Modeling catalyst deactivation during hydrocracking of atmospheric residue by using the continuous kinetic lumping model

Fuel Processing Technology 123 (2014) 114–121

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Modeling catalyst deactivation during hydrocracking of atmospheric residue by using the continuous kinetic lumping model Ignacio Elizalde ⁎, Jorge Ancheyta Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, México 07730 , México Escuela Superior de Ingeniería Química e Industrias Extractivas (ESIQIE), UPALM, Zacatenco, México 07738, México

a r t i c l e

i n f o

Article history: Received 4 September 2012 Received in revised form 21 March 2013 Accepted 8 February 2014 Available online 27 February 2014 Keywords: Residue oil Continuous kinetic model TOS Deactivation

a b s t r a c t The kinetics of the hydrocracking of residue and catalyst deactivation were studied by using the continuous kinetic lumping approach. Catalyst activity decay was represented with an empirical equation. Experimental information was obtained in a continuous stirred tank reactor at liquid-hourly space velocity of 0.5 h−1, three reactor temperatures (380, 400 and 410 °C), 9.8 MPa of pressure, 5000 ft3/bbl of H2-to-oil ratio and 200 h of time on stream. The parameters of the continuous kinetic model showed dependence with time on stream and temperature. Due to the marked changes on catalyst activity during time on stream, it was proposed that some pore blockage occurs apart from catalyst deactivation by site coverage. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The processing of non-conventional crude oils is increasing, and this trend will continue in the next years. Among all the commercially available technologies hydrotreatment and hydrocracking are excellent options to upgrade the heavy petroleum [1,2]. Because heavy oil and residua contain significant amounts of asphaltenes, the main problems associated with their processing are the excessive coke deposit on catalyst at the first hours of time on stream (TOS) and the difficulty for contact of these complex molecules with active sites due to mass transfer limitations [3], which in turn provokes the catalytic deactivation. For longer TOS, metal-bearing species are the main cause of permanent deactivation of catalyst [4–7]. The deposits of coke and metals cause loss of catalytic surface area and decrease of mean pore diameter and volume [8,9]. The effective diffusivity shows stronger correlation with coke content because the more the deposited coke, the more difficult the access to pores in which the chemical transformation is carried out. As a consequence, a decrease in effectiveness factor is observed [10]. Modeling these changes and other aspects of catalyst deactivation during heavy oil processing is not an easy task. Different approaches to model the deactivation in different reactions have appeared in the literature. For instance, Moustafa and Froment [11] have related the

⁎ Corresponding author at: Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, México 07730, México. Tel.: +52 55 9175 8418. E-mail address: [email protected] (I. Elizalde).

http://dx.doi.org/10.1016/j.fuproc.2014.02.006 0378-3820/© 2014 Elsevier B.V. All rights reserved.

loss of catalyst activity to coke deposition on catalyst surface, while others have used the time on stream [12,13]. Recently Jiménez-García et al. [14] have correlated the catalytic deactivation with the effectiveness factor in FCC process. They argue that as coke is deposited on catalyst surface, the smallest molecules present in the feed exhibit the easiest access to catalytic pores, and the contrary behavior is expected for larger ones. That behavior changes as catalyst pore diameter is reduced by effect of coke deposition. Galiasso [15,16] has also found that even for light cycle oil (LCO), rapid loss of activity is observed during hydrocracking, and this change on activity was related to loss of weak acid sites. Similar observations were pointed out by Castaño et al. [17] and Gutiérrez et al. [18], who confirm that some plugging of small catalytic pores together with loss of acid sites are responsible for catalyst deactivation due to the hydrocracking of LCO. Beckman and Froment [19] have developed deactivation models for coke deposition on catalyst surface that proceeds following two mechanisms: site coverage and pore blockage, both limiting the diffusion of reactants to enter into the pore structure. Also, experimental information confirms the fact that under the hydrocracking of liquid hydrocarbons, both site coverage and pore blockage are responsible for loss of activity during the initial deactivation period [20]. Another important feature associated with the hydrocracking of heavy oils is the kinetic approach. On the one hand, very simple kinetics is used when modeling catalyst deactivation even if the employed feed is complex in nature, and on the other hand, if complex kinetic approach is used, no deactivation effects are taken into account. In previous publications, it has been demonstrated that the hydrocracking of crude oils and residua can be properly modeled by the continuous kinetic lumping approach [21,22]. The main attractiveness of such a model is the use of

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

fixed reaction order and the accurate predictions of the entire boiling point curve with few parameters. Also, because the use of modern chromatographic apparatus for simulated distillation allows for obtaining almost the entire distillation curve of hydrocracked products, it is desirable to use a kinetic model compatible with those experimental results. The use of continuous lumping approach for the hydrocracking of heavy oils is relatively new, and up until now, it has been applied to experiments collected at steady-state conditions, but nothing has been reported for its application to the hydrocracking of heavy oil experiments affected by catalyst deactivation. It is then the aim of the present contribution to use the continuous lumping to represent the reaction kinetics and catalyst deactivation of the hydrocracking of heavy oil at moderate reaction conditions.

Table 1 Complementary equations for the hydrocracking kinetic model. TBP−TBPðlÞ θ ¼ TBP ðhÞ−TBPðlÞ

(8)

¼ θ1=α

(9)

kHDC kmax



2 a0 1 S0 ¼ ∫0 pffiffiffiffiffiffi e−½fðx=K Þ −0:5g=a1  −A þ B  DðxÞ  dx 2π  k2
C 1;2 ¼ ∫k c x; τ  DðxÞ  dx K

Relating catalyst deactivation with coke formation requires considerable amount of long-term experiments to measure the amount of coke deposited on catalyst to collect representative samples for characterization than in case of relating deactivation phenomenon with time on stream. Although the first approach is a rational way of modeling the catalyst deactivation high cost of experiments limits their use apart from other features of that approach, such as the ex situ analysis of coke content on catalyst that could be different than that deposited at reaction conditions. The simplest way to take into account the loss of catalyst activity is by means of averaged power deactivation function that relates activity coefficient with time on stream. It is assumed generally that a simple function allows for modeling the deactivation by coke during the first hours of TOS without distinction between sites coverage and pore blockage. Another assumption frequently done is that the final activity reduces to zero, which is not the case for deactivation by coke in hydrocracking reactions according experimental evidence [17,18,20,23,24]. 2.2. Kinetic model The rate of reaction for species with reactivity “k” can be written as [25]
 k −r A ¼ k  c k; τ −∫kmax ½ pðk; xÞ  x  cðx; τÞ  DðxÞdx ð1Þ

kmax 1 DðxÞ N ∫0

a0 and a1 are model parameters that determine the position of peak on the interval k ∈ (0, K) and δ is a small finite value that warranties that p(k, K) takes a finite value when k = 0. All these model parameters are dependent on feed impurities (sulfur, metals content, heaviness of feed, etc.), catalyst activity and operating conditions. The species-type distribution or change factor from discrete to continuous approach is given by the following relationship: DðkÞ ¼

Nα α−1 k kα Ä

Such a relationship permits to keep the invariance during transforming discrete mixture to a continuous one. Physically, D(k) expresses the interdependence between the reactivity of the various components [26]. Table 1 reports complementary equations of the kinetic model. The description of each variable is given in the Nomenclature section. In the continuous kinetic model, α, a0, a1, δ and kmax are the model parameters.

τ¼

and S0 is calculated as

Z K 2 1 − ðk=xÞa0 −0:5g=a1  pffiffiffiffiffiffi e ½f S0 ¼ −A þ B  DðxÞ  dx 2π 0

The experiments were carried out in a continuous stirred tank reactor (CSTR). A pseudohomogeneous model is used to represent the reactor. Proper care has been taken to minimize the fluid-to-particle mass transfer resistance. Thus, kinetic information is affected only by intraparticle mass transfer resistance. Based on this, the CSTR model is used as follows [27]:

τ¼

Eq. (2) accounts for the amount of formation of species with reactivity k from species of reactivity K (being K greater than k). Other features related to p(k, K) are [25]:

C A0 −C A1 −r A jC A ¼C A1

ð13Þ

Substituting Eq. (1) in Eq. (13),

ð4Þ

ð5Þ

ð7Þ

mAx

where A and B are given by the following expressions: ð3Þ

ð6Þ

• a positive function between the ranges of validity of model parameters. • a yield distribution biased toward the reactivity of crackate K. • p(k, K) = 0 if k N K, which means that dimerization effects are not significant.

2.3. Reactor model

B ¼ δ½1−ðk=K Þ

(12)

 dx ¼ 1

The first term of the right-hand side (rhs) of Eq. (1) allows for representing the rate of the hydrocracking of species with reactivity “k”, whereas the second term accounts for the species that being longer produces the species in question by hydrocracking. τ is the reciprocal of space velocity. The yield species distribution (p(k,K)) is given by
 i  2 1 h  a p k; K ¼ pffiffiffiffiffiffi e− ðk=K Þ 0 −0:5 =a1 −A þ B ð2Þ S0 2π

−ð0:5=a1 Þ

(11)

1


 K ∫0 p x; K DðxÞdx ¼ 1

2.1. Consideration to develop the model

A¼e

(10)

• equal to zero for k = K. • satisfies the mass balance criterion:

2. The models

2

115

cðk; 0Þ−cðk; τÞ k  cðk; τÞ−∫kkmax ½ pðk; xÞ  x  cðx; τÞ  DðxÞdx

ð14Þ

Solving for hydrocracking product concentration, one arrives at [28,29]
 cðk; 0Þ þ τ∫kk ½pðk; xÞ  x  cðx; τÞ  DðxÞdx max c k; τ ¼ 1þkτ

ð15Þ

116

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

2.4. Deactivation model

For the heaviest compound (c (kmax,τ)), Eq. (15) reduces to 
cðkmax ; 0Þ c kmax ; τ ¼ 1 þ kmax  τ

ð16Þ

In order to solve Eq. (15), discretization of the integral term was done, and after some arrangements, the following expression was obtained [22]: h i  n
 c ki ; 0 þ τ ∑nþ1 j¼iþ1 cðk j ; τ r ÞI 1 j þ ∑ j¼iþ1 cðk j ; τ r ÞI 2 j c ki ; τ ¼ 1 þ τ ½k i  I 1 i 

− ψt

φ ¼ φS þ ð1−φS Þe ð17Þ

where I1i, I1j and I2j are given as follows:


 x−kiþ1 kiþ1 I1i ¼ ∫k p ki ; x  x   DðxÞdx i ki −kiþ1
 k I 1 j ¼ ∫k j p ki ; x  x 

x−k j−1 k j −k j−1


 p ki ; x  x 

x−k jþ1 k j −k jþ1

j−1

k jþ1

I 2 j ¼ ∫k

j

ð18Þ

!  DðxÞdx

ð19Þ

 DðxÞ  dx

ð20Þ

!

After calculation of c(k, τ), the following integral is solved in order to obtain the weight faction of individual pseudocomponent:
 wt 1;2 ðτ Þ ¼ ∫k c k; τ DðkÞdk k2

ð21Þ

1

wt i ¼ 1

ð22Þ

i¼1

Species distribution in feed (c(k, 0)) can be determined with the following equation: Wt ¼ AðkÞ cðk; 0Þ

ð23Þ

where 0

a1;1 B 0 B AðkÞ ¼ B B 0 @ ⋯ 0

a1;2 a2;1 0 ⋯ 0

0 a2;2 a3;1 ⋯ 0

⋯ ⋯ ⋯ ⋱ ⋯

0 0 0 ⋯ an;1

1 0 0 C C 0 C C ⋯ A an;2

ð24Þ

and
     c k2;0 c k3;0 c k; 0 ¼ c k1;0

 T ⋯ c knþ1;0

ð25Þ

W is a vector containing the experimental information of individual weight fraction of feed. Also, matrix coefficients in Eq. (24) are calculated as follows:

ai1 ¼

1 Nα ki −kiþ1 kαmax

ai2 ¼

1 Nα kiþ1 −ki kαmax

"

"

ð28Þ

where φ is the activity, ψ is the parameter decay and φS is the steadystate catalyst activity. These model parameters are characteristic for different feed, catalyst and operating conditions, mainly temperature. Also, Eq. (28) is applied because it is considered that reactant composition surrounding the catalyst is constant with time. Because in our experiments some sharp change in activity was observed, two intervals of TOS can be identified. The time that marks such a change was denominated tb. According to some reports in the literature [5,24,31], the proper way for modeling the deactivation kinetics by two simultaneous and different causes is done by multiplying a partial activity due to cause one by the activity due to cause two. During the first hours of time on stream, only site coverage due to coke precursors occurs so that only cause one is present. After certain time, simultaneous sites coverage and pore blockage provoke loss of activity. On the basis of these ideas, the following function defined by intervals is proposed:  φ¼

φ1 φ1  φ2

0≤ t ≤t b t b bt

ð29Þ

where φ1 was taken to be equal to Eq. (28) and φ2 is defined as

And total mass conservation is verified by using the following equation at each residence time: n X

To model the deactivation by sites coverage and pore blockage, two functions were chosen for each cause both of power law type considering first-order dependence on activity [30]. According to Monzón et al. [24], modeling the deactivation as time on stream function with the above conditions can be done with the following expression:

! !# αþ1 α kαþ1 kαþ1 ki k iþ1 − iþ1 − −kiþ1 i αþ1 α αþ1 α

ð26Þ

! !# αþ1 αþ1 kαþ1 kα ki k iþ1 −ki iþ1 − − i αþ1 α αþ1 α

ð27Þ

−ψ ðt−t b Þ

φ2 ¼ φS þ ð1−φS Þe

ð30Þ

It is believed that the ψ parameter is the same with and without pore plugging because it allows for representing average decay rate. 2.5. Strategy for estimation of model parameters Prior to parameter estimations, dimensionless curves from experimental results were prepared by calculating the normalized temperature for each point, taking as reference the maximum and minimum boiling points in the feed and product mixtures and normalizing the weight fractions by adding the gas yields to liquid product [22]. The kinetic model was solved firstly by using simulated distillation data curve at three different temperatures and 20 h of TOS. In order to avoid overparameterization, it was firstly assumed that α, a0, a1 and δ are only a function of temperature while the reactivity coefficient (kmax) depends additionally on TOS. The former model parameters were calculated at each temperature. After that, the values of kmaxφ were determined at all values of TOS. Finally, the refinement of model parameters was followed. All routines were coded in Matlab. fmincon routine was used for finding the apparent kinetic and deactivation model parameters. Details of solution of Eq. (1) can be found elsewhere [22]. 3. Experimental A CSTR of 1 L equipped with a basket for catalyst was used to carry out the hydrocracking of residue. It was operated under the following conditions: 9.8 MPa of total initial pressure, three temperatures: 380, 400 and 410 °C; LHSV of 0.75 h−1, hydrogen-to-oil ratio (H2/HC) of 5000 scf/bbl and 1000 rpm. One hundred milliliters of extruded catalyst was loaded into the reactor basket. The catalyst properties are as follows: nominal size of 1/18 inches, Ni content of 0.58 wt%, Mo content of 2.18 wt%, specific surface area of 197.2 m2/g, pore volume of

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

100

a

80

wt%

0.85 ml/g and average pore diameter of 172.6 Å. Feedstock consists of atmospheric residue of crude oil of 13° API whose main properties are listed in Table 2. Feed and products were characterized by simulated distillation method. The duration of the test at each condition was 200 h, and samples were taken at 20 h intervals.

117

4. Results and discussion

60 40 20

4.1. Experimental results

0 100

b

wt%

80 60 40 20 0 100

c

80

wt%

Figs. 1a–c show the curves of liquid composition versus boiling temperature of hydrocracked products obtained at 380 °C, 400 °C and 410 °C of reaction temperature, respectively, and 0.50 h−1 of space velocity at different TOS. Only selected curves and points are presented in order to avoid overlapping. The maximum boiling point for products at all conditions is of about 720 °C. Typical trends of distillation curves are observed, that is, for longer TOS, the curves are displaced to the right. The displacement of the curves to the right means that for certain cut temperature, the weight percent is lower, which is indicative of the diminution of desired product yields due to decay on catalyst activity. At 380 °C (Fig. 1a), the yield of the fraction with high boiling points (N500 °C) undergoes small changes at increased TOS. This behavior can be attributed to the difficulty to react of those compounds (mainly resins and asphaltenes) at the moderate reaction conditions studied here. On the other hand, the yield of fraction with lower boiling point is more TOS-dependent because marked differences in the trends of the curves are observed. It is believed that deactivation occurs mainly in small pores so that its effect is more pronounced in the yield of lighter boiling point fractions, although large pores are also reduced in size because they are covered with coke in some extent. Also, it is observed that a sharply change in distillation curves occurs between the curve at 80 h and 100 h of TOS, which can be attributed to changes in catalyst activity due to pore mouth plugging of significant fraction of total pores. At 400 °C of reaction temperature (Fig. 1b), all compounds undergo changes at different TOS, including those contained in the heavy fraction, probably because at this temperature the reactions begin to be more dominated by the hydrocracking of heavy compounds instead of by hydrogenation. Because hydrocracking occurs in higher extent, more changes in activity are observed. At 200 h, an apparent steadystate activity is reached. At 410 °C (Fig. 1c), appreciable changes in distillation curves are noticed for all fractions as TOS increases. Due to high temperature, hydrocracking affects product yields obtained at 180–200 h of TOS although that effect is small. It is seen in all figures that some curves are close to each other in certain intervals of TOS, which could be interpreted as pseudo-steady-state activity at those conditions. A separate plot of distillation curves as a function of reaction temperature for two TOS, namely, 20 and 200 h, was prepared in order to clearly observe the effect of these variables on distillate yields, which is

60 40 20 0 0

200

400

600

800

Temperature (ºC) Fig. 1. Effect of time on stream on distillation curves at (a) 380 °C, (b) 400 and (c) 410 °C and LHSV of 0.50 h−1. (\) Feed; (●) 20 h, (■)40 h, (▲)60 h, ( )80 h, ( )100 h, (○)120 h, (□)140 h, (△)160 h, (▪) 180 h and (+) 200 h of TOS.

shown in Fig. 2. As expected, the higher the temperature, the higher the yield of distillates at the shortest TOS studied. It is worth noting that the yields at 200 h TOS are comparable for the three curves obtained at different reaction temperatures. This behavior has been already observed experimentally [9] and is attributed to a steady-state coke deposition, which has reached a maximum value, and its effect on catalyst provokes that similar residual activity is attained even for different reaction temperatures. In order to verify the changes in catalyst surface area and average pore volume, the characterization of fresh and spent catalysts at the 100

Table 2 Properties of feedstock. 5.60 82.51 10.05 5.80 1.09 664 774.41

wt%

API gravity Elemental analysis, wt% Carbon Hydrogen Sulfur Nitrogen Metals, ppmw Ni + V Kinematic viscosity at 110 °C, cSt Distillation, °C IBP/5 wt% 10/30 wt% 37.8 wt%

80 60 40 20 0 0

200

400

600

800

Temperature (ºC) 268/338 374/397 546

Fig. 2. Effect of reaction temperature on distillation curves: (●,○) 410 °C, (■,□) 400 °C and (▲,△) 380 °C. (Full symbols) 20 h of TOS and (void symbols) 200 h of TOS. (\) Feed.

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

20

0.4

200

16

0.3

150

12

100

8

α

250

APD (nm)

SSA (m2/g)

118

a

0.2

0.1 4

50

0.0 0

0 Fresh

Spent 380°C

Spent 400°C

2.0

Spent 410°C

Fig. 3. Textural properties of fresh and spent catalyst. (■) Specific surface area; ( ) average pore diameter.

1.5

a0

different operating temperatures was carried out. In Fig. 3, the diminution of SSA at increased reactor temperature is shown. It is observed that comparable surface area is available for spent catalysts after 200 h TOS at 380° and 400 °C but with an area reduction of almost 50% with respect to fresh sample at 410 °C. This can be attributed to extradeposits of carbon due to some thermal hydrocracking at the most severe conditions. The average pore diameter follows similar trend. On the one hand, smaller pores disappear, and on the other hand, larger pores are partially plugged hence resulting in a net reduction of average pore diameter.

b

1.0

0.5

0.0 30.0

c

4.2. Model results 20.0

δ x106

4.2.1. Dependence of model parameters on TOS Initially, no dependence of some kinetic model parameters on TOS was assumed, but poor fitting was observed. In order to improve predictions, all kinetic model parameters were calculated at each level of TOS and averaged, except kmax. However, even with this modification, significant deviation between simulated and experimental points was encountered. The only model parameter that did not undergo changes was a1. Ulterior refinement was conducted to formulate the linear dependence of the other kinetic model parameters (α, a0 and δ) on TOS on the basis on their trends. The optimized curves of these parameters are shown in Fig. 4. It is observed that, in general, at the lowest reaction temperature, the dependence of model parameters on TOS is slight and increases at higher temperature. Thus, it is confirmed that those model parameters are a function of catalyst activity as was previously suggested by Laxminarasimhan et al. [25]. This connection indeed reduced the deviations between model and experimental results found when constant activity was assumed a priori despite of exhaustive parameter optimization. Fig. 5 shows the dependence of kmax on TOS together with calculated trends by using Eq. (29). These trends remained unchanged even when the other model parameters were kept constant. Remarkable changes in activity at 380 °C and 400 °C of reaction temperature at 80 and 100 h TOS, respectively, are observed (Fig. 5a and b), while at 410 °C, less change is seen at 60 h (Fig. 5c). With reference to Fig. 5a and b, the first part of curve allows for representing the loss of catalyst activity by site coverage, and the sharp changes on reactivity can be attributed to some catalyst pore constrictions together with deactivation by coke precursors. No well-defined curve is shown in Fig. 5c, and such a behavior can be attributed to severe reaction conditions, where the catalytic function is the main cause for hydrocracking, but also some thermal cracking could modify the dependence of kmax on TOS. Another salient feature that deserves to be mentioned here is that besides the empiricism of expression to describe the loss of activity, the

10.0

0.0 0

40

80

120

160

200

TOS (h) Fig. 4. Effect of time on stream on α, a0 and δ model parameters at (\) 380 °C, (—) 400 °C and (∙∙∙) 410 °C.

deactivation function given by Eq. (29) allows for capturing well the changes of reactivity as a function of TOS. 4.2.2. Dependence of model parameters on reaction temperature Derived kinetic model parameters at the shortest TOS were plotted against reaction temperature, except a0, which was constant for all conditions (Fig. 6). The linear dependence of α and δ with reaction temperature is observed in Fig. 6a and b, respectively. Some deviation from linearity was found for a0 (Fig. 6c). Excellent correlation between reciprocal of absolute reaction temperature and logarithm of kmax is seen in Fig. 6d. These observations perfectly agree with previous reports in which at short TOS, the linear correlation of kinetic model parameters with reaction temperature was reported [21,22]. 4.2.3. Comparison of predicted and experimental results The optimized model parameters were used to simulate the dimensionless curves (θ against wt), and they were compared with

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

0.5

a

119

a

0.4

α

kmax•φ

0.50

0.3 0.2 0.1

0.25 20

3

b δx106

kmax•φ

2

10 5

1

0 3.0

0

c

2.0

a0

c

15 12

kmax•φ

b

15

1.0

9 0.0 360

6

380

400

420

440

Temperature (ºC)

3 3.0

0 0

40

80

120

160

200

kmax

Fig. 5. Effect of time on stream on kmax model parameter at (a) 380 °C, (b) 400 °C and (c) 410 °C.

d

2.0

TOS (h)

1.0 0.0

4.2.4. Deactivation model parameters It was found for all reaction temperatures that residual activity (φs) is present because its value was higher than zero, as reported in Table 3. It is observed that as reaction temperature increases, the corresponding

-1.0

1.4

1.5

1.6

1000/K Fig. 6. Dependence of kinetic model parameters on reaction temperature at 20 h of TOS.

residual activity diminishes. This behavior is anticipated since at the most severe reaction conditions faster decay of catalyst activity is expected. Parameter tb, that marks the sharply change on reactivity, is different for experiments conducted at different reaction temperatures. The observe values of tb can be attributed to relative contributions of 1.00

Experimental point (wt)

experimental points in a parity plot shown in Fig. 7. Good correspondence can be observed. The simulation of selected complete composition curves at 410 °C as a function of dimensionless boiling temperature is shown in Fig. 8 together with experimental results. In general, good agreement is confirmed, although some predictions deviate from experimental points as was already seen in Fig. 5c. The representation of this figure was chosen because plots obtained at different TOS are clearly observed while the simulated and experimental results at the other reaction temperatures are closer than for the case of 410 °C. In Fig. 9, all predicted curves at 380 °C and 400 °C of reaction temperature are plotted. From this figure, sharp changes are clearly observed to occur at certain TOS in line with variations of reactivity commented from Fig. 5a and b, which can be attributed to changes of mechanism from deactivation of active sites to combined deactivation of sites and pore plugging. Fig. 9b depicts slight differences in gas yields (θ b 0.25) for the different TOS. This could mean that gases are produced in short TOS, and then only small amounts of such a fraction are added due to the loss of ability of catalyst to produce them. Similar behavior was found for fraction containing the heaviest compounds, perhaps because the ability to react to such a fraction is high initially, but as TOS becomes longer, less active sites able to hydrocrack heavy molecules are available, and thus a slight increase in heavy compounds yield is observed. Gas formation requires high activity, while heavy compounds need clean pores to enter the active sites, and such conditions are only present during first the hours of TOS.

0.75

0.50

0.25

0.00 0.00

0.25

0.50

0.75

1.00

Calculated point (wt) Fig. 7. Parity plot of simulated and experimental data at three temperatures and all TOS (20–200 h).

120

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

wt

1.00

Table 3 Model parameters for deactivation function.

0.75

Model parameter

0.50

k0max, h−1 −1

ψ, h ϕS tb, h

0.25

0.00 0.00

0.25

0.50

0.75

1.00

Dimensionless temperature Fig. 8. Simulated and experimental dimensionless distillation curves as a function of TOS at 410 °C. (●) 20 h, (▲) 60 h, (□) 100 h and (○) 140 h. (Lines) Simulated results, (points) experimental.

reaction mechanisms, i.e.,. hydrocracking, hydrogenation and thermal cracking, as the reaction severity is increased.

4.3. Final remarks The use of advanced characterization equipment such as high temperature simulated distillation (HTSD) is more and more a requirement to properly obtain experimental information of distillation curves that are needed for an accurate description of the hydrocracking of heavy oils. The HTSD method allows for generating more information of the end part of distillation curve that represents the most complex compounds, whose conversion is the main goal of hydrocracking. Its data are not available in this zone, and extrapolation of the curves by using any correlation can be used. However, this latter approach is questionable. Regarding the collection of data, much care must be put because deactivation by coke deposition is indeed present at short TOS, and if catalyst activity is assumed to be constant, that could provoke the misinterpretation of kinetics. 1.00

a

wt

0.75

0.50

0.25

0.00 1.00

b

wt

0.75

Temperature (°C) 380

400

420

0.65 0.070 0.660 80

3.2 0.061 0.588 110

16 0.025 0.356 60

From the good agreement between model predictions and experimental information, it is clear that the continuous lumping approach captures some of the main features of activity decay during the hydrocracking of heavy oil and reflects the need of more accurate kinetic models and more research in this area. 5. Conclusion The effect of temperature and TOS on the hydrocracking of residue oil was studied by using the continuous kinetic lumping approach and an empirical deactivation model that considers two causes: site deactivation by coverage and pore mouth constrictions. It was observed that kinetic model allows for capturing the general trend of hydrocracking, and the derived model parameters undergo changes at the different TOS, which confirms the fact that these parameters are a function of catalyst activity. The dependence of model parameters on reaction temperature was also confirmed. Experimental data with simulation results allow for corroborating that during the first hours of TOS, accelerated deactivation of catalyst occurs, and for longer TOS, pseudo-steadystate activity is reached. Nomenclature a0, a1, S0 Parameters of yield distribution function Eq. (2) c(k, τ) Concentration of the species with reactivity k at residence time τ c(k, 0) Concentration of the species with reactivity k in the feed wt1,2(τ) Concentration in weight fraction of any pseudocomponent with arbitrary boiling point range as a function of residence time D(k) Species-type distribution function for hydrocracking reaction e Exponential function basis k Hydrocracking reactivity of any species (h−1) kmax Hydrocracking reactivity of the species with the highest TBP in the mixture (h−1) N Total number of species in the mixture TBP True boiling point of any pseudocomponent (K) TBP(h) Highest boiling point of any pseudocomponent in the mixture (K) TBP(l) Lowest boiling point of any pseudocomponent in the mixture (K) x Hydrocracking reactivity of any species (h−1); variable of integration wt Weight fraction of species Greek letters α Model parameter in Eq. (6) δ Model parameter of hydrocracking yield distribution function (p(k, K)) θ Normalized TBP as defined in Eq. (7), dimensionless τ Inverse of space velocity or residence time (h)

0.50

0.25

0.00 0

0.25

0.5

0.75

1

Acknowledgements

Dimensionless tempetature (θ) Fig. 9. Simulated dimensionless curves as a function of TOS at (a) 380 °C and (b) 400 °C.

J. Ancheyta acknowledges the Marcos Moshinsky foundation for providing financial support by means of a “Cátedra de Investigación.”

I. Elizalde, J. Ancheyta / Fuel Processing Technology 123 (2014) 114–121

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