Development of a model for an industrial acetylene hydrogenation reactor using plant data – Part I

Chemical Engineering Journal 379 (2020) 122390

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Development of a model for an industrial acetylene hydrogenation reactor using plant data – Part I

T

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Bruna Rijoa, Francisco Lemosa, , Isabel Fonsecab, André Vilelasc a

CERENA, Departamento Engenharia Química, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal REQUIMTE/CQFB, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Lisboa, Portugal c REPSOL Polímeros, Complexo Petroquímico, Aptd. 41 Monte Feio, Sines, Portugal b

H I GH L IG H T S

development of a dynamic model for an acetylene hydrogenation reactor. • Successful describes acetylene concentration at the outlet under different disturbances. • Model describes temperature at the outlet under different disturbances. • Model • A model was successfully developed based on plant data and published kinetics.

A R T I C LE I N FO

A B S T R A C T

Keywords: Acetylene hydrogenation Carbon monoxide Dynamic model Front-end configuration

In this work, a dynamic model of an industrial acetylene hydrogenation reactor with a front-end configuration was developed, based on plant operation data. This type of reactor operates in transient state, not only due to the natural fluctuations in operating conditions but also due to the effects caused by the deactivation of the catalyst. To develop the dynamic model of the acetylene hydrogenation reactor a thorough study of the effect of operating conditions was performed; the influence of variables such as the inlet temperature of the 1st reactor, the flowrate, carbon monoxide concentration, on the activity, selectivity and stability of the catalyst was examined by choosing adequate periods of the operation of the reactor. To understand the reaction mechanism of this system, several published kinetics were tested but only one was finally fitted to the industrial data, to interpret the operation of the acetylene hydrogenation reactor. A set of operation periods was used to develop the model which was then validated by applying the model to a different set of operation periods. As a conclusion, the dynamic model that was developed and validated, using actual plant operation data, was able to adequately describe the outlet temperatures of the three reactors in the system as well as the outlet acetylene concentration of the 3rd reactor.

1. Introduction Acetylene is an impurity in the olefin feed of polyolefin production plants, with the potential to poison the catalysts in the polymerization reactors [1–7]. As such, the acetylene in the ethylene stream to be fed to the polymerization reactors should be reduced to 1–5 ppm or less [1–7]. Acetylene can be eliminated from ethylene stream through two different methods: by hydrogenation or by solvent extraction. The solvent extraction method is usually unfavourable due to the high cost and operational difficulties; as a consequence, hydrogenation has become the most common method for the reduction of acetylene concentration. Acetylene is selectively hydrogenated into ethylene in

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Corresponding author. E-mail address: [email protected] (F. Lemos).

https://doi.org/10.1016/j.cej.2019.122390

Available online 30 July 2019 1385-8947/ © 2019 Elsevier B.V. All rights reserved.

adiabatic fixed-bed catalytic reactors in series, with heat exchangers which are installed between the different stages in order to limit the temperature rise [1,2]. The multi bed catalytic reactor system can be set-up in three configurations which depend on the feedstock, acetylene concentration, and the manufacturer [1,2]. The more frequently used configurations are the tail-end (or back-end), front-end and, lastly, raw gas catalytic hydrogenation, which is the least used. In tail-end configuration, the lighter compounds like H2, CH4 and CO are removed in demethanizer column, following the deethanizer distillation column prior to being fed to the reactor. Thereafter, the C2 rich stream (C2H2, C2H4 and C2H6) is fed into the reactor. Hydrogen and CO are removed before they enter

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(temperature controllers). These controllers manipulate the hot-stream flow control valves of 3 heat exchangers. Before the acetylene gas stream enters the 1st reactor, it is heated by three heat exchangers. Downstream of each bed a heat exchanger is installed, in which the gas is cooled by manipulating the cooling water flow rate to control the inlet temperature of the next bed. The inlet temperatures of the second and third reactors are controlled by the TC, which act on the flow control valves in the main and bypass lines of the respective exchangers and cooling water. The hydrogenated C2 gas stream is sent to a knock-out drum equipped with a demister. In it the green oil formed coalesces and is accumulated to be sent to a flare. The gas phase is sent to the low temperature section. The analyzer of acetylene concentration indicator is located on the stream leaving the knock-out drum that goes to the low temperature section. When the product goes out of specification, the information of the analyzer reaches the cascade controller in which the TC will manipulate the hot-stream flow control valves of the heat exchangers in front of the first reactor to appropriately increase the inlet temperature into the first reactor. This control is essential in order to guarantee product specification. The inlet temperatures of all reactors, considered in the model, are those measured online. In this way, the model simply uses the independently measured inlet temperatures as inputs to the present model. In case of any future simulation run in which no plant data are available beforehand, the model will simply use the selected set point of the TC as the inlet temperature into the respective second and third reactor.

the reactor and then added individually [1–3]. Carbon monoxide is usually used to improve the selectivity of catalyst. In this system, variables such as the hydrogen/acetylene ratio, inlet temperature of 1st reactor and CO concentration can be easily adjusted according to the requirements of the process. In the front-end deethanizer configuration, the reactor is placed after the deethanizer and before the demethanizer. In this case, the stream entering the reactor is composed by hydrogen, carbon monoxide, CH4, C2H2, C2H4 and C2H6. The composition of the reactants, including CO concentration, are determined by the pyrolysis conditions in the furnaces, and, in this case, the only variable that can be adjusted in the hydrogenation unit is the inlet temperature in 1st reactor [1–3]. Inside the hydrogenation reactors both the hydrogenation of acetylene (1) and ethylene (2) can occur: 1) C2 H2 + H2 → C2 H 4 2) C2 H 4 + H2 → C2 H6 3) C2 H2 + 2H2 → C2 H6 Reaction (1) is the desired reaction, whereby acetylene is selectively hydrogenated to ethylene. Simultaneously ethylene may also be hydrogenated to ethane in reaction (2), which will imply a reduction of the ethylene selectivity of the process. There is also the possibility of a direct hydrogenation of acetylene to ethane (3). Usually this reaction is ignored because it is much slower when compared to the two former ones [3]. In the case of front-end reactors, hydrogenation of methylacetylene (4), propadiene (4) and propylene (5), which may also be present in the feed, are also likely to occur in addition to the ones above [4].

2.2. Disturbances

4) C3 H 4 + H2 → C3 H6 5) C3 H6 + H2 → C3 H8

In this work, the system under analysis has a front-end deethanizer configuration. The plant data from the industrial reactor corresponds to operation data for extended periods of time. From the complete set of available information different subsets were chosen so as to allow the model development and model validation. The first step was the choice and collection of the data to be used for the different purposes. Also, to develop the dynamic model, deliberate disturbances were introduced in the reactor operation to allow us to study the dynamics of the process under conditions such as the reduction of the flow rate and the increase of CO concentration into the 1st reactor. Figs. 1 and 2 depict deliberate disturbances that were separately introduced in the process, both on CO concentration and on the feed flowrate in Period #1. The only variable that was not possible to vary independently in a controlled manner in this work was the concentration of CO that depends on the amount of coke that is formed in the furnaces used to produce the feed to the reactor. However, indirect disturbances were also possible in CO concentration by turning off the DMDS (dimethyl disulphide) injection system in the furnaces; the sulphur additives are added to decrease the amount of coke formed in the furnaces and, thus, have a direct impact on the concentration of CO. The introduction of CO in the reactor is important to control the

2. Industrial data collected 2.1. Acetylene hydrogenation unit description The data available from the industrial reactor consisted of a set of flowrate and the temperatures profiles in all reactors measured online for an extended period of time. The initial concentrations of acetylene and carbon monoxide, at the inlet of the 1st reactor and the acetylene concentration at the outlet of the 3rd reactor, were also measured online. However, there were no online measurements at the outlet of the 1st and 2nd reactors for acetylene or CO. Although there are no online measurements for the main compounds, such as hydrogen, methane, ethylene, ethane, propylene and propane, once a week samples were taken to check the detailed composition of the inlet and outlet streams of the all reactors. A typical feed mixture consists of 17.2 M % H2, 43.8 M % CH4, 32.8 M % C2H4, 5.3 M % C2H6, 0.47 M % C2H2, 0.35 M % C3H6 and 0.09 M % CO as main components. The flow rate is usually between 90,000 Nm3/h−119,000 Nm3/h, the total pressure is about 27 bar, and the inlet temperature in the first reactor usually lies between 360 K and 385 K. The reactor that was studied, in this work, is coupled to a SteamCracker. The feedstock used in Steam-Cracker is a mixture of naphtha, propane and butane. The catalytic bed has a volume of 4.5 m3, with a Pd catalyst promoted by silver on an alumina support. The overall process consists of a deethanizer distillation column followed by three adiabatic reactors in series in a typical front-end hydrogenation configuration. The acetylene in gas streamC2 , will be hydrogenated in the three adiabatic reactors in series. Since the reactors are adiabatic and hydrogenation reactions (1)–(5) are exothermic, there will be a significant increase of temperature at the exit of the catalytic beds. The reactor’s output currents will be cooled by heat exchangers placed between the reactors. The inlet temperature of the first reactor is controlled by the TC

Fig. 1. Flowrate at the entrance of 1st reactor. 2

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significant changes in the temperature profile along the reactor. It was observed that there were some deviations of the temperature along the reactor, on indicators 2, 4 and 6 which were assigned to sensor problems as it is unlikely that the preferred path issues would give rise to these differences in the readings. 3. Development of fixed bed reactor model The model developed, in this work, combined kinetic rate laws presented in the literature and industrial operation data necessary to estimate the kinetic parameters and to validate the model. 3.1. Model assumptions

Fig. 2. CO concentration at the entrance of 1st reactor.

Based on the work found in the literature, a pseudo-homogeneous model was chosen as this is a common approach by authors [8–16]. In order to reduce the complexity of the resulting model, additional simplifications were introduced:

hydrogenation activity and ensure ethylene selectivity by poisoning some of the hydrogenation sites in the catalyst and, thus, reducing the activity: when there is an increased CO concentration, acetylene conversion decreases, due to lack of hydrogenation activity; when there is a decreased CO concentration, the acetylene conversion increases. This is associated with the fact that carbon monoxide will adsorb in the same active sites of the catalyst as acetylene (and ethylene). When there is a decreased in acetylene conversion, for whatever cause, including an increase in CO concentration, the way to counteract this situation is to increase the inlet temperature of 1st reactor and this also had to be done during the disturbances that were introduced so as to ensure that the outlet is always within the required specification. As an example, in Figs. 2 and 3, it is possible to observe that when there is an increase in CO concentration an increase in the inlet temperature of the first reactor is also induced to prevent the product from being out of specification due to high acetylene concentrations resulting from the loss of activity.

• All reactors were described by the 1-dimensional pseudo-homo-

•

•

2.3. Catalyst deactivation analysis

• • •

The operation data available for this part of the work included all the operation conditions (flowrate, compositions of streams and inlet and outlet temperatures), and also included the temperature profiles inside all three reactors (consisting of six temperature measurements for each reactor) represented schematically in Fig. 4. After a detailed analysis of the operation data provided, data was chosen, on different dates that had very similar flows and acetylene and carbon monoxide concentrations. Under these conditions, the inlet temperature of the reactor must be substantially the same and no deactivation of the catalyst occurs; otherwise, a gradual increase of the reactor inlet temperature should be observed. Regarding temporal evolution of the temperature along the first reactor, shown in Fig. 4, there is no gradual increase in the reactor inlet temperature, and it is found that the deactivation of this catalyst is very slow. During these periods we can also observe that there are no

geneous plug-flow reactor model and adiabatic; axial and radial dispersion of mass and heat were considered as negligible; this assumption can be justified by the short residence time in the reactors and was tested in the model where it was found that including axial dispersion in the plug-flow approach did not improve the fittings. Carbon monoxide and methane were considered unreactive under the conditions used in the reactor; it should be noted, however, that CO, although unreactive, is considered in the kinetic rate law for the hydrogenation reactions since its adsorption on the catalyst is relevant for the hydrogenation activity. Carbon monoxide acts as a reversible poison [13]. Since the approach used was to develop a pseudo-homogeneous model, it was implicitly assumed that all adsorption equilibria are fast and there was no significant accumulation of the components on the catalyst. Catalyst deactivation was very slow; this assumption was based on the preliminary analysis detailed above (see Fig. 4). No pressure drop through the fixed beds was considered. Heat capacity of the solid (catalyst) was considered negligible.

3.2. Mass and heat balances A complete description of the equations that compose the model of the acetylene hydrogenation is given in this section. As the reactor operates under unsteady-state conditions and the objective is to provide an operational account of the reactor, all equations written in this section for the mass and heat balances are dynamic. The mass balance of main compounds can be written as:

ε

∂Ci, n ∂Ci, n + ρs . (1 − ε ) = − ε . ug , n ∂z ∂t

∑ r j, n (1)

j

where i stands for the different chemical species (C2H2, C2H4, C2H6, C3H6), j stands for the reaction number and n the number of reactor. The thermal balance is given by the following equation:

ρg . ε . Cpg, n

∂Tn ∂T = −ε . ρg . Cpg, n. ug, n n + ρs . (1 − ε ) ∂t ∂z

∑ rj,n (−ΔHr )j,n j

(2) 3.3. Kinetic model Most kinetic studies reported in the literature were relative to tailend configurations in the acetylene hydrogenation process. Authors such as Men'shchikov et al. [17], Gva and Kho [18], Bos et al. [19,20] and Mostoufi et al. [8] proposed kinetic expressions based on a tail-end

Fig. 3. Inlet temperature in the 1st reactor. 3

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Fig. 4. Arrangement of temperature indicators along the 1st reactor (left figure) and temporal evolution of the temperature along the 1st reactor (right figure).

quantitative analysis was done for the values of the pre-exponential factor for the acetylene and ethylene hydrogenation reactions so that the temperature values obtained by the model were close to the plant data. After the semi-quantitative analysis, a kinetic equation was chosen by considering the one that best describes the plant data, where the sum of squared error has the lowest value. Once the kinetic equation is chosen, all kinetic parameters were fitted to the plant data.

configuration. Nevertheless studies related to front-end configurations can also be found. Some authors like Adúriz et al. and Gigola et al. [21,22] studied the dependence of the rate order for acetylene on the particle size of the palladium, in front-end conditions. Duca et al. [23,24] developed a model assuming a Langmuir-Hinshelwood mechanism for the conversion of acetylene, in a front-end configuration. Cider et al. [25] developed a mathematical model based on the Horiuti-Polanyi mechanism for ethylene hydrogenation. Mcgown et al. [26] studied the hydrogenation of acetylene in the presence of ethylene and carbon monoxide and reported that the rate of disappearance of acetylene was controlled by pore diffusion at low acetylene concentrations and was independent of acetylene at high acetylene pressures. Zea et al. [27] considered that the surface reaction of ethylene is the controlling step of the mechanism and that the adsorption of ethylene, hydrogen and carbon monoxide takes place on the same kind of active site. The rate equation of acetylene consumption is obtained by applying a Langmuir–Hinshelwood–Hougen–Watson mechanism. Godinez et al. [4] proposed power-law type kinetic laws for frontend acetylene hydrogenation and considered the influence of CO in the acetylene hydrogenation process. Schbib et al. [10] published several expressions for the kinetic law in the formation of ethylene and ethane using front-end configuration. Gobbo et al. [14] adopted a kinetic expression of Schbib et al. and fitted it to their experimental data. In this work, the configuration used is front-end and, as such, the study of kinetic models will focus on authors who have used this configuration. A careful choice was made of the kinetic expressions that were studied by Schbib et al. and the ones that were found to be better suited to describe the experimental data were selected. Several hypotheses have been considered before the final choice was made, such as: if the hydrogen will adsorb at different active sites (Schbib 1) or in the same active sites (Schbib 2) than hydrocarbons and CO or if hydrogen reacts directly with adsorbed C2H2 and C2H4 (Schbib 3), thus leading to three different approaches. From Section 2.2, it was possible to observe that when there is an increased CO concentration, acetylene conversion decreases. This implies that CO adsorbs in the same active sites of the catalyst as acetylene (and ethylene). Where,

1 ⎞⎞ ⎛ Ea, i ⎛ 1 ki = k 0, i exp ⎜− − ⎜ ⎟ R ⎝T Tref ⎠ ⎟ ⎠ ⎝

(3)

1 ⎞⎞ ⎛ Eads, i ⎛ 1 Ki = K 0, i exp ⎜− − ⎜ ⎟ R ⎝T Tref ⎠ ⎟ ⎠ ⎝

(4)

3.4. Numerical solution The model equations were solved using a program developed in the Visual Basic for Applications environment within Excel. The PDE that describes the transient behaviour of a plug flow reactor was solved using the method of lines (MOL). The spatial coordinate (the reactor volume) was discretized approximating the space coordinate derivatives using the finite differences method. By this process, a set of ordinary differential equations were obtained and these were solved using a fourth-order Runge–Kutta method (RK4). 4. Results and discussion 4.1. Rate-law selection As discussed previously, one of the aims of this study is to develop a reactor model capable of representing the behaviour of the acetylene hydrogenation system. As detailed above, three different versions of the kinetic rate laws were preliminarily selected. In this section the kinetic rate equations presented in Table 1 will be analysed so that only one will be selected for further use in this work. The kinetic parameters proposed by Schbib et al. [10] are shown below with the exception of the pre-exponential factors of acetylene and ethylene reactions. The pre-exponential values proposed by Schbib et al. were 31.1 and 26.6, respectively for acetylene and ethylene reaction but as these pertained to a specific catalyst, in the continuation we assumed that the same kinetic rate-laws apply and only the pre-exponential factor for the acetylene and ethylene hydrogenation reactions were change to fit them to the catalyst being used in the facility. In a first stage the pre-exponential factors were varied so that the values obtained with the model described well the actual temperatures at the exit of the first reactor. When these temperatures, obtained by the model, were close to the actual temperatures, the second stage proceeded to compare the values obtained by the model for the outlet temperatures of the 2nd and 3rd reactors and the outlet acetylene concentration of the 3rd reactor. The initial kinetic parameters values of acetylene and ethylene reactions are shown in the Table 2. The purpose of this section is to choose the kinetic equation that best describes the plant data. In Fig. 5 a comparison of the values calculated by the model, using the above mentioned kinetic rate laws, based on Schbib kinetics equations [10], and the actual plant data. This

The initial guesses of kinetic parameters were taken as the ones proposed by the Schbib et al. [10]. The procedure for the development of the acetylene hydrogenation reactor model, using the kinetic expressions presented in Table 1, was the following: first, a semi4

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Table 1 Kinetic rate equations for the selective hydrogenation of C2H2 and C2H4 proposed by Schbib et al. [10]. Schbib 1

kA P C2 H2 P H2

r C2 H2 =

1

1 2

( 1 + KC2 H2 PC2 H2 + KC H PC2 H4 + KC2 H6 PC2 H6 + KCO PCO ) ⎜⎛1 + K H2 2 P H2 2 ⎞⎟ 2 4 ⎝

r C2 H6 =

r C2 H2 = r C2 H6 =

r C2 H2 = r C2 H6 =

1 1 2 ( 1 + KC2 H2 PC2 H2 + KC H PC2 H4 + KC2 H6 PC2 H6 + KCO PCO ) ⎜⎛1 + K H2 2 P H2 2 ⎟⎞ 2 4 ⎝ ⎠ kA P C2 H2 P H2 1 (1 + KC2 H2 P C2 H2 + KC H P C2 H4 + KC2 H6 P C2 H6 + (K H2 P H2 ) 2 + KCO PCO )3 2 4 k E P C2 H4 P H2 1 (1 + KC2 H2 P C2 H2 + KC H P C2 H4 + KC2 H6 P C2 H6 + (K H2 P H2 ) 2 + KCO PCO )3 2 4

kA P C2 H2 P H2 1 + KC2 H2 P C2 H2 + KC H P C2 H4 + KC2 H6 P C2 H6 + KCO PCO 2 4 k E P C2 H4 P H2

6

kC2H2 (m /(s gcat kmol))

kC2H4 (m6/(s gcat kmol))

KH2 (m3/kmol)10 KCO (m3/kmol)10 KC2H4 (m3/kmol)10 KC2H6 (m3/kmol)10 K C2H2 (m3/kmol)10

Schbib 2

Schbib 3

1 + KC2 H2 P C2 H2 + KC H P C2 H4 + KC2 H6 P C2 H6 + KCO PCO 2 4

reactor when there are significant disturbances. If we analyse Fig. 2, during Period #1, there is an increase in CO concentration, and it is observed that the values given by the model show a larger deviation in this period. It is also observed that all models, show larger deviations in temperature during Period #1, in the 1st reactor, when there is an increase in CO concentration. This shows that the kinetic parameters, presented in Table 2, need to be fitted to our plant data, mainly to their daily variability. All kinetic parameters were proposed by Schbib et al. for a catalyst different from that used in this work. As previously stated, the preexponential factors of the acetylene and ethylene reactions were changed so that the temperatures obtained by the model in the 1st reactor were similar to those of the industrial temperatures. However, the kinetic parameters for the adsorption of the different compounds were those proposed by Schbib et al. [10]. As such, the values of the temperatures obtained by the models and industrial ones have a lower error than the error of the difference between the values of the acetylene concentrations. As such, these parameters need to be fitted to our industry data. The chosen of model was the one that, based on the following sum function, using the least squares method, achieved the lowest value:

Table 2 Initial values of kinetics parameters. Kinetics parameters

⎠

k E P C2 H4 P H2

log k0,i 35.4 37.9 28.3 28.9 31.3 22.7 log K0,i 20.2 13.6 0.26 −0.012 −16

Ea,i (kJ/mol) Schbib Schbib Schbib Schbib Schbib Schbib

1 2 3 1 2 3

190.210

179.4

10

Eads,i(kJ/mol) 88.7 41.6 0.021 0.004 0.004

procedure was carried-out using the three variations of the kinetic rate laws presented in Table 1 and that will be referred from here on as Schbib 1, Schbib 2 and Schbib 3. From Fig. 5 it can be seen that all variations of the kinetic rate laws that were used describe well the overall temperature evolution with time. However, in relation to the evolution of the acetylene concentration the situation is rather different. The acetylene concentration of 3rd reactor is not predicted as accurately, however the same behaviour is observed but at different concentration scales. The kinetic parameters need to be fit to our plant data. The values calculated by the model using the kinetic equations from Schbib 2, present major differences with the plant data. This model varies widely and does not approach the plant data. The kinetic equation of Schbib 2 cannot describe the industrial acetylene concentration. This model also presents significant deviations from the plant in relation to the temperature. One of the reasons for oscillations in the temperature calculated by the model may be that the power in the denominator is higher. This model could not be used to explain the outlet temperatures off all reactors and acetylene concentration of 3rd reactor. As a consequence, the kinetic parameters were not fitted to the experimental data. The model using Schbib 3 kinetic expression can adequately describe the plant temperature data in the beginning. However, after an initial period this model presents significant differences between the plant data and the temperature values obtained by the model in the first two reactors when there is a decrease in the flow rate and in CO concentration and an abrupt decrease in the inlet temperature of the first reactor, see Figs. 1–3. It is also possible to observe that this model is not able to describe the trends in the outlet acetylene concentration of the 3rd reactor. Comparing the values obtained by all models, it can be seen that the models cannot predict the acetylene concentration at the exit of the 3rd

⎛ Sum = ⎜∑ ∑ (Tcalc, t , n − Tmeas, t , n )2 + ⎝ t n

∑ (C2 H2calc,t − C2 H2meas,t )2⎞⎟ t

⎠ (5)

where Tmeas, t , n represents the temperature measurement taken at the time instant t, in the reactor n, Tcalc, t , n represents the temperature values calculated by the model, C2 H2meas, t and C2 H2 calc, t are the concentration measurement of acetylene in the outlet of 3rd reactor at the time instant t and acetylene concentration values obtained by the model, respectively. The following Table 3 shows the sum function values for each kinetic model used. It should be mentioned that the kinetic parameters of the expressions were not fitted to our industrial data. Analysing all models, it is observed that the model Schbib 1 has the objective function with the lowest value. This model is the only that can describe the temporal evolution of the temperature of all reactors with a good approximation, but the kinetic parameters need to be fitted so that the model can predict the values of the acetylene concentration at the exit of the 3rd reactor when there is a daily variability of the operating conditions. So, in this work, the model based on Schbib 1 kinetic expression will be used to describe the temporal evolution of the temperature in three reactors and acetylene concentration in outlet of 3rd reactor. The kinetic parameters fitted of Schbib 1 expression will be presented in the next section.

5

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Fig. 5. Comparison between the plant data and model using kinetics equations of Schbib: left part is shown temporal evolution of temperature; right part corresponds to the temporal evolution of C2H2 concentration.

and #3. The chosen date, for the collection of industrial data, in the development of the model was from Period #1 (one day continuous operation). As was said previously, during these days, some disturbances were deliberately introduced in the process, namely in the flow rate, increase in carbon monoxide concentration and inlet temperature of the first reactor. The plant data presented previously was used to develop the model and to fit the necessary kinetics parameters. In this section, the model based on Schbib 1 rate equations will be developed and validated for the three reactors. As it was seen above, in particular in the Fig. 5, the acetylene concentration that was computed by the initial model was very high and did not coincide with the experimental data. Since the catalyst that was used in the industrial facility was not the same upon which the reaction rate equations were developed in the literature references

Table 3 Sum values for each model. Schbib 1

Error

Schbib 2 6

3.75 × 10

Schbib 3

1.59 × 10

8

8.72 × 106

4.2. Model fitting While the model developed in this work incorporates previous kinetic information, plant data are required for parameter estimation and model validation. The parameters to be estimated were the constants of the acetylene and ethylene consumption kinetic constant and the adsorption terms (k 0, i , K 0, i , Ea, i and Eads, i ), using the data set in Period #1. After the kinetic parameters of the model were fitted, using the data from Period #1, the model was validated using data from Periods #2

Table 4 Comparison of the values obtained by the model and the sample data. Mole fraction

H2 C2 H2 C2 H 4 C2 H 6 CO

Inlet 1st reactor

Outlet 1st reactor

Outlet 2nd reactor

Process/Model

Process

Model

Process

Model

Process

Model

0.172 4.65E−03 0.326 0.052 9.00E−4

0.167 4.25E−4 0.331 0.052 9.00E−4

0.167 5.52E−4 0.330 0.052 9.00E−4

0.167 1.92E−05 0.332 0.052 9.00E−4

0.167 2.09E−5 0.331 0.052 9.00E−4

0.167 9.06E−7 0.332 0.052 9.00E−4

0.167 9.26E−7 0.331 0.052 9.00E−4

6

Outlet 3 reactor

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fraction of inlet of 1st reactor used to initialize the model and the mole fraction of process of all reactors were an average of the samples taken before and after the disturbances were carried out. It is possible to conclude that the values obtained by the model are in agreement with the sample data. The parity plots for the outlet temperatures and acetylene concentration are presented in Fig. 7. These values were calculated for the chosen periods when there were disturbances in flow rate, inlet temperature in 1st reactor and carbon monoxide concentration. The diagrams of Fig. 7 shows that the model is able to predict reasonably well the outlet temperatures of all reactors even when the process had significant disturbances and, consequently, had the highest variability. The diagram of acetylene concentration shows, also, that the model is able to predict the outlet acetylene concentration of 3rd reactor. However, the model did not predict the acetylene concentration as well as temperature because the acetylene concentrations are very low and a small change in the operating conditions has a large impact on the final acetylene concentration. The model is able to predict the temporal evolution of the temperature in all reactors and acetylene concentration, within the observed daily variability. Other criteria used for model validation are the root mean square error (RMSE) and the average absolute relative deviation (AARD):

some corrections to this model in order the amount of acetylene in the outlet of 3rd reactor can describe the real quantity of acetylene in the industry. In the sum function used above, the absolute error definition was used to choose the kinetic rate laws to be used. However, this function (Eq. (5)) needs to be improved before fitting the kinetic parameters since the acetylene concentration values are much lower than the temperature values; this improvement was introduced in the form of a different weight to ensure that the objective function is adequately dependent on both concentration and temperature. With this correction, the square of the difference value between the temperatures obtained by the model and industrial and the square of the difference value between the acetylene concentrations obtained by the model and industrial ones have results of the same order of magnitude. Thus, the kinetic rate expressions were kept as described in the literature and the kinetic parameters were fitted to the available reactor data by minimizing the objective function using the least squares method, Eq. (6). The minimization of the objective function was made by using Solver from Excel for multiple response.

⎛ min ⎜∑ ∑ (Tcalc, t , n − Tmeas, t , n )2 + Fobj ⎝ t n

∑ 10 × (C2 H2calc,t − C2 H2meas,t )2⎞⎟ t

⎠ (6)

In next Fig. 6, the outlet temperature data of all reactors and the acetylene concentration data at the outlet of the 3rd reactor using the model with the kinetic parameters fitted are shown. From Fig. 6, it can be concluded that all temperatures are reasonably well predicted by the model. However, even though the outlet temperature is predicted within its estimated daily variability, significant deviations may occur. The temporal evolution of acetylene concentration, in the outlet of 3rd reactor, is also predicted by the model. As previously stated, samples are taken once a week from all streams at the inlet and outlet of all reactors so as to ensure that there are no changes in the compositions of those streams. As such, it is not possible to compare the concentration values obtained by the model with respect to the H2, C2H4, C2H6 and nor it is possible to compare the outlet acetylene concentration of the 1st and 2nd reactors. The mole

⎡1 RSMEx = ⎢ N ⎣

1 2

N

∑ (xcalc,t,n − xmeas,t,n )2⎤⎥ ⎦

t=1

AARDx (%) = 100 ×

1 N

N

∑ t=1

x calc, t , n − x meas, t , n x meas, t , n

(7)

(8)

where x meas, t , n represents the temperature or acetylene concentration measurement taken at the time instant t, in the reactor n and x calc, t , n the temperature or acetylene concentration given by the model and N the number of samples. The RSMEx for outlet temperatures of the 1st, 2nd and 3rd reactors and outlet acetylene concentration for the 3rd reactor are, respectively: 1.78, 0.78, 0.29 and 0.4. From RMSE it is possible to observe that differences between values predicted by the model and the values measured is higher in acetylene concentration than the value

Fig. 6. Comparison between the plant data and model in all reactors. 7

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Fig. 7. Parity plot for the outlet temperature of all reactors and concentration of acetylene in 3rd reactor.

development of the model with the new catalyst. If the acetylene adsorption parameters were low, hydrogenation of this compound would be low because while in the 1st reactor the acetylene concentration is much higher than the carbon monoxide concentration, in the 2nd and 3rd reactors this situation changes. In the 2nd and 3rd reactors, the concentration of carbon monoxide is higher than that of acetylene (see Table 4). As such, if the acetylene adsorption rate is much lower and if it is in less concentration when compared to the carbon monoxide rate and amount, the latter will occupy rapidly the same active centres of acetylene. This is consistent with the assumption that acetylene and carbon monoxide are adsorbed molecularly and compete for the same adsorption sites. Therefore, the fitting procedure changed the kinetic parameters to make acetylene adsorption more competitive and, the adsorption rate must be higher than that proposed by Schbib et al. [10]. These changes are reasonable as, although we assumed that the same mechanism applies, the catalyst used in this study is different from the one in the original work by Schbib et al. [10]. By the values obtained by fitting of the kinetic parameters to our industrial data, presented in Table 5, it is observed that the adsorption rate of acetylene is higher than that proposed by Schbib et al. [10] and, on the other hand, the rate of carbon monoxide adsorption is lower than that was observed by these authors. This shows that, in our catalyst, there is a greater competition, by the same active centres, between the acetylene and the carbon monoxide than in the of Schbib et al. catalyst. Thus, in this case, the adsorption rate of the acetylene needed to be increased so that the acetylene would have higher coverage of the active sites than the carbon monoxide in the 2nd and 3rd reactors, even though it is present in smaller amounts. In this way, the hydrogenation reaction of acetylene is present in the 2nd and 3rd reactors and, by Fig. 6, it can be observed that the model can predict the acetylene concentration, even if there are changes in the concentration of carbon monoxide. Although the catalyst of Schbib et al. [10] was completely different from the one in this study, as was previously noted, the parameters were fitted in this work due to the similarity of industrial conditions namely the presence of carbon monoxide in this acetylene hydrogenation process which plays a very important role in this type of front-end configuration.

presented by the outlet temperatures of all reactors. This means that acetylene presents an error higher than the other errors presented by the outlet temperatures of all reactors. The AARDx (%) for outlet temperatures of the 1st, 2nd and 3rd reactors and outlet acetylene concentration for the 3rd reactor are, respectively: 0.39%, 0.15%, 0.06%, 36.08%. The acetylene concentration shows an AARD much higher than the value presented by the outlet temperatures of all reactors due to the same reasons discussed above: as previously stated, the acetylene concentration is very low and a slight change in the operating conditions causes a more significant variation in the final concentration than in the temperature values at the exit of the reactors. However, this developed dynamic model can predict the outlet temperatures of all reactors and the concentration of acetylene at the exit of the 3rd reactor, within the daily variability observed in this industrial unit. The numerical model was fitted to the set of operational data. The fitting parameters were presented in Table 5. A more visible difference between these fitted kinetic parameters, presented in Table 5, and Schbib et al. parameters, see Table 2, is in values of the adsorption parameters of the acetylene and carbon monoxide in the catalyst, KC2H2 and KCO, respectively. These parameters are important in the kinetic model because, in these catalysts, acetylene has a great affinity with the active centres, like the other compounds, H2 and CO. Using the same kinetic parameters for acetylene adsorption, proposed by Schbib et al. [10], the acetylene adsorption rate becomes very slow and, in the 2nd and 3rd reactors, the acetylene hydrogenation reaction was practically non-existent. This was observed in the Table 5 Kinetic parameters fitted for the catalyst. Kinetics parameters

log k0,i

Ea,i (kJ/mol)

kC2H2 (m /(s gcat kmol)) kC2H4 (m6/(s gcat kmol))

36.2 30.6

180.0 177.5

KH2 (m3/kmol) KCO (m3/kmol) KC2H4 (m3/kmol) KC2H6 (m3/kmol) KC2H2 (m3/kmol)

log K0,i 22.7 10.3 0.26 −0.012 8.6

Eads,i (kJ/mol) 101.6 10.10 0.021 0.004 0.011

6

8

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Fig. 8. Model validation of Period #2 and Period #3.

4.3. Model validation

4.4. Axial dispersion effect

In this section the simulation concerning the chosen validation data sets are presented, in order to check if the developed model describes these datasets as well. The criterion used to select the validation dataset was based on the existence of variations of inlet conditions, such as: flow rates, CO concentration and inlet temperature in the first reactor. From Fig. 8, it can be observed that all temperatures and temporal evolution of acetylene concentration, in the outlet of 3rd reactor, are reasonably well predicted by the model. This implies that the model developed is, in fact, capable of describing the reactor operation in a variety of conditions.

As previously discussed, axial dispersion effects were neglected since the ratio between reactor length and catalyst particle diameter is larger than 100 [28]; other authors also suggests that, for the flow velocities used in industrial applications, axial dispersion can be considered as negligible when the reactor length exceeds by 50 times the value of the catalyst particles diameter [29]. All of these criteria to neglect axial dispersion are satisfied in the reactor under study in this work. Moreover, since the reactor is adiabatic, radial dispersion is also expected to be negligible because there is no driving force for temperature gradients to develop in the radial direction. Nevertheless, a 9

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Fig. 9. Time evolution of the temperature and acetylene concentration along the 1st reactor.

rate, inlet temperature of the first reactor and the concentration of carbon monoxide. This model assumes that the deactivation of the catalyst has characteristic time which is much longer than the characteristic time of the observed disturbances. From the data presented in Fig. 4, it was possible to confirm that the deactivation of this catalyst is very slow. It has been observed, both from the model and from the plant data, that the concentration of carbon monoxide is the variable that causes the most significant impact on the process. It is usually accepted that carbon monoxide adsorbs on the same active sites of the catalyst as acetylene and this assumption was consistent with the results obtained. If there is an unexpected increase in CO concentration the reaction rate will drop and one way of preventing off spec product, due to the decrease in acetylene conversion, is to increase the inlet temperature of the first reactor. One way of controlling the acetylene concentration at the outlet of the 3rd reactor is through the inlet temperature of the 1st reactor. The model used a published reaction rate law and only the kinetic and equilibrium constants were fitted to the actual plant data. The fitted kinetic model was able to accurately predict the outlet temperatures of the 3 reactors as well as the acetylene concentration at the exit of the 3rd reactor even in the case of significant variability of the inlet conditions. The developed model was validated with a second set of plant data and were able to predict the outlet evolution of the temperature of all reactors, as well as of the acetylene concentration at the exit of the 3rd reactor, along time in the presence of these disturbances. From the results that were presented we can conclude that it is possible to develop models based on plant data that can be used to describe the reactor performance in a wide variety of conditions. This type of models can be useful not only for long-term planning of the operation but also for short-term operation of the reactor and can potentially be used for the reactor operation to analyse possible strategies in face of unforeseen disturbances in reactor operating conditions. The developed model has a calculation time faster than the real time, allowing to predict the output variables in unforeseen situations.

brief sensitivity analysis was also performed on the influence of including axial dispersion in the model. Considering the mass dispersion of the gas, the mass balance equation should be rewritten:

ε

∂Ci, n ∂2Ci, n ∂Ci, n + ρs . (1 − ε ) − ε . ug , n = ε . Dax ∂z ∂z 2 ∂t

∑ r j, n j

(9)

Such as, the thermal balance with axial heat dispersion is shown in the following equation:

∂Tn ∂t ∂2Tn ∂T = λax . ε 2 ε . ρg . Cpg, n. ug, n n + ρs . (1 − ε ) ∂z ∂z

ρg . ε . Cpg, n

∑ rj,n (−ΔHr )j,n j

(10)

λax is the axial heat dispersion calculated by [30,31]: λax = 7 + 0.5PrRe kg

(11)

The results obtained are compared with plant data and the results obtained by using pure plug flow model without dispersion and considering dispersion. In the next Fig. 9, axial dispersion model with temporal evolution of the temperature and concentration for 1st catalyst bed is plotted. The mass dispersion/thermal dispersion ratio is very high, more than 200. As such, the thermal dispersion, in this work, can be neglected [8]. For the case of gas–solid catalytic reactions that take place in packed-bed reactors, the axial dispersion coefficient, Dax, can be estimated [32,33]. The value of Dax, axial dispersion coefficient obtained is 0.68 dm2/s. The influence of the axial dispersion was also studied, increasing by 5 times the previously obtained value, to 3.4 dm2/s. The purpose of this increase is to analyze the effect of axial dispersion on temperature and acetylene concentration values. The values of temperature and concentration provided by the model with and without dispersion were then compared. In Fig. 9, it is possible to observe that, comparing the values of the temperatures and concentration along the 1st reactor, obtained by the model, the effect of the axial dispersion is negligible in comparison with the values obtained without dispersion. Even with an increase of 5 times of the axial dispersion coefficient, it is possible to observe that this effect is not significant. It is concluded that the hypothesis of not considering axial dispersion in the model is a good approximation.

Acknowledgments B. Rijo thanks the Fundação para a Ciência e Tecnologia (FCT) and Repsol Polímeros S.A for financial support doctoral grant (PDE/BD/ 52612/2014). And also to CERENA for the project UID/ECI/04028/ 2013. References

5. Conclusion

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A dynamic model of the set of reactors in acetylene hydrogenation process was developed for an actual industrial plant using a commercial catalyst. This model comprised the three fixed bed reactors that operate adiabatically, in series, with inter-reactor cooling. The dynamic model was developed using actual plant data from a set of selected periods, representative of disturbances in the main operating variables: the flow 10

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