Address: Laboratorio del Carbón y Residuales de Petróleo. USB. Apartado Postal 89000. Caracas. Venezuela. E-mail: naperez@usb.ve.

COKING REACTION KINETICS FOR VENEZUELAN CRUDE 1N. A. Pérez , 1G. Rincón.

1 Departamento de Procesos y Sistemas - Universidad Simón Bolívar.

Abstract. In the Delayed Coking process (DC), it is well known the influence of the type of feedstock on coke characteristics and overall yield products for a given set of operation condition. Considering that Venezuela is the world’s second producer of oil coke, it is important to understand the mechanisms of transformations taking place inside the coke drum. To this end reaction systems should be developed, which simulate the product concentration data. Therefore, the objective of this paper is to propose a mechanism to predict kinetic of DC using Venezuelan vacuum residual as feed. The chemistry of the DC process suggests that kinetic studies of such a complex system can be carried out considering a few reactions. Three kinetic models (two proposed by Del Bianco and one by Yue) were used to simulate the reaction kinetics of DC with four series of experimental data (each series at a different temperature), obtained from one Venezuelan crude type. Finding out, first, that one of Del Bianco kinetic model is which best replicates the experimental values. This model assumes coke is produced from condensation reactions both of the feed as well as the light crude previously cracked. And second, the order of reactions involved in the process can be grouped as third order, which is indicative of a cubic proportion between the concentration of reactive and the reaction rate.

Keywords: Coke, Reaction Kinetics, Delayed Coking

1. Introduction

The economic challenge in last years has been the production of distilled, naphthas and gasoleos, from

vacuum residuums of heavy oil with a high content of metals and impurities. In order to convert these residuums

in distilled is required deep conversion processes, one of these is Delayed Coking Process (DC). In this process,

cracking and polymerization reactions are carried out to obtain a mix of: gases, condensables, and petroleum

cokes (Rodriguez-Reinoso et al., 1999).

The productivity of the DC process is found limited for petroleum coke production. This product has a

smaller commercial value that condensables, reason why is necessary to look for alternatives that increase

selectivity of the condensable reaction (Udaja et al., 1992). In order to determine the effect of operational

variables on the selectivity of involved reactions, is required to know which reactions are carried out inside the

reactor, but the number of these reactions is enormous and simulation of the reactor turns over very difficult.

The objective of this work is to establish models that simplify the reaction group that occur in the coking

drum, based as much on type of developed reactions like in pseudo-components that represent the types of

substances in the equipment. Developed supposed models are validated fitting them with experimental values

obtained from a little scale DC plant that use as feed, vacuum residuums of Venezuelan Refineries. The product

of the validation is the best fit to DC kinetic.

2. Kinetic Considerations

Initial considerations of DC chemical suggest that is possible to make on little scale, kinetic studies of these

complex systems. Global kinetic data that are obtained, describe the accumulative effect of numerous reactions

that are carried out simultaneously in an independent form one of the other, involving intermediary reactive

radicals and with different rate constants and activations energies. This indicates that although, there are

difficulties in the measurement of appropriated parameters, the system can be described in terms of the kinetic of

consecutive reactions. (Faúndez et al., 2001)

In complex reactions like heavy oil’s, basic kinetic concepts aren’t simple to apply. To overcome this

difficulty, chemical models and computational chemistry are employing (Kocaefe et al., 1995).

In DC process take part thousand of substances that in general have different molecular weights. Previous

studies have supposed that a mix of feed and products can be simplified to estimate kinetic parameters if it’s

supposed pseudo-components with an average molecular weight within the range of known substances. In this

work was established that feed (A), distilled (D) and coke (C) consisted of one pseudo-component, each one with

molecular weight equal to 1000, 200 and 1000 respectively.

It is important to understand under what mechanisms are carried out reactions within the coking drum,

reason why it’s necessary to model possible reactions to find a clear idea of how temperature and reactive

concentration affect concentration of products that were obtained from Venezuelan oils subject to DC process.

Due to feed properties are fundamental variables in DC process yield, it’s important to indicate that obtained

results are reproducible only for feeds with similar characteristics to the feed employed. To validate developed

models, were utilized three series of experimental data that were obtained for cuts of Venezuelan oils feed to

batch reactors. These series are shown in the figure 1.

Fig. 1. Experimental data

Reaction rate is only a function of reactive substance properties (reactive concentration, temperature, and

pressure or catalyst type, if this is employed) in one point of the reactor, and is independent of the type of reactor

in that the reaction takes place. (Fogler, 1986)

Supposing models of reaction that take place within the reactor is possible to obtain mass balance equations

for each case, and subsequently a convenient fix of variables within balance equations would allow to evaluate

these variables from graphs, in which are compared values obtained from balance equations and experimental

data. The proposed configuration of present reactions in the drum that gives as result a reaction order with a

better fix to experimental data will be the correct configuration.

The kinetic parameter that will be estimated from reaction rate is the K constant of reaction rate. This rate

can be expressed for a simple reaction from a mass balance in a batch reactor, like is shown below in Eq. (1):

inA

dNA r K·CAV·dt

= − = (1)

In where: dNAV·dt

is the Mol variation of A in a volume and time unit; Ar− is the Reaction rate of A; K is the

Reaction rate constant; CA is the Reactive concentration within the drum; ni is the Reaction order.

3. Kinetic Models Studied

Three models was proposed for DC process, the first is based in coke production from series reactions, the

second is based in a system of parallel reactions and the third where coke is produced as much by series

reactions as by parallel reactions. Proposed configurations will be developed next.

3.1. Petroleum Coke production from two series reactions (model 1)

In figure 2 is shown the proposed configuration. In this model is supposed that feed is transformed in

distilled (D) and a part of this last one reacts to produce coke (C) (Yue et al., 1998). According to this model,

first reactions that take place are cracking reactions and next polymerization’s, the last is that make possible the

coke formation.

Fig. 2. Configuration supposed for model 1

In where:-r1, Reaction rate with respect to consumed feed; -r2, Reaction rate with respect to consumed

distilled.

Mass balance expressions for the batch reactor with model 1 are shown below in Eq. (2), (3) and (4).

1n1

dNA K ·CAV·dt

= − (2)

1 2n n1 2

dND d K ·CA K ·CAV·dt a

= − (3)

2n2

dNC c K ·CAV·dt d

= (4)

In the first place for this work, was supposed that both reaction orders were equals and could have entire

values between 1 and 3. It was begun with the lower order, later to continue with superior orders.

When reaction orders (both) are equal to 1, analytical solutions of the differential equation system shown

before are the next expressions (Eq. (5) and (6)):

1 CAt ·lnK CAo1

⎛ ⎞= − ⎜ ⎟⎝ ⎠

(5)

( )1K ·t1

2 1

CD K ·CAo·e1t ·lnK CDo K ·CAo

−⎛ ⎞−= − ⎜ ⎟⎜ ⎟−⎝ ⎠

(6)

From equations 5 and 6 were obtained figures 3 and 4, where were established as parameters to represent in

the graph, those that for what the slope of fitted curves allow to obtain the rate constant of the reaction involved

in the process.

-r1 -r2aA dD cC

Fig. 3. K1 obtaining for model 1 and reaction order equal to 1

In figure 3 is possible to observe that model deviation from experimental data is high (never less than 3%

and sometimes over 15%). The same study was made with reaction constant K2, and the obtained deviation for

K2 was more even elevated that for K1 (up 4%). In case that this model was evaluated with larger reaction orders,

it wasn’t possible to obtain smaller deviations that those were obtained with model 1, in conclusion it was

considered the better fit that could be obtained with model 1. Because this fit has elevated deviations, it was

discharged as a possible expression of kinetic of reactions that take place in DC process.

3.2. Petroleum Coke production from two parallel reactions (model 2)

This configuration is shown in figure 4. It is based in that feed (A) is converted in two products: D and C,

when cracking and polymerization reactions take place at the same time (parallel), competing between

themselves (Del Bianco et al., 1993).

Fig. 4. Configuration supposed for model 2.

Mass balance expressions for a batch reactor in model 2, are shown below in Eq. (7), (8) and (9):

1 2n n1 2

dNA K ·CA K ·CAV·dt

= −− (7)

ndND b 1·K ·CA1V·dt a= (8)

2n

2dNC c·K ·CAV·dt a

= (9)

This equation system was resolved with conditions supposed in model 1. When reaction orders are equal to

1, the analytical solution of this system is represented with following equations (Eq. (10) and (11)):

1 2K K K+ = (10)

-r1

-r2aA

dD

cC

( )Aln 1 Xt

K− −

= (11)

Where: XA is the Feed conversion.

Also, if it’s possible to adapt variables involved to a form in which the curve obtained is a straight, from its

slope can be calculated the reaction rate constant, K. This curve is shown in figure 5.

Fig.5. K obtaining from model 2 and order equal to 1.

It can be observed in figure 5, that calculated values of K1 are exactly the same that K values obtained from

model 1when A consumption is evaluated, because analytical solution of model 2 when reaction orders are equal

to 1 is the same that model 1’s when K1 is determined.

Due to fit obtained wasn’t better than when model 1 was evaluated, was necessary to suppose configurations

with reaction orders equal to 1,5 and 2, to evaluate the effect of this change over the deviation of the model with

respect to experimental data. Results of this case are shown in figures 6 and 7.

Fig. 6. K obtaining from model 2 to reaction orders equal to 1,5

Curves obtained for configurations with reaction orders equal to 1,5 and 2, fit better that when reaction

orders were equal to 1, showing that when reaction orders were increased, deviation obtained decreased. This

can be observed comparing obtained deviations in figure 7 with figure 6’s, in which when reaction order is

elevated, maximum deviation decrease (from almost 14% to 13%).

In based on it, it possible to think that elevate more reaction orders, is the solution to improved the fit, but if

it’s observed how much the fit get better when reaction order changed from 1,5 to 2, it can be demonstrated that

this improve is not decisive, reason why it’s considered that this configuration is the best approximation that can

be made to reactions that are taking place in the drum.

Fig. 7. K obtaining from model 2 to reaction orders equal to 2.

It is important to emphasize that, when figures 3, 5, 6, and 7 are reviewing, it can be observed that an

increase in temperature changes the value of rate constant, then can be said that reactions which are taking place

in the reactor are depending of temperature.

Due to fit that was obtained was not good enough, it was necessary to modelate another configuration.

3.3. Petroleum Coke production from two parallel and one series reactions (model 3)

This configuration supposed that feed (A) is become to two products: distilled (D) and coke (C), but at the

same time a part of this distilled reacts to produce coke, too. Cracking and polymerization reactions take place at

the same time, besides not only feed but also distilled can be converted into coke (Del Bianco et al., 1998). A

graphic representation of this configuration is shown in figure 8.

Fig. 8. Configuration supposed for model 3.

Mass balance expressions for a batch reactor, if process is taking place in a constant volume system, are

shown below in Eq (12), (13) and (14):

1 2n n1 2

dCA K ·CA K ·CAdt

= −− (12)

31 nn1 3

dCD d d·K ·CA ·K ·CDdt a c

= − (13)

2n

2dCC c·K ·CA

dt a= (14)

To resolve this differential equation system was considered that reaction orders are equal, and could have

values of 1, 2 and 3. It was begun with reaction orders equal to 1, and next was supposed reaction orders highest.

It was found that analytical solution of this system is not simple, reason why it’s required to use numerical

methods to obtain desired results. To solution equations (12), (13) and (14) was utilized Runge-Kutta-Fehlberg

-r3

-r1

-r2aA

dD

cC

method, which is a fourth order method, reason why gives an acceptable precision to the level of evaluation that

is carried out in this work.

Due to, results for different temperatures that were studied had the same behavior, it was made an analysis

of model 3 fitting them to a serie of experimental data, which was selected at random and corresponded to 425ºC

data. Results of comparing this experimental data with respect of solution for orders equal to 1, 2 and 3 of the

equation system are shown in figure 9.

Fig. 9. Changes on the feed quantity contain within reactor with the time.

In figure 9 is possible to observe that when reaction orders are increased, fit with experimental data gets

better until the point in which a reaction order is supposed to be 3, moment in which model hasn’t only the same

tendency that experimental data also it superposes over several of them. It’s indicates that model has similar

behavior that experimental data.

With the objective to establish that model 3 is which fits better experimental data was made figure 10, where

are shown obtained results with best fits using each model.

Fig. 10. Evaluation of feed consumption to the different models

In figure 10 is observed how model 3 (order equal to 3) is the best fit to experimental data of feed

consumption, comparing with the others. Due to coke and distilled production depend on reactive consumption,

and how was shown later, the best fit of A consumption is found with model 3. It can be said that this model

would be the best fit to production of both, too.

To know if production of coke and distilled can be better fitting to model 3 with order equal to 3 was made a

graph in which were represented obtained results for production of distilled and coke with model 3 and reaction

orders equal to 1, 2 and 3, these are shown in figure 11 and 12, respectively.

Fig. 11. Changes of distilled quantity containing within reactor with time

In figure 11, it can be observed how model 3 using three different reactions orders before named doesn’t fit

correctly distilled production, reason why this model is not adequate to predict distilled production. Then it can

be said that model 3 with reaction orders equal, fits better feed consumption that does distilled production.

Nevertheless, the fact that experimental data is found between other results indicates that reaction orders that fit

better has values between 2 and 3.

The same study for coke production is shown in figure 12.

Fig. 12. Changes of coke quantity within reactor with time

Results shown in figure 12 indicates again that model 3 with orders between 1 and 3 doesn’t fit well

experimental data, this fact suggest that exists a different level of dependency of distilled and coke production

with feed concentration. It for this reason why it’s possible to verify, in first place, dependency of selectivity

with feed concentration, and in second place, existence of infinite configurations that are necessary to study to

obtain the best reaction orders.

In based on figure 12, it were looked for reaction orders from 1 to 3 different between themselves, but with

only entire values. It was found that was possible to reduce infinite configurations before named to 27, three of

which already were studied (which had equal reaction orders), being left 24. This number of configurations is too

high, yet, and based on the fact that every configuration already studied which had an reaction order equal to 1

didn’t fit well the data, it was decided that all of them that had order equal to 1 of at least one of reactions

involved, were discharged. It this by that left only 6 configuration resting.

These 6 configurations were simulated and it was obtained which of them is the better fit to experimental

data of distilled and coke production, these were that for which reaction orders were equal to 2 for distilled

production and 3 for the rest of reactions involved.

But this result isn’t the best could be obtained, reason why it was proceed to utilize fractional reaction orders

between 2 and 3 for distilled production, maintaining equal to 3 the others. Results are shown in figures 13, 14

and 15.

Fig. 13. Feed quantity present within reactor with time using fractional orders

As results of figures 13, 14 and 15, it can be said that model 3 when reaction order is equal to 2,55 for

distilled production and equal to 3 for the rest, is the better average fit with respect to all reactions. This is the

most important result of this work, because it’s possible to probe that coke production is more dependent of feed

concentration than distilled production, based on the fact that coke reaction order is higher than distilled one’s.

Fig. 14. Distilled quantity present within reactor with time using fractional orders

Fig. 15. Coke quantity present within reactor with time using fractional orders

This could indicate that DC plant should be operated in a point in which feed concentration has to be smaller

as possible to favor distilled production. It is convenient to emphasize that those studies with a higher exactitude

in reaction orders are not justified, based on that the number of reactions involve in DC process is enormous and

then to know punctual values of reaction orders is less important (because they change with the number of

reactions that are taken into account) than to know dependency of every reaction with feed concentration and

temperature.

4. CONCLUSIONS

Conversion of reactions are taking place within the drum is dependent of temperature.

Use of pseudo-component is a viable alternative to predict kinetic parameters for chemical reactions when

they are complexs.

Model in which coke production is reached from polymerization of distilled and feed is the best fit for DC

process.

Reaction orders are higher than 2, which indicate a clear dependency of rate reaction with feed

concentration.

This dependency is higher for coke production than for distilled production.

5. SUGGESTIONS

It’s necessary to make simulations with model 3, but modifying the number of pseudo-components

supposed to verify that this variable doesn’t change obtained results for kinetic parameters.

To make studies in little scale with inerts feed to the drum, to verify the influence of feed concentration over

process selectivity.

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