Article pubs.acs.org/EF
Effect of Palm Oil Content on Deep Hydrodesulfurization of Gas Oil−Palm Oil Mixtures A. Vonortas, Ch. Templis, and N. Papayannakos* †
National Technical University of Athens, School of Chemical Engineering, Heroon Polytechniou 9, 157 80 Zografos, Athens, Greece. ABSTRACT: Co-processing of gas oil and vegetable oils for the production of diesel−green diesel mixtures aims at producing deep hydrodesulphurized fuels at an acceptable cost. Gas phase analysis and data treatment can effectively provide knowledge for catalyst selectivity and hydrogen consumption. In this work, the reactor outlet gas composition was calculated from laboratory data and then the catalyst selectivity was estimated. Apart from CO and CO 2, CH 4 was also present in significant amounts in the effluent gas, indicating that methanation reaction occurs in the gas phase. The water−gas shift reaction was found to be at equilibrium, which does not allow distinguishing the two reactions mechanisms, decarboxylation and decarbonylation. Deep hydrodesulfurization (HDS) was simulated by two sulfur pseudocomponents, one of high reactivity and one of low reactivity. Experiments were carried out in a bench-scale tricklebed reactor at typical HDS conditions.
1. INTRODUCTION The ever increasing energy demands and environmental pollution problems, combined with the current rise in prices of petroleum-derived fuels and the decline in petroleum reserves, lead to the necessity for the development of new technologies to produce environmental friendly and economically acceptable renewable substitutes of fossil fuels. Many countries worldwide encourage the use of renewable fuels in several sectors. EU, especially, boosts the use of renewable fuels in the transport sector and has set the aim to raise the proportion of biofuels and other renewable fuels to 10% of the total gasoline and diesel consumption by 2020.1 For the last two decades, the most common alternative fuel to petro-diesel has been biodiesel. Biodiesel is associated with FAME (fatty acid methylesters) produced by the transesterification of triglyceridecontaining feedstocks.2 Despite its advantages, biodiesel has certain disadvantages, mainly concerning its stability, which has been shown to be significantly lower than that of both fossil diesel and other alternative fuels.3 A new promising technology that overcomes the majority of the biodiesel production disadvantages is the hydrotreatement (HDT) of vegetable oils. The HDT of the triglyceride-containing feedstocks leads to the production of a stable product, due to the elimination of organic oxygen from the ester bonds of triglycerides (HDO) and saturation of the olefinic double bonds. This fuel is paraffinic in nature and is fully compatible with petroleum-derived diesel.4 For the hydrotreatment of the vegetable oils, hydrogen is consumed for the saturation of the double bonds in triglycerides as well as for the deoxygenation reactions of the ester bonds. Depending on the catalyst selectivity, hydrogen consumption ranges from 1 molecule for hydrodecarboxylation of one ester bond to 4 molecules per ester bond for hydrodeoxygenation, while for the hydrodecarbonylation of an ester bond, two molecules of hydrogen are needed. These routes are depicted in Figure 1. © 2012 American Chemical Society
Figure 1. Possible reaction routes of hydrogenation of triglycerides.
Since the method of producing renewable diesel through the HDT process has been recently introduced, there is an increasing interest in it. Laurent and Delmon5,6 performed tests that focused on the catalytic performance of sulfided CoMo catalysts of various supports for the HDT of model compounds containing oxygen. Krause et al.7−10 investigated the HDO of model compounds containing or resembling molecules with ester groups existing in wood-derived biooils. Murzin et al.11 also used model compounds to check the performance of a number of catalysts for the production of molecules similar to those of petroleum-derived diesel. Using these model compounds, a reaction mechanism and kinetic modeling have been proposed.12−15 Besides model compounds, experiments with neat vegetable oils16 or blends with heavy and light gas oil have been conducted.17 More specific experiments with blends of vegetable oils and heavy petroleum fractions have shown that coprocessing can be successfully applied. The hydrodesulfurization (HDS) catalysts used in refinery units have been proven to be active at HDO conditions, with their deactivation remaining at acceptable levels. The product of the coprocessing has a higher cetane number and lower sulfur content than the neat diesel.18 Kubicka et al.19−21 Received: March 7, 2012 Revised: May 13, 2012 Published: May 18, 2012 3856
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avoid liquid maldistribution in the catalyst bed and to achieve full wetting of the catalyst particles, the catalytic bed was diluted with 48 g of inert carborundum (SiC) particles with a mean diameter of 0.25 mm. The catalyst/SiC ratio was 40/48 w/w. The loading of the catalytic particles performed in small portions (1−2 g each time), with continuous gentle shaking of the reactor, to achieve better distribution of the catalyst and to avoid void zones inside the bed. The reactor loading is presented in Figure 2.
showed that the product obtained from the simultaneous HDS and HDO had, in general, improved fuel properties. The main drawback was the poor cold-flow properties of the final product, due to the long chain paraffins produced from the HDO reactions. A crucial parameter of the vegetable oil’s hydrotreatment is the catalyst selectivity, which controls the liquid products, the composition of the gas produced during reaction, and the hydrogen consumption. As stated before, the cleavage of the ester bonds in the triglyceride molecules can follow three different reaction pathways: hydrodecarboxylation, hydrodecarbonylation, and hydrodeoxygenation. For the first two reaction pathways, the hydrocarbon products are the same and carbon oxides are produced. The analysis of the liquid products cannot distinguish the hydrocarbons stemming from the triglycerides, especially for the mixtures with low vegetable oil content. Another way to distinguish these pathways and determine the catalytic selectivity is by analyzing the gaseous products. As shown in Figure 1, these are different in each occasion. Therefore, the study of the gaseous phase composition and its dependence on the process conditions can give important information on hydrogen consumption and catalyst selectivity. The aim of the present work is dual, that is, the study of the deep HDS of blends of refined palm oil with heavy gas oil using a commercial CoMo/γ-Al2O3 catalyst and the study of the gas phase composition and its relation with the HDO reaction selectivity. Then, the estimation of the hydrogen consumption has been attempted along with the calculations for the hydrotreatment of the vegetable oil. These parameters are very important for the process economics, and the presented analysis will allow their estimation from laboratory and industrial data.
Figure 2. Schematic loading of the reactor.
2. EXPERIMENTAL SECTION
The preparation and sulphidation of the catalyst took place in situ. At the beginning, the unit was pressurized at the desired pressure with hydrogen and purged with a flow of 15 NL/h for about 2 h, before the temperature rose to 100 °C, for the removal of trapped humidity. Consequently, the catalyst was sulphided with dimethyl disulfide (DMDS, 2% w/w) diluted in light gas oil, by raising the temperature from ambient to 370 °C. After almost 48 h of activating the catalyst and estimating the initial activity, 25 experiments were conducted, each one lasting about 12−14 h. Deactivation was monitored by repetition of a selected standard experiment. To achieve steady state operation in each experiment, the unit was operated for a minimum of 8 h and afterward liquid samples were taken for the measurement of the final sulfur concentration. Gas analysis was performed for three experiments at T = 330 °C and three WHSVs (0.85, 1.0, 1.4 h−1). The gas samples were collected in plastic sample bags of 5 L total volume. The sample analysis was carried out at Motor Oil Hellas refinery in a gas chromatography (GC) system with both a flame ionization detector (FID) and a thermal conductivity detector (TCD). In Table 1, the fatty acid composition of the refined palm oil used is shown. In a previous communication,18 total conversion of the triglycerides was proven to occur at experimental conditions similar to those applied in this work. In Tables 2 and 3, the basic properties and the distillation data of the gas oil used are shown.
Experiments were conducted in an integrated, isothermal, micropilot bench-scale trickle-flow reactor. The inner diameter of the reactor tube was 2.54 cm, and its overall length was 47.5 cm. The temperature of the catalytic bed was controlled and monitored via four thermocouples (K-type), placed inside a thermowell of 4 mm inside diameter. Temperature control was achieved, within ±1 °C of the desired value, by software proportional−integral−derivative (PID) controllers, which through a system of solid-state relays, supply with the electrical energy required in each of the four individual resistors that “embrace” the reactor tube. A positive displacement piston-bearing pump leads the liquid feed at the top of the catalytic bed where it is mixed with the gas feed (hydrogen). The two phases flow concurrently downward in the reactor. The whole unit is fully automated, with all the operating conditions controlled by a personal computer equipped with several data acquisition modules to digitalize the analogue signals obtained from the “field” instruments. All the signals have been collected and intensified by a multiplexer card. User-friendly software allows the easy handling of the signals for either their surveillance or control. The experiments were carried out at three different temperatures 330, 350, and 365 °C. These high temperatures were selected to achieve deep HDS of the gas oil. Total pressure was maintained at 33 bar. The flow rate of the hydrogen feed was kept 19−20 NL/h. Three different liquid mass flow rates were tested, 34, 40, 56 g/h, which correspond to WHSV = 0.85, 1.0, and 1.4 h−1 respectively. The liquid feed was neat gas oil and mixtures of 5 and 10% w/w of refined palm oil in gas oil. Gas oil had a low initial sulfur concentration of 5000 ppm in order to achieve low sulfur content in the final product. The catalyst used was a commercial CoMo/ γ-Al2O3 in cylindrical form with a mean diameter of 1.4 mm. To
3. RESULTS AND DISCUSSION The present work has two objectives. The first one is to estimate the gas phase composition at the reactor outlet and by using the collected data to estimate the catalytic selectivity for the HDO of palm oil. The second one is to examine the effect 3857
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separator vessel two cubic equations of state, Soave− Redlich−Kwong (SRK) and Peng−Robinson (PR) were used, and the calculations of the molar fractions at the reactor outlet (separator inlet) were made by fitting the molar fractions measured by gas analysis at the separator gas outlet (Figure 3), as described in the Appendix.
Table 1. Composition of the Palm Oil Used fatty acid type
form
formula
% w/w
lauric myristic palmitic palmitoleic stearic oleic linoleic linolenic
12:0 14:0 16:0 16:1 18:0 18:1 18:2 18:3
C12H24O2 C14H28O2 C16H32O2 C16H30O2 C18H36O2 C18H34O2 C18H32O2 C18H30O2
0.3 0.8 44.3 0.2 5.0 39.1 10.1 0.1
Table 2. Basic Properties of the Gas Oil Used property
value
density (g/mL) cloud point (°C) water content (ppm) sulfur content (S% w/w) cetane index
0.865 3 250 0.5 48.3
of the diluted vegetable oil on the deep HDS of heavy gas oil via the estimation of HDS kinetic parameters and also to examine the effect of the presence of the vegetable oil on the catalyst activity. 3.1. Gas Phase Modeling. The hydroconversion of the palm oil occurs via three different reaction pathways: hydrodeoxygenation, decarbonylation, and decarboxylation.22 So, except for the formation of n-alkanes from alkyl and alkylene groups of the triglycerides, the hydrotreatment of palm oil molecules also produces CO, CO 2 , H 2 O, and C 3 H 8 . Hydrodeoxygenation leads to the production of H 2O, decarbonylation gives CO and H2O, and finally, decarboxylation gives only CO2. Propane is produced in all three cases. However, to completely understand how the catalyst converts the triglycerides, the selectivity of the three reaction pathways should be determined. For this purpose, gas samples were collected from the unit’s outlet, and subsequently, the gas analysis was carried out. In this way both qualitative and quantitative results were obtained. The results showed that all three reaction routes of the triglycerides can occur simultaneously with the HDS of heavy gas oil as carbon monoxide and dioxide, propane and hydrogen sulfide were present in the gas samples. It must be noted here that these molecules are the only ones present in the gas phase if no other side reactions occur. Apart from these molecules, a significant amount of methane was also detected. Water was collected with the liquid sample from the bottom of the separator which was located between the reactor and the gas sampler. The separator operates at room temperature and at the unit’s pressure (33 bar), so no water was expected in the gaseous phase. To correctly estimate the catalyst selectivity, the gas composition at the reactor outlet must first be estimated from the gas analysis at the separator outlet taking into account dilution of the gaseous products in the liquid phase inside the separator. For the phase equilibrium in the
Figure 3. Schematic representation of the system reactor−separator; yi denotes the molar fractions at the point of gas sampling, and zi denotes the molar fractions at the reactor outlet.
Thus, using either the SRK or PR method, the gas composition at the reactor outlet is calculated using only experimental data of the gas composition at the separator outlet. With the molar fractions of the gaseous products known at the reactor outlet, the selectivity of the CoMo/γ-Al2O3 catalyst can be estimated. However, it has to be taken into account that, simultaneously with the HDO and HDS reactions of the ester bond and sulfur bearing molecules in the liquid molecules, two other reactions seem to happen among the molecules of the gas phase. The first is the methanation reaction of CO with H2, which leads to the production of CH4, which was present in the gas sample. The second one is the water−gas shift (WGS) reaction. Both reactions are shown as follows: CO + 3H 2 → CH4 + H 2O
CO2 + H 2 ↔ CO + H 2O
The procedure for the estimation of the catalyst selectivity commences by finding the actual moles of palm oil contained in the liquid feed. Taking into account that every mole
Table 3. Distillation Data of the Gas Oil Used distillation curve of gas oil (% recovered, °C) IBP 174
5% 233
10% 248
20% 264
30% 274
40% 284
50% 294
60% 305 3858
70% 317
80% 331
85% 338
90% 348
95% 360
FBP 368
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of triglyceride has three ester bonds, the total number of triglyceride molecules is multiplied by three to obtain the total number of ester bonds contained in the feedstock. Then, from the gas molar fractions calculated before, the molar flows of CO, CO2, and CH4 are calculated at the exit of the catalytic bed. By adding these three flows and deducting the sum from the total molar inflow of ester bonds, the ester bonds that followed the hydrodeoxygenation pathway could be calculated, as CH4 is produced from CO while CO and CO2 are produced from decarbonylation and decarboxylation reactions. In this way, the hydrodeoxygenation percentage for all three experiments was calculated as 38%, and the remaining 62% corresponds to the two other mechanisms, decarboxylation and decarbonylation. The distinction between decarboxylation and decarbonylation is not possible because of the WGS reaction. The gas composition at the reactor exit indicates that the WGS reaction is at equilibrium in all three cases examined. This indicates that the WGS reaction is very fast, and therefore, the calculation of the molar flow of CO produced from decarbonylation and CO2 coming from decarboxylation reaction is not possible. The methanation reaction proved to be a practically oneway reaction with a large equilibrium constant (Keq = 1.61 × 106 at T = 330 °C) at the reactor experimental conditions, whereas the WGS reaction is a reversible reaction with an equilibrium constant of about 25 (Keq = 23.43 at T = 330 °C). For both reactions, the equilibrium constants were calculated using the Van’t Hoff equation. However, the methanation reaction appears to be not very fast for the system examined in this work, as both CH4 and CO are present in the reactor exit gas. 3.2. Liquid Phase Simulation. 3.2.1. Reaction Kinetics. For the research of the effect of the presence of the vegetable oil on the deep HDS of the gas oil in its mixtures with palm oil, the desulphurization kinetics will be determined in each case. The deep HDS of the neat gas oil and the mixtures gas oil− vegetable oil cannot be studied using a general power law kinetic form for the total sulfur removal. This happens because in the deeply desulphurized oil the refractory sulfur compounds prevail. As the HDS kinetics of each compound is of first order and their reactivity lies in a narrow spectrum, the kinetics of the total sulfur removal of this group is close to first order.23 Thus, the sulfur bearing compounds in gas oil can be distinguished in two pseudocomponents. The first one represents all the molecules that contain sulfur, and their HDS is easy (high and medium reactivity molecules, HR); the second one stands for the molecules that contain sulfur, and their HDS is difficult (low reactivity, LR). The low reactivity sulfur compounds in gas oils are mainly dibenzothiophenes with substituents at 4 and 6 positions.23 In the HR pseudocomponent, all the other sulfurbearing molecules are included. The wide spectrum of HDS reactivity of the easy to desulphurize sulfur bearing molecules justify the use of the power law, nth order, kinetic form for this group, although the desulphurization kinetics of each compound appears to be of first order.26 The reaction order, n, depends on the type and the distribution of the sulfur compounds in the gas oil fraction as well as on the catalyst used. Accordingly, the HDS kinetic equation used in this study is
where kHDS, i = k 0, i exp( −Eαi /RT )PH2
For both pseudocomponents, the kinetic parameters (kHDS,LR, kHDS,HR, n, and CS0,HR) and activation energies will be estimated by fitting the predicted total sulfur concentration values into the experimental data. 3.2.2. Mass Balances. The developed mathematical model for the simulation of the reactor operation was based on the following conditions: the gas and liquid flow through the void space of the catalyst bed is well approximated by the plug flow model, since the dilution of the catalyst bed with fine particles (SiC) ensures the full wetting of the catalyst particles and the elimination of liquid axial and radial maldistribution and dispersion. Palm oil is fully converted at the experimental conditions of this work, as shown in a previous communication.18 The mass balances of the two pseudocomponents are expressed by the following eqs 3 and 4: dCS,HR dmcat dCS,LR dmcat
= kHDS,LR CS,LR +
⎛ −E ⎞ n = k 0,HR exp⎜ α HR ⎟PH2CS,HR ⎝ RT ⎠
(3)
⎛ −E ⎞ = k 0,LR exp⎜ α LR ⎟PH2CS,LR ⎝ RT ⎠
(4)
where CS = CS,HR + CS,LR and CS denotes the total sulfur concentration in the liquid. 3.3. Results. The two mass balances were integrated analytically while the estimation of the kinetic parameters was achieved by applying the Simplex optimization method. It is observed that the reaction order for elimination of the high reactivity sulfur molecules has been estimated as 1.25, which corroborates the wide range of reactivity of the individual sulfur compounds in gas oil. It is also noticeable that the initial concentration of the sulfur contained in the difficult to react molecules was estimated 130 ppm. However, as it is shown later, the latter molecules control the sulfur concentration of the deeply desulphurized samples. In Figure 4, the parity plot for the three different experimental series (0, 5 and 10% w/w palm oil in gas oil) is
Figure 4. Parity plot of the product sulfur concentration for the three experimental series (0, 5, and 10% w/w palm oil in gas oil).
RHDS = RHDS,LR + RHDS.HR n kHDS,HR CS,HR
(2)
drawn. The relative error for all three series remains close to 3.5%, and it is observed that the model predictions are in a good agreement with the experimental data.
(1) 3859
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of the kinetic constants increases as before from 1.4 to 1.9 and finally to 2.3 when the temperature increases from 330 to 350 and finally to 365 °C. It is observed that the effect of the vegetable oil on both pseudocomponents’ desulphurization is almost identical. The decrease of the neat gas oil reaction rate constant when palm oil was added in the feed, either 5 or 10% w/w, was 64% more for the high reactivity pseudocomponent than for the low reactivity one for all three temperatures tested in this research. This clearly indicates that the two pseudocomponents, despite their different reactivity, are equally affected by the palm oil presence in the whole range of the experimental temperatures. These results are in agreement with a previous communication24 where the dependence of the reaction rate constant for the HDS reaction was examined for lower desulphurization levels and heavier gas oil in which case a global power law was sufficient to describe the process. In Tables 4 and 5, the calculated values of the frequency factors and activation energies are presented for the two
For the estimation of the effect of the presence of the vegetable oil on the HDS rates of the gas oil molecules, a comparison of the reaction rate constant for the neat gas oil and its mixtures with vegetable oil is presented. In Figure 5, a
Figure 5. Dependence of the HDS reaction rate constant for the high reactivity pseudo-S-component on the palm oil percentage in the liquid feed, for all three experimental temperatures.
Table 5. Activation Energies Calculated for the Three Experimental Temperatures and the Three Different Feed Mixtures
decline of the reaction rate constant is observed from 0 to 5% w/w palm oil content for the high reactivity pseudocomponent. However, from 5 to 10% w/w, no further effect on the HDS rates is indicated. The ratio of the neat gas oil HDS rate constant to that estimated for the 5% w/w vegetable oil blend at 330 °C is 2.3 implying that due to the presence of the palm oil the reaction rate of HDS declined by 2.3 times. A similar decrease in the HDS reaction rate constant is observed from Figure 6 for the other two reaction
EαHR (J/mol) EαLR (J/mol)
0% w/w
5% w/w
10% w/w
137197 147536
92538 105030
88959.8 102761.2
pseudocomponents and the three different feedstocks, respectively. It is obvious that in both cases the frequency factor and activation energy decrease when palm oil is added to the feed. This decrease is sharp for the transition from neat gas oil to 5% w/w mixture and becomes negligible when palm oil in the reactor feed increases from 5 to 10% w/w. This is due to the fact that the reaction rate constant is not practically different for 5 and 10% w/w palm oil in the feed mixtures but alters significantly from neat gas oil to 5% w/w palm oil in the feed. In Figure 7, the dependence of the activation energies for the gas oil-palm oil blends is shown.
Figure 6. Dependence of the HDS reaction rate constant for the low reactivity pseudo-S-component on the palm oil percentage in the liquid feed, for all three experimental temperatures.
temperatures. However, the decrease becomes steeper with the temperature increase. So, at 350 °C, the calculated ratio is about 3, and the corresponding value at 365 °C is 3.8. Figure 6 shows the same trend for the low reactivity HDS kinetic constant. It initially decreases from the neat gas oil to the blend with 5% w/w palm oil and then remains almost unaffected from the presence of the vegetable oil. The ratio
Figure 7. Dependence of the activation energies on the palm oil content in the feed.
Table 4. Frequency Factors, k0, Calculated for the Three Experimental Temperatures and the Three Different Feed Mixtures k0HR ((kgoil ppms
−1
)/(kgcat barH2 ))
(1−n)
−1
k0LR ((kgoil ppmS)/(kgcat barH2 ))
0% w/w
5% w/w
3.86 × 10
2.25 × 10
3.61 × 105
1.31 × 10
1.91 × 10
5.08 × 106
10 11
3860
10% w/w 6 7
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sulfur removal rates in the neat gas oil and its mixtures with palm oil, although for milder HDS levels the simple power law kinetics corresponding to one pseudocomponent is sufficient.24
The evolution of the total sulfur concentration as well as of the easy and difficult to desulphurize pseudocomponents can give an indication on why this kinetic model is appropriate to be applied for successful simulations. In Figure 8, the evolution of the pseudocomponents’ concentration and the total sulfur content is presented for the
4. CONCLUSIONS The presence of palm oil in gas oil feeds with up to 10% wt/wt vegetable oil affected the deep HDS of the mixtures over a commercial CoMo/γ-Al2O3 catalyst. The addition of palm oil up to 5% w/w resulted in a steep decrease of the desulphurization reaction rates, while further addition of vegetable oil up to 10% w/w did not affect them. From the simulation of the separator operation, the percentage of the triglycerides contained in the feedstock that follow the hydrodeoxygenation path was calculated as 38%. The other 62% follows the two other reaction paths, decarbonylation and decarboxylation, which cannot be separated due to the fast equilibrium of WGS reaction. The sulfur compounds in the liquid feed were distinguished in two pseudocomponents, one of high and one of low reactivity. The HDS reaction order of the high reactivity pseudocompound and the initial sulfur concentration of the low reactivity pseudocompound were estimated 1.25 and 130 ppm, respectively. Gas phase analysis indicated that apart from CO and CO2, CH4 is also produced from the methanation reaction of CO. Finally, catalyst deactivation was followed and found to be typical, as in the corresponding HDS process of the neat gas oil.
Figure 8. Sulfur concentration corresponding to the two pseudocomponents (Cs,HR, Cs,LR) and all sulfur compounds (CS) vs 1/WHSV for the neat gas oil (365 °C).
neat gas oil. It is observed that when WHSV increases the concentration of the total, high and low reactivity sulfur bearing molecules also increases. It is also obvious that for the very deep HDS levels the remaining sulfur is more than 95% represented by the low reactivity pseudocomponent because the high reactivity sulfur has been removed and the low reactivity molecules remain present mainly contributing to the final sulfur concentration. Thus, the HDS reaction rate is governed by the low reactivity pseudocomponent, and the power-law form does not describe well the desulphurization rates. When palm oil is added in the gas oil feed, the HDS reaction rates of both pseudocomponents are affected. For the mixture with 10% palm oil, Figure 9,
■
APPENDIX: PHASE EQUILIBRIUM CALCULATIONS The two equations in the form of fugacity coefficient, φi, are given as follows:25 SRK: Bi (z − 1) − ln(z − B) B B⎞ ⎛ A ⎛ 2 ∑ xjAij B⎞ − × ⎜⎜ − i ⎟⎟ × ln⎜1 + ⎟ ⎝ B ⎝ A B⎠ z⎠
ln(ϕi) =
PR: Bi A (z − 1) − ln(z − B) − 2B 2 B ⎛ 2 ∑ xjAij ⎞ ⎛ z + 2.414B ⎞ B ⎟ × ⎜⎜ − i ⎟⎟ × ln⎜ ⎝ z − 0.414B ⎠ A B ⎝ ⎠
ln(ϕi) =
where A= Figure 9. Sulfur concentration corresponding to the two pseudocomponents (Cs,HR, Cs,LR) and all sulfur compounds (CS) vs 1/WHSV for the 10% palm oil in gas oil feed (365 °C).
aP (RT )2
Aij =
aijP (RT )2
Bi =
biP RT
B=
bP RT
z = compressibility factor, a, b, ai, and bi parameters are determined below. For each component, the critical constants ai and bi, used in the mixing rules are determined as
even for total sulfur concentration of 123 ppm, the difficult to desulphurize molecules represent more than 50% of the total sulfur, although the initial sulfur concentration corresponding to the low reactivity pseudocomponent was estimated as low as 130 ppm. Thus, for deep HDS, the desulphurization kinetics consisting of two pseudocomponents reacting with different kinetics describe much better the 3861
ai =
CR2TC2 f (Tr ) PC
bi =
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In Table 6, the coefficients C and D are given for both equations.26
Both cubic equations produced similar results for all the seven components of the gas mixture which participate in the phase equilibrium. Table 8 shows the estimations with both equations for the three experimental runs for which gas analysis was performed.
Table 6. Coefficient Values Used for the Calculation of ac and bc for Both Equations of State SRK PR
C
D
0.42747 0.45724
0.08664 0.07780
■
*Tel.: +30 210 772 3239. Fax: +30 210 772 3155. E-mail:
[email protected].
The function f(Tr) is a function of the temperature and the parameter S:25 f (Tr ) = [1 + S(1 −
Notes
The authors declare no competing financial interest.
■
2
Tr )]
ACKNOWLEDGMENTS The authors are thankful to Motor Oil Hellas Refinery for the financial support of this work and the analysis of the gas samples.
The S parameter is given by the equation:25 S = D1 + D2ω + D3ω 2
■
where ω is the acentric factor of each molecule. It Table7, the coefficients D1, D2, and D3 are given for both equations.26
D1
D2
D3
0.48508 0.37464
1.55171 1.54226
−0.15613 −0.26992
The same mixing rules were used for both equations and given by Graboski and Daubert for SRK equation:25 Liquid phase a=
∑ ∑ xixjaij
b=
∑ xibi
b=
∑ yb i i
Gas phase a=
∑ ∑ yyi j aij
where aij = (1 − kij)(aii − ajj)0.5
The interaction parameters kij between the different molecules were taken from Knapp et al.27 Especially for H2 and only for SRK equation, assuming interaction parameters are equal to zero (kij = 0), ai = 1.202 exp( −0.30228Tr )
Table 8. Comparison of the Two Cubic Equations of State Used for the Calculation of zi Molar Fractions for the Three Experiments
H2 CO CO2 H2S CH4 C3H8 oil
Expt. 1 (T = 330 °C, WHSV = 0.85 h−1)
Expt. 2 (T = 330 °C, WHSV = 1.0 h−1)
Expt. 3 (T = 330 °C, WHSV = 1.4 h−1)
molar fractions
molar fractions
molar fractions
zi (SRK)
zi (PR)
zi (SRK)
zi (PR)
zi(SRK)
zi (PR)
0.7386 0.0027 0.0043 0.0045 0.0040 0.0059 0.2400
0.7380 0.0027 0.0047 0.0047 0.0040 0.0059 0.2400
0.7312 0.0052 0.0060 0.0073 0.0039 0.0060 0.2400
0.7306 0.0054 0.0059 0.0078 0.0039 0.0064 0.2400
0.7322 0.0048 0.0037 0.0087 0.0043 0.0063 0.2400
0.7314 0.0050 0.0038 0.0092 0.0044 0.0062 0.2400
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Table 7. Coefficient Values for the Equations Used to Calculate the S Parameter for the Two Equations of State SRK PR
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