Kinetic Modeling Approaches Part 1 (Petroleum Refining)

Various approaches to kinetic modeling of reactions that take place in the petroleum refining industry have been reported in the literature. On the one hand, kinetic studies considering each compound and all the possible reactions are complex due to the huge number of hydrocarbons involved. However, they permit a mechanistic description based on detailed knowledge of the mechanism of the various reactions. Most of the time, applying this method to reactions with real feeds is difficult because of analytical complexity and computational limitations. The situation is clear: The more compounds a model includes intrinsically, the more kinetic parameters that need to be estimated; and consequently, the more experimental information that is required. On the other hand, the problem can be simplified to consider the partition of the species into a few equivalent classes, called -umps or the -umping technique, and then assume that each class is an independent entity (Wei and Kuo, 1969). These two approaches are very well known as being the two extreme cases for kinetic modeling of complex mixtures. The second approach is most used nowadays due to its simplicity. There are other models that can be considered as a combination of these two methods; of course, their complexity is based on the experimental information available.

In the following sections, a detailed description of the approaches to kinetic modeling of petroleum refining reactions is reported. Hydrocracking has been chosen as a base for discussing the various kinetic models. The particular kinetics of other reactions, such as hydrotreating, reforming, and catalytic cracking, is described with more detail in subsequent topics. For better organization of this section, the kinetic model approaches have been classified as (1) models based on the lumping technique, (2) models based on continuous mixtures, and (3) structure-oriented lumping and single-event models.


Traditional Lumping

Models Based on Fractions with a Wide Distillation Range The kinetics of hydrocracking of gas oil was studied by Qader and Hill (1969) in a continuous fixed – bed tubular flow reactor. These authors found that the rate of hydro-cracking is of first order with respect to feed concentration, with an activation energy of 21.1 kcal/mol. The kinetic data were obtained at 10.34 MPa pressure, 400 to 500°C temperature, 0.5 to 3.0h- space velocity, and a constant H-/oil ratio of 500 standard m3/m3. The liquid product was distilled into gasoline (IBP to 200°C), middle distillate (200 to 300°C), and diesel (300°C+). This seems to be the first experimental study in which kinetics of hydrocracking of real feed was reported.

Callejas and Mart-nez (1999) studied the kinetics of Maya residue hydrocracking. They used a first-order kinetic scheme involving a three-lump species: atmospheric residuum (AR; 343°C+), light oils (343°C-), and gases. The experiments were conducted continuously in a stirred-tank reactor (1 L) in the presence of a NiMo catalyst supported on /-Al2O3. All tests were carried out at 12.5 MPa hydrogen pressure at temperatures of 375, 400, and 415°C, and WHSV in the range 1.4 to 7.1L/g-at -h. The total liquid products from each experiment were analyzed by simulated distillation using the ASTM D-2887 method, which was employed to estimate the boiling distribution of the oil samples. Rate constants at various temperatures are listed in Table 2.6. The authors reported that experimental data at 375 and 400°C are in agreement with the model proposed (r > 0.82), but at 415°C the fits were bad (r < 0.70). Better agreement between experimental and calculated yields was reported with optimized k values, particularly for gas lumps. The original recalculated values of activation energies are reported in Table 2.6 .

Aboul-Gheit (1989) determined the kinetic parameters of vacuum gas oil (VGO) hydrocracking, expressing composition in molar concentration. The experiments were carried out at 400, 425, and 450°C, 0.5 to 2h- LHSV, and 12 MPa pressure. Two different NiMo catalysts with HY zeolite supported on silica-alumina matrix were used. He proposed that VGO reacts to form gases, gasoline, and middle distillates. Kinetic parameters and activation energies are summarized in Table 2.6. The same problem as that seen in the previous model was observed, which was also due to individual determination of each parameter by lineal regression. The exact values of k0 are reported in parentheses in Table 2.6, which are very close to the original values. Consequently, the activation energies determined with the two series of k0 values are similar.

Another kinetic model for gas oil hydrocracking was proposed by Yui and Sanford (1989), who performed experiments in a pilot plant with a trickle-bed reactor at different operating conditions (350 to 400°C, 7 to 11 MPa, 0.7 to 1.5 h-1 LHSV, and an H2/oil ratio of 600 std m3/m3). They used Athabasca bitumen-derived coker and hydrocracker heavy gas oils (HGOs) as feed and two different commercial NiMo/Al2 O3 hydrotreating catalysts. A three-l ump model was considered [HGO, LGO (light gas oil), and naphtha], which can follow parallel, consecutive, and combined reaction schemes. The model includes first-order reactions and considers the effects of partial pressure (in MPa), temperature (in °C), and space velocity on the total liquid products yield [Eqs. (2.49), (2.50), and (2.51), Table 2.7]. Fitted parameters are Y„ = 1.0505, a = 0.2517, b = 0.0414, and c = -0.0163 for the coker gas oil; and Y„ = 1.0371, a = 0.1133, b = 0.0206, and c = -0.0134 for the hydrocracker gas oil. The kinetic parameters are presented in Table 2.6. According to the authors, it was not possible to fit a set of parameters for the combined reaction scheme.

TABLE 2.6. Kinetic Data Reported for Various Lump Models

Kinetic Data Reported by Callejas and Martmez (1999)

375°C

and Anch 400 ° C

eyta et al. 415 ° C

(2005) Ea

tmp364-122

1.13

3.26

9.20

45.32

tmp364-123

1.13

3.18

7.22

41.32

tmp364-124

0.07

0.25

1.52

64.40

tmp364-125

0.30

0.46

1.45

32.57

tmp364-126

0.21

1.5

5.12

70.43

tmp364-127

0.79

2.72

5.77

43.90

Kinetic Data Reported by Aboul-Gheit (1989)

tmp364-128

Catal

st 1

Cataly

st 2

400 ° C

425°C

450 ° C

EA

400 ° C

425 °C

450 ° C

Ea

tmp364-129

0.286

0.500

0.688

17.51

0.469

0.612

0.916

13.09

tmp364-130

0.040

0.083

0.140

24.02

0.111

0.216

0.350

22.23

tmp364-131

0.026

0.048

0.069

18.67

0.040

0.074

0.106

18.96

tmp364-132

0.352

0.631

0.897

18.14

0.620

0.902

1.372

15.35

tmp364-133

(0.333)

(0.667)

(1.059)

22.51

(0.714)

(1.125)

(1.75)

17.15

Kinetic Data Reported by Yui and Sanford (1989)

Parallel Scheme (k3=0)

Coker Feed

Hydrocracker Feed

A

EA

A

Ea

tmp364-134 tmp364-135

17.75

tmp364-136

17.24

tmp364-137 tmp364-138

15.02

tmp364-139

14.32

tmp364-140 tmp364-141

29.78

tmp364-142

32.17

Consecutive scheme (k2=0)

tmp364-143 tmp364-144
tmp364-145 tmp364-146

17.75

tmp364-147

17.24

tmp364-148 tmp364-149

26.96

tmp364-150

20.46

*Values in parentheses correspond to tmp5C-151_thumb in kcal/mol.

The kinetics of hydrocracking of vacuum distillates from Romashkin and Arlan crude oils was studied by Orochko (1970) in a fixed – bed reactor over an alumina-cobalt molybdenum catalyst using a first-order kinetic scheme involving four lumps. This model is similar to that proposed by Aboul-Gheit (1989). The rate of a first-order heterogeneous catalytic reaction was expressed by the Eq. (2.52) (Table 2.6), where a is the rate constant, t the nominal reaction time, y the total conversion, and fi the inhibition factor of the process by the reaction products formed and absorbed on the active surface of the catalyst and also by their effect on mass transfer in the heterogeneous process. These authors indicate that in this case the consecutive reactions predominate, the parallel reactions in the calculations being comparatively minor and negligible to a first approximation. All experiments were carried out at 5 and 10.13 MPa of hydrogen pressure and temperatures of 400, 425, and 450°C. For the case of Arlan petroleum vacuum distillate at 425°C and 10.13 MPa, a value of fi = 1 was reported. Rate constants and activation energies based on the experimental data reported by others are given in Table 2.8. The kinetic model is represented by Eqs. (2.53), (2.54), and (2.55) for diesel, gasoline, and gases, respectively (Table 2.6). In these equations, k and k" are kinetic factors with a meaning similar to that of the rate constants, which are determined from the experimental data and are dependent on the equivalent kinetic temperature of the process and the catalyst activity. For the Romashkin petroleum vacuum distillate at 10.13MPa, the values of k and k" are 1.3 and 2.0, respectively.

TABLE 2.7. Equations for Kinetic Models Based on Traditional Lumping

Criterion

Eq.

Criterion

Eq.

tmp364-152

(2.49)

tmp364-153

(2.59)

tmp364-154

(2.50)

(2.51)

tmp364-155

(2.60) (2.61)

tmp364-156

(2.52)

tmp364-157

(2.62)

tmp364-158

(2.53)

(2.54)

(2.55)

tmp364-159

(2.63)

(2.64)

(2.65)

tmp364-160

(2.56)

tmp364-161

(2.66)

tmp364-162

(2.57)

(2.58)

tmp364-163

(2.67)

(2.68)

Botchwey et al. (2004) studied overall conversion kinetic models within specified, short-range temperature regimes for the hydrotreating of bitumen-derived heavy gas oil from Athabasca over a commercial NiMo/Al2O3 catalyst in a trickle-bed reactor. All experiments were carried out at various reaction temperatures between 340 and 420°C, 8.8 MPa of pressure, LHSV of 1 h-1, and a H2/oil ratio of 600 standard m3/m3. The oil samples (feed and products) were grouped into four different boiling cuts with temperature ranges of D (IBP to 300°C), C (300 to 400°C), B (400 to 500°C), and A (500 to 600°C). The boiling-point distribution was derived from gas chromatography simulated distillation. It should be noted that the product analyses were limited to liquid samples, because negligible amounts of gaseous hydrocarbon products were formed from mass balances. The proposed kinetic model included the four lumps (A, B, C, and D) and five kinetic parameters (k1,^,k5).The low-severity temperature regime was considered to be that at the lowest operating temperature range (340 to 370°C), and the reactions A to C and C to D were negligible. In the intermediate-severity temperature regime (370 to 400°C), only the reaction A to C was negligible. The value of k5 is equal to zero in both kinetic schemes derived from both temperature regimes. The high-severity temperature regime covered the most severe operating temperature range (400 to 420°C). All kinetic parameter values for the three regimes are tabulated in Table 2.8 .

Aoyagi et al. (2003) studied the kinetics of hydrotreating and hydrocracking of conventional gas oils, coker gas oils, and gas oils derived from Athabasca bitumen. They were interested in studying the influence of feed properties on product yield and composition. The experiments were fixed as follows: a temperature of 380°C, an operating pressure at 13.8 MPa, a liquid hourly space velocity of 0.75 h-1,and a H2/oil ratio of400std m3/m3.The feedswith different properties were obtained mixing hydrotreated gas oils with gas oil without hydrotreating. A kinetic model was developed and the parameters were adjusted with experimental data from a system with two reactors in series, each with a different catalyst. In the first reactor, a commercial NiMo//-Al2O3 catalyst was used, and in the second reactor, a commercial hydrocracking catalyst with NiMo/boria USY was employed. The model considers that in the first hydrotreating reactor, the modifications in molecular weight are due to reactions of hydrodesulfurization and hydrogenation of polycyclic aromatic compounds. Hydrocracking is the most important reaction in the second reactor. The model uses a first-order expression to describe the rate of disappearance of heavy gas oil (HGO), given by Eq. (2.56), where kH is the overall hydrocracking rate constant. Its value depends on both hydrotreating and hydrocracking reactions and is calculated with Eqs. (2.57) and (2.58), in which the last term includes the nitrogen content’s inhibitor effect. HGOin and HGOout are the inlet and outlet concentrations of heavy gas oil; and [S], [PA], and [I] are the contents of sulfur, polycyclic aromatic compounds, and inhibitors. The best set of model parameters reported by the authors is a = 9.5 x 10-4, b = 1.8 x 10-3, c = 0.32, d = 9.1 x 10-4- and n = 2. Figure 2.8 presents the reaction schemes proposed for developing the previous kinetic models, which contain no more than four lumps.

TABLE 2.8. Activation Energies Reported for Various Kinetic Models

Activation Energies Reported by Orochko (1970)

Feedstock

Total Pressure (MPa)

Ea (kcal/mol)

Romashkin petroleum

5.06

56.7

vacuum distillate

10.13

63.8

Arlan petroleum vacuum

5.06

63.0

distillate

10.13

64.8

Activation Energies Reported by Sanchez et al. (2005, 2007)

tmp364-164

400 ° C

Ea (kcal/mol)

tmp364-165

400 ° C

tmp364-166
tmp364-167

0.147

48.5

tmp364-168

0.007

37.1

tmp364-169

0.022

44.2

tmp364-170

0

tmp364-171

0.020

38.0

tmp364-172

0.003

53.7

tmp364-173

0.098

27.3

tmp364-174

0

tmp364-175

0.057

39.5

tmp364-176

0

 

Reaction schemes for hydrocracking models with two to four lumps.

Figure 2.8. Reaction schemes for hydrocracking models with two to four lumps. 

Another reaction pathway was proposed by Botchwey et al. (2003) – The pathways describe the conversion of gas oil to products via heteroatom removal, aromatics saturation, and hydrocracking. Typical hydrotreating reactions are represented by solid lines and cracking reactions are shown by dashed lines. These authors consider conversion to take place according to different regimes: the hydrotreating regime (reactions 1 to 7) at temperatures of 340 to 390°C and the mild hydrocracking regime (reactions 1 to 9) at 390 to 420°C. They arrived at this conclusion after performing experiments in a micro-trickle-bed reactor. The study covered a pressure range between 6.5 and 11 MPa at temperatures of 360, 380, and 400°C. The liquid hourly space velocity and the H2/oil ratio were maintained constant at 1 h-1 and 600 std m3/m3- respectively. However, kinetic expressions and rate constants are not given.

Mosby et al. (1986) reported a model to describe the performance of a residue hydrotreater using lumped first-order kinetics which divides residue into lumps that are easy and difficult to crack. This lumping scheme was used by Ayasse et al. (1997) to fit experimental product yields from catalytic hydro-cracking of Athabasca bitumen obtained in a continuous-flow mixed reactor over a NiMo catalyst at 430°C and 13.7MPa. To develop the model, stoichi-ometry concepts of a complex reacting mixture were applied. The resulting compact model was fitted to data from single-pass hydrocracking and used to predict the performance of multipass experiments. The liquid product was distilled into four cuts: naphtha (IBP to 195° C), middle distillates (195 to 343°C), gas oil (343 to 524°C), and residue (>524°C). Residue fraction was then distilled under vacuum to obtain the gas oil and residue fractions using the ASTM D-1160 procedure. After all the data had been utilized to estimate the parameters of the general lumped model, it was found that the model was overdetermined. The number of parameters was too large, and it was concluded that seven lumps are not required to give the experimental data a satisfactory fit. Afterward, three new models were proposed, two with six lumped components and one with five lumps, which were considered to be adequate to describe the data with an equivalent sum of squared residuals. In model 1, hard and soft residues were lumped as a single component under "hard residue." The initial concentration of lump 2 was zero, and the kinetic parameters of this lump (k2, sM, s25, s26, and s27) were not determined. In model 2, all the gas oil, whether it originated with the feed or was formed by cracking of the residue, was lumped as a single component under "product gas oil." The initial concentration of lump 3 was zero, and the kinetic parameters of this lump (k3, s35, s36- and s37) were not determined. Consequently, the simplest model that could capture this chemistry was a five- l ump model (model 3), consisting of one residue lump (hard residue), one gas oil lump (product gas oil), middle distillates, naphtha, and light ends. The resulting five – lump model had seven independent parameters (two rate constants and five independent stoichiometric coefficients). After determining the optimal parameter values, it was found that model 1 overpredicted the yield of middle distillates and underestimated the yield of naphtha at high residue conversion in experiments with bitumen as feed. Model 1 was therefore satisfactory for fitting yields over a wide range of residue conversion. Model 2 was inferior to model 1 in predicting the products, with large errors in the proportions of naphtha and gas oil. However, model 3 underestimated the yield of middle distillates and tended to overpredict the yield gas oil. The models with six and seven lumps are unnecessarily complex for these data, whereas the simpler five – lump model is satisfactory.

Recently, Sanchez et al. (2005- 2007) proposed a five-lump kinetic model for moderate hydrocracking of heavy oils: (1) unconverted residue (538°C+ ), (2) vacuum gas oil (VGO: 343 to 538°C), (3) distillates (204 to 343°C), (4) naphtha (IBP to 204°C), and (5) gases. The model includes 10 kinetic parameters which were estimated from experimental data obtained in a fixed – bed downflow reactor, with Maya heavy crude and a NiMo/Y-Al2O3 catalyst at a 380 to 420°C reaction temperature, 0.33 to 1.5 h- LHSV, a H–oil ratio of 890m3/m3, and a 6.9 MPa pressure. Activation energies reported by these authors are given in Table 2.8. The kinetic model was developed for basic reactor modeling studies of a process for hydrotreating of heavy petroleum oils, which, among several characteristics, operates at moderate reaction conditions and improves the quality of the feed while keeping the conversion level low. Figure 2.9 presents the kinetic models reported by Mosby et al. (1986), Botchwey et al. (2003), and Sanchez et al. (2005).

Reaction schemes for hydrocracking models with more than four lumps.

Figure 2.9. Reaction schemes for hydrocracking models with more than four lumps.

Models Based on Pseudocomponents: Discrete Lumping Krishna and Saxena (1989) reported a detailed kinetic model with seven lumps in which different cut temperatures are considered. The lumps are sulfur compounds, heavy and light aromatics, naphthenes, and paraffins. The pseudocomponents are considered light if they are formed from fractions with boiling points lower than the cut temperature (Tcut). Sulfur compounds are assumed to be a heavy lump. Experimental data reported by Bennett and Bourne (1972) were used to test the model; the values of the 60 kinetic parameters are presented in Table 2.9. The authors proposed a second model based on the analogy between reactions of hydrocracking and the phenomena of axial dispersion of a tracer in a flow; this model used only two parameters. Figure 2.10 shows the reaction scheme proposed and a comparison of the experimental data with the results predicted. The dispersion model is based on a study of the TBP (true boiling point) curves of hydrocracking products. An increment in residence time causes a reduction in the average molecular weight of the product and a drop in the distillation curve -s middle boiling point (T50). TBP curves at different residence times are normalized to obtain values of T* according to Eq. (2.59), where FBP; is the final boiling point of the feed. Krishna and Saxena (1989) used Bennett and Bourne – s (1972) pilot-plant experimental data to develop the model. The normalized temperature data of feed and products, shown in Figure 2.11, can be described roughly by Eq. (2.60); the solid line is the representation of the axial dispersion model with Pe = 14. The middle boiling-point temperature is obtained using Eq. (2.61)- which assumes a first-order decay function.

TABLE 2.9. First-order Rate Constants for the Kinetic Model Proposed by Krishna and Saxena (1989) and Comparison of Calculated and Plant Data Obtained by Mohanty et al. (1991)

tmp364-179

Tcut

( ° C) (Krishna and Saxena, 1989 )

371

225

191

149

82

0

tmp364-180

8.3000

tmp364-181

1.2633

0.4943

0.4799

0.4624

0.4345

0.4000

tmp364-182

0.6042

0.1809

0.1105

0.0397

0.0034

0.0000

tmp364-183

0.0421

0.3131

0.2719

0.2593

0.2501

0.2302

tmp364-184

0.5309

0.0211

0.0096

0.0095

0.0095

0.0095

tmp364-185

0.0397

0.0383

0.0249

0.0131

0.0086

0.0000

tmp364-186

1.1855

0.2772

0.2134

0.1117

0.0073

0.0000

tmp364-187

0.1619

0.0474

0.0275

0.0275

0.0275

0.0275

tmp364-188

0.4070

0.2391

0.1993

0.1518

0.0978

0.0299

tmp364-189

0.2909

0.5434

0.5219

0.4509

0.4391

tmp364-190

0.0818

0.0740

0.0709

0.0618

0.0608

Mohanty et al. (1991)

Calculated

Plant Data

Error (%)

Total feed to second stage (kg/h)

183,236

183, 385

-0.08

Hydrogen consumption (kg/h)

first stage

2816

3267

-13.8

second stage

1196

1363

-12.2

Reactor outlet temperature (°C)

first stage

693.3

714 (max.)

second stage

677.7

700 (max.)

Diesel (wt%)

48.79

50.5

-3.46

Jet fuel (wt%)

30.53

29.4

+3.83

Naphtha (wt%)

16.17

15.8

+2.51

Butanes and lights (wt%)

4.51

4.5

+0.22

Furthermore, Krishna and Saxena (1989) developed empirical correlations to predict the values of the decay rate of T50 (k50) with respect to residence time (t) and Peclet number (Pe). Both parameters are functions of the paraffin content in the feedstock (P). Equations (2.62) to (2.65) permit the estimation of these parameters considering an n-order decay function.

Next post:

Previous post: