world.
2. Derivation of global reaction rate for GSR in the presence of selected catalyst.
3. Simulation of light-off curve for GSR using global reaction rate and one dimensional catalyst modelling technique
1.3 Article Structure
First, the need for reforming of glycerol has been discussed in section 1. Section 2 will discusses the effort by different authors in the field of glycerol reforming. Various reforming processes practiced at present will be summarized in section 2.1. Section 2.2 talks about different catalyst options for GSR. The appropriate condition to promote maximum hydrogen through Le Chatelier’s principle is discussed in section 2.3. Section 2.4 will discuss the possible reaction pathway for GSR followed by section 2.5 which talks about kinetics and reaction mechanism. Under section 3, a global reaction rate will be derived. Section 4 will discuss about the kinetic parameters required to evaluate a reaction rate. The simulation of light-off curve of glycerol will be presented in section 5. Section 6 demonstrates the effect of pressure on glycerol conversion light-off curve. Finally, section 7 will summarize the findings of this project and it will present recommendations for future work.
2. Literature Review
2.1 Various Reforming Process
Adhikari et al. and Schwengber et al. have presented literature reviews on the reforming technologies applied to the glycerol along with advantages and problems of these methods [5, 7]. Various glycerol reforming processes expressed in their reviews are: steam reforming (SR), partial oxidation reforming (POR), auto-thermal reforming (ATR), aqueous-phase reforming (APR) and supercritical water reforming (SWR). The main reactions involved are [7]:
Global reaction:
C3H8O3 + 3H2O →3CO2+7H2 (1) ∆H °298 = +128 kJ/mol
Water-gas shift (WGS) reaction:
CO + H2O ↔ CO2+H2 (2) ∆H °298 = -41 kJ/mol
Glycerol decomposition:
C3H8O3 ↔ 3CO+4H2 (3) ∆H °298 = +250 kJ/mol
Methanation
CO2 + 4H2 ↔ CH4 + 2H2O (4) ∆H °298 = -165 kJ/mol
Glycerol oxidation:
C3H8O3 + 0.5O2 ↔ 2CO2+4H2 (5) ∆H °298 = -32 kJ/mol
C3H8O3 + O2 ↔ CO+2CO2+ 4H2 (6) ∆H °298 = -315 kJ/mol
C3H8O3 + 1.5O2 ↔ 3CO2+4H2 (7) ∆H °298 = -598 kJ/mol
C3H8O3 + 3.5O2 ↔ 3CO2+4H2O (8) ∆H °298 = -1565 kJ/mol
Steam reforming (SR) is an endothermic process in which the substrate is reacted with steam to produce hydrogen, carbon dioxide and carbon monoxide in the presence of catalysts. The global reaction expression for glycerol steam reforming is represented by equation 1. SR method is the most commonly used glycerol reforming method mainly because it facilitates hydrogen production without significant changes in the current hydrogen production industry. Moreover, hydrogen yield rate is higher for the SR method in comparison to other methods.
Figure 5: Summary of five reforming methods
Partial oxidation reforming (POR) is an exothermic process in which the substrate is reacted with oxygen in the presence or absence of a catalyst at lean conditions. The global POR reaction can be expressed as Equation 7. The auto-thermal reforming (ATR) process combines the effects of PO and SR, combining fuel, air and water in the presence of catalyst. The benefit of this process over SR is that ideally the reactor itself supplies the amount of heat required for the reaction. However, the hydrogen yield rate for SR method is more than for the ATR method. The reaction in ATR can be expressed by Equation 1 and 5 through 8 [7]. The aqueous- phase reforming (APR reaction occurs at relatively higher pressure (60 bar) and lower temperatures (270 °C). An advantages of APR over SR is the greater heat recovery efficiency. However, the selectivity for hydrogen is lower for APR. The supercritical water reforming (SWR) reaction occurs at a high-pressure and low-temperature (374°C, 218 atm) in which the water is at or over its critical point. The advantages of SWR methods are:
1. Hydrogen is produced under high pressure and can therefore store in cylinders, requiring less energy for its compression
2. Even without the addition of catalyst, conversion of glycerol is almost complete.
Unfortunately, higher yield of hydrogen is possible only at higher temperature. As a result, the cost for building such infrastructures is high. An analysis of different techniques suggest that SR is the most effective method to produce hydrogen using catalysts (Figure 5). For the ATR method, either the velocity, temperature, or pressure needs to be higher for better selectivity of hydrogen. Furthermore, APR and SWR method must operate at a very high pressure to promote higher glycerol conversion rate and hydrogen selectivity rate.
2.2 Selection of Catalyst
Catalysts are essential for steam reforming reactions to lower the activation energy and the catalyst must be highly active and stable, generate smallest amount of coke, be sintering-resistance and not facilitate undesirable parallel reactions (e.g. methanation) [7]. Using these conditions, methane production is minimized and carbon formation is inhibited. This is important as carbon weakens catalyst activity. Among several metals including Ir/CeO2, Co/CeO2, Ni/CeO2, Ru/Y2O3, Ni/Al2O3 and Rh/CeO2, Adhikari et al. has stated Ni/Al2O3 and Rh/CeO2/Al2O3 are the best performing catalysts in terms of hydrogen selectivity and glycerol conversion [5]. Schwengber et al. has suggested Ni-based catalysts with various supports and promoters are the most effective catalyst for the SR method [7]. Tran et al. states that Rh, Ru, Pt, Ni, Co, and Fe based catalysts are equally active towards Equation 3 or Equation 2 or both. However, H2 yield rate was found in following order: Ru= Rh > Ni > Ir > Co > Pt > Pd > Fe under similar conditions [8].
Bobadilla et al. state that nickel is the most used active metal for glycerol steam reforming because of its good activity for C-C, C-O, and C-H bond cleavage, as well as its ability to remove the adsorbed CO by the WGS reaction (Equation 2) [8]. According to Silva et al., Ni, Pt, Co, Rh, Ir, Pd, and Ru-based catalysts have been investigated for the steam reforming of glycerol [9]. Among these catalysts, Ni-based catalysts have been most extensively studied mainly because of their lower price in comparison to other metals. Suffredini et al have mentioned that generation of hydrogen from glycerol relies on the cleavage of C-C and C-H bonds but preserving C-O bonds (Figure 6) [10]. As a result, Pt and Ni-based catalyst emerge as the most active systems [10]. Ni has advantage over Pt primarily due to its lower cost and remarkable ability to break the C-C bond. However, Ni-based catalysts can promote catalyst deactivation by formation of carbon [10. It has also been reported that carbon deposition can be inhibited by adjusting the catalyst structure or by adding various promoters [10].
Figure 6: C-C and C-H bond cleavage for H2 formation [8]
Tran et al have stated that catalysis is a surface process and activity is greatly increased by a higher surface area [1] also represented by Figure 7. This higher surface area can be created by decreasing the size of the catalyst material, however, high density of unsaturated coordinated atoms increases the tendency of sintering. Consequently, the surface area will be reduced along with the catalytic activity. One way to maintain this activity of the Nano-scale catalyst is to introduce supporting materials because their interactions with the catalytic material will reduce sintering effects [1]. Supports tabulated in the report of Tran et al. includes SiO2, CeO2, MgO, ZrO2 and Al2O3. Among them, gamma aluminum oxide is the most widely used support.
Figure 7: Schematic catalyst dispersion effect [8]
According to Papageridis et al. and Wu et al., researchers have investigated a variety of metal oxide supports (MgO, CaO, SiO2, CeO2, MgO, ZrO2, Al2O3 and Y2O3) in an effort to improve stability and activity [6, 11]. Aluminum oxide has attracted considerable interest due to its high specific surface area along with its mechanical and chemical resistance under typical reaction conditions [6, 11]. Experimental results from the literature to produce hydrogen using the steam reforming process have been summarized in Table 1.
Table 1: Summary of different experimental results
| Catalyst | Operating Conditions | Results | Ref |
| Ir/CeO2 | 400°C, 11,000 h-1 GHSV | C3H8O3 conversion=100%; H2 selectivity= 85% | [5] |
| Ru/Y2O3 | 600°C, 1 atm, 3.3 S/C | H2 yield= 82.8% | [5] |
| Pt/Al2O3 | 880°C, 1 atm, 2.5 S/C | C3H8O3 conversion= 100%; H2 selectivity= 70% | [5] |
| Pd/Ni/Cu/K/γ-Al2O3 | 850°C, 1 atm, 3.0 S/C | H2 yield= 42% | [5] |
| Ni/Al2O3 | 750°C, 1 atm, 4 S/C | H2 yield = 45% | [5] |
| Ni/Al2O3 | 600 °C, 1 atm, 3 S/C*, 6.6 h-1 WHSV** | Mole of H2/ Mole of C3H8O3= 5.5 | [6] |
| Ni/γ-Al2O3 | 750 °C, 1 atm, 3, 10,000 h-1 GHSV*** | C3H8O3 conversion =94.1 %; H2 Selectivity= 65.3 % | [12] |
| Co-Ni/Al2O3 | 550°C, 1 atm, 3.98 S/C | Mole of H2/ Mole of C3H8O3= 5.5212 | [13] |
| Ni-Fe-Ce/Al2O3 | 550°C, 1 atm, 6.82 S/C | H2 yield= 65% | [14] |
| Ru/Al2O3 | 500°C, 1 atm, 3 S/C | H2 yield= 45% | [15] |
S/C means steam to carbon ratio; WHSV means weight hourly space velocity; GHSV means reactant gas flow rate.
Table 2: Cost of metals used in GSR
| Metal | Cost ($/lb) |
| Nickel (Ni) | 4.40 |
| Platinum (Pt) | 15,636 |
| Palladium (Pd) | 12,392 |
| Iridium (Ir) | 14,160 |
| Rhodium (Rh) | 16,400 |
| Ruthenium (Ru) | 1,040 |
Table 1 shows the glycerol conversion rate and hydrogen yield rate using Ni, Ru, Pt, Pd, and Ir based catalysts. Except for Ru/Y2O3 catalyst where, the experiment was done with a higher catalyst loading, the conversion and yield rates for other results are almost comparable. The cost of these catalysts has been listed in Table 2. From the table, it can be noticed that the cost of nickel is at least 200 times cheaper than for other metals. Based on these result, nickel based catalyst can be considered among the active metals for GSR. Moreover, they are the cheapest metals for GSR. So, nickel based catalyst supported by aluminum oxides has been used in this study.
2.3 Application of Le Chatelier’s Principle
Le Chatelier’s principle states that equilibrium will always be displaced in such a way as to minimize the changes imposed from outside the system [16]. This equilibrium can be affected in three ways: 1. Change in concentration of a constituent; 2. Change in pressure or 3. Change in temperature. Implementing Le Chatelier’s principle for the global steam reforming reaction represented by Equation 1 generates the following points.
1. When the concentration of H2O is increased, the reaction moves in the forward direction to decrease the concentration of H2O. Likewise, if the H2 in the products is removed, the reaction again moves in forward direction to reproduce the lost hydrogen. Both these methods enhance the production of hydrogen.
2. Pressure can be related to the number of molecules in a container. If the pressure is increased in a reaction, it tends to move in the direction with lowest number of molecules. So, if the pressure in Equation 1 is increased, it will shift towards the reverse direction as the number of moles are less (4) than in forward direction (10). Hence, to produce greater number of moles of hydrogen, the pressure of the system should be minimized.
3. The reaction always tends to minimize the effect of temperature change. Therefore, when the temperature of Equation 1 is increased, it will shift in the forward direction because this direction is endothermic and will minimize the increased temperature effect.
Therefore, maximum theoretical production of hydrogen is possible at higher concentrations of water, lower pressures and at a greater temperature of the reactor. However, these facts are limited by cost, equipment set up and the nature of the catalyst. Pant et al. has stated that the hydrogen generation increased with temperature from 773 to 993 K, but at 1023 K, coke formation was significant and hydrogen generation reduced drastically [17]. This may be linked to the sintering of catalyst. Furthermore, higher concentrations of water increase the vaporization cost [7]. According to several studies [5, 6, 12, 13, 14,15], the best results for glycerol steam reforming process are obtained at temperature in the rage of 500 °C to 750 °C, atmospheric pressure, and water/glycerol ratios of 9 to 12.
2.4 Reaction on catalyst surface
Owing to the complexity of GSR surface reaction, different glycerol reforming pathways have been proposed. Wang et al. has presented a reaction mechanism where, dehydrogenation of adsorbed glycerol molecule first takes place on the metal surface of the catalyst [4]. It gives rise to adsorbed intermediates. And finally, the adsorbed molecules are further reacted through breakage of C-C or C-O bond (Figure 8) [4].
Likewise, Papageridis et al. has stated that the conversion of hydrogen to glycerol takes places through the formation of variety of chemical intermediates, such as alcohols and ketones [11]. Since glycerol is not a thermally stable molecule, the extent of pyrolysis reaction phenomena is critical [11]. The author also suggested that the presence of alumina enhances activities like dehydration, isomerization and polymerization [11]. Finally, hydrogen is produced by the dehydrogenation of the adsorbed glycerol molecules and reaction of organic fragments [11]. The reaction mechanism proposed by Pant et al. is similar to the mechanism stated by Wang et al. [17].
Figure 8: Various intermediates during GSR reaction [4]
Finally, Dieuzeide et al. has presented the reaction scheme as follow [18]:
1. Conversion of glycerol to condensable products via dehydration, dehydrogenation and decarboxylation.
2. Conversion of condensable products by C-C bond break.
3. Formation of gaseous products from condensable ones.
Figure 9: Reaction pathway for GSR with coke formations [18]
Despite of different reaction scheme, most papers agree that the reaction is initiated by adsorption of glycerol on the surface and it is followed by breakage of C-C and C-H bonds.
2.4 Kinetics and Reaction Mechanism
As discussed in the previous section, the surface reaction involves adsorption of glycerol on the surface. However, there are different ways of adsorption for example Langmuir-Hinshelwood (L-H) model and Eley-Rideal (E-R) model. According to L-H model, both reactant molecules adsorb on the surface and undergo a bimolecular reaction. In contrast, according to E-R model, only one molecule adsorbs and other molecule reacts with it directly from the gas phase. Cheng et al. has derived both Langmuir-Hinshelwood (L-H) and Eley-Rideal (E-R) detailed kinetic models for glycerol steam reforming over bimetallic Co-Ni/Al2O3 [13]. Power-law modeling (Equation 9) was used to estimate the glycerol consumption rate and the formation rates of H2, CO2, CO and CH4. The resulting parameter estimations for glycerol is activation energy (Ea) of 63.3 kJ/mol and reaction order with respect to glycerol (B) and steam (Y) of 0.253 and 0.358 respectively .
(9)
Cheng et al. has further divided L-H models into eight different categories by varying the adsorption type (associative or dissociative), number of sites (single or dual sites) and adsorption type of either glycerol or steam. Likewise, E-R model is divided into four subcategories based on first and last criteria. Twelve such models have been listed below. First eight models are L-H models and last four of them are E-R model.
1. Associative adsorption of both Glycerol (G) and Water (W) on the single site with bimolecular surface reaction
2. Dual site associate adsorption of both G and W with bimolecular surface reaction
3. Single site associative adsorption of G and dissociative adsorption of W with bimolecular surface reaction
4. Dual site associative adsorption of G and dissociative adsorption of W with bimolecular surface reaction
5. Single site associative adsorption of W and dissociative adsorption of G with bimolecular surface reaction
6. Dual site associative adsorption of W and dissociative adsorption of G with bimolecular surface reaction
7. Single site dissociative adsorption of both G and W with bimolecular surface reaction
8. Dual site associative adsorption of W and dissociative adsorption of G with bimolecular surface reaction
9. Eley- Rideal model with associative adsorption of G with W in gas phase
10. Eley- Rideal model with dissociative adsorption of G with W in gas phase
11. Eley- Rideal model with associative adsorption of W with G in gas phase
12. Eley- Rideal model with dissociative adsorption of W with G in gas phase.
Models based on E-R mechanism (R2=0.5), produced poor fits to the rate data, in comparison to L-H mechanism (R2=0.98). For adsorption constant to have physical meaning in the Langmuirian sense, two rules must be satisfied:
i. 10 ≤ ∆Sexp (a)
ii. -∆Sexp≤ 12.2- 0.0014 ∆Hexp (b)
The values may be obtained from:
Ln (K) = ∆Hexp/RT + ∆Sexp/R (10)
Here, ∆Sexp and ∆Hexp are adsorption entropy and adsorption enthalpy respectively, K is the reaction equilibrium constant, R is the universal gas constant and T is the temperature.
After incorporating this information, it was concluded that only models 1 and 2 exhibited obvious trends with variation in reaction temperature. Furthermore, model 2 was successful in predicting Ea closely as estimated by power- law model. However, model 2 is based on double reaction sites which results in complex reaction mechanism and hence complex reaction rates. From the analysis, model 1 is also capable in predicting obvious trends. Moreover, model 1 is based on single sites which results in comparatively simpler reactions and reaction rates. So, for the study, reaction is based on model 1. Some accuracy of model 2 has been traded off to derive comparatively easier reaction rate. Detailed single site associative adsorption of both glycerol and steam (Model 1) can be expressed as [13]:
C3H8O3 + X↔C3H8O3X (11)
H2O +X↔H2OX (12)
C3H8O3X + H2OX ↔ HCOOX + CH2OHCHOHX + 2H2 (13)
HCOO X↔CO2 + HX (14)
CH2OHCHOH X+ HX↔ 2CH3OX (15)
CH3OX + X↔CH2X + OHX (16)
CH2X + HX↔CH3X + X (17)
CH3X + HX↔CH4 + 2X (18)
CH3OX + X↔CH2OX + HX (19)
CH2OX + X↔HCOX + HX (20)
HCOX + X↔COX + HX (21)
COX ↔CO + X (22)
HX + HX↔H2 + 2X (23)
In addition, Sundari et al. has investigated the reaction mechanism and its associated kinetics of GSR using Ru/Al2O3 catalyst [15]. They have stated that GSR involves the diffusion of the reactants from the bulk gas phase to the catalyst surface and intra-particle diffusion followed by chemical reactions at the active centers. Any of these mass transfer process can affect the reaction rates. The authors have used the Madon-Boudart method of metal dispersion to limit mass transfer. The glycerol consumption rate at various temperatures was expressed as:
(24)
Here, X is the glycerol conversion (%), W is the weight of the catalyst (kg) and FAO is the glycerol molar flow rate (mol/min). The reaction rate was assumed to be first order with respect to glycerol and zero order with respect to water. Furthermore, the Arrhenius equation was plotted and the activation energy was evaluated as 21.2 kJ/mol. The lower activation energy is due to the high loading level of Ru and uncertainty in the evaluation of reaction rates. The following kinetic model has been proposed for GSR:
(25), (26), (27)
Here, A and B represents glycerol and water respectively and S represents an active site on the catalyst surface. Values of K represent the rate constant for the reaction. Decomposition of ABS to form intermediate products has been assumed as the rate determining step (RDS). The dependence based on partial pressure was expressed as [15]:
(28)
In other paper, Adhikari et al has presented the kinetics of the glycerol steam reforming process over a Ni-based CeO2-supported catalyst. The power law model (Equation 10) was used to express the reaction kinetics [19]. Concentration of water was not included because water was present in excess as compared to the concentration of glycerol so Y=0. Kinetic data were collected by minimizing mass transfer limitations and film diffusion reactions. The value of activation energy and reaction order based on the power law model were estimated with nonlinear regression analysis. The activation energy and reaction order were found to be 103.4 kJ/mol and 0.233 respectively.
The other paper on reaction kinetics for GSR is by Go et al. where, the author has investigated the kinetics in a Ni catalyst supported with y-Al2O3 and added Fe and Ce as the promoters [20]. The glycerol reaction order and activation energy were evaluated by the power-law method and Arrhenius equation, respectively. The glycerol consumption rate at various temperatures was expressed as equation 24. Rate of GSR was also expressed as the power law equation (Equation 10). The reaction order of steam y was assumed to be zero. So, Equation 24 can be expressed as:
(29), (30)
The slope of the line of the plot versus gives the reaction order with respect to glycerol and was calculated as 0.06. However, the coefficient of determination (R2) for the slope was only 0.4765. Using, the Arrhenius equation (Equation 30) the activation energy was calculated from the slope of the Arrhenius plot (1/T vs. ) and indicated as 32.9 kJ/mol [20].
To sum up the literature, GSR is the most practical method to produce hydrogen from glycerol. Furthermore, nickel- based catalysts supported by aluminum oxides have been widely used for GSR and the literature suggest that these catalysts are quite effective in hydrogen yield and glycerol conversion. The papers also suggest that L-H model is more appropriate than E-R model in prediction of reaction rates. Based on the summary from the papers, nickel supported by aluminum oxides catalyst has been selected for this study. Similarly, the reactions on the catalyst surface are assumed to follow L-H model with single site adsorption. Using this information, global reaction rate is derived in the next chapter.
3. Global Reaction Kinetics
Implementing the information from previous section, L-H model was used to determine detailed reactions for GSR. Using the detailed reactions, reaction rates can be evaluated. Fundamentally, reaction rates are expressed in terms of concentration. However, concentration can be expressed as a product of number of moles and density as shown in Equation 31.
Concentration (C) = Number of mole (n) * Density () (31)
n = Partial pressure (p)/ Total pressure (P) (32)
Therefore, for constant density, reactions rates can be expressed in terms of number of moles or partial pressure. In our study, as will be discussed later, constant density case is considered. So, the reaction rates can be expressed in terms of partial pressure or number of moles. Here, reaction rates are expressed in terms of partial pressure along with rate constant (k) and coverage fraction (θ). From Cheng et al., Pant et al. and Sundari et al., it can be inferred that equation 34 is the rate determining step [13, 15, 17]. Representing, CH3O by ‘B’ and by ‘C’ for simplification, we can get reaction rates. As the rate determining step is the slowest process, all other reactions will have more time; thus, they are considered to be in quasi-equilibrium state and the global rate can be expressed as RG = R4.
Using these information and simplifying, the global rate expression is:
(33)
Here, k4 is the reaction rate constant which can be expressed by Arrhenius equation (Equation 34), where k, is the pre-exponential coefficient that depends upon number and frequency of collision. E1 is the activation energy, Ru is the universal gas constant and Tm is monolith temperature.
k4 = k * exp[-E1/(Ru*Tm)] (34)
And, K1 is the equilibrium constant given by Equation 35, where A1 is the adsorption pre-factor and H1 is the adsorption heat.
K1 = A1 * exp[-∆H1/(Ru*Tm)] (35)
For the global reaction rate we have three equilibrium constants which have been expressed by Equation 65 to 67.
The quantitative value of global reaction rate is possible only after determining adsorption heat and adsorption pre-factor for C3H8O3, CH2OHCHOHNi and H2. The required parameters were approximated or imported from various literature as discussed in the next section.
4. Kinetic Parameters
Adsorption heat for C3H8O3, CH2OHCHOHNi and H2 has been listed in Table 3. Values for and were taken from Cheng et al and Davis et al respectively while the value foris approximated to be between and [13, 21]. Similarly, Table 4 lists the adsorption pre-factor for C3H8O3, CH2OHCHOHNi and H2. Values for and were imported from Cheng et al. and Tuchin et al. respectively while the value for has been approximated [13, 22].
Table 3: Value of adsorption heat
| Parameters | Values | Units | Reference |
| C3H8O3 | -40 | kJmol-1 | Cheng et al. [13] |
| CH2OHCHOHNi | -35 | kJmol-1 | Approximation |
| H2 | -30.295 | kJmol-1 | Davis et al. [21] |
Table 4: Value of adsorption pre-factor
| Parameters | Values | Units | Reference |
| C3H8O3 | 0.0145 | kPa-1 | Cheng et al. [13] |
| CH2OHCHOHNi | 0.0312 | kPa-1 | Approximation |
| H2 | 0.0685 | kPa-1 | Tuchin et al. [22] |
Activation energy, total pressure, universal gas constant, monolith temperature and reaction rate constant at 823 K have been listed in Table 5. This information is sufficient to determine the reaction rate at 823 K. However, to determine the reaction rate at all temperatures, pre-exponential coefficient needs to be evaluated. Since, we know all other parameters except pre-exponential coefficient in Arrhenius equation (Equation 63), pre-exponential can be calculated. Evaluation of this value, listed in the Table 5, will help to find reaction rate at all the temperatures.
Table 5: Kinetic parameters
| Parameters | Values | Units | Reference |
| Inlet pressure (P) | 1 | Atm | Cheng et al. [13] |
| Activation Energy (E1) | 103.4 | kJ/mol | Adhikari et al.[19] |
| Universal gas constant (Ru) | 8.314 | J/(mol.K) | |
| Reaction constant (k1) @823 K | 5.0 * 10-7 | mol/(m2s.kPa) | Cheng et al. [13] |
| Pre exponential component (k) | 1.45 * 10-13 | mol/(m2s.kPa) | From Arrhenius equation |
Numerical value of reaction rates can be calculated by using the information from Table 3, Table 4 and Table 5. However, the information is not sufficient to simulate a light-off curve which will be discussed in next section. Table 6, 7 and 8 have listed the parameters required for the modeling of catalyst. Table 6 lists the catalyst model parameters including the length and hydraulic diameter of the catalyst along with the velocity of flow in the catalyst. Table 7 lists the mole fraction of the species entering the catalyst. Diffusivity of glycerol, water, carbon dioxide and hydrogen are listed in Table 8.
Table 6: Catalyst model parameters
| Parameters | Values | Units | Reference |
| Catalyst length (L) | 30 | mm | Adhikari et al. [21] |
| Channel hydraulic diameter (d) | 10.16 | mm | Adhikari et al. [21] |
| Void fraction () | 0.22 | – | Adhikari et al. [21] |
| Inlet velocity (u) | 0.0515 | m/s | Adhikari et al. [21] |
| Sherwood number (Sh) | 3.0 | – | |
| Number of points (N) | 30 | – |
Table 7: Inlet mole fraction
| Parameters | Values | Reference |
| C3H8O3 | 0.076 | Adhikari et al. [21] |
| H2O | 0.760 | Approximation as as H2O is generally 6-12 times C3H8O3 |
| CO2 | 0.076 | Approximation as CO2 and H2 are in 3:7 ratio |
| H2 | 0.088 |
Table 8: Diffusivity value
| Parameters | Values | Units | Reference |
| C3H8O3 | 7.57 * 10-5 | cm2/s | Adhikari et al. [21] |
| H2O | 0.282 | cm2/s | Cussler [23] |
| CO2 | 0.165 | cm2/s | Cussler [23] |
| H2 | 0.417 | cm2/s | Cussler [23] |
5. Catalyst Model
Kinetic and catalyst reactor parameters determined in the previous section has been used along with one dimensional (1-D) catalyst model to simulate a glycerol conversion light-off curve.1-D Catalyst model is based on the efforts of Depcik et al which discusses the history of the monolith one-dimensional catalyst [16]. Physical phenomena present in the catalyst surface include: bulk gas flow, interphase transfer, chemical reaction, heat generation, washcoat diffusion and axial heat conduction. For an isothermal and adiabatic condition, heat generation and axial heat conduction are neglected. Furthermore, the model assumes dynamically incompressible flow since the Mach number is relatively low and uses source terms to account for boundary layer effects. There are two regions within the channel; the bulk gas and the surface (Figure 10).
Figure 10: Schematic monolith channel indicating the bulk gas and the surface regions [16]
The bulk gas region consists of the full governing equation of the fluid mechanics. Based on the above assumptions presented in the paper, the equation for bulk gas species was derived. The equation included the advection of the species (Cj) as a function of the gas velocity u, and the mass transfer of species through Fick’s law of diffusion,Ga the geometric surface area of the channels per unit volume as is given by:
(36)
(37)
With the void fraction (percentage of catalyst that is open channel space) and d is the hydraulic diameter of the channels. The variable kj is a measure of mass transfer to the surface and can be computed from the Sherwood number (Sh) and the diffusivity (Dj) of the species:
(38)
Where, the Sherwood number is evaluated under fully developed flow. At the surface (assuming that the washcoat is simulated as a single point), the researchers assumed that the mass transfer to the surface is balanced by the reaction rates occurring within the washcoat:
(39)
Where, the left hand side balances the source term in the bulk gas species equation and represents mass flow to the surface as a function of concentration gradient. The right hand side describes the reactions lumped within the washcoat as one expression. The above equation is currently in an algebraic state and can be numerically stiff as the reactions rates are exponentially dependent. As a result, the equation can be expressed in a time differential form as follows to take the advantage of available ordinary differential equations.
(40)
Now, the bulk gas species can be obtained by solving Equation 36. In this study, Equation 36 was solved by using an Euler Implicit solver. Similarly, surface gas species can be obtained by solving Equation 40. In this study, Equation 40 was solved to steady state by using a Matlab ordinary differential equation (ODE) solver. A light-off curve for glycerol conversion was generated by solving these equations (Equation 36 and 40) throughout the catalyst domain. Furthermore, a light-off curve for glycerol conversion was extracted from a literature [3] as a reference and plotted alongside the model. The light-off curve along with the reference light-off curve is illustrated in Figure 11. From the plot, the modeled light-off curve has maximum conversion of glycerol at around 775 K. From the experimental results in previous sections, suitable temperature for GSR is around 500°C to 750 °C which is equivalent to 775 K to 1000 K. In this aspect, simulated light-off curve closely matches the experimental result. However, there are few differences between the reference and modeled light-off curve. The differences between the 1-D catalyst model and reference model might be because of following reasons:
1. Reference plot has used Ni-Cu-Al catalyst and has higher activation energy
2. Reference plot is done for non-isothermal kinetics, some heat might be lost during endothermic reaction so, conversion occurs at higher temperature.
3. Due to some approximation in 1-D model.
Figure 11: Light off curve of GSR for 1-D model compared with a reference
6. Parametric Study
An analysis was done to study the effect on GSR light-off curve by varying various input parameters. Pressure was selected as the parameter to be changed and it was increased to 2 atmospheric pressure (atm) and decreased to 0.5 atm. The effect of variation in pressure on GSR light-off curve is illustrated by Figure 12.
Figure 12: Effect of pressure on GSR light-off curve
As analyzed from section 2.3, according to Le Chatelier’s principle, the reaction rate will increase with decrease in pressure. In the plot, the reaction rate is faster for pressure of 0.5 atm than for 2 atm. Therefore, the simulation result supports the principle.
However, simulation was carried out taking kinetic and catalyst model parameters for a packed –bed reactor while the tested model is for a monolith design. There is a difference in bulk gas species flow for monolith and packed bed reactor. But, the difference is negligible for a higher flow rate where the results of monolith reactor can be compared with the results of packed- bed reactor.
7. Conclusions and Future Work
To sum up, there were two main goals for this study. The first goal was to select the most effective catalyst for GSR process so that GSR becomes more practical and excess glycerol in the world market is utilized properly. Second goal was to derive a global reaction rate and model a catalyst for GSR with high accuracy along with least computational cost so that the model can be used in the future to enhance research in the field of GSR. The first goal was accomplished by conducting literature review to determine most effective catalyst. Selection of Ni-based catalyst which is active in breakage of bond and is at least 200 times cheaper cost than other metals, makes GSR practical. Global reaction rate based on L-H model and simulation of light-off curve based on 1-D model was conducted to achieve second goal. The simulation result closely matching the experimental data and Le Chatelier’s principle validates the accuracy of simulation. Furthermore, the simulation run time of only about two minutes, supports that the computational cost is low. Therefore, the catalyst model can be used to check the catalytic activity of other metals. It can also be used to check the effect of other operating parameters like fluid velocity, catalyst length. For the future work, simulation can be done for a packed-bed reactor at non-isothermal conditions to confirm the result with reference model. Furthermore, the global reaction rate can be derived using different detailed reaction mechanism and the result can be compared with this study.
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