Stationary Thermal Stability Analysis of a Gas Oil Hydrotreating

In this work, the thermal stability of the LCO hydrotreating reactor is investigated based ..... The thermal stability or parametric sensitivity behav...
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Ind. Eng. Chem. Res. 2010, 49, 10581–10587

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Stationary Thermal Stability Analysis of a Gas Oil Hydrotreating Reactor R. Sardella Palma,† J. M. Schweitzer,*,‡ H. Wu,§ C. Lo´pez-Garcı´a,‡ and M. Morbidelli§ Residue and HeaVy Crude Processing Department, PDVSA-InteVep, 76343, Caracas 1070 A, Venezuela, Process DeVelopment and Engineering DiVision, French Petroleum Institute, IFP Lyon, PO Box 3, 69360 Solaize, France, and Institute for Chemical and Bioengineering, Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland

Thermal stability analysis is imperative to ensure the safe operation of chemical reactors carrying out highly exothermic reactions. We present a thermal stability study for a fixed bed gas oil hydrotreating reactor working at industrial operating conditions, which involves three phases, 15 lumped hydrocarbon chemical families (saturates, olefins, sulfur containing compounds, triaromatics, diaromatics, and monoaromatics), and distributed in 3 boiling point cuts to differentiate light and heavy hydrocarbons. The influence of various system parameters on the reactor thermal stability has been investigated using the sensitivity-based Morbidelli-Varma criterion. It is found that most of the operating parameters can be used in principle to tune the reactor thermal stability, except for the inlet feed temperature, which, though shifting the occurrence of runaway to different parameter regimes, does not improve the reactor thermal stability behavior. In addition, the convective heat removal plays an important role in changing the reactor thermal stability. The obtained results are given in various operating parameter planes, which are divided by the criticality curves for parametric sensitivity into three regimes, LTO (low-temperature operation), HTO (high-temperature operation), and M (multiplicity), thus forming various reactor operation diagrams, which can be used to guide the reactor design and operation. Introduction The past decade has been subjected to stringent targets concerning on-road fuel specifications. The main objective has been to take measures to reduce road transport emissions and attain new air quality standards. For instance, in Europe, the maximum total sulfur emission standard has been progressively reduced from 2000 ppm in 1996 to 10 ppm in 2009. The latter requires using the so-called ultra-low-sulfur diesel (ULSD). Many other countries and regions (e.g., North America, Japan, and Australia) have also tightened their diesel vehicle emission standard to ULSD level. Because of the increasing car fleet, demand for ULSD has increased in recent years. Therefore, refiners have to face a dual challenge: increasing fuel production while respecting current legislations. Diesels are obtained from gas oils, currently mainly coming from fossil resources (petroleum). Gas oil compositions depend on operations and processes in the refining chain. The most common process to attain diesel commercial specifications is called hydrotreating. A great number of hydrotreating units are installed all around the world covering a capacity of about 44 millions of barrels per calendar day.1 It is one of the most important processes in the oil refining industry. The main objectives of hydrotreating are to reduce the total sulfur and the aromatics content, to increase the cetane number and to improve some other physicochemical properties. Gas oil hydrotreating reactions mainly consist of hydrogenation of aromatics, olefins and hydrodesulfurization reactions, which are all highly exothermic. There are different kinds of gas oils. Straight Run (SR) gas oils are directly obtained from atmospheric distillation of crude oils. In general, they have low total aromatics content (typically 20 to 30 wt %). Gas oils can also be produced by conversion processes, such as fluid catalytic * To whom correspondence should be addressed. E-mail: [email protected]. † PDVSA-Intevep. ‡ French Petroleum Institute. § ETH Zurich.

cracking (FCC), usually referred to as Light Cycle Oils (LCO). These gas oils have a high aromatics content (70-80 wt %), and they also contain olefinic compounds (5-10 wt %). Before hydrotreating, LCO are usually diluted with other gas oils having lower aromatics content (e.g., SR). This is a choice based not only on the poor LCO properties (high sulfur and low cetane number) but also on safety concerns since LCO hydrotreating is extremely exothermic. Thus, it is necessary to make sure that in the defined ranges of operating conditions, the reactor operation is reliable and safe. The aim of this study is to investigate the effects of main operating parameters on the thermal stability of the LCO hydrotreating reactor. Thermal stability of reactors has been largely studied in literature works,2-19 most of them based on parametric sensitivity analysis. Van Heerden2 studied exothermic reactions under stationary conditions. This author showed that a diagram representing the heat consumption and production enables to determine if the reactor temperature is stable. Bilous and Amundson,3 introduced parametric sensitivity analysis which has been widely applied to analyze thermal stability and to establish various runaway criteria for different chemical systems and reactors.4-18 However, all the reaction systems adopted in those studies are rather simple, including no more than three reactions, and the reactors are assumed to be homogeneous or pseudo-homogeneous. In this work, the thermal stability of the LCO hydrotreating reactor is investigated based on parametric sensitivity and the occurrence of multiplicity of steady states. Applications of the parametric sensitivity analysis to complex reaction systems like the LCO hydrotreating are seldom found in the literature. The LCO hydrotreating reactive system involves three phases, a reaction scheme including 15 lumped hydrocarbon chemical families (saturates, olefins, sulfur-containing compounds, triaromatics, diaromatics, and monoaromatics) all distributed in 3 boiling point cuts to differentiate light and heavy hydrocarbons. Operating conditions are representative to actual industrial conditions. In particular, we apply the MorbidelliVarma criterion, based on the normalized objective sensitivity,10

10.1021/ie100471h  2010 American Chemical Society Published on Web 07/27/2010

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to identify the parametrically sensitive regions under industrial operating conditions for the main system parameters, including kinetic and thermodynamic properties, operating conditions, reactor geometry, etc. Such parametric sensitivity analysis allows one to have a clear view about the controlling parameters affecting the thermal stability of the reactor, thus providing guidance for reactor design and operation. Reactor Model and Thermal Stability Analysis Gas Oil Hydrotreating Reactor Model. The model used for the parameter sensitivity analysis has been developed in a previous work20 and validated by simulation of experiments carried out in a representative pilot plant under industrial operating conditions. Without going into the details of the model and its validation, we summarize in the following the most relevant aspects to this work. The model considers a three-phase reactor with a fixed bed of solid industrial catalyst, and describes the liquid flow by an axial dispersion model, while the gas flow is considered to be in plug flow. A power law kinetic model was developed and validated with pilot plant experiments carried out with commercial catalyst and real LCO feeds in the range of conditions of interest for industrial operations. The most important reactions from the thermal point of view are aromatics hydrogenation (HDA), olefins saturation (HDO), and hydrodesulfurization (HDS). The gas oil cuts are described by 15 chemical lumps (triaromatics, diaromatics, monoaromatics, saturates, sulfur compounds, and olefins) distributed in 3 boiling point cuts (initial boiling point, 200 °C, 200-300, and 300 °C, final boiling point). The reaction scheme and the assumptions in the reactor model development are detailed elsewhere.20 The main reactor model equations are as follows: ∂(εg · Cgi + (εl + εs · εpor) · Cli) ∂Cli ) -ul · εl · ∂t ∂z g 2 l ∂(ug · Ci ) ∂ Ci + Dlax · εl · εg · + νij · rj · εs · Fs ∂z ∂z2 j

∑

(

∂T · εg · Cpg · Fg + εl · Cpl · Fl + εs · Cps · Fs + ∂t Swall ∂ ∂T · Cpsteel · Fsteel ) εl · λ · Sr ∂z ax ∂z ∂T + (Fl · Cpl · εl · ul + Fg · Cpg · εg · ug) · ∂z rj · εs · Fs(-∆Hj) - Uwall · Awall · (T - Tc)

)

(

(1)

)

∑

(2)

j

∂

()

(

∑

ug ∂ Cli T R i + ) · - (εl + εs · εpor) · ∂z εg · Pt ∂t ∂2

Dlax · εl ·

∑C

l i

i

2

∂z

- ul · ε l ·

∂

∑C

l i

i

∂z

+

εg · Pt 1 ∂T · 2 · + R ∂t T

∑ ∑ν

ij

i

j

)

· rj · εs · Fs

(3)

Equations 1-3 represent, respectively, the transient material balance for each lump, the transient thermal balance (where the heat generated by all the reactions is taken into account), and the gas velocity changes along the reactor, due to temperature changes, H2 consumption, H2S production and partial vaporiza-

tion of the hydrocarbon lumps. To be able to calculate the latter, we have summed the transient material balances (eq 1) for all species. At each time step and reactor axial coordinate, the momentum balance must be satisfied, which leads to the differential eq 3 for the gas velocity. The hydrotreating performances were validated by comparison between experimental and calculated contents of aromatics and sulfur compounds. The dynamic behavior of the model was also validated with transient experimental runs.20 In all cases, the temperature profiles measured in the pilot plant were in good agreement with the model predictions. Thermal Stability Analysis. In this work the thermal stability of the reactor at steady state is analyzed based on its parametric sensitivity behavior. In particular, we analyze the response of the maximum temperature along the reactor to the variations of parameters controlling the reaction system. The generalized criterion, developed by Morbidelli and Varma,10 is used to define the critical conditions for the parametrically sensitive region. This criterion is based on the normalized objective sensitivity. We take the temperature maximum along the reactor, Tmax, as the objective, and the objective sensitivity index reads s(Tmax ;φj) )

dTmax dφj

(4)

where φj is the generic j-th input parameter, and the corresponding normalized objective sensitivity is S(Tmax ;φj) )

φj ∂ ln Tmax · s(Tmax ;φj) ) Tmax ∂ ln φj

(5)

The critical condition for parametric sensitivity is defined as the situation where the normalized sensitivity, S(Tmax;φj), with respect to any of the system input parameters (kinetic constants, activation energies, heat-transfer coefficients, heat exchange surfaces, control parameters, etc.) reaches a maximum or minimum. Such a critical condition defines a parametrically sensitive region where small variations in any of the operating parameters would lead to thermal runaway of the reactor. There are mainly three (direct differential, finite difference, and the Green’s function) methods for computing the sensitivity index.12 Because of the complexity of the reactor model and reaction kinetics, the most realistic one is the finite difference method S(Tmax, φj) )

φj dTmax φj ∆Tmax · ≈ · Tmax dφj Tmax ∆φj

(6)

In the following parametric sensitivity analysis, the sensitivity of the temperature maximum along the reactor (Tmax) with respect to the following parameters (φj) have been investigated: wall cooling temperature (Tc), total pressure (Pt), feed composition (Z ratio), feed inlet temperature (Tinlet), liquid hourly spatial velocity (LHSV), Peclet number (Pe), and heat transfer coefficient (Uwall). The numerical procedure in computing the parametric sensitivity may be described as follows: For a given set of system parameters, the temperature maximum of the reactor (Tmax) is computed through the reactor model as a function of a selected operating parameter, which in this work is the wall cooling temperature (Tc). Along the Tmax versus Tc curve, for each given Tc value we compute the Tmax values, corresponding to a variation in each of the input parameters equal to 0.1% of its absolute value. From this we compute the corresponding variation in the temperature maximum, ∆Tmax, and then the

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Figure 1. Mean temperature along the reactor axis (Tmean) as a function of the wall cooling temperature (Tc) at steady state, at various values of the total pressure (Pt). Numbers on each curve indicate the bifurcation points between which multiple steady states occur. Z ) 100%; LHSV ) 2 h-1; Pe ) 4.3; Tinlet ) 200 °C; Uwall ) 20 W/m2/K; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3.

normalized objective sensitivity, S(Tmax;φj) from eq 6. It is worth noting that, due to the possibility of having multiple steady states, we found that to obtain the Tmax versus Tc curve, it is more convenient to set Tmax to search for Tc, using the regulation system developed in our previous work,20 instead of setting Tc to search for Tmax. Results and Discussion Parametric Sensitivity versus Steady-State Multiplicity of the Reactor. For simple reaction systems, previous studies for CSTRs, single catalyst pellets and fixed bed reactors,12 demonstrated that the steady-state multiplicity behavior is a subset of the parametric sensitivity behavior. Under a given condition, if multiplicity exists, parametrically sensitive behavior certainly exists as well. However, the converse is not true, that is, although multiplicity is not possible under certain conditions, parametrically sensitive behavior may occur. In the following we investigate for the present complex reaction systems, the relation between the parametric sensitivity and the steady-state multiplicity. Let us consider the LCO hydrotreating in the pilot plant. Figure 1 shows the mean temperature (Tmean) along the reactor axis at steady state as a function of the wall cooling temperature (bifurcation parameter) at various values of the total pressure (unfolding parameter). It is seen that, as the total pressure increases, the shape of the Tmean curve changes from a monotonic function of Tc to the S-shape, representing typical multiple steady states (3 possible Tmean values for a given Tc value) or S curve. In Figure 1, the occurrence of the steady-state multiplicity starts at Pt ) 140 barg, and the region of the Tc values where three steady states exist is shown by the two bifurcation points (turning points), as indicated by numbers 2 and 3 in the figure. Turning points for higher total pressures (150, 160, and 170 barg) are marked with numbers 4-9 in the same figure. It should be noted that the term bifurcation used in this work corresponds to the stationary jump from lower branch to upper branch (and vice versa) in the operating curves (locus of steady states) having a hysteresis behavior. It is shown that as total pressure increases, the stationary unstability range is also enlarged. It is known

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that reactor operation within the multiplicity region is extremely unstable and small perturbations in the system input parameters may lead to the reactor behavior jumping between lowtemperature operation (LTO) and high-temperature operation (HTO) states. Now, we apply the normalized objective sensitivity analysis to investigate the thermal stability behavior for the systems in Figure 1. In the case of Pt ) 140 barg, we have computed the normalized objective sensitivity, S(Tmax;φj), with respect to various input parameters, φj, as a function of Tc, which together with the operating curve are shown in Figure 2a. It is seen that when the reactor operates along the lower branch of the operating curve, starting from a Tc value far from the bifurcation point, all the S(Tmax;φj) values are low. Then, as Tc increases, the S(Tmax;φj) values increase, and become substantially large when Tc approaches the bifurcation point. At the bifurcation point (Tc ) 272.4 °C), in fact the S(Tmax;φj) reaches its maximum (infinity in this case). Thus, Tc ) 272.4 °C defines the critical condition for parametric sensitivity. When the reactor operates around this criticality, small perturbations in any of the input parameters would lead to runaway (i.e., jumping to the HTO state). After the bifurcation point, when the reactor operates in the HTO state, the S(Tmax;φj) values are very small and do not change very much with Tc, indicating that the reactor operates safely and insensitive to small perturbations in the input parameters. On the other hand, if the reactor operates in the HTO state, by reducing the wall cooling temperature, one would find that the S(Tmax;φj) values increase and reach their maximum or minimum at another bifurcation point (out of the Tc range in the figure), defining another criticality for parametric sensitivity. A similar behavior for the thermal stability of the reactor is obtained at operating pressure values Pt > 140 barg. Therefore, we can conclude that when steady-state multiplicity occurs, the critical conditions for parametrically sensitive (runaway) operation correspond to the bifurcation points. In the case of Pt ) 130 barg, it is seen from the operating curve in Figure 1 that no steady-state multiplicity occurs. The corresponding S(Tmax;φj) curves for various input parameters, φj, together with the operating curve, are shown in Figure 2b. It is seen that all the S(Tmax;φj) curves exhibit a sharp maximum or minimum at the same value of Tc ) 282.8 °C, which based on the Morbidelli-Varma criterion defines the criticality around which the system becomes sensitive to small perturbations in the input parameters. A similar situation occurs also for Pt ) 125 barg as shown in Figure 2c, even though small deviations in the locations of the sensitivity maxima and minima are observed for different choices of the input parameter, φj. Since in both cases, no steady-state multiplicity occurs, this confirms that even for such a complex reacting system, the steady-state multiplicity behavior is a subset of the parametric sensitivity behavior, that is, occurrence of steady-state multiplicity certainly implies parametric sensitivity, while the opposite is not true. In Figure 2d, the S(Tmax;φj) curves correspond to the reactor operation at an even lower pressure, Pt ) 120 barg. In this case, although all the S(Tmax;φj) curves do exhibit a maximum or minimum, the sensitivity value at the maximum or minimum is very small, and especially its location depends substantially on the specific choice of the input parameter, φj. The latter, from the Morbidelli-Varma criterion, indicates that the reactor is operating in the parametrically insensitive regime. From the operating curve in Figure 1 (or Figure 2d), it is in fact seen that the mean (or maximum) temperature increases rather smoothly as the wall cooling temperature increases.

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Figure 2. Normalized sensitivities of Tmax, S(Tmax;φj), with respect to different choices of the input parameter, φj, as a function of Tc: (a) 140, (b) 130, (c) 125, and (d) 120 barg; Z ) 100%; LHSV ) 2 h-1; Pe ) 4.3; Tinlet ) 200 °C; Uwall ) 20 W/m2/K; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3. Secondary y axis: Tmax vs Tc.

Figure 3. Reactor operating diagram in the Pt-Tc plane, obtained from the parametric sensitivity analysis, where the two solid curves are the criticality curves for the reactor runaway, which divide the plane into three regions: LTO (low-temperature operation), HTO (high-temperature operation), and M (multiplicity). Z ) 100%; LHSV ) 2 h-1; Pe ) 4.3; Tinlet ) 200 °C; Uwall ) 20 W/m2/K; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3.

Effect of Various System Parameters on the Reactor Thermal Stability. Total Pressure. On the basis of the above analysis, we can summarize the effect of the total pressure (Pt) on the thermal stability of the LCO hydrotreating reactor, in terms of the reactor operation diagram in the Pt-Tc plane shown in Figure 3. The information obtained from the stationary stability curves (Figure 1), as well as the normalized sensitivity calculations (Figure 2), was combined to trace a stability map (Figure 3). The stable/unstable regions are illustrated in the

Pt-Tc plane. The values of the turning points illustrated in Figure 1 (numbers 2-9) corresponding to the stationary boundaries at several total pressures (intermediate branch of the S curves) were reported to Figure 3 with the same numbers. The zone inside these critical points encloses the unstable stationary region. It is clearly illustrated that the unstable region is larger when total pressure increases. Hence as Pt decreases, the bifurcation interval in terms of Tc shrinks leading to a larger safe operating conditions range. Figure 3 is divided by two criticality curves for parametric sensitivity into three regions: LTO, multiplicity (M), and HTO regions, as indicated in the figure. It is seen that as the total pressure decreases, the M region shrinks, and at the cusp point (1) where the two criticality curves merge, the reactor operates in the single steady state regime but parametric sensitivity is still possible. In particular, the solid curve originating from the cusp represents the critical conditions for parametric sensitivity, that is, for every given Pt value this gives the Tc value at which the reactor operation becomes very sensitive to small variation in any input parameters. The broken curve represents the region, where the normalized objective sensitivities do exhibit local maxima or minima, but their locations depend on the specific choice of the input parameter, as shown in Figure 2d, thus corresponding to parametrically insensitive region. Hydrocarbon Feed Composition and Heat Transfer Coefficient. As mentioned in the Introduction, the high aromatics-containing LCO gas oil is commonly diluted by the low aromatics-containing SR gas oil for hydrotreating. Then, it is necessary to investigate how the thermal stability behavior is affected by the volumetric ratio between LCO and SR, which is defined by the parameter Z ) LCO/(LCO + SR). In this way,

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Figure 4. Reactor operating diagram in the Z-Tc plane. LHSV ) 2 h-1; Pe ) 4.3; Tinlet ) 200 °C; Uwall ) 3 and 20 W/m2/K, respectively; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3; Pt ) 150 barg.

the pure LCO and pure SR gas oils are represented by Z f 1 and Z f 0, respectively. The reactor operation diagram obtained from the parametric sensitivity analysis is shown in the Z-Tc plane in Figure 4, where two sets of results are reported with the same values of the system parameters except for the heat transfer coefficient Uwall, which is 3 and 20 W/m2/K, respectively. Let us first consider the case with Uwall ) 3 W/m2/K in Figure 4, whose multiplicity (M) region labeled by 1 divides the plane into the LTO and HTO regions. It is seen that the occurrence of steady-state multiplicity starts at Z ) 63%. As Z increases, the M region enlarges. This arises because the higher the LCO content in the hydrocarbon feed, the higher the amount of aromatics, which are the dominant heat producers during hydrotreating. This enlarges the difference in the generated heat between LTO and HTO, thus enlarging the M region. For the same reason, the critical conditions for parametric sensitivity move toward smaller wall cooling temperature as Z increases. These results confirm that by properly playing with the ratio between LCO and SR, one can control the thermal stability of the reactor. It can be expected that changing the heat removal capacity would change dramatically the reactor thermal stability behavior. In fact, when all the other parameters are fixed and the heat transfer coefficient Uwall increases to 20 W/m2/K, the reactor operation diagram in Figure 4 becomes substantially different from that at Uwall ) 3 W/m2/K. The M region (labeled by 2) becomes much narrower, and starts at a larger Z (80%) value. The critical Tc values for parametric sensitivity become less sensitive to the Z value. In this case, the difference between LTO and HTO is smaller and the reactor thermal runaway becomes less dramatic. Inlet Temperature. In practice, one of the most frequently adopted operating parameter to control thermal runaway is the feed temperature at the reactor inlet (Tinlet). Therefore, it is important to evaluate if Tinlet is an effective measure to avoid thermal instability. In Figure 5 are shown the reactor operation diagrams in the Tinlet-Tc plane, at Pt ) 120 barg and 150 barg. All the other parameters are fixed, as given in the figure caption. It is seen that in both cases the multiplicity region M is present in the entire range of Tinlet values, but that at Pt ) 150 barg is much larger than that at Pt ) 120 barg. This is consistent with the results in Figure 3. The most important result in Figure 5 is that the two criticality curves enclosing the M region are basically parallel. This means that although reducing the feed temperature would shift the occurrence of runaway at a larger Tc value, the consequences of runaway would not change

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Figure 5. Reactor operating diagram in the Tinlet-Tc plane. Z ) 100%; LHSV ) 2 h-1; Pe ) 4.3; Uwall ) 3 W/m2/K; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3; Pt ) 120 and 150 barg, respectively.

Figure 6. Reactor operating diagram in the LHSV-Tc plane. Z ) 100%; Tinlet ) 200 °C; Pe ) 0.5 to 6.4; Uwall ) 3 W/m2/K; Dax ) 2.1 × 10-4 m2/s; H2/HC ratio ) 1000 N m3/m3; Pt ) 110, 120, and 150 barg, respectively.

substantially, that is, the difference for example between the maximum temperature values before and after runaway remains practically unchanged. On the other hand, when controlling the reactor stability with another parameter, say the total pressure, Pt, one observes in Figure 3 that as Pt decreases the bifurcation interval in terms of Tc shrinks, which corresponds to a smaller difference between Tmax before and after runaway, and then a safer operation. Therefore, the feed temperature at the reactor inlet is not an effective parameter to improve the reactor thermal stability. Liquid Hourly Spatial Velocity. Under industrial operating conditions, the liquid hourly space velocity (LHSV) is adjusted to attain the commercial diesel fuel specifications at the reactor outlet. The LHSV value is determined by the hydrocarbon feed composition and the target conversions of specific reactions such as hydrodesulfurization and aromatics hydrogenation. The reactor operation diagrams obtained from the parametric sensitivity analysis are shown in the LHSV-Tc plane in Figure 6 for three different Pt values. Let us first consider the case with Pt ) 150 barg in Figure 6. Both the criticality curves in the LTO and HTO regions are nonmonotonic functions of Tc, resulting in rather peculiar shapes of the M region. Starting from the cusp point at LHSV ) 0.16 h-1, the M region enlarges as LHSV increases. This is understandable because an increase in the reactants flow rate

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results are in agreement with Perlmutter21 where it is shown that less backmixing leads to higher stability. Conclusions

Figure 7. Reactor operating diagram in the Pe-Tc plane. Z ) 100%; LHSV ) 2 h-1; Tinlet ) 200 °C; Uwall ) 3, 20, and 40 W/m2/K, respectively; Dax ) 2 × 10-4 to 1.7 × 10-3 m2/s; H2/HC ratio ) 1000 N m3/m3; Pt ) 150 barg.

enlarges the difference between the heat generated under the LTO and HTO conditions, thus requiring a larger difference in the Tc values for the coolant. After LHSV becomes larger than 1.3 h-1, the M region shrinks as LHSV further increases. To understand this behavior, we have examined the heat balance in the reactor. It turns out that this arises because at such large LHSV values, the convective heat removal by the fluid is dominant, leading both to runaway occurring at a larger Tc value and to the M region shrinking. As the total pressure decreases to Pt ) 120 and 110 barg, because of the reduced heat generation capacity, the parametrically sensitive region shrinks progressively and moves toward larger Tc values, while the shape of the M region remains similar. Peclet Number. In the model for the liquid phase, axial dispersion of each component is considered. Through the analysis of the effect of the Peclet number (Pe ) L · ul/Dax) on the parametric sensitivity behavior, one can understand the effect of axial mass dispersion on the reactor thermal stability. Thus, in Figure 7 are shown the reactor operation diagrams in the Pe-Tc plane for three different Uwall values. It is seen that in all cases, similarly to the situation in Figure 6, the two criticality curves bind the multiplicity region in a closed form. Let us start from extremely small Pe(f0) values where the axial dispersion effect is maximized and the reactor behaves like a CSTR. Due to the dilution effect of axial dispersion, the reactor operates safely in the single steady state regime, except for the case with a very small value of Uwall ) 3 W/m2/K, where multiple steady states occur. As Pe progressively increases, that is, the axial dispersion (dilution) effect decreases, the difference in the heat generated between LTO and HTO increases, leading to thermal instability and presence of multiple steady states. Above a sufficiently large Pe value, because of the high fluid velocity, the convective heat removal becomes dominant, thus improving the reactor thermal stability, and the M region shrinks. Such an effect becomes more evident and occurs at smaller Pe values for smaller heat transfer coefficients. At substantially large Pe values, the reactor behaves like a PFR, and for the given set of system parameters in Figure 7, the reactor operates in the single steady-state regime for all three Uwall values. These

The thermal stability or parametric sensitivity behavior in a stationary, three-phase, gas oils hydrotreating reactor has been investigated using the parametric sensitivity criterion developed by Morbidelli and Varma.10 The Light Cycle Oils (LCO) system containing 70-80 wt % aromatics has been used as the main reacting system, and its dilution by the Straight Run (SR) gas oils (containing 20-30 wt % aromatics) has also been considered. The complex multicomponent reacting mixture has been lumped into 6 chemical species and 3 boiling point cuts. The reactor and reaction kinetic models used in this study have been developed and validated for the operating conditions of interest in the industrial practice in a previous work.20 It has been confirmed that for such a complex reacting system, similar to simpler systems, the steady-state multiplicity behavior is only a subset of the parametric sensitivity behavior. In other words, in the region where the steady-state multiplicity occurs, the parametrically sensitive behavior or runway takes place as well, but in the region where the parametrically sensitive behavior occurs, the steady-state multiplicity is not necessarily present. The effect of six main system input parameters, that is, reactor cooling temperature, total pressure, liquid hourly spatial velocity (LHSV), inlet feed temperature, feed composition, and Peclet number, on the thermal stability of the hydrotreating reactor has been investigated. It is found that all the parameters can be used to tune the reactor thermal stability, except for the inlet feed temperature, which, though shifting the occurrence of runaway to different parameter regimes, does not improve the reactor thermal stability. Pertaining to Peclet number effect, it is shown that less backmixing leads to higher stability. These results are in agreement with literature. In addition, it is found that convective heat removal may play an important role in determining the reactor thermal stability. The results of the parametric sensitivity analysis are presented in terms of the reactor operating condition planes, which are divided by the criticality curves for parametric sensitivity into three regimes, LTO (low-temperature operation), HTO (hightemperature operation), and M (multiplicity). These can be used to guide the proper reactor design and operation. Acknowledgment IFP authors are grateful to “AXELERA” FUI French research project for financial support. Nomenclature A ) heat exchange area per reactor volume (m2/m3) C ) concentration (mol/m3) Cp ) specific heat capacity (J/kg/K) Dax ) axial dispersion coefficient (m2/s) L ) length of the reactor (m) Pt ) Total pressure (barg) Pe ) Peclet number R ) ideal gas constant (J/mol/K) r ) reaction rate (mol/s/kgcatalyst) S ) normalized sensitivity S curve ) stationary stability curve with multisteady state behavior Sr ) reactor section surface (m2) t ) time (s)

Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010 T ) temperature (K) Tmean ) average temperature along the reactor (K) Tmax ) maximum temperature along the reactor (K) u ) superficial liquid velocity (m/s) U ) heat transfer coefficient (W/m2/K) y ) variable z ) axial coordinate (m) Z ) LCO/(LCO + SR) volumetric ratio related to feed composition Subscripts and Superscripts c ) cooling g ) gas i ) pseudocomponent index j ) reaction index or parameter index l ) liquid por ) porosity s ) solid steel ) reactor steel wall ) reactor external wall Greek Symbols ε ) holdup φ ) parameter ∆H ) heat of reaction (J/mol) λax ) effective thermal conductivity (W/m/K) ν ) stoichiometric coefficient F ) density (kg/m3)

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ReceiVed for reView March 3, 2010 ReVised manuscript receiVed June 28, 2010 Accepted July 15, 2010 IE100471H