Hydrogen solubility in heavy oil systems: Experiments and modeling

Fuel 137 (2014) 393–404

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Hydrogen solubility in heavy oil systems: Experiments and modeling Meri Saajanlehto ⇑, Petri Uusi-Kyyny, Ville Alopaeus Aalto University, School of Chemical Technology, Department of Biotechnology and Chemical Technology, P.O. Box 16100, FI-00076 Aalto, Finland

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Hydrogen solubility was measured in

heavy oil systems at high temperature and pressure.  Measurements were performed with a continuous flow apparatus with visual method.  Hydrogen solubility in heavy oil systems was predicted with four models.

a r t i c l e

i n f o

Article history: Received 20 May 2014 Received in revised form 30 July 2014 Accepted 5 August 2014 Available online 19 August 2014 Keywords: Hydrogen solubility Heavy oil Experiments Modeling PC-SAFT

572 K 547 K 498 K

a b s t r a c t Hydrogen solubility measurements in heavy oils are required in order to develop accurate process models. Nevertheless, these solubility measurements are challenging at elevated temperatures and pressures and the amount of data points is scarce in the literature. This paper presents measured hydrogen solubilities in heavy oil systems at a temperature range from 498 to 598 K and a pressure range from 2 to 11 MPa. The experiments were conducted with a continuous flow apparatus. One of the well-characterized heavy oil systems was a hydrocracked vacuum gas oil and the second system consisted of a modified vacuum residue from Urals crude and toluene. The modified vacuum residue and toluene mixtures were prepared gravimetrically (mass fractions of vacuum residue: 0.25, 0.34 and 0.50). The experiments demonstrated that increasing the partial pressure of hydrogen and temperature increased the hydrogen solubility. Another finding was that the amount of toluene in the system had great impact to the hydrogen solubility. Four modeling approaches were compared based on their predictions on the hydrogen solubility in heavy oil systems measured in this work and four heavy oils found from the literature. The chosen models were PC-SAFT, Peng–Robinson, a simple correlation based on the corresponding theory and a method based on the Scatchard–Hildebrand theory. PC-SAFT with applied a heavy oil characterization method and the correlation based on the corresponding theory were found to predict the hydrogen solubility equally well and accurately. The benefit of using PC-SAFT instead of the simple correlation is that with PC-SAFT, phase behavior of multicomponent systems can be predicted and other properties, such as densities, can be obtained simultaneously. Peng–Robinson with a single carbon number characterization method overestimated the hydrogen solubility in the studied heavy oils and the method based on the Scatchard–Hildebrand theory could model the hydrogen solubility well after parameter regression. Ó 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +358 50 434 9070. E-mail addresses: meri.saajanlehto@aalto.fi, [email protected] (M. Saajanlehto). http://dx.doi.org/10.1016/j.fuel.2014.08.015 0016-2361/Ó 2014 Elsevier Ltd. All rights reserved.

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Nomenclature A AAD B EoS F k l m M N P PS RAD SCN SH2 T u Vm w wt%

parameter in the generalized distribution model average absolute deviation parameter in the generalized distribution model equation of state flow rate (cm3 min1) binary interaction parameter in the PC-SAFT equation of state property: density (g cm3) or pressure (MPa) number of segments in PC-SAFT equation of state molar mass (g mol1) number of measured data points pressure (MPa) pseudocomponent relative average deviation single carbon number hydrogen solubility (mol(H2) kg(liquid)1) temperature (K) uncertainty molar volume of ideal gas (22 414 cm3 mol1) mass fraction mass percent

q r

density (g cm3) segment diameter (Å) in PC-SAFT equation of state

Subscripts 0 parameter in the generalized distribution model 2-P two-phase region A aromatic fraction b boiling point C cumulative calc calculated value H2 hydrogen i component i j component j L liquid sample Li liquid phase region P polyaromatic fraction S saturate fraction Superscripts ⁄ equilibrium point

Greek letters e/ j segment energy parameter (K) in PC-SAFT equation of state

1. Introduction Energy consumption is increasing worldwide all the time. One third of the consumed energy is produced from petroleum, and the most of the liquid fuels are refined from oil. Meanwhile, light crude oil wells are being exhausted and the utilization of heavy and extra-heavy oils is increasing. Simultaneously, refineries are maximizing their capacity and the heaviest fractions are processed into an even more valuable form [1]. Heavy crude oil is dense and viscous and usually has a high content of asphaltenes. In addition, heavy oil contains usually a high amount of heteroatoms, such as sulfur and nitrogen, and metals, mostly nickel and vanadium. Vacuum residue has similar properties in comparison to heavy crude oil and it is normally classified as heavy oil. In addition, heavy crude oil and vacuum residue is refined in similar process units [1]. Refining of heavy oils is challenging due to their complex nature. However, processing increases the value of the product substantially. Refining is usually conducted in hydroprocesses, where heavy hydrocarbons are hydrocracked to the more valuable light components. In addition, most of the heteroatoms and metals have to be removed from the system due to the environmental legislation and the subsequent refining processes [1]. Knowledge of hydrogen solubility in heavy oil is required for designing and operating hydroprocesses and it has a major role in process models [2–4]. Hydrogen solubility data is also needed in kinetic models of hydrocracking and hydrotreating reactions [4,5]. Unfortunately, the hydrogen solubility measurements are challenging due to the thermal instability of heavy oils at elevated temperatures and pressures. Further challenges are the complex phase behavior of heavy oils and the low hydrogen solubility in such systems [2]. Only three data sets for hydrogen solubility in heavy oils and heavy oil cuts were found in the literature [2,5,6]. In addition, there are a few measurements of hydrogen solubility in coal liquids [7–14]. Hydrogen solubility in hydrocarbons and oils

are reviewed in details in the paper by Chávez et al. [4]. As to conclude, there is still a need for hydrogen solubility data in well-characterized heavy oil systems. Accurate hydrogen solubility predictions are an essential part in hydroprocess models as discussed above. Challenge to the modeling work is caused by the complexity of heavy oils – a huge number of components of which a large fraction is unidentified [15] – hence oil characterization must be conducted carefully. In the previous studies, hydrogen solubility in heavy oils is predicted with several models. At early stages, correlations for predicting hydrogen solubility in hydrocarbons and hydrocarbon mixtures have been suggested by Chao and Seader [16], Grayson and Streed [17] and Sebastian et al. [18]. Shaw [19] has proposed a correlation for predicting hydrogen solubility in alicyclic and aromatic solvents based on the corresponding theory. The correlation has predictive nature. It requires mean boiling point and density of the solvent and estimation of density difference between the lightest and the heaviest component of oil sample. Lal et al. [5] has predicted the hydrogen solubility in Athabasca bitumen with the Peng–Robinson with a modified repulsive term. One challenge of applying the cubic equations of state is defining critical properties for heavy oil or alternatively for pseudocomponents. In addition, binary interaction parameters may easily be unreasonable with the cubic equations of state [5]. Riazi and Vera [20] and Riazi and Roomi [3] has developed a method for modeling H2 + hydrocarbons and H2 + heavy oil systems based on the Scatchard–Hildebrand theory. The method requires mean boiling point and density of solvent but not require the critical parameters or binary interaction parameters. In addition, user might have to estimate one solvent depended parameter if the solvent is highly aromatic. Luo et al. [21] are proposed a model, which combines the Pierotti method together with the Henry’s law. In practice, four oil specific parameters are regressed against measured data of H2 + oil system. Thus, the model cannot be applied for modeling hydrogen solubility without experimental data. Torres et al. [22] modeled hydrogen

M. Saajanlehto et al. / Fuel 137 (2014) 393–404

solubility in heavy oil cuts with the Grayson Streed and the augmented Grayson Streed methods. They concluded that the Grayson Streed and the augmented Grayson Streed methods gave inaccurate results for hydrogen solubility in heavy oils. One interesting model for predicting hydrogen solubility in heavy oils is the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) [23] equation of state. This equation of state has been applied for modeling hydrogen solubility in hydrocarbons (for example in Refs. [24,25]) but not used for predicting hydrogen solubility in heavy oils. In this study, hydrogen solubility was measured in heavy oil systems with the continuous flow apparatus [25,26]. The measurements were conducted at high pressures (2–11 MPa) and high temperatures (498–598 K). One of the measured heavy oil systems was a hydrocracked vacuum gas oil (Oil1) and the other system consisted of a modified vacuum residue from Urals crude (Oil2) and toluene. In addition, the hydrogen solubility was predicted in heavy oil systems measured in this work and in four heavy oils found from the literature [2,5,6] with four models. Two of the models were equations of state: PC-SAFT [23] and Peng–Robinson [27]. The equations of state were combined with a single carbon number (SCN) type characterization [28–30] in order to conduct the calculations. The characterizations were based on the distillation curve of oil samples. Two other models evaluated were a correlation proposed by Shaw [19] and a method suggested by Riazi and Roomi [3]. These four models were selected due to their demonstrated potential in predicting hydrogen solubility in hydrocarbons accurately and predictive nature. From the literature, such H2 + heavy oil systems were selected into further examination that had a distillation curve or a distillation range for heavy oil available. Distillation curve or mean boiling point was required in the models applied in this work. 2. Experimental 2.1. Samples The hydrogen solubility was measured in hydrocracked vacuum gas oil (Oil1) and mixtures consisted of modified vacuum residue from Urals crude (Oil2) and toluene. The purities and the suppliers of hydrogen and toluene are listed in Table 1. These components were used without further purification. The oil samples were characterized and distillation curves, densities, mass fraction of SARA and elementary analysis for Oil1 and Oil2 were obtained in the work by Saajanlehto and Alopaeus [28] and they are listed in Appendix A in Tables A1 and A2. The mixtures of Oil2 and toluene were prepared gravimetrically with a balance (Kern 572). The accuracy of the balance was ±0.1 g, according to the manufacturer. The mass fractions of Oil2 in the samples were 0.25, 0.34 and 0.50. All liquid samples were degassed in an ultrasonic bath applying a vacuum pump before the samples were fed into the continuous flow apparatus. The time for degassing was approximately 1.5 h. The Oil2 + toluene samples were weighed before and after the degassing. The lost mass from the system was assumed to be toluene and based on this assumption the mass fractions of Oil2 was corrected if needed. Table 1 Suppliers and purities of hydrogen and toluene. Component Hydrogen Toluene a b c

CAS number 1333-74-0 108-88-3

Supplier AGA Sigma–Aldrich

Purity as reported by the supplier. Mole fraction. Mass fraction.

Puritya

Purification method b

0.99995 P0.997c

None None

395

2.2. Density measurements In this work, densities for toluene + Oil2 systems were measured in order to be able to calculate the mass of liquid and thus the content of hydrogen in the liquid system. Density for Oil1 was measure earlier [28]. The density measurements for toluene + Oil2 systems were conducted with a vibrating tube densimeter (DMA HP connected to a DMA 5000 M densimeter manufactured by Anton Paar GmbH). The densimeter was calibrated with degassed distilled water and dry air. The uncertainty for density is ±0.0002 g cm3 at 293–353 K according to this calibration. The accuracy of the densimeter temperature is ±0.001 K according to the manufacturer of the densimeter. 2.3. Hydrogen solubility measurements 2.3.1. Apparatus Fig. 1 shows the experimental set-up. The hydrogen solubility measurements were performed with the continuous flow apparatus as described in the work by Saajanlehto et al. [25] with a small modification: the liquid and gas lines were connected with a Tpiece placed in an oven. The pressure calibration was conducted at 318 K. The overall pressure uncertainty was estimated to be ±0.02 MPa including the uncertainty from the measurement method and the pressure sensor. The apparatus and the measurement method were validated for gas solubility measurements in the previous study by Saajanlehto et al. [25]. 2.3.2. Procedure The experimental procedure is based on finding the gas solubility point visually. The measurements were conducted by observing the phase of the fluid in the equilibrium cell with the aid of a camera and changing the fluid composition until the phase boundary was reached at constant pressure and temperature. The experiments were conducted by feeding the liquid sample and gas through the system continuously. The flow rates of liquid and gas was calculated beforehand in order to have desired fluid composition. The flow rates for liquid varied from 0.5 cm3 min1 to 4.4 cm3 min1 and flow rates for gas between 5.0–10.5 cm3 min1 (the gas flow rate reading given at normal conditions, 273.15 K and 101.3 kPa). The maximum residence time of the fluid in the oven was 15 min. The mixing of gas and liquid was monitored visually with the camera system. The phase of the fluid was visually observed from the video. If the phase of the system was liquid, in other words, no bubbles were observed, the hydrogen content was increased and vice versa, if the system was in the two-phase region, the amount of hydrogen was decreased in the system. Fig. 2 shows two still frames from the video. The frame on the left hand side represents the liquid phase and on the right hand side, the bubble can be seen in the twophase region. After composition change, the flow was let to stabilize and a new composition of fluid mixture reached typically the equilibrium cell in less than 10 min. The amount of hydrogen in the liquid was changed until the phase boundary was zoomed into a composition step of 0.015 mol(H2) kg(liquid)1 or less. 2.3.3. The hydrogen content in the heavy oil system The amount of hydrogen in the oil systems was calculated from the flow rates of the fluids as following:

SH2 ¼

1000 FVH2 m F L qL

ð1Þ

where SH2 is amount of hydrogen in liquid (mol(H2) kg(liquid)1), FH2 is flow rate of hydrogen (cm3 min1) from the mass flow controller, the reading is given at normal conditions (273.15 K and

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Fig. 1. Schematic figure of experimental set-up for hydrogen solubility measurements.

Fig. 2. Still frames from the video: on the left hand side the liquid phase and on the right hand side the bubble in the two-phase region.

101.3 kPa), Vm is the molar volume of ideal gas (22 414 cm3 mol1, at 273.15 K and 101.3 kPa), FL is flow rate of liquid (cm3 min1) from the feeding pump, qL is density (g cm3) of liquid. The density of liquid was calculated with a correlation. The density correlation was obtained by regressing parameters against measured density values of each system (see Chapter 4.1). The actual hydrogen solubility point (Eq. (2)) was calculated as an average of the last observed point of the liquid region and the first observed point of the two-phase region after the phase transition was zoomed into as small step as possible with the current apparatus set-up.

SH2 ¼

SH2;LI þ SH2;2-P 2

ð2Þ

where SH2 is hydrogen solubility (mol(H2) kg(liquid)1) at equilibrium point, subscript ‘‘LI’’ denotes liquid phase and subscript ‘‘2-P’’ two-phase region. The uncertainty of hydrogen solubility was calculated as presented below:

uðSH2 Þ ¼

      1000 DF H2  DF L  DqL  þ þ  SH2   V F H2   F L   qL  m

ð3Þ

where u(SH2) is the uncertainty of hydrogen solubility (mol(H2) kg(liquid)1), Vm is molar volume of ideal gas (22 414 cm3 mol1, at 273.15 K and 101.3 kPa), FH2 is flow rate of hydrogen (cm3 min1, the reading given at normal conditions, 273.15 K and 101.3 kPa), FL is flow rate of liquid (cm3 min1), qL is density (g cm3) of liquid, DFH2 is uncertainty of the mass flow controller (5% of set point, based on calibration), DFL is uncertainty of the feeding pump

(0.5% of set point according to the manufacturer of the pump) and DqL is uncertainty of density (estimated to be 0.1%). 3. Characterization of heavy oils for modeling with equations of state The hydrogen solubility was predicted in Oil1 and mixtures consisting of Oil2 and toluene as well as in LVGO, HVGO [2], HCGO [6] and Athabasca bitumen (AB) [5] found from the literature with PC-SAFT [23] and Peng–Robinson [27]. In order to conduct the calculations, the characterization of heavy oils into pseudocomponents was required. Distillation curve of the heavy oils were applied as input data for both characterization procedures. Extensive distillation curve information was available for Oil1 and Oil2 [28] but for LVGO, HVGO, HCGO, only a begin and end-point of the distillation curve was presented in the papers [2,6] and for Athabasca bitumen, distillation curve was measured up to 42.5 wt% of AB [5]. In addition, due to amount of asphaltenes in AB was not given in the original paper [5], the amount of asphaltenes was estimated based on the data in Refs. [31,32]. The generalized distribution model [33,34] was used for obtaining the pseudocomponent composition for oil samples as presented in Eq. (4):

T b ¼



 1B A 1 ln B w

ð4Þ

0 where T b ¼ T bTT , w⁄ = 1  wC, Tb is normal boiling point, wC is 0 cumulative mass fraction, T0, A and B are specific parameters for each sample.

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At first, the auxiliary parameters T0, A and B were regressed against the distillation curve data, and then the pseudocomponent compositions for the both characterization procedures were calculated with the same auxiliary parameters. The parameter T0 represents the boiling point temperature of the lightest component in the mixture [34]. In this study, the parameter was set to approximately 10 K lower than the measured initial boiling point temperature of the distillation curve, rounding to the nearest ten of Kelvin. 3.1. Heavy oil characterization method for PC-SAFT The heavy oil characterization procedure [28] applied in this work was developed for PC-SAFT [23] and it was based on dividing the pseudocomponents first by their boiling point and further by distribution of three types of compound: saturates, aromatic and polyaromatics. The detailed description of the procedure is presented in the paper by Saajanlehto and Alopaeus [28]. The pseudocomponent composition was calculated with Eq. (4) and as explained in the study by Saajanlehto and Alopaeus. The mass fraction of each pseudocomponent for Oil1 and Oil2 was obtained from the study by Saajanlehto and Alopaeus and for LVGO, HVGO, HCGO and AB, the compositions were calculated in this work. The compositions for heavy oils are presented in Appendix B in Table B1. All the PC-SAFT and the binary interaction parameters for pseudocomponent pairs were obtained from work by Saajanlehto and Alopaeus. The PC-SAFT parameters for toluene were obtained from the study by Gross and Sadowski [23] and for hydrogen from the work by Ghosh et al. [24]. The PC-SAFT binary interaction parameter for toluene + saturate pseudocomponent pair was set to 0.02 and for toluene + aromatic/polyaromatic pseudocomponent pairs 0.01 as suggested by Saajanlehto and Alopaeus [28]. The PC-SAFT binary interaction parameter for hydrogen + pseudocomponent/toluene pairs was first set to zero. Then the parameter was estimated to be 0.1 in order to enhance the performance of the model.

of 2–11 MPa and in the temperature range of 498–598 K. The densities for vacuum residue + toluene systems were also measured in order to enable calculation of the mass of liquid sample and further the hydrogen content in liquid with Eq. (1). The hydrogen solubility was predicted in Oil1 and Oil2 + toluene systems as well in LVGO, HVGO [2], HCGO [6] and Athabasca bitumen (AB) [5] with four models. The selected models were PC-SAFT [23], Peng–Robinson [27], a correlation proposed by Shaw [19] and a method developed by Riazi and Roomi [3]. In order to conduct the predictions with PC-SAFT and Peng–Robinson, characterization of heavy oil were required: the single carbon number type characterization was applied as presented in Chapter 3 [28– 30]. In addition, the densities of Oil2 + toluene systems were predicted with PC-SAFT combined with the heavy oil characterization method [23,28] introduced in Chapter 3.1. Simple correlations for densities of Oil2 + toluene were also regressed in order to calculate the mass of the liquid sample with Eq. (1). 4.1. Density Densities for Oil2 + toluene systems were measured with the vibrating tube densimeter at temperature range from 293 to 353 K and atmospheric pressure. The results are listed in Table 2. Simple correlations were regressed against the data points (see Eqs. (5)–(7)). In addition, a correlation (Eq. (8)) was obtained for Oil1 with the density values listed in Appendix A in Table A2. The correlations were applied when determining the mass of liquid fed to the system.

q0:25 ¼ 0:00086ðT  273:15Þ þ 0:91222

ð5Þ

q0:34 ¼ 0:00083ðT  273:15Þ þ 0:92236

ð6Þ

q0:50 ¼ 0:00078ðT  273:15Þ þ 0:94015

ð7Þ

qOil1 ¼ 0:00065ðT  273:15Þ þ 0:926783

ð8Þ

3

3.2. Characterization for cubic equation of state For the calculations with Peng–Robinson, heavy oils were characterized with a single carbon number (SCN) type method. The pseudocomponents for SCN method were obtained so that the temperature difference between boiling points of SCN pseudocomponents was less than 15 K. The mass fraction of pseudocomponents for each heavy oil sample was obtained with Eq. (4) in this work. These compositions are presented with boiling point of pseudocomponents in Appendix B in Table B2. The molar mass and specific gravity of SCN pseudocomponents was obtained with correlations presented by Riazi and Al-Sahhaf [29]. The critical temperature and pressure and acentric factor for SCN pseudocomponents were obtained with the Kesler–Lee correlations [30]. Parameters for the asphaltene pseudocomponent were an exception: molar mass was estimated to be 2250 g mol1, critical pressure and omega were calculated as proposed by Modaresghazani [32] and the rest of the properties were obtained with the Kesler–Lee correlations [30]. Critical parameters for hydrogen were obtained from DIPPR [35].

where q is density (kg m ), T is temperature (K), subscripts ‘‘0.25’’, ‘‘0.34’’ and ‘‘0.50’’ denote the mass fraction of Oil2 in the sample and subscript ‘‘Oil1’’ refers to sample Oil1. In addition, the densities of Oil2 + toluene systems were predicted with the heavy oil characterization method for PC-SAFT [23,28]. The data points and predictions are shown in Fig. 3. Average absolute deviation (AAD) (given in Eq. (9)) and relative average

Table 2 Densities (q) for Oil2 + toluene systems (wOil2 = mass fraction of Oil2) at temperature (T) and atmospheric pressure. wOil2

T (K)

q (g cm3)

0.25

293.15 308.15 313.15 318.15 333.15 353.15

0.8948 0.8821 0.8778 0.8736 0.8606 0.8431

0.34

293.14 308.15 313.15 318.15 333.15 353.15

0.9055 0.8932 0.8891 0.8849 0.8724 0.8554

0.50

293.15 308.15 313.14 318.15 333.15 353.15

0.9244 0.9130 0.9091 0.9051 0.8934 0.8776

4. Results and discussion The hydrogen solubility in hydrocracked vacuum gas oil (Oil1) and mixtures consisting of modified vacuum residue from Urals crude (Oil2) and toluene were measured with the continuous flow apparatus [25,26]. From the vacuum residue and toluene, three solutions were prepared: mass fractions of Oil2 were 0.25, 0.34 and 0.50. The measurements were conducted in the pressure range

Standard uncertainties u are u(q) = ±0.0002 g cm3, u(T) = ±0.001 K.

M. Saajanlehto et al. / Fuel 137 (2014) 393–404

1.00

12

0.95

10

0.90

8

P/MPa

ρ/g cm-3

398

0.85

6 4

0.80

2

0.75

0

0.70 280

300

320

340

360

0

0.2

T/K Fig. 3. Measured and predicted densities for Oil2 + toluene systems: the measured mass fraction of Oil2 0.25 (), 0.34 (j) and 0.50 (N) and the predictions with the heavy oil characterization method for PC-SAFT [23,28] (—).

deviation (RAD) (given in Eq. (10)) for density predictions were 0.009 g cm3 and 1 %, respectively.

AAD ¼

N   1X li;meas  li;calc  N i¼1

ð9Þ

RAD ¼

  N  li;meas  li;calc  1X N i¼1 li;meas

ð10Þ

where N is number of the measured data points, l is property, density (g cm3) or pressure (MPa), and subscript ‘‘meas’’ denotes measured value and ‘‘calc’’ calculated value. 4.2. Measurements of hydrogen solubility in heavy oil systems Hydrogen solubility in Oil1 was measured with the continuous flow apparatus. The measurements were conducted at temperatures of 498 K, 547 K and 596 K and in the pressure range of 2–10 MPa. The data points are presented in Table 3 with the uncertainties. The uncertainty of hydrogen solubility (u(SH2)) was estimated to be ±1 %. Feeding the Oil1 sample into the apparatus was challenging due to the high viscosity and low vapor pressure of the sample. Another challenge was encountered when oil was pumped through the apparatus. Oil1 blocked the l-mixer and the mixer had to be

0.4

0.6

SH2/mol(H2) kg-1(liquid) Fig. 4. Hydrogen solubility in Oil1: measured data points at 498 K ( ), 547 K ( ), 596 K ( ).

removed from the system and replaced with a T-piece. The camera was used to confirm that mixing was appropriate after installing the T-piece by monitoring visually that any unexpected stripes were not appearing in the fluid. Fig. 4 presents the measured hydrogen solubilities in Oil1. The solubility of hydrogen in Oil1 increased as the temperature and pressure were increased. This behavior can be considered as typical for systems containing hydrogen. A linear behavior of increasing hydrogen solubility was observed with increasing pressure. For comparison, Fig. 5 presents hydrogen solubility in Oil1 (at 498 K and 547 K) as well in HVGO (at 523 K) [2] and HCGO (at 523 K) [6]. HVGO (boiling point range: 547–868 K, density: 0.973 at 293 K, CH: 7.8 [2]) and HCGO (boiling point range: 543–791 K, density: 0.9691 at 293 K, CH: 7.9 [6]) has similar properties with each other as well as with Oil1 (boiling point range: 508–800 K, estimated density: 0.914 at 293 K, CH: 7.2 [28]) in some extent. As can be seen from the figure, hydrogen solubility in Oil1 corresponds well with hydrogen solubility in HVGO whereas clearly more hydrogen is dissolved in HCGO than in Oil1 or HVGO according to the measurements. With the current apparatus set-up, measuring hydrogen solubility in Oil2 was only possible by adding solvent, toluene, due to

12 10

Table 3 Hydrogen solubility (SH2) in Oil1 at temperature (T) and pressure (P) with uncertainty of hydrogen solubility (u(SH2)). P (MPa)

SH2 (mol(H2) kg(liquid)1)

u(SH2)

497.6 497.5 497.5 498.1 497.4 547.2 547.1 546.9 546.9 546.9 596.4 596.4 596.3

2.04 4.02 6.05 8.04 10.06 2.05 4.04 6.06 8.07 10.06 5.04 7.58 10.07

0.082 0.170 0.250 0.345 0.436 0.103 0.195 0.307 0.410 0.528 0.295 0.450 0.609

±0.001 ±0.001 ±0.002 ±0.003 ±0.004 ±0.001 ±0.002 ±0.003 ±0.003 ±0.004 ±0.002 ±0.004 ±0.005

Standard uncertainties u are u(T) = ±0.2 K, u(P) = ±0.02 MPa.

P/MPa

T (K)

8 6 4 2 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

SH2/mol(H2) kg(oil)-1 Fig. 5. Hydrogen solubility in Oil1 at 498 K () and at 547 K (j), in HVGO at 523 K (—) (calculated with the given hydrogen solubility coefficient) [2] and in HCGO at 523 K ( ) [6].

M. Saajanlehto et al. / Fuel 137 (2014) 393–404 Table 4 Hydrogen solubility (SH2) in Oil2 + toluene systems at temperature (T) and pressure (P) with uncertainty of hydrogen solubility (u(SH2)). wOil2

T (K)

P (MPa)

SH2 (mol(H2) kg(liquid)1)

u(SH2)

0.25

497.4 497.4 497.4

5.04 7.52 10.00

0.292 0.501 0.704

±0.002 ±0.004 ±0.006

0.26

547.0 547.0 546.9

5.04 7.52 10.00

0.275 0.547 0.798

±0.002 ±0.005 ±0.007

0.34

497.6 497.6 497.5 547.1 547.0 547.0 571.8 571.7 571.6

5.04 7.52 10.00 5.04 7.53 10.01 5.05 7.53 10.01

0.262 0.430 0.630 0.254 0.478 0.711 0.212 0.463 0.727

±0.002 ±0.004 ±0.005 ±0.002 ±0.004 ±0.006 ±0.002 ±0.004 ±0.006

0.50

497.6 497.6 497.6 497.6 547.1 547.0 547.0 547.0 571.8 571.8 571.7 596.4 596.3 596.3 596.2

4.04 6.04 8.02 10.00 4.05 6.04 8.03 10.01 6.03 8.03 10.01 6.04 8.03 10.01 11.01

0.167 0.281 0.406 0.513 0.140 0.282 0.421 0.572 0.257 0.421 0.586 0.220 0.405 0.571 0.665

±0.001 ±0.002 ±0.003 ±0.004 ±0.001 ±0.002 ±0.003 ±0.005 ±0.002 ±0.003 ±0.005 ±0.002 ±0.003 ±0.005 ±0.005

Standard uncertainties u are u(T) = ±0.2 K, u(P) = ±0.02 MPa.

the very high viscosity of Oil2 at room temperature. Hydrogen solubility was measured in three mixtures consisting of Oil2 and toluene (the mass fractions of Oil2 were 0.25, 0.34 and 0.50). The experiments were performed in the temperature range of 497– 596 K and in the pressure range of 4–11 MPa. Table 4 presents the measured hydrogen solubilities for all three systems with the

399

uncertainties. The uncertainty of hydrogen solubility was estimated to be ±1%. During the experiments, it was visually observed that as the temperature was increased, more light was transmitted through the fluid. As a result, the picture from the equilibrium cell seemed clearer. For the mixture of 0.50 mass fraction of Oil2, the measurements were only possible at temperatures higher than 497 K with the current illumination arrangement. Fig. 6 illustrates this finding. In addition, increasing the amount of Oil2 in the fluid increased the absorbance of the light used for illumination at a constant temperature. Fig. 7a–c show the measured hydrogen solubilities in Oil2 + toluene systems. Increasing the partial pressure of hydrogen improved the hydrogen solubility linearly in all systems and the greater the temperature was the better the hydrogen solubility was. Fig. 8 compares hydrogen solubility in three mixtures of Oil2 + toluene at 548 K. As can be seen, hydrogen solubility decreased as the amount of Oil2 is increased in the liquid. It should be noticed that the amount of toluene in the fluid had great impact on the hydrogen solubility. On the other hand, due to this great impact, the hydrogen solubility in Oil2 could be predicted or extrapolated with appropriate models. 4.3. Modeling hydrogen solubility in heavy oil systems The hydrogen solubility was predicted in Oil1 and Oil2 + toluene systems as well in LVGO, HVGO [2], HCGO [6] and Athabasca bitumen (AB) [5] with four models. The selected models were PC-SAFT [23], Peng–Robinson [27], a correlation suggested by Shaw [19] and a method proposed by Riazi and Roomi [3]. These models were chosen due to their demonstrated good capability to predict hydrogen solubility in hydrocarbons and predictive nature. In order to conduct the predictions with PC-SAFT and Peng– Robinson, heavy oils were characterized with the SCN type characterization procedures presented in Chapter 3 [28–30]. The criterion for selecting the heavy oils listed above was the availability of distillation curve or distillation range in the paper [2,5,6]. This was necessary since the distillation curve or mean boiling point

Fig. 6. Pictures from video of H2 + Oil2 + toluene system (the mass fraction of Oil2: 0.50) at temperatures 596 K, 547 K and 478 K.

Fig. 7. Measured data points for the hydrogen solubility in Oil2 + toluene systems: (a) 0.25, (b) 0.34, (c) 0.50 for the mass fraction of Oil2 at 498 K ( ), 547 K ( ), 572 K (N) and 596 K ( ).

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M. Saajanlehto et al. / Fuel 137 (2014) 393–404

12 10

P/MPa

8 6 4

572 K 2

547 K 0

498 K 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

SH2/mol(H2) kg(liquid)-1 Fig. 9. Measurements and predictions for hydrogen solubility in Oil2 + toluene systems: the measurements for 0.34 mass fraction of Oil2 at 498 K ( ), 547 K ( ) and 572 K ( ), the prediction with PC-SAFT [23] (—) and the prediction with Peng– Robinson [27] (- - -).

Fig. 8. Measured data points of hydrogen solubility in Oil2 + toluene systems at 547 K where the mass fractions of Oil2 are 0.25 (), 0.34 ( ), 0.50 (d).

was needed as an input parameter in the models applied in this examination. For every modeling case and system, the average absolute (AAD) (Eq. (9)) and the relative average pressure deviation (RAD) (Eq. (10)) were calculated and these deviations are presented in Table 5. The deviations were calculated between the predicted values and values either measured in this work or presented in the studies [5,6]. For H2 + LVGO and H2 + HVGO systems, hydrogen solubility was only given in the form of hydrogen solubility coefficient at each temperature [2]. Thus, the comparison was conducted against this data. Table 5 also presents overall deviations for each model. The overall RADs were also calculated without contribution of H2 + HCGO system due to the deviations for this system differed from the common line. PC-SAFT with the heavy oil characterization method [23,28] predicted the hydrogen solubility in heavy oil systems well in general, especially in Oil1 and Oil2 + toluene systems. Slightly higher deviations for LVGO, HVGO and AB might be caused from the incomplete distillation curve data presented for these heavy oils in the papers [2,5]. For H2 + HCGO system, the deviations were

large but as presented in Fig. 5 the measured data for H2 + HCGO system differs from the H2 + Oil1 and H2 + HVGO systems. Overall, PC-SAFT with the applied characterization underestimated the hydrogen solubility in heavy oil systems. To correct this underestimate, the binary interaction parameter for every hydrogen and pseudocomponent/toluene pair was set to 0.1. This action enhanced the hydrogen solubility predictions for every system except for the H2 + HVGO system. Peng–Robinson with the SCN method characterization [27,29,30] described the hydrogen solubility in studied heavy oil systems inaccurately. Peng–Robinson clearly overestimated the hydrogen solubility in heavy oil systems. Binary interaction parameter was regressed but the results indicated relatively large binary interaction parameter, approximately 0.5. Fig. 9 presents measured and predicted values for H2 + Oil2 + toluene system (the mass fraction of Oil2: 0.34) with PC-SAFT (kij = 0) and Peng–Robinson. As can be seen, PC-SAFT describes the hydrogen solubility in Oil2 + toluene system well whereas Peng–Robinson overestimates the hydrogen solubility significantly.

Table 5 Average absolute (AAD) and relative average pressure (P) deviation (RAD) for hydrogen solubility predictions with PC-SAFT, Peng–Robinson, the correlation by Shaw and the method by Riazi and Roomi.

a b C d e f g

System

Trange (K)

Prange (MPa)

PC-SAFT [23]a

PC-SAFT [23]a (kij = 0.1c)

Peng–Robinson [27]b

Correlation by Shaw [19]

Method by Riazi and Roomi [3]

RADd (%)

AADe (kPa)

RADd (%)

AADe (kPa)

RADd (%)

AADe (kPa)

RADd (%)

AADe (kPa)

RADd (%)

AADe (kPa)

H2 + Oil1

497–596

2.0–10.1

6

422

4

183

26

1623

13

882

6

206

H2+Oil2+toluene 0.25f 0.34f 0.50f H2 + LVGO [2] H2 + HVGO [2] H2 + HCGO [6] H2 + AB [5] Overall

497–547 498–572 498–596 353–653 353–523 423–623 323–573

5.0–10.0 5.0–10.0 4.0–11.0 1.0–10.0 1.0–10.0 1.8–10.0 0.3–24.8

8 7 5 15 14 42 19 19 (13g)

658 625 481 651 738 2205 1593 1251

2 3 3 10 19 31 8 12 (7g)

187 267 197 386 994 1629 566 669

33 34 37 28 38 13 25 26 (29g)

2501 2661 2910 1582 1995 695 2575 2055

17 25 74 15 31 (15g)

861 1272 4103 1524 2075

14 21 23

735 1192 1103

17 (12g)

836

Combined with the heavy oil characterization method [28]. Combined with the SCN characterization [29,30]. The recommended PC-SAFT binary interaction parameter (kij) for hydrogen + component pairs. Relative average deviation (RAD) as given in Eq. (10). Average absolute deviation (AAD) as given in Eq. (9). Mass fraction of Oil2. RADs without H2 + HCGO system.

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M. Saajanlehto et al. / Fuel 137 (2014) 393–404

498 K 547 K

596 K

Fig. 10. Measurements and predictions for hydrogen solubility in Oil1: the measured data points at 498 K ( ), 547 K ( ), 596 K ( ), the prediction with PCSAFT [23] (—) and the prediction with the correlation by Shaw [19] (- - -).

12 10

P/MPa

8 6 4 2 0 0.0

posed by Riazi and Roomi due to this method also only predicts the partial pressure of hydrogen and only the total pressure of the system was measured. Thus, it was impossible to conduct the comparison as discussed above. In addition, hydrogen solubility in AB was not predicted with the method by Riazi and Roomi. The method gave unreasonable large activity coefficients (even hundreds) with the given molar mass of AB (522 g mol1 [5]) and due to this fact the predicted pressures were huge. To conclude, the method is simple and predictive for paraffinic systems but for system containing large amount of aromatics, the method requires the parameter optimization and is not purely predictive. In addition, the method needs to be modified in order to predict hydrogen solubility in heavy oils with high molar mass. As conclusion, PC-SAFT and the correlation by Shaw predicted the hydrogen solubility in studied systems equally well if the H2 + HCGO system was left out from the examination. PC-SAFT could describe the systems even more accurately when the binary interaction parameter was set to 0.1. The method by Riazi and Roomi could estimate the hydrogen solubilities well only after parameter regression. Peng–Robinson was clearly the most inaccurate model of these four. As PC-SAFT and the correlation by Shaw produced the most accurate predictions, the hydrogen solubility in Oil2 was predicted with these models. Fig. 11 presents measured data points for H2 + Oil2 + toluene at 548 K (mass fractions of Oil2 0.25, 0.24 and 0.5) as well as the predictions for H2 + Oil2 + toluene system (mass fraction range of Oil2: 0.25–1) with PC-SAFT (kij = 0) and predictions for H2 + Oil2 system with the correlation by Shaw. All models studied in this work have their advantages and disadvantages. The equations of state are simple to use, phase behavior of multicomponent systems can be predicted easily, and other properties, such as densities, can be obtained simultaneously. This Table A1 Distillation curves for Oil1 and Oil2 obtained from the work by Saajanlehto and Alopaeus [28].

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

SH2/mol(H2) kg(liquid)-1 Fig. 11. Measurements and predictions for hydrogen solubility in Oil2 + toluene systems: the measurements at 547 K where the mass fractions of Oil2 are 0.25 (), 0.34 ( ), 0.50 (d), the prediction with PC-SAFT [23] (—), and the prediction with the correlation by Shaw [19] (- - -).

The correlation by Shaw [19] predicted the hydrogen solubility in the fluids well except in HCGO. The density difference between the lightest and the heaviest component in the oil (required in the model) was estimated to be 0.1 g cm3 for every studied system. Hydrogen solubility in Oil2 + toluene systems was not predicted with the correlation by Shaw due to the model predicts the partial pressure of hydrogen and only the total pressure of the H2 + Oil2 + toluene system was measured in this work. Thus, the comparison could not be performed without knowledge of partial pressure of hydrogen in this system. For the other systems, total pressure of the system could be estimated to be equal to partial pressure of hydrogen because the oils are heavy and in practice, vapor pressure of heavy oils is negligible. However, vapor pressure of toluene is considerable in the conditions where the hydrogen solubility measurements were conducted. Fig. 10 compares measurements and predictions for H2 + Oil1 system with PC-SAFT (kij = 0) and the correlation by Shaw. Both models underestimated the hydrogen solubility but the prediction with PC-SAFT was slightly closer to the measured values than the prediction with the correlation by Shaw. The method by Riazi and Roomi [3] described the hydrogen solubility in heavy oil systems well after parameter regression L (reduced fugacity of pure hypothetical hydrogen, f r ). The H2 + Oil2 + toluene systems was not modeled with this method pro-

a B

wt%

Tb (K)

wt%

Tb (K)

wt%

Tb (K)

wt%

Tb (K)

wt%

Tb (K)

Oil1a 0.5 2 4 5 8 10 12 14 16 18 20

508 540 560 567 583 591 598 604 611 615 620

22 24 26 28 30 32 34 36 38 40

625 629 634 638 641 645 649 652 656 659

42 44 46 48 50 52 54 56 58 60

662 665 669 672 675 678 681 684 687 690

62 64 66 68 70 72 74 76 78 80

693 696 700 703 707 710 714 718 722 726

82 84 86 88 90 92 94 95 98 99.5

730 735 740 745 751 757 764 768 784 800

Oil2b 0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

713 734 753 764 772 778 784 788 793 796 800 803 806 809 811 814 816 819 821 823

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

826 828 830 832 834 836 838 840 842 843 845 847 849 851 853 855 856 858 860

39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

862 864 866 867 869 871 873 875 877 879 881 883 885 887 889 891 893 896 898

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

900 902 905 907 909 912 914 916 919 921 924 927 929 932 935 938 941 944 947

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 94.6

950 954 957 961 965 968 971 975 978 982 985 989 993 996 1001 1004 1009 1014 1017

Measurement method: ASTMD2887. Measurement method: simulated distillation HT750.

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M. Saajanlehto et al. / Fuel 137 (2014) 393–404

Table A2 Mass fractions of SARA, densities (q) and elementary analysis (C, H, N and S) for Oil1 and Oil2 obtained from the work by Saajanlehto and Alopaeus [28]. SARAa (wt%)

Oil1

Oil2

Saturates Aromatics Resins Asphaltenes

46.2 46.1 6.3 <0.1

14.1 40.2 42.8 <0.1

q (kg m3)

T (K) Oil1 298b 313c 333c 348c 353c 363c

a b c d e

Oil2

900.7 887.6

958.2 949.2

874.6 939.8

Elementary analysis

Oil1

Oil2

Cd (wt%) Hd (wt%) Nd (wt%) Se (wt%)

87.3 12.1 0.3 0.3

85.3 11.1 0.4 2.5

Measurement Measurement Measurement Measurement Measurement

method: method: method: method: method:

ASTMD2007M. EN15326. ENISO12185. ASTMD5291. ENISO8754.

study also demonstrated that PC-SAFT with the used characterization have potential for modeling hydrogen solubility in heavy oils. Disadvantage of utilizing equations of state is that obtaining the parameters for heavy oil is challenging. For proper application of equations of state, careful oil characterization is required. The correlation by Shaw is a simple correlation and quick to apply. However, this correlation does not provide any other information of the studied system besides the hydrogen solubility in the solvent. 5. Conclusion Reliable hydrogen solubility measurements in heavy oil are a key factor in developing models for hydroprocesses and they are needed for designing these processes. It is essential that the models describe the hydrogen solubility accurately. The accuracy of models can be evaluated by comparing model predictions against measured data. However, the hydrogen solubility measurements are challenging and only a very limited amount of measurements of hydrogen solubility in heavy oils were found from the literature. This paper presents a study of hydrogen solubility in heavy oil systems. The hydrogen solubility was measured in hydrocracked vacuum gas oil (Oil1) and in mixtures consisting of modified vac-

uum residue (Oil2) and toluene with the continuous flow apparatus. The measurements of H2 + Oil1 system was conducted on the temperature range of 498–596 K and in the pressure range of 2– 10 MPa. The experiments demonstrated that increasing the temperature and the pressure increased the hydrogen solubility in Oil1. The hydrogen solubility was measured in mixtures consisted of modified vacuum residue and toluene: the mass fractions of Oil2 were 0.25, 0.34 and 0.50. These experiments were performed at temperatures between 497–596 K and pressures between 4 and 11 MPa. Increasing the partial pressure of hydrogen and the temperature improved the hydrogen solubility in Oil2 + toluene systems. In addition, an important finding was that the amount of toluene in the fluid had great impact on the hydrogen solubility. The uncertainty for hydrogen solubility was estimated to be ±1 % and for the set-up of the pressure measurement ±0.02 MPa and the temperature measurement ±0.2 K. In addition, densities for Oil2 + toluene systems were measured in order to be able to determinate the mass of liquid fed to the apparatus. In the modeling part of this work, hydrogen solubility was predicted in Oil1 and Oil2 + toluene systems as well in LVGO, HVGO [2], HCGO [6] and AB [5] with four models. The selected models were PC-SAFT [23], Peng–Robinson [27], a correlation proposed by Shaw [19] and a method suggested by Riazi and Roomi [3]. The heavy oils were characterized with single carbon number type characterization method in order to conduct the calculations with the equations of state. PC-SAFT with the applied characterization and the correlation by Shaw were found to predict the hydrogen solubility in studied system most accurately. The method by Riazi and Roomi could describe the systems well only after parameter regression and Peng–Robinson clearly overestimated the hydrogen solubility in heavy oils. PC-SAFT with the used characterization and the correlation by Shaw can be applied for describing phase behavior of H2 + heavy oil systems. Since PC-SAFT has not been applied for modeling hydrogen solubility in heavy oils earlier, one interesting finding of this study was that PC-SAFT can predict the hydrogen solubility accurately and more precise than Peng–Robinson. Acknowledgments The authors acknowledge Dr. Olli Visuri for the technical guidance with the camera system. Meri Saajanlehto acknowledges Fortum Foundation for the financial support, and Petri Uusi-Kyyny acknowledges Academy of Finland for financial support.

Appendix A See Tables A1 and A2.

Table B1 Pseudocomponent composition of heavy oils with the heavy oil characterization method for PC-SAFT. Tb (K)

Heavy oil Oil1 [28] wS

473 523 573 623 673 723 773 823 873 923 973 1023

0.003 0.036 0.048 0.049 0.029 0.015 0.008

wA 0.006 0.086 0.132 0.159 0.109 0.071 0.048

Oil2 [28] wP 0.002 0.024 0.040 0.052 0.038 0.026 0.019

wS

0.001 0.013 0.019 0.019 0.010 0.003 0.000

wA

0.004 0.061 0.114 0.151 0.129 0.089 0.107

LVGO wP

0.001 0.023 0.045 0.063 0.056 0.041 0.050

HVGO

wS

wA

wP

0.015 0.091 0.077 0.051 0.005 0.007

0.028 0.193 0.185 0.140 0.017 0.027

0.006 0.049 0.052 0.043 0.006 0.009

wS 0.001 0.038 0.086 0.034 0.032 0.004 0.004 0.000

wA 0.001 0.091 0.239 0.110 0.122 0.017 0.025 0.002

HCGO wP 0.000 0.025 0.073 0.036 0.043 0.006 0.010 0.001

wS

0.037 0.098 0.045 0.020 0.005

wA

0.090 0.271 0.146 0.075 0.022

AB wP

0.025 0.083 0.048 0.026 0.008

wS

wA

wP

0.002 0.012 0.012 0.017 0.015 0.016 0.012 0.011 0.006 0.005 0.002 0.000

0.003 0.025 0.029 0.047 0.047 0.061 0.055 0.063 0.052 0.057 0.043 0.046

0.001 0.006 0.008 0.014 0.015 0.021 0.020 0.025 0.022 0.025 0.019 0.022

wAsp

0.165

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M. Saajanlehto et al. / Fuel 137 (2014) 393–404 Table B2 Pseudocomponent composition of heavy oils with the single carbon number type characterization method for Peng–Robinson. Heavy oil Oil1

Oil2

LVGO

HVGO

HCGO

AB

Tb (K)

w

Tb (K)

w

Tb (K)

w

Tb (K)

w

Tb (K)

w

Tb (K)

w

Tb (K)

w

521 538 555 570 585 599 612 625 638 649 661 672 682 692 702 711 720 729 737 745 753 761 768 775 782 789 795

0.009 0.021 0.032 0.042 0.050 0.057 0.061 0.063 0.063 0.062 0.060 0.057 0.053 0.049 0.045 0.041 0.037 0.033 0.029 0.026 0.023 0.020 0.017 0.016 0.013 0.012 0.010

711 720 729 737 745 753 761 768 775 782 789 795 801 807 819 830 840 850 859 868 876 884 892 899 906 912 918 924 933 940 948 955 961 967 974 981 989 996 1003 1008 1014 1021

0.001 0.003 0.004 0.006 0.008 0.010 0.012 0.014 0.015 0.017 0.018 0.019 0.020 0.021 0.066 0.025 0.067 0.025 0.066 0.022 0.062 0.018 0.058 0.013 0.053 0.009 0.049 0.005 0.068 0.005 0.044 0.006 0.038 0.001 0.044 0.001 0.032 0.001 0.026 0.002 0.012 0.012

503 521 538 555 570 585 599 612 625 638 649 661 672 682 692 702 711 720 729

0.201 0.014 0.197 0.023 0.190 0.004 0.149 0.007 0.094 0.007 0.056 0.004 0.026 0.002 0.014 0.003 0.006 0.000 0.004

555 570 585 599 612 625 638 649 661 672 682 692 702 711 720 729 737 745 753 761 768 775 782 789 795 801 807 819 830 840 850 859

0.006 0.013 0.024 0.034 0.046 0.054 0.062 0.066 0.070 0.069 0.068 0.064 0.061 0.055 0.050 0.043 0.038 0.032 0.028 0.022 0.020 0.015 0.013 0.010 0.009 0.006 0.006 0.010 0.001 0.004 0.002 0.001

555 570 585 599 612 625 638 649 661 672 682 692 702 711 720 729 737 745 753 761 768 775 782 789

0.043 0.045 0.086 0.078 0.105 0.084 0.101 0.072 0.084 0.052 0.063 0.033 0.046 0.017 0.032 0.006 0.014 0.016 0.004 0.009 0.000 0.006 0.001 0.003

503 521 538 555 570 585 599 612 625 638 649 661 672 682 692 702 711 720 729 737 745 753 761 768 775 782 789 795 801 807

0.022 0.010 0.018 0.013 0.020 0.015 0.022 0.016 0.022 0.016 0.022 0.016 0.022 0.015 0.021 0.014 0.020 0.013 0.019 0.013 0.018 0.012 0.018 0.011 0.017 0.010 0.016 0.009 0.015 0.008

819 830 840 850 859 868 876 884 892 899 906 912 918 924 933 940 948 955 961 967 974 981 989 996 1003 1008 1014 1021 Asp

0.036 0.005 0.033 0.003 0.031 0.001 0.018 0.022 0.005 0.020 0.003 0.019 0.002 0.017 0.010 0.015 0.008 0.013 0.006 0.012 0.010 0.010 0.012 0.007 0.010 0.005 0.009 0.011 0.165

Appendix B See Tables B1 and B2.

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