ARTICLE pubs.acs.org/EF
Prediction of Sulfur Content, API Gravity, and Viscosity Using a Continuous Mixture Kinetic Model for Maya Crude Oil Hydrocracking in a Slurry-Phase Reactor Hector J. Martinez-Grimaldo,† Juan C. Chavarria-Hernandez,‡ Jorge Ramirez,*,† Rogelio Cuevas,† and Hugo Ortiz-Moreno† †
Unidad de Investigacion en Catalisis (UNICAT), Facultad de Química, Universidad Nacional Autonoma de Mexico, Mexico Distrito Federal 04510, Mexico ‡ Unidad de Energía Renovable, Centro de Investigacion Científica de Yucatan, Calle 43 No. 130, Colonia Chuburna de Hidalgo, Merida, Yucatan, CP 97200, Mexico ABSTRACT: A continuous mixture kinetic model was applied to describe the hydrocracking reactions of Maya crude oil in a slurryphase reactor. Besides the prediction of simulated distillation curves, complementary models were developed to predict American Petroleum Institute (API) gravity, viscosity, and total sulfur content as the reaction proceeds. Experiments were carried out in a batch-type reactor under 800 psig of hydrogen and 400 °C at several reaction times. Powder ammonium heptamolybdate (1000 ppm Mo) was added and activated in situ. Vacuum residue (VR) conversion reached 88 and 96% after 7.5 and 24 h of reaction, respectively. The formation of liquid products (bp < 538 °C) was maximum and fairly constant (6566 wt %) for VR conversions from 37 to 88%. Feed and liquid reaction products were characterized by thermogravimetric analysis (TGA). Total sulfur, viscosity, and API gravity were also measured. The mathematical model accurately describes TGA distillation curves for VR conversions up to 88%, and the developed models for the calculation of sulfur content, viscosity, and API gravity predict with good accuracy the values of these properties.
1. INTRODUCTION Because of the increasing need of processing heavy petroleum, several efforts are being made to efficiently transform this type of feedstocks into lighter and more valuable products.1,2 The use of slurry-phase technology for the hydrocracking of heavy feedstocks is a strategy that is gaining more attention in recent years,24 because of the favorable characteristics of this technology for the processing of heavy feeds with large amounts of heteroatoms and coke precursors. In the slurry-phase technology, either a bulk solid powder or homogeneously dispersed catalysts are employed, favoring an effective contact between the catalyst and the reactive species. Solid powder catalysts are mainly based on Mo, Fe, Ni, or V precursor salts or oxides, while homogeneous dispersed catalysts, divided into oil-soluble and water-soluble, are generally organometallic compounds, such as naphthenates or water-soluble salts, respectively. These precursors are activated in situ to produce the active form of the catalyst, generally a metal sulfide. In general, Mo-based catalysts have been found more active.5,6 The breakdown of molecules in slurry-phase reactors mainly proceeds through thermal cracking.7 Therefore, the role of the catalyst is to hydrogenate aromatic rings and olefins to enhance cracking and hydrotreating reactions [hydrodesulfurization (HDS), hydrodenitrogenation (HDN), hydrodemetallization (HDM), etc.] while avoiding coke formation. Typical operating conditions for slurryphase hydrocracking are 400460 °C, 1020 MPa, and liquid hourly space velocity (LHSV) of 0.52.0 h1. Single pass conversions from 70 to 85% have been reported,2 while conversions higher than 90% are reported for several technologies.3 r 2011 American Chemical Society
Kinetic modeling of the hydrocracking of heavy oils is a complex task that has experienced significant advances in the last few years because of the improvements in analytical techniques and the availability of more powerful computers. Kinetic models based on the theory of continuous mixtures have been recently developed and applied for the simulation of the hydrocracking process. Laxminarasimhan et al.8 presented the basis for the application of the continuous mixture approach to hydrocracking of heavy petroleum fractions. More recently, Elizalde et al.9 simulated the hydrocracking of Maya crude oil in fixed-bed reactors, including the effect of the temperature in their model. In this work, the continuous mixture approach was applied to simulate the hydrocracking of Maya crude oil in a batch slurry-phase reactor up to vacuum residue (VR) conversions of about 90%. A set of equations for the estimation of American Petroleum Institute (API) gravity, viscosity, and total sulfur content was proposed and coupled to the main kinetic model. To our knowledge, this is the first time that API gravity and viscosity are predicted using the continuous mixture approach during the hydrocracking of heavy oil or petroleum fractions. Finally, the results of the model were compared to the experimental data obtained at different contact times.
2. EXPERIMENTAL SECTION The experiments were carried out in a batch slurry-phase reactor and can be described in two stages: (1) Stage 1: pretreatment or catalyst Received: April 15, 2011 Revised: June 9, 2011 Published: June 20, 2011 3605
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activation. In this stage, the reactor was charged with 143 mL of Maya crude oil and ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor, pressurized with 600 psig of hydrogen, and heated to 350 °C. Thereafter, the temperature was kept constant (at 350 °C) for 2 h. After that, the system was allowed to cool at room temperature. During this stage, a VR conversion of 9% took place. (2) Stage 2: the reactor was pressurized with 800 psig of hydrogen and heated to 400 °C. Thereafter, the reaction temperature was kept constant (at 400 °C) for the desired reaction time (1, 2, 3, 4, 7.5, 11.5, 17, and 24 h). A method based on thermogravimetric analysis (TGA) was used to obtain the distillation curve of feed and hydrocracking liquid products. The experiments were conducted in a SDT 2960 TA Instruments analyzer, using nitrogen as a carrier gas (100 mL/min). Because of the sweeping action of the carrier gas, evaporation in the TGA pan takes place against virtually zero vapor pressure of the evaporating species; therefore, the boiling points must be corrected. For this, a calibration curve was built with the boiling points of pure components (decane, 174.1 °C; naphthalene, 218 °C; fluorene, 298 °C; 4,6-DMDBT, 365 °C, pyrene, 393 °C; triphenylbenzene, 460 °C; n-hexatriacontene, 499 °C; and n-tetracontane, 522 °C). No solvent was used, and the samples were heated from 30 to 450 °C at 4 °C/min. API gravity, total sulfur, and viscosity analysis were also performed for the feedstock and the liquid reaction products. Determination of density at 15.5 °C for the API gravity calculation was performed using a pycnometer. The total sulfur content was obtained by means of wavelength-dispersive X-ray fluorescence. Viscosity of liquid reaction products was measured with an Ostwald viscometer, while viscosity of Maya crude oil before and after pretreatment was obtained with a Brookfield viscometer (DV-2 + RV version 5, 28 spindles, 120 rpm). Liquid and solid products were separated and weighted, while the mass of gas produced was determined by material balance. Detailed explanation about the experimental determinations can be found elsewhere.10
in which kmax is the reactivity coefficient of the species with the highest TBP and R is a model parameter. Calculation of the concentrations of species for the generation of distillation curves requires the solution of the following Volterra-type integrodifferential equation: Z kmax ∂cðk, tÞ pðk, KÞKcðK, tÞDðKÞdK ð3Þ ¼ kcðk, tÞ þ ∂t k In eq 3, c(k,t) represents the concentration of species with reactivity k, K is the reactivity of species with a higher boiling point, and t is the reaction time. The first term on the right-hand side of this equation accounts for the disappearance of species with reactivity k because of cracking reactions, while the integral term accounts for the formation of the same species because of the cracking of species with higher boiling points. p(k,K) is a probability density function given by eqs 4 and 5 and determines the probability that species with reactivity K form species with reactivity k. D(k) is the Jacobian given by eq 6, which transforms the discrete coordinate i (associated with the ith species) into the continuous coordinate k, associated with species having concentration c(k,t). N in eq 6 is the total number of species in the mixture. h 1 expð½fðk=KÞa0 0:5g=a1 2 Þ pðk, KÞ ¼ pffiffiffiffiffiffi 2πSðKÞ k expðf0:5=a1 g2 Þ þ δ 1 ð4Þ K Z S0 ðKÞ ¼
K
pðk, KÞDðkÞdk
ð5Þ
0
3. KINETIC MODEL The kinetic model applied in this work is based on the continuous mixture approach, whose theoretical basis can be reviewed elsewhere.1128 Previous applications of the method2938 include models for cracking and hydrocracking of paraffins and heavy feedstocks.8,9,12,3943 In addition to the continuous mixture kinetic model for the prediction of distillation curves, complementary equations are proposed in this work to describe API gravity, viscosity, and sulfur content in hydrocracking products of heavy feedstocks. 3.1. Estimation of the Distillation Curves. A continuous mixture kinetic model based on the work by Laxminarasimhan et al.8 for the simulation of hydrocracking was applied to describe the hydrocracking of Maya crude oil in a batch slurry-phase reactor. According to the mathematical model, each temperature in the boiling temperature curve is associated with a reactivity coefficient, k. A dimensionless temperature is defined as follows: θ¼
TBP TBPðlÞ TBPðhÞ TBPðlÞ
ð1Þ
where TBP is the boiling temperature in the distillation curve corresponding to θ. TBP(l) and TBP(h) are the lowest and highest boiling temperatures (IBP and EBP) in the distillation curve, respectively. Laxminarasimhan et al.8 proposed eq 2 for the relationship between the dimensionless temperature, θ, and its associated reactivity, k k ¼ θ1=R kmax
ð2Þ
DðkÞ ¼
NR R 1 k kmax R
ð6Þ
To account for the concentration of all species in the complete interval of boiling points, the solution of the integral given by eq 7 is required. This term, referred to as the total concentration, is used for the calculation of distillation curves and will be applied with some modifications in the following subsections for the estimation of sulfur content, API gravity, and viscosity of hydrocracking products. Z kmax cðk, tÞDðkÞdk ð7Þ CðtÞ ¼ 0
The kinetic model given by eqs 17 has five adjustable parameters (kmax, R, δ, a0, and a1). The values of these parameters depend upon the feedstock composition, the reaction conditions, and the catalyst activity. More details about the mathematical formulation of the continuous mixture approach applied to hydrocracking kinetics can be found elsewhere.8 The kinetic model described thus far was developed by Laxminarasimhan et al.8 to predict the evolution of distillation curves as hydrocracking proceeds. In the following three subsections, we propose a set of mathematical expressions for the calculation of sulfur content, API gravity, and viscosity, using the continuous mixture approach. 3.2. Estimation of the Total Sulfur Content. It is possible to estimate the sulfur content in a petroleum fraction defined in terms of the boiling temperature interval (θ,θ + dθ), such that the sulfur species occurring in that fraction have HDS reactivities 3606
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DS(kS) in eq 8 is the Jacobian for the transformation of the discrete coordinate i (associated with the ith species) into the continuous coordinate kS, associated with species having a sulfur concentration s(kS,t). We propose eq 9 to relate the HDS reactivity, kS, to the dimensionless temperature, θ.
in a defined interval (kS,kS + dkS). Using a suitable discrete-tocontinuous transformation and after integration for the whole boiling temperature interval, the total sulfur content can be obtained using the mathematical expression of eq 8, in which s(kS,t) is the sulfur content of species with HDS reactivity kS, while kSL and kSH are the HDS reactivities of the species with the lowest and highest boiling points in the distillation curve, respectively. Z SðtÞ ¼
kSH
sðkS , tÞDS ðkS ÞdkS
kS ¼ kSL expðσθÞ
ð9Þ
Because θ is bounded between 0 and 1, eq 9 implies that the upper bound in the integral in eq 8 is given by eq 10, in which kSL and σ are adjustable parameters of the model.
ð8Þ
kSL
kSH ¼ kSL expðσÞ
ð10Þ
Starting from eq 10, the Jacobian of transformation in eq 8, DS(kS), is given by eq 11. DS ðkS Þ ¼
N σkS
ð11Þ
A kinetic equation for the HDS reactions is required. We propose the following power law kinetic equation: ∂sðkS , tÞ ¼ kS sðkS , tÞn ∂t
ð12Þ
in which n is the order of reaction, which for simplicity was assumed to be a unique value for all of the sulfur species. According to the above, the model that we propose here for the calculation of the total sulfur content has three adjustable parameters, kSL, σ, and n. These parameters depend upon the distribution and type of sulfur species present in the feed. Similar kinetic models can be developed for other reactions, e.g., HDN and HDM.
Figure 1. TGA distillation curves of Maya crude oil and hydrocracking products obtained at several reaction times in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor.
Table 1. Experimental Results for Hydrocracking of Maya Crude Oil in a Batch Slurry-Phase Reactor at 400 °C and 800 psig of H2 (Initial Pressure at 20 °C), using Ammonium Heptamolybdate (1000 ppm Mo) as the Catalyst Precursor reaction time (h)a
Maya
0.0
1.0
2.0
36.74
3.0
4.0
7.5
11.5
17.0
24.0
Conversion % VR conversion
0.00
9.06
% HDS conversion
0.00
4.47
57.03
70.17
% solid
0.00
0.00
1.40
5.50
9.70
% liquid
100.00
95.49
88.32
82.89
77.85
% gas
0.00
4.51
10.28
11.61
12.45
API gravity
19.98
20.51
weight % S
3.50
3.51
34.37
81.06
87.71
91.48
94.58
95.59
45.35
56.78
61.57
67.35
71.95
12.82
14.74
16.36
19.78
22.82
73.73
71.09
66.29
59.94
54.02
13.45
14.17
17.35
20.28
23.16
Weight Percent of Solid, Liquid, and Gas Products
Feed and Product Mixture Properties 21.36
23.96
26.95
2.77
29.01
32.99
33.89
35.51
36.61
2.60
2.13
2.03
1.91
1.82
weight % CR
10.39
9.67
9.25
7.12
5.51
2.97
3.36
2.44
1.44
1.27
viscosity (cP)
719
643
42.11
15.25
8.89
5.44
3.20
2.47
2.11
1.78
IBP177 °C
0.1
0.1
0.12
0.15
0.15
0.2
0.25
0.29
0.32
0.36
heavy naphtha, 177204 °C
0.03
0.04
0.04
0.05
0.07
0.08
0.09
0.1
0.12
0.13
jet fuel, 204274 °C kerosene, 274316 °C
0.09 0.06
0.09 0.06
0.13 0.07
0.14 0.09
0.17 0.1
0.19 0.1
0.22 0.11
0.25 0.1
0.24 0.1
0.24 0.09
Weight Percent in Liquid
a
LGO, 316364 °C
0.07
0.07
0.08
0.1
0.09
0.09
0.1
0.08
0.06
0.06
HGO, 364454 °C
0.13
0.14
0.14
0.14
0.16
0.15
0.11
0.09
0.08
0.05
VGO, 454538 °C
0.11
0.11
0.12
0.12
0.1
0.08
0.05
0.04
0.04
0.04
VR, >538 °C
0.41
0.39
0.3
0.21
0.16
0.11
0.07
0.05
0.04
0.03
After 2 h of catalyst activation. 3607
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Figure 2. Weight fraction of petroleum cuts in Maya crude oil and hydrocracking products obtained at several reaction times in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor.
Figure 3. Experimental yield of hydrocracking liquid products with bp < 538 °C versus the reaction time in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor.
3.3. Estimation of the API Gravity. API gravity can be estimated using a similar approach to that proposed for the calculation of sulfur content. Estimation of API gravity requires defining a probability distribution function, APID(k), that assigns an API gravity value to the species with reactivity k. We propose the following function for the relationship between these two variables:
API D ðkÞ ¼ λAPI eηk
ð13Þ
where λAPI and η are adjustable parameters of the model. In this way, estimation of average API gravity for the whole mixture is given by eq 14. Z kmax API D ðkÞcðk, tÞDðkÞdk ð14Þ APIðtÞ ¼ 0 Z kmax cðk, tÞDðkÞdk
Figure 4. API barrel of products obtained in hydrocracking of Maya crude oil versus the reaction time in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor.
the distribution function of viscosity logarithm, we selected the Laplace-type expression given by eq 15. This equation establishes the relationship between viscosity, μD ln(k), and the reactivity coefficient, k. μD ln ðkÞ ¼ λvis expðωjðk=kmax Þβ 0:5jÞ
λvis, ω, and β in eq 15 are adjustable parameters of the model. Estimation of average viscosity is calculated with eq 16. Z kmax cðk, tÞDðkÞμD ln ðkÞdk ð16Þ ln μðtÞ ¼ 0 Z kmax cðk, tÞDðkÞdk
0
3.4. Estimation of the Viscosity. Estimation of viscosity
follows a similar procedure to the API gravity calculation. For
ð15Þ
0
3.5. Estimation of the Liquid, Solid, and Gas Formations. Because the kinetic model for the prediction of distillation curves only gives the distribution of liquid reaction products, we used 3608
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the following set of empirical equations to estimate the total amount of liquid, solid, and gas formed during the reaction: dL kL ðL LL Þ ¼ dt ð1 þ KL L þ KS S þ KG GÞγ
ð17Þ
dS kL ðL LL Þ ¼ PS dt ð1 þ KL L þ KS S þ KG GÞγ
ð18Þ
dG kL ðL LL Þ ¼ PG dt ð1 þ KL L þ KS S þ KG GÞγ
ð19Þ
In eqs 1719 L is the liquid fraction, including the dispersed solids in it, S is the fraction of sedimented solids, and G is the gas fraction, while kL, KL, KS, KG, PS, PG, and γ are adjustable parameters of the model. Parameters PS and PG have to satisfy the following material balance criteria: PS þ PG ¼ 1
ð20Þ
Figure 5. Weight fraction of CR in products of Maya crude oil hydrocracking versus the reaction time in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor: experimental (b) and calculated (—) data.
3.6. Carbon Residue (CR) Calculation. Figure 1 shows that experimental TGA distillation curves do not reach unity in the y axis. This is because, after heating the sample in the TGA analysis, nondistillable solid remains. This solid, called CR, is modeled by means of eq 21
dCR ¼ kCR CR ξ dt
ð21Þ
in which kCR and ξ are adjustable parameters. The calculation of CR is required for the mathematical model to predict the TGA distillation curves with the behavior that they show in Figure 1
4. RESULTS AND DISCUSSION 4.1. Experimental Results. The experimental determinations for Maya crude oil and the hydrocracking products are summarized in Table 1. VR conversion, defined as the conversion of the liquid fraction with the boiling temperature above 538 °C, was calculated with eq 22
% VR conversionð > 538 °CÞ ¼
MM ð > 538 °CÞ Mð > 538 °CÞ 100 MM ð > 538 °CÞ
ð22Þ
where MM(>538 °C) is the mass of VR in Maya crude oil and M(>538 °C) is the mass of VR in the liquid products. On the other hand, HDS percent conversion was defined according to eq 23, in which STM is the total sulfur content in Maya crude oil and ST is the total sulfur content in the liquid products. % HDS ¼
STM ST 100 STM
ð23Þ
Figure 1 shows the TGA distillation curves corresponding to Maya crude oil and hydrocracking products for reaction times up to 24 h. The curve labeled “0 h” (zero hours) belongs to the oil after two hours of pretreatment or catalyst activation. During the stage of pretreatment, a VR conversion of 9% took place, which explains the separation between the curves labeled “Maya” and “0 h”.
Figure 6. Distillation curves of Maya crude oil and hydrocracking products obtained in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor. Experimental (b, 0, 2, , 9, and 4) and simulated (—) results for reaction times up to 7.5 h.
The flat zone on the right side of the distillation curves in Figure 1 indicates that there is a weight fraction of the sample, which is nondistillable. This fraction is referred to as CR. For higher reaction times, hydrocracking of dispersed solids increases and the amount of CR is smaller. This explains that CR changes from 10.4% for Maya crude oil up to a value of 1.27% after 24 h of reaction. It is evident from Figure 1 that TGA distillation curves and, thus, composition of products change rapidly from 0 to 7.5 h of the reaction (e.g., % VR conversion reached 87.7% at 7.5 h). For higher reaction times, changes in the distillation curves are less pronounced. Figure 2 shows the weight fractions of Maya crude oil and hydrocracking products, lumped in boiling point petroleum cuts. The weight fractions are referred to the mass of Maya crude oil fed to the reactor. As seen in the figure, the production of gasoline and naphtha (IBP204 °C) increases continuously with the reaction time. After 7.5 h of reaction, the weight fraction of this lump was almost twice compared to that of the feed: 24 and 13 wt %, respectively. The weight fraction of middle distillates, kerosene, and jet fuel (bp = 204316 °C) increased from 14 wt % in 3609
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Figure 7. Normalized distillation curves of Maya crude oil and hydrocracking products obtained in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor. Experimental (b, 0, 2, , 9, and 4) and simulated (—) results for reaction times up to 7.5 h.
Figure 8. Weight percent sulfur in Maya crude oil and hydrocracking liquid products versus the reaction time in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor: experimental (b) and calculated (—).
ARTICLE
Figure 10. Viscosity of Maya crude oil and hydrocracking liquid products versus the reaction time in a batch slurry-phase reactor at 400 °C and 800 psig of H2 (initial pressure at 20 °C), using ammonium heptamolybdate (1000 ppm Mo) as the catalyst precursor: experimental (b) and calculated (—).
and VR (bp > 538 °C) decreased continuously with the reaction time, with the diminution being more drastic for the case of VR, as seen in the figure. With regard to the quality of products, it can be seen in Table 1 that API gravity increased from nearly 20 for Maya crude oil to nearly 33 for the hydrocracking products after 7.5 h of reaction. This value of API gravity is comparable to those of light oils. The sulfur content was reduced from 3.5 wt % in Maya crude oil to 1.82 wt % after 24 h of reaction, obtaining a HDS conversion of nearly 72%. Although the experimental results show an improvement in product quality, the yield of liquid products gradually decreased with an increasing reaction time, because of the formation of sedimented solids as well as the generation of gaseous products. However, the formation of liquid (distillable) products (bp < 538 °C) was at a maximum (66 wt %) at 7.5 h of reaction (VR conversion of 87.7%). Indeed, as seen in Figure 3, this variable was almost constant from 2 to 7.5 h of reaction. The yield of liquid products (bp < 538 °C) in Figure 3 was calculated using eq 24 % YLð < 538 °CÞ ¼
Lð < 538 °CÞ 100 MM0
ð24Þ
in which L(538 °C) = mass of VR in liquid products MM(>538 °C) = mass of VR in Maya crude N = total number of species in the mixture n = hydrodesulfurization order rate PG = gas model parameter PL = liquid model parameter p(k,K) = distribution function of species formation S = solid product (wt %) S(t) = total sulfur content of reactants at time t (wt %) ST = total sulfur content (wt %) STM = total sulfur content in Maya crude oil (wt %) S(kS,t) = continuous sulfur content (wt %) TBP = boiling temperature in the distillation curve (°C) TBP(h) = highest possible boiling temperature in the distillation curve (°C) TBP(l) = lowest possible boiling temperature in the distillation curve (°C) t = reaction time (h) XN = normalized distillation fraction X = distillation fraction of the liquid cut R = distillation curve model parameter β = viscosity model parameter γ = liquid, solid, and gas model parameter δ = distillation curve model parameter η = API gravity model parameter θ = normalized temperature λAPI = API gravity model parameter λvis = viscosity model parameter (cP) μ(t) = viscosity at reaction time t (cP) μD ln(k) = distribution function of viscosity logarithm (cP) ξ = carbon residue order rate σ = sulfur content model parameter ω = viscosity model parameter % HDS = hydrodesulfurization conversion % YL(
