H2 Solubility and Mass Transfer in Diesel: An Experimental and

Jul 25, 2016 - 103 type distillation analyzer according to GB/T6536. H2 with a purity of 99.99% (mass fraction) was purchased from Beijing Longkou Cit...
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H2 Solubility and Mass Transfer in Diesel: An Experimental and Modeling Study Zhigang Lei,*,† Yanyan Guo,† Lu Zhao,† Chengna Dai,† Biaohua Chen,† and Xiangchen Fang*,‡ †

State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 266, Beijing 100029, China ‡ Fushun Research Institute of Petroleum and Petrochemicals, SINOPEC, Liaoning, Fushun 113001, China ABSTRACT: In this work, the solubility and liquid-phase mass transfer coefficient of hydrogen (H2) in catalytic diesel at temperatures (353.2−453.2 K) and pressures (1−6 MPa) were measured experimentally. The solubility increases with the increase of pressure and temperature, and the Henry’s constant follows the relation of ln H (MPa) = 2447.02/T (K) − 0.11 with temperature. The molar fraction of H2 and system pressure at different equilibrium time were measured to estimate the liquidphase mass transfer coefficient, and the results showed that with the increase of pressure the mass transfer coefficient increases. Furthermore, the solubility of H2 in diesel was predicted by the COSMO-RS model using six virtual model compounds. Both the experimental data and predicted values agree well. Then, the solubility of H2 in several hydrocarbon components with the same carbon atom but different ratios of C to H atoms was also predicted, and the results showed that the solubility decreases with the increase of the degree of unsaturation for hydrocarbons. Moreover, the H2 solubility behavior in catalytic diesel was further explained from a molecular point of view by means of the COSMO-RS model.

1. INTRODUCTION After the process of catalytic cracking, the diesel also contains high sulfur, nitrogen, and unsaturated hydrocarbon, which leads to diesel with undesirable properties such as dark color and weak stability. It is known that sulfur content in diesel must be controlled to an ultralow level to reduce harmful emissions and meet the environmental request for vehicle exhaust. Thus, the hydrorefining of catalytic diesel is needed to improve the quality of the product. In recent years, liquid-phase hydroprocessing as a novel technology has been developed, but the still unsolved issues are the dissolved hydrogen (H2) concentration and the mass transfer limitations in catalytic diesel.1,2 The solubility of H2 and mass transfer coefficient are required to develop accurate process models for hydrogenation processes. Besides, H2 solubility data are also needed for the development of kinetic models. Therefore, the research on H2 solubility in diesel is of great importance, which can provide the fundamental data for the process design and optimization in liquid circulation hydrogenation.3 However, H2 solubility data in the petroleum fractions have rarely been reported. Kikic et al.4 measured the solubility of H2 in some pure hydrocarbon solvents and found that H2 solubility in hydrocarbons increases with pressure, in accordance with the general law of gas solubility. However, at constant pressure, especially at high pressure, H2 solubility in a pure hydrocarbon solvent increases with the temperature, which conforms to the general rule of H2 solubility in common solvents. Saajanlehto et al.5 measured the solubility of H2 in heavy oil systems with a continuous flow apparatus at different temperatures and pressures. d’Angelo et al.6 investigated the solubility of H2 in four kinds of alcohol, and concluded that H2 solubility in the solvent increases with the pressure and temperature, and also increases with the number of carbons in the alcohol. Zhou et al.7 studied the H2 solubility in benzene, toluene, BTXS © 2016 American Chemical Society

(benzene, toluene, xylene, and styrene), and pyrolysis gasoline. The SRK (Soave−Redlich−Kwong) equation was used to model the H2 solubility in solvents. They found that the calculated results and experimental data agree well, indicating that the SRK equation has a good practicability for modeling the H2 solubility. Schofield et al.8 studied the H2 solubility in white oil as a function of temperature and pressure. The calculated results by the Krichevsky−Ilinskaya and van’t Hoff model exhibited a small deviation from experimental data, suggesting that the thermodynamic model is applicable. Nevertheless, H2 solubility and mass transfer data in diesel are scarce in the literature, and the aforementioned thermodynamic models are correlative but not predictive models, which require experimental data to correlate the model parameters. For most chemical engineers, the predictive thermodynamic models are quite desirable to reduce the amount of experimental work. The conductor-like screening model for real solvent (COSMO-RS) models is independent of any experimental data, and it is a powerful thermodynamic and quantum mechanical approach to predict the thermodynamic properties of pure and mixed liquids based on unimolecular quantum chemical calculations.9−13 Klamt and Eckert14 developed the COSMO-RS method to predict gas solubility, Henry’s law constant, vapor pressure, etc.15 The COSMOthermX16 is a commercial program under continuous improvement based on the COSMO-RS model, by which the σ-profiles and the potentials of individual compounds as well as a complete set of thermophysical, equilibrium, and transport properties of pure compounds and mixtures, etc., can be obtained.17 As an a priori Received: March 29, 2016 Revised: July 10, 2016 Published: July 25, 2016 6257

DOI: 10.1021/acs.energyfuels.6b00733 Energy Fuels 2016, 30, 6257−6263

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cell. (3) When the system temperature reached the desired value, H2 was rapidly loaded into the cell. The initial pressure was recorded as Pint (t = t0). Then, the cell was agitated by a magnetic stirrer at a constant speed, while the pressure began to decline as a function of time. During the experiment, the system pressure (Pt) was recorded every 5 min until the pressure remained constant (Peff), indicating that the gas−liquid equilibrium was reached. Each experiment was performed in triplicate under similar conditions to verify the reproducibility of experimental data, and its accuracy should be controlled within ±5%.27,28 2.3. Calculation Method. The solubility of H2 (x) can be calculated according to the following equations:

predictive method, the COSMO-RS model has received wide attention for predicting gas solubility in organic solvents and ionic liquids.18−20 Thus, in this work we will explore the possibility of the COSMO-RS model to predict the solubility of H2 in diesel. In this work, the solubility and liquid-phase mass transfer coefficient of H2 in catalytic diesel at appropriate temperatures (353.2−453.2 K) and pressures (1−6 MPa) were measured. In addition, H2 solubility in diesel was predicted by the COSMORS model using the COSMOthermX software package (version C30_1301), and the predicted values were compared with the experimental data. To the best of our knowledge, it is the first work to extend the COSMO-RS model to predict gas solubility in oil.

x=

nH2 nH2 + ndiesel

2.1. Materials. The catalytic diesel was supplied by Sinopec Fushun Research Institute of Petroleum and Petrochemicals, and its properties are listed in Table 1. The digital densimeter (type DA-650)

Table 1. ASTM Distillation Data for the Diesel Investigated in This Work (initial boiling point), °C (5%), °C (10%), °C (20%), °C (30%), °C (40%), °C (50%), °C (60%), °C (70%), °C (80%), °C (90%), °C (95%), °C (end), °C

(1)

m,eff

VL,int =

range range range range range range range range range range range range range

nH2 nH2 + mdiesel /Mdiesel

⎛ 1 1 ⎞ 1 ⎟⎟ nH2 = (Vcell − VL , int )⎜⎜ − Vm,eff ⎠ 1 − VH̃ 2 ⎝ Vm,int V

2. EXPERIMENTAL SECTION

distillation distillation distillation distillation distillation distillation distillation distillation distillation distillation distillation distillation distillation

=

mdiesel ρdiesel

(2)

(3)

Here, Mdiesel is the molecular weight of diesel; nH2, ng,int, and ng,eff represent the amount of H2 in the diesel liquid phase and in the gas phase at initial and equilibrium states, respectively. Vcell is the total volume of the equilibrium cell; VL,int and VL,eff represent the initial and equilibrium volumes of liquid phase in the equilibrium cell, respectively. Vm,int and Vm,eff represent the mole volumes of H2 at the corresponding pressures Pint and Peff, respectively, which can be obtained from the NIST database (http://webbook.nist.gov/ chemistry/fluid/). VL,eff can be obtained by

194.7 231.3 241.4 252.9 263.7 274.7 289.1 304.8 323.4 343.8 366.2 382.3 385.0

VL,eff = VL,int + VH̃ 2nH2

(4)

where Ṽ H2 represents the partial molar volume of H2 at the equilibrium state calculated by the method as proposed by Kumełan et al.29 The accuracy and reliability of the experimental apparatus and procedure were validated by comparing the experimental solubility data of H2 in toluene at 50 °C with those reported in literature.30 As shown in Figure 1, it can be seen that the experimental data measured in this work agree well with literature data, indicating the reliability of experimental method presented in this work. On the other hand, in the calculation of the mass transfer coefficient in the liquid side (kLa), the influence of H2 volume in the liquid phase (Ṽ H2nH2) on the total liquid-phase volume (VL,eff) can be neglected because H2 solubility in diesel is very small. The liquid-phase mass transfer coefficient (kLa) was measured by the dynamic pressure step

was used to obtain the density of the diesel by a type U tube vibration method; the determination of kinematic viscosity of diesel was done at 20 °C with the Petroleum Products kinematic viscosity tester instrument (JZ-A033). The average molecular weight was measured by vapor pressure osmotic method at the temperature of 20 °C; the ASTM distillation data as listed in Table 1 were obtained using a BSY103 type distillation analyzer according to GB/T6536. H2 with a purity of 99.99% (mass fraction) was purchased from Beijing Longkou City Gas Plant and was used without further purification. 2.2. Experimental Setup and Procedure. A magnetic agitated view-cell apparatus was applied to measure the solubility and mass transfer coefficient of H2 in catalytic diesel, and the details of the apparatus can be seen in our previous publication.21 The system pressure was measured by a pressure sensor with an accuracy of ±0.01 MPa in the range 0−6.00 MPa, and the temperature was controlled with an accuracy of ±0.1 °C, which can make the total uncertainty of temperature and pressure within 1%. The masses of samples were measured by an electronic balance (CPA 1003S, Sartorius) with an accuracy of ±0.001 g. The technique to measure the hydrogen solubility and the liquid-phase mass transfer coefficient is similar to that of the previous works reported by Dai et al.22 and Heintz et al.23 During the experiment, the initial pressure, the varied dynamic pressure as a function of time, and the balance pressure were all recorded. The procedure is somewhat similar to that from previous works,23−26 and briefly described here: (1) To start, the equilibrium cell was evacuated with a vacuum pump until the pressure −0.01 MPa (P0) to make sure that there is no air. (2) A certain amount (mdiesel) of diesel determined by measuring the mass difference of the container before and after the loading of diesel was added into the equilibrium

Figure 1. Comparison of H2 solubility in toluene between experimental data obtained in this work and those in ref 30 at 323.2 K: black ■, experimental data obtained in this work; red ●, ref 30. 6258

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Energy & Fuels Table 2. Physicochemical Properties of Catalyst Diesel Investigated in This Work density (g cm−3)

kinematic viscosity (mm2 s−1)

MW (g mol−1)

C wt %

H wt %

S (mg L−1)

N (mg L−1)

0.9428

6.37

206

89.99

10.01

341.1

116.0

Figure 2. Optimized geometries of six virtual model compounds C15H20 (A) and the polarized screening charge distribution on the molecular surface (B). which exhibits a linear relationship between ln((Pint − Peff)/(Pt − Peff)) and the time t. Thus, kLa can be deduced from the slope of the straight line.34−36

method,31−33 as described. (1) After the desired liquid temperature was reached, the cell headspace was flushed with the gas solute and the liquid was saturated at low pressure (P0). (2) Then the stirring was stopped, and the gas solute pressure was rapidly increased to Pint. (3) At t = t0, the stirrer was started again, and the pressure was recorded as a function of time until it remained constant (a new equilibrium pressure Peff). The liquid-phase mass transfer coefficient kLa between t = 0 (P = Pint) and t(P = Pt) was calculated by

⎛ P − Peff ⎞ ⎛ Pint − P0 ⎞ ln⎜ int ⎟=⎜ ⎟kLa(t − t0) ⎝ Pt − Peff ⎠ ⎝ Peff − P0 ⎠

3. COSMO-RS MODEL In this work, H2 solubility in solvents was estimated directly by the COSMOthermX software package (version C30_1301). It is known that the compositions of catalytic diesel are extremely complex, and thus in this work several virtual model compounds consisting of elements C and H were introduced. The virtual model compounds have physicochemical properties similar to those of catalytic diesel, such as similar density,

(5) 6259

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Energy & Fuels Table 3. Experimental Solubility Data of H2 in Diesel and Predicted Results for Six Model Compounds at Different Temperatures and Pressures predicted results by COSMO-RS model for six model compounds (100xpred) T (K)

P (MPa)

100xexp

(1)

(2)

(3)

(4)

(5)

(6)

av

ARD (%)

u(T) (K)

u(P) (MPa)

u(x)

453.2 453.2 453.2 453.2 453.2 423.2 423.2 423.2 423.2 423.2 423.2 403.2 403.2 403.2 403.2 403.2 403.2 373.2 373.2 373.2 373.2 373.2 373.2 353.2 353.2 353.2 353.2 353.2 353.2 353.2

1.50 2.28 3.15 3.94 5.00 1.17 2.22 3.04 3.90 4.99 5.86 1.29 2.06 2.95 4.06 5.12 5.53 1.15 2.04 3.00 4.07 4.95 5.78 1.31 2.30 3.33 3.87 4.19 4.86 5.46

2.05 3.02 3.95 4.86 5.82 1.44 2.52 3.42 4.19 5.24 6.05 1.41 2.25 3.15 4.21 5.28 5.71 1.19 1.95 2.69 3.69 4.35 5.19 0.94 1.68 2.49 2.92 3.12 3.64 4.24

1.60 2.42 3.34 4.16 5.27 1.28 2.42 3.31 4.23 5.40 6.32 1.41 2.26 3.25 4.47 5.65 6.11 1.33 2.35 3.45 4.65 5.64 6.57 1.55 2.70 3.91 4.53 4.90 5.68 6.39

1.57 2.39 3.29 4.101 5.20 1.26 2.39 3.28 4.18 5.33 6.25 1.40 2.24 3.21 4.42 5.59 6.05 1.32 2.33 3.41 4.61 5.60 6.52 1.54 2.68 3.88 4.50 4.87 5.64 6.33

1.59 2.41 3.32 4.14 5.24 1.27 2.41 3.29 4.21 5.37 6.30 1.40 2.23 3.18 4.36 5.49 5.92 1.33 2.34 3.44 4.65 5.64 6.57 1.55 2.71 3.91 4.54 4.87 5.69 6.38

1.58 2.40 3.31 4.13 5.23 1.27 2.41 3.29 4.21 5.36 6.28 1.41 2.22 3.18 4.36 5.48 5.91 1.32 2.34 3.43 4.64 5.63 6.56 1.55 2.70 3.90 4.53 4.90 5.68 6.37

1.58 2.39 3.30 4.11 5.21 1.27 2.40 3.28 4.20 5.33 6.27 1.39 2.22 3.17 4.35 5.47 5.90 1.33 2.34 3.44 4.65 5.64 6.57 1.55 2.71 3.92 4.55 4.92 5.70 6.39

1.58 2.39 3.29 4.11 5.20 1.267 2.40 3.28 4.19 5.35 6.26 1.39 2.22 3.17 4.34 5.46 5.90 1.32 2.34 3.43 4.64 5.63 6.55 1.55 2.70 3.91 4.54 4.91 5.68 6.37

1.58 2.40 3.31 4.13 5.22 1.27 2.40 3.29 4.20 5.36 6.28 1.40 2.23 3.19 4.38 5.52 5.96 1.32 2.34 3.43 4.64 5.63 6.56 1.55 2.70 3.90 4.53 4.89 5.68 6.37

22.82 20.55 16.28 15.09 10.29 11.73 4.59 3.96 0.32 2.32 3.80 0.84 0. 85 1.32 4.14 4.60 4.41 11.16 20.00 27.55 25.74 29.38 26.31 64.62 60.76 56.77 55.17 56.99 55.96 50.14

0.2 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.1 0.2 0.1 0.1

0.002 0.002 0.002 0.003 0.002 0.002 0.002 0.003 0.001 0.003 0.002 0.003 0.001 0.003 0.003 0.002 0.002 0.001 0.001 0.002 0.001 0.002 0.001 0.003 0.003 0.002 0.002 0.002 0.003 0.002

0.0007 0.0012 0.0017 0.0023 0.0032 0.0006 0.0012 0.0018 0.0024 0.0034 0.0044 0.0007 0.0012 0.0018 0.0028 0.0039 0.0044 0.0006 0.0014 0.0020 0.0030 0.0041 0.0049 0.0008 0.0015 0.0029 0.0031 0.0034 0.0043 0.0050

molecular weight, and C/H atom ratio, as listed in Table 2. These model compounds all have the same atom ratio of C to H (3/4), relative molecular weight, and molecular formula (C15H20). The geometries of these virtual model compounds are first optimized, and the optimized geometries are shown in Figure 2. The excess enthalpy of the gas−oil mixture was also estimated by the COSMO-RS model, and expressed by the sum of three contributions associated with the interactions of hydrogen bonding HE (H-bond), polar misfit HE (misfit), and van der Waals forces HE (vdW)36 HE = HE(misfit) + HE(H ‐ bond) + HE(vdW)

(6)

which can provide some theoretical insight into the physicochemical solute−solvent interaction and help understand the solubility behavior of H2 in catalytic diesel at the molecular scale.

Figure 3. H2 solubility in diesel at different temperatures and pressures: black ■, 353.2 K; red ●, 373.2 K; blue ▲, 403.2 K; purple ▼, 423.2 K; orange ★, 453.2 K.

4. RESULTS AND DISCUSSION The solubility of H2 in catalytic diesel at temperatures (353.2− 453.2 K) and pressures (1.00−6.00 MPa) were first measured, and the data are listed in Table 3, in which the uncertainties of temperature u(T), pressure u(P), and solubility u(x) were obtained by error propagation calculations. The P-x diagram is illustrated in Figure 3. It clearly shows that H2 solubility increases with the increase of temperature and pressure, which conforms to the general rule of H2 solubility in common

solvents.37 The Henry’s law constants were deduced by linear extrapolation at xH2 → 0, and then were fitted using the b

equation of ln H = a + T . It can be seen from Figure 4 that lnH exhibits a good linear relationship with 1/T, and the values of a and b are given as well. The H2 molar fraction at different times at temperature of 373.2 K and different initial pressures is shown in Figure 5. It 6260

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− Peff) and time t, i.e., ln(Pint − P0)/(Pt − Peff) = 0.0012t − 0.0568 as expressed by eq 5. The liquid-phase mass transfer coefficient (KLa) as a function of pressure at temperature of 353.2 K is illustrated in Figure 7. With the increase of pressure, the mass transfer coefficient also increases, indicating that H2 dissolves in diesel oil more rapidly at high pressures.

Figure 4. Henry’s constants of H2 in diesel at different temperatures.

Figure 7. Mass transfer coefficient KLa as a function of pressure at temperature of 353.2 K.

Figure 8 shows the H2 solubility in six virtual model compounds with the same atom ratio of C/H at 403.2 K. It can

Figure 5. Molar fraction of H2 in diesel as a function of time at different initial pressure at 373.2 K: ■, 1.15 MPa; red ●, 2.04 MPa; blue ▲, 3.00 MPa; purple ▼, 4.07 MPa; orange ★, 4.95 MPa; green ◆, 5.78 MPa.

can be seen that with the increase of time, the molar fraction of H2 in diesel increases first rapidly and then tends to be constant. It will take about 2 h to achieve the gas−liquid equilibrium. The system pressure as a function of time at temperature 353.2 K and pressure 3.33 MPa is shown in Figure 6. It is seen that there exists a linear relationship between ln(Pint − P0)/(Pt

Figure 8. Comparison between experimental data and predicted results by COSMO-RS model at 403.2 K: ■, experimental data; solid lines, predicted results for six model compounds with different molecular structures.

be seen that the predicted results by the COSMO-RS model are in good agreement with experimental data, with the average relative deviation, ARD % =

xexp −

1 N

N

∑i = 1 xi ,pred xexp

× 100, where

xi,pred is the predicted solubility for virtual model compound i, 2.69%. The detailed results are listed in Table 3. It is noted that most of the predicted results are close to the experimental data except for those at the low temperature 353.2 K, which may be due to the very small solubility values at low temperature resulting in the large relative deviations. Anyway, this work proves that the COSMO-RS model can be used to predict the H2 solubility in catalytic diesel which, however, contains complex compositions. This work goes a further step to predict the H2 solubility in several hydrocarbon components with the same carbon atom

Figure 6. System pressure as a function of time at temperature of 353.2 K and pressure of 3.33 MPa. 6261

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Table 4. Predicted H2 Solubility in Hydrocarbons with Different Ratios of C/H by the COSMO-RS Model at 403.2 K

role, whereas the hydrogen bonding interaction makes a negligible contribution to the excess enthalpy. Moreover, the excess enthalpy coming from the contribution of van der Waals force is positive, indicating that the H2 dissolution process is endothermic. This explains the H2 “inverse” temperature effect that H2 solubility in common solvents increases with the increase of temperature. In addition, the repulsive van der Waals force between H2 and the hydrocarbon with high C/H atom ratio is higher than that between H2 and the hydrocarbon with low C/H atom ratio (see Figure 9B). This is consistent with the fact that H2 solubility decreases with an increase of the degree of unsaturation for hydrocarbons.

but different ratios of C/H atoms by the COSMO-RS model, and the results are listed in Table 4. It can be seen that the solubility decreases with the increase of the ratios of C/H, revealing that H2 solubility decreases with the increase of the degree of unsaturation for hydrocarbons.38−41 Moreover, the solubility in aromatics is lower than that in alkanes, as confirmed by previous experimental findings.42,43 The COSMO-RS model can not only predict the H2 solubility in catalytic diesel accurately, but also provide a theoretical insight into the solute−solvent interaction at the molecular level. As shown in Figure 9, it is evident that the repulsive van der Waals force is the main part of intermolecular interaction between H2 and virtue model compounds (or other hydrocarbons). The electrostatic interaction plays a secondary

5. CONCLUSION The hydrogenation process can reduce the impurities in diesel such as sulfur, oxygen, and nitrogen contents, in which H2 dissolved in oil participates in the main reaction. In this case, the solubility data and liquid-phase mass transfer coefficients of H2 in catalytic diesel are required to better understand the whole hydrogenation process. It was confirmed that H2 solubility increases with the increase of pressure and temperature, and the natural logarithm of Henry’s law constant ln H shows a linear relation with 1/T. The molar fraction of H2 in diesel as well as system pressure at different equilibrium time was measured to estimate the liquid-phase mass transfer coefficient (kLa). With the increase of pressure, the mass transfer coefficient also increases. Furthermore, the solubility of H2 in diesel was predicted by the COSMO-RS model using six virtual model compounds. The predicted results were compared with the experimental data, indicating the accuracy of COSMO-RS model. Then, the solubility of H2 in several hydrocarbon components with the same carbon atom but different ratios of C to H atoms was predicted. It was concluded that H2 solubility decreases with the increase of the degree of unsaturation for hydrocarbons. In summary, the COSMO-RS model was used for the first time to predict gas solubility in oil, and successfully explain the H2 solubility behavior observed experimentally from a molecular point of view. The results obtained from experiment, calculation, and theoretical analysis remain consistent.

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AUTHOR INFORMATION

Corresponding Authors

*Phone: +86-1064433695. E-mail: [email protected]. *E-mail: [email protected].

Figure 9. Interaction energies between H2 and virtual model compounds (A) and between H2 and the compounds with different C/H atom ratio (B) at 403.2 K.

Notes

The authors declare no competing financial interest. 6262

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ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China under Grants 21476009, 21406007, and U1462104.

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DOI: 10.1021/acs.energyfuels.6b00733 Energy Fuels 2016, 30, 6257−6263