Continuous Pseudohomogeneous Models
Steady-State Continuous Pseudohomogeneous Models Among different approaches, steady-state continuous pseudohomogeneous models have been widely reported in the literature. This is due to their reliability and simplicity. A pseudohomogeneous model generally assumes a power–aw kinetic type, although sometimes Langmuir-Hinshelwood expression has been employed. Use of the power law for kinetics has been questioned due to its meaningless; that is, it does not permit following the phenomena occurring intrinsically, such as the reaction mechanism and inhibitory effects, however, for a certain range of temperature and composition, the power-law kinetic model has been employed successfully for preliminary designs and to explore related phenomena, such as hydrogen consumption, catalytic deactivation, quench studies, and dynamic behavior, among others.
The reactor is modeled assuming no gradients of mass or temperature between two adjacent phases. Generally, one- dimensional analysis and few reports of two-dimensional modeling reactors for HDT have appeared in the literature. The main contributions toward modeling TBR systems applied to an HDT process by pseudohomogeneous models are described briefly below.
Shah et al. (1976) discussed the proper location for a quench in an exothermic, time-dependent catalyst activity system. The system chosen for study was a trickle -bed reactor, and the feedstock was residue oil. Empirical catalyst activity functions for HDS and HDM were developed from pilot-plant data. Differential mass balances for irreversible first-order reactions of HDS and HDM were written assuming ideal plug-flow conditions, whereas the energy balance was formulated under adiabatic conditions. They concluded that the value of the maximum cycle life and the quench position depend significantly on reaction variables such as feed temperature, feed concentrations of sulfur and metals, activation energies of sulfur and metals removal reactions, residence time, and the sulfur conversion level. This model seems to be the first attempt to predict, although empirically, deactivation in a TBR system sustaining HDT reactions. Although this report is interesting in itself, almost all the studies performed with quench systems take the maximum allowable temperature as a criterion for the localization of quench, that is, the temperature at which the quality of products may become undesirable, and they propose that the quench location is dependent on maximum catalyst life.
Kodama et al. (1980) developed a simulation model of residue HDS reaction based on a catalyst deactivation model. To represent the fouling process, an improved model that included both interaction of the coking reaction and vanadium removal of the pore plugging was proposed. Both rate equations of desulfurization and vanadium removal were expressed by second-order reactions, and they were assumed to be proportional to the hydrogen concentration in the liquid phase. The material balances for sulfur and metals in a plug-flow reactor were carried out, the energy balance was developed considering an adiabatic reactor, and the heat of reaction was attributed only to the HDS reaction. Mass transfer in the porous catalyst was taken into account through the effectiveness factor. The model allows for prediction of the actual operations of bench-scale fixed- and moving-bed reactors. This model was validated with enough data, and thus its predictions can be expected to be reliable.
By using plug – flow reactor model and power-law kinetics, Akgerman et al. (1985) showed the effect of liquid volatility on the conversion, arriving at the conclusion that the difference between predictions of models, assuming either volatile or nonvolatile liquid phases, is significant. For the first – order case, differences range from 24 to 38%. At high conversions, the difference between the models, volatile and nonvolatile, diminishes, due to depletion of the limiting reactant. This can be attributed to a change in concentration in the liquid phase. In another work of Akgerman and Netherland (1986), several equations of state for prediction of partial vaporization of feed in reactor performance were compared. Although VLE has to be performed at each step of integration through the length of the reactor, these authors bypassed this feature, supposing linear variation of equilibrium constant between the inlet and outlet conditions. They assumed almost complete wetting, and no appreciable influence of vaporization effects was observed in the conversion. Further studies in this direction have confirmed the importance of taking into consideration the volatility of the light feedstock in HDT reactions, because it can cause incomplete wetting and thus poor performance of the catalytic bed, increase of conversion of refractory species, and depletions on conversion of reactive species and related phenomena.
Dohler and Rupp (1987) performed laboratory-scale experiments with the same feed and catalyst as those in an industrial VGO hydrotreating unit, in order to simulate the adiabatic behavior of the industrial reactor using a plug-flow pseudohomogeneous one-dimensional reactor model. The model was validated only with HDS, HDN, and hydrodearomatization (HDA) reaction data. They pointed out that calculation of the weight-average bed temperature (WABT) in an adiabatic reactor having a AT value of 55°C or higher does not agree well with the isothermal temperature of experimental reactors because there is a nonlinear relationship between the temperature and the rate of reaction.
Used oil hydrotreating in a pilot TBR was simulated by Skala et al. (1991) employing a pseudohomogeneous model with a power term for LHSV, where HDS, hydrodeoxygenation (HDO), and HDM reactions were used for validation. Those reactions were described by first – order power- law kinetic models, which were then used for the simulation of an industrial TBR. Catalyst deactivation by coke and metals was also simulated according to the model of Shah et al. (1976) – and a similar model was used to predict the pressure drop dependence on decrease of the bed porosity. Good agreement between the model and industrial data of the pressure drop was reported. The model for pressure drop dependent on catalyst activity could be useful for industrial analysis of reactor performance affected by continuous plugging of a catalyst bed.
Tsamatsoulis and Papayannakos (1998) employed real feeds and operating conditions such as those encountered in hydroprocessing of heavy VGO and a set of four nonporous catalysts to derive a correlation for predicting the Bodenstein number (Bo) as a function of bed characteristic and Reynolds number. Two-thirds of their data fell within the Bo range given by Gierman (1988) – In another work of the same authors, the effects of liquid dispersion in a bench-scale HDT on the determination of the intrinsic desulfurization kinetics and on reactor performance for three porous catalysts with different activity were studied. Porous catalysts were used. Only two reactions, hydrode-sulfurization and hydrogen consumption, were considered. Activation energies for HDS and HCON were almost the same for each catalyst, but higher values were estimated when an axial dispersion model was used instead of plug flow, although the difference was negligible. Some observations given by these authors were that the plug-flow model can be employed successfully for HDS and hydrogen consumption predictions when the conversion is kept low, but that for higher values such as deep desulfurization (>95%), deviation of up to 40% can be estimated when axial dispersion effects are incorporated in the plug – flow model. Therefore, the influence of dispersion effects on reaction kinetics must be taken into account when using data at high conversions.
A commercial kero-HDS reactor was simulated successfully by Sau et al. (1997) by means of a pseudohomogeneous plug-flow model. The novel continuum theory of lumping was employed for kinetics, and very good predictions were observed. This work is a good example of how, with a simple reactor model but following the chemistry closely, it is possible to achieve reliable predictions with an important reduction in the total number of model parameters.
The HDS, HDN, and olefin hydrogenation (HGO) reactions were simulated in a commercial diesel HDT reactor by Cotta and Maciel Filho (1996) employing a one-dimensional pseudohomogeneous model. Each reaction was described by a power–aw kinetic model because they found the Langmuir-Hinshelwood model to be inconsistent with their results. They observed higher experimental values than were calculated for HDS, while the opposite effect was found for HDN. This behavior could be attributed to the fact that the model does not take into account the inhibiting effect of H2S.
A deterministic quasi-steady-state model of the reaction section of the atmospheric residue desulfurization unit was developed by Lababidi et al. (1998) to simulate the long-term behavior of the catalyst bed. A single fixed-bed experimental reactor was first considered, followed by an industrial-scale reactor. An appropriate correlation was used to determine the dissolved hydrogen concentration in the oil. Simulation results of the single-bed reactor showed a perfect match with Kodama et al. (1980) work, which validate the main assumptions of the model proposed. After validation, a series of four industrial- scale reactors were simulated. Their conclusions were that actual industrial profiles of concentration and temperature with respect to time were very similar to the profiles predicted. Deviations were observed at start-of-run (SOR) and end-of-run (EOR), whereas the model was capable of predicting perfectly the middle-of-run (MOR). According to the authors, the simulation program developed might be useful for predicting the life of the catalyst if the product temperature is considered as an acceptable measure.
To select the best rate expression to predict the industrial reactor behavior, an adiabatic diesel hydrotreating trickle-bed reactor packed with commercial NiMo catalyst was simulated by Cotta et al. (2000). The HDS, HDN, and HDO reactions were considered. Power-l aw kinetics was employed in this system, and parameters for HDN and HDS were obtained from an experimental isothermal downflow pilot – plant fixed-bed reactor, while for HDO, kinetic parameters were obtained from the literature .A one-dimensional pseudohomogeneous model was employed in this work. On the basis of their results, the authors determined that it is necessary to use the most severe processing conditions (pressure of about 95 atm and temperature of 390°C) to increase HDN conversion, and the best model to represent HDN and HDS processes is a power-law kinetic instead of a Langmuir-Hinshelwood kinetic under typical conditions. Due to the complex composition of different feedstocks, the intrinsic kinetics assumed for estimating HGO conversion might not be adequate, and results obtained from the model might not be reliable.
Mejdell et al. (2001) modeled an experimental plug-flow TBR reactor for the HDS of oil products based on a discretization of the entire spectrum of sulfur components into small pseud ocompon en ts of only 1°C boiling -point range (132 pseudocomponents), and identifiable components with low reactivity such as 4-Me-DBT and 4,6-DMe-DBT (six real components) were modeled separately. A Langmuir-Hinshelwood kinetic type of expression was used. Experimental data to estimate the 277 kinetic parameters were obtained on a reactor operated in upflow mode, employing light gas oil (LGO) as feed. Predictions of conversion were carried out and results were compared with experimental results, showing good agreement. An observation derived from this work was its utility for simulating the HDS process at high conversions because it permits prediction of the conversion of pseudocomponents with high reactivity and also that of refractory components which suffer from large deviations from a TBP-reactivity tendency. This approach may also have a certain generality for other feedstocks if one assumes that the reactivity for the lumps is the same for other oils. Although the authors have reported the implementation of this model in an industrial TBR, and they claimed very accurate predictions in conversion, they did not give any evidence of such a study.
Bellos and Papayannakos (2003) studied the HDS and hydrogen consumption kinetics of a straight-run heavy gas oil in a microreactor loaded with a diluted bed of commercial catalyst which was simulated by means of two models, one of them a plug-flow pseudohomogeneous model assumming no liquid evaporation, and the other an improved model that took into account feed evaporation and gas- and liquid-phase equilibrium along the reactor axis. The former was developed only to derive the initial values for the kinetic parameters of the improved model. Predictions of gas- and liquid-phase equilibrium were carried out at each step of integration over the entire length of the reactor. Miscalculation in the mass balance of the improved model was observed when the catalyst mass was taken as a constant value, since the mass of catalyst was also a function of the bed length.
Melis et al. (2004) employed a pseudohomogeneous axial dispersion reactor model for the interpretation of the HDA reaction during gas oil HDT. This model only considers the HDA reaction by means of a lumped scheme for aromatics composition in gas oil and assumes that hydrogenation and dehy-drogenation reactions occur according to the Langmuir-Hinshelwood mechanism. The model developed was capable of predicting experimental results with different types of feed containing different concentrations of aromatics.
A process for LGO HDS via catalytic distillation was proposed by Vargas-Villamil et al. (2004) – It was compared with an optimized conventional HDS process using similar flow conditions, which represented an industrial plant. A compromise was established among the production of diesel and naphtha and the operating costs in order to optimize the conventional HDS process. The kinetics of HDS employed was represented by a Langmuir-Hinshelwood equation, using DBT as a representative of all sulfur compounds to HDS via two parallel pathways, hydrogenolysis and hydrogenation. A pseudohomoge-neous plug-flow model of an industrial TBR was developed and incorporated in an HDS unit, which was modeled using commercial software. The energy balances and the distribution of the components between the phases were defined by isoenthalpic equilibrium. An effectiveness factor was included to describe an industrial-size catalyst, which accounts for the intraparticle transport phenomena. Some remarks were made with respect to the use of catalytic distillation, such as the possibility of improving the quality of products to a level even higher than that of a conventional process, keeping lower fixed and operational costs. This technology is very prominent in meeting future requirements in specifications of low sulfur contents in diesel fuel.
A simple one-dimensional pseudohomogeneous plug-flow reactor model for a multicatalyst system was developed by Kam et al. (2005) to study the deactivation mechanisms of hydroprocessing catalysts in atmospheric residue desulfurization (ARDS) units due to coking and metal deposition. Three different stages of deactivation are considered: SOR, MOR, and EOR. The reactions considered were HDS, HDM (the removal of vanadium and nickel were considered separately), and HDAsph, the latter accounting for catalyst deac-tivation. The equations for the mass and heat balances are pseudo-steady-state because of catalyst deactivation. The model was applied further to a parametric study that examines the effects of LHSV, temperature, and maximum capacity on the performance catalyst systems.
A steady-state pseudohomogeneous plug-flow model to predict HDS conversions in an experimental TBR was developed by Sertic-Bionda et al. (2005). The simple reactor and kinetic models proposed in this work were used to investigate the influence of some reaction parameters (i.e., H2/oil ratio, pressure, and LHSV) on HDS, using atmospheric gas oil and LCO from FCC as feeds.
Toulhoat et al. (2005) have presented a plug-flow pseudohomogeneous model to predict the performance and cycle length of fixed – bed residue hydro-processing units. The model simulates catalyst activity in a pseudo-steady-state regime and resistance to deactivation by metals and coke deposition. Both HDS and HDAsph reactions described by pseudo Langmuir-Hinshelwood kinetics were considered; coke deposition was assumed to be first order with respect to a driving force equal to the difference between actual and equilibrium coke concentrations in the solid phase.
By taking the model developed by Kam et al. (2005) and adding hydrother-mal treatment as a term modeled as a power law, Juraidan et al. (2006) simulated the long-term behavior of a catalyst and reactor considering the same reactions studied previously by Kam et al. (2005) and also carried out the same parametric study. The additional term (coefficient and exponent) was obtained from the results of blank experiments in a laboratory-scale reactor (i.e., experiments carried out with inert materials without a catalyst). Other conditions were the same as those employed by Kam et al. (2005) – Kinetic parameters for HDM (HDV and HDNi) and HDasph reactions using Boscan crude were estimated. The model was utilized to predict the complete accelerated test run of experimental results obtained from a pilot plant after verification. Simulated results from this model matched quite well with those of the pilot plant. A marked improvement over the original model of Kam et al. (2005) was achieved.
A two-stage micro-TBR for HDT of heavy gas oil derived from Athabasca bitumen was simulated by Botchwey et al. (2006). A one-dimensional pseudo-homogeneous mass transfer model and a two-dimensional heat transfer model were developed. Kinetic models for HDS and HDN reactions used in simulations were based on the Langmuir-Hinshelwood approach. This paper represents an earlier work on the modeling of a two-stage micro-TBR for HDT with interstage H2S removal. It was observed that removing H2S improved the levels of HDN and HDS.
Galiasso (2006) developed a simplified pseudohomogeneous plug-flow model for isothermal TBR and gas- and liquid-phase reactors to optimize a scheme of reactors and to minimize investment. The effect of adding reactor volume to existing units to produce a low-emission diesel fuel was compared by using the new scheme of reactors and the conventional TBR. The model reproduced HDS, HDA, and HDN reactions. It was shown that by using the new gas- and liquid-phase reactors, the aromatic hydrogenation and hydroge-nolysis reactions can be enhanced. Simplified kinetic rate models (Langmuir-Hinshelwood type) in the gas and liquid phases for simple lumps of HDA reactions were used in the simulations, and kinetics and fluid – dynamic – related parameters were calculated previously through an optimization algorithm.
Dynamic Continuous Pseudohomogeneous Models Since perturbations can occur in the various HDT processes due to changes in composition of reac-tants, flows, inlet temperatures, and so on, it is highly desirable to account for a robust model capable of predicting the performance of the reactor system under such sudden changes. In this direction, some work has been reported in the literature; the main contributions are summarized below.
Chao and Chang (1987) showed a one-dimensional pseudohomogeneous model incorporating the effects of mass and heat dispersion, mass and heat transfer resistance inside catalyst particles, and catalyst deactivation in order to investigate the dynamic behavior of an adiabatic residue HDS trickle-bed pilot reactor system. The reactions taken into account were HDS, HDV, and the coking deposition rate on catalyst. This dynamic model was validated using the experimental data of Kodama (1980) and producing step changes on feed composition, feed rate, and inlet temperature. This rigorous model could be used only for off-line studies, because it involves a large number of equations, and as a consequence its solution requires a huge amount of time.
Oh and Jang (1997) presented a rigorous modeling and simulation of commercial naphtha HDS reactor in the dynamic regime. The mathematical model is two-dimensional pseudohomogeneous and uses a kinetic model of Langmuir-Hinshelwood type to describe an HDS reaction. They have also studied the influence of changing the hydrogen flow rate by 10%, showing how it influences conversion and temperature. The agreement between predictions and design data can be attributed to well-established correlations for gas-solid systems.
Chen et al. (2001) proposed a pseudohomogeneous two-dimensional reactor model to describe the dynamic and steady states of a fixed-bed pilot-plant hydrotreater used for the hydrotreating of partially stabilized light-coker naphtha; therefore, the reaction system was gas-solid. The rate reaction parameters were obtained in an experimental pilot-plant reactor, and kinetics was assumed as nth-order power. Dynamic behavior was induced by changes in hydrogen volumetric flow rate. As a main conclusion, it was reported that the thermowell can provoke heat conduction within the reactor; thus, temperature measurements in the thermowell could differ from those of the bed, and due to that, special care must be taken when interpreting pilot-plant data.
Heterogeneous Models
Steady-State Heterogeneous Models
1. continuous models The main reason for developing heterogeneous models (i.e., models that distinguish the phases in a trickle-bed reactor) is to account for inhibitory effects. In the literature, the majority of reports have supposed no significant resistance to mass transfer from the gas phase to the gas–iquid interface. On the other hand, several researchers have modeled heterogeneous adiabatic systems based on an isothermal bed catalyst, due to the lack of proper correlations accounting for this feature. Generally, the energy balance is carried out by supposing pseudohomogeneous behavior even though material balances are considered heterogeneous. Different features remain for discussion, such as the influence of axial dispersion in coun-tercurrent operation, the level of vaporization during HDT reactions, and the degree of saturation of liquid-phase and phase equilibria, among other relevant aspects. Some important contributions considering different aspects of this type of model applied to HDT processes are reviewed below.
Van Parijs and Froment (1984) simulated an adiabatic reactor for hydrode-sulfurization of naphtha, using a one-dimensional heterogeneous reactor model, Hougen-Watson kinetic expressions, and internal concentration gradients. The thiophene was chosen as a model sulfur compound for HDS reaction. A review of equations accounting for interfacial and intraparticle gradients was presented by Froment (1986), who also recommended a Hougen-Watson approach for expressing rates of catalytic reactions, since power-law equations account insufficiently for interaction of the reacting species with the catalyst. It was also pointed out that kinetics and transport phenomena have to be treated separately to simulate and design the reactor successfully. These models seem to be the first rigorous heterogeneous models presented in the literature for an HDT process.
Trambouze (1990) carried out comparative simulations of co-current and countercurrent fixed-bed heterogeneous reactors. The criterion selected to make the comparison was the conversion of one of the reactants, with the quantity of catalyst employed used as a reference. It was remarked that a countercurrent reactor requires less catalyst than the co- current reactor to obtain the same conversion in irreversible reactions, equilibrium reactions, or those inhibited by one of the reaction products that are typical cases of hydro-genation of aromatics and hydrotreating of petroleum fractions. It is known that axial dispersion is more important when operating in the countercurrent mode compared with the co- current downflow mode; however, Trambouze neglected this feature, probably because the objective of his work was only to show a potential for countercurrent operation, although some miscalculation can affect the results quantitatively by taking into account, or overlooking, axial dispersion in a real system.
A one-dimensional heterogeneous model was also employed by Froment et al. (1994) to simulate diesel HDS using a kinetic model for HDS of DBT and alkyl-substituted dibenzothiophenes based on structural contributions. This kinetic approach, which retains the details of the complex reaction network of every feed component, allowed us to reduce significantly the number of parameters with respect to the molecular approach and satisfactorily represented experimental data of HDS. It was proposed that the kinetic approach can also be applied to nitrogen-containing compounds. This approach gives good results, but the model is complex and involves extended analytical work to identify the components (Mejdell et al., 2001).
A set of differential first-order equations was solved by Korsten and Hoffmann (1996) to simulate the performance of a pilot trickle-bed reactor. The main reaction was the desulfurization of VGO, which was assumed to be saturated with hydrogen at the inlet of the reactor bed. Mass transfer coefficients, pressure drop, and physical properties were estimated with correlations reported in the literature, and kinetic parameters of Langmuir-Hinshelwood type were obtained from pilot-plant experiments. Although the correlations employed were developed for nonreacting systems and ambient pressure and temperature, the mathematical formulation showed reasonably good agreement with experimental results. On the basis on their observations, these authors pointed out that scale-up of pilot-plant data to an industrial trickle-bed reactor can yield some miscalculation, due to differences in mass-superficial velocity, which strongly affect the contact effectiveness between the fluid phase and the catalyst. It seems that the correlation used for the solubility of H2S in oil is not applicable at other conditions because it neglects the influence of pressure.
An attempt to address the main requirements by relaxing many of the assumptions used in previous models was proposed by Khadilkar et al. (1999), who also reported three models. The first model, at the pellet-scale level, assumed power-law kinetics; the second, at the reactor-scale level, considered dry and wet zones but without a distinction between external and internal wetting of catalyst pellets; and the third was a combination of both levels: rigorous multicomponent mass and energy balances at the reactor scale and its extension to the pellet scale. The model was formulated by a set of steady-state one-dimensional differential equations and tested with data available for cyclohexene hydrogenation, giving accurate predictions of conversion and temperature profiles at the reactor scale. Additional features, such as capillary effects, incomplete catalyst filling, and evaporation, were incorporated in the third-level model. They recommended their rigorous approach, level three, for future models with complex reaction systems and volatiles. This model could be implemented for the HDS of diesel when considerable volatilization occurs.
Van Hasselt et al. (1999) developed a novel model for the countercurrent three-levels-of-porosity reactor and for the internally finned monolith reactor and compared them with traditional co-current reactor model in the hydrode-sulfurization of VGO. To develop the simulation, a combination of continuous approach and discrete cells were employed; the former approximation was used to simulate the reactions occurring in a cell package and the latter to simulate gas–iquid contact through channels existing through a packed bed conceived as quench; hence modeling a reactor can be visualized as a combination of continuous and discrete models. For comparison, the TBR model was simulated with a one-dimensional heterogeneous model, and equations were written for mass and energy balances. Deep conversion was chosen as 98%. It was observed that the catalyst volume required for countercurrent flow is lower than that for co-current flow, but the main disadvantage of countercur-rent flow was observed to be cooling because it is less effective since hydrogen flows from high to low temperature areas. Due to the high degree of freedom for developing this new model, packing could be adapted to satisfy demands imposed by mass transfer mechanisms.
A one-dimensional heterogeneous model for simulation of commercial trickle -bed reactor was presented by Lopez and Dassori -2001) – The fluid pattern in the gas and liquid phases was approximated by plug flow. Kinetics was of the Langmuir-Hinshelwood type for the main reactions considered: hydrodesulfurization and hydrodenitrogenation. The model incorporated catalyst deactivation caused by metal deposition, coking, and the decrease in effective diffusivity. Parameters of the model were obtained from the literature as well as information compiled from runs in VGO hydrotreater units for HDN and frequency factor, activation energies, absorption equilibrium constant, and catalyst deactivation coefficient. Also, they have reported on an ammonia profile within the reactor but did not report the correlation employed for this prediction.
Bhaskar et al. (2004) used a three-phase heterogeneous model to analyze the performance of a pilot-plant trickle-bed reactor employed for the hydrode-sulfurization of an atmospheric gas oil fraction and to show the influence of intrinsic kinetics and hydrodynamics. Effects of pressure, temperature, space velocity, and H2/oil ratio were discussed on a model results basis. The simulation showed good agreement with the experiments carried out in a wide range of operating conditions.
A one-dimensional heterogeneous model was employed by Vanrysselberghe and Froment (2002) to illustrate the performance of an industrial hydrotreat-ing reactor. The continuity, energy, and momentum equations were formulated, and appropriate correlations were employed to determine physical properties. A synthetic diesel mixture was chosen, and detailed Hougen-Watson kinetics based on structural contributions was used. Predictions on the evolution of the content of a number of sulfur components and on the molar flux of hydrogen in the liquid phase were shown.
A heterogeneous adiabatic plug-flow model reactor for trickle-bed reactor based on previous works (Korsten and Hoffmann, 1996; Vanrysselberghe and Froment, 2002) was employed by Marroqum et al. (2002) to represent diesel hydrodesulfurization and hydrogen consumption. Model compounds were chosen and kinetic parameters were taken from the literature, although some changes were finally necessary to fit monoaromatics in the bench-scale data and sulfur content in the industrial diesel product.
Avraam and Vasalos (2003) employed a steady-state model for a trickle-bed reactor to simulate the hydroprocessing of light oil feedstocks. Plug-flow conditions and uniform pellet conditions were assumed. Four general chemical processes were modeled: HDS, HDN, HGO, and hydrogenation of mono-, di-, and tri-aromatics, taking into account equilibrium aromatic and inhibition by hydrogen sulfide, ammonia, and aromatics. This is an important contribution and seems to be the first one to consider changes in liquid and gas holdup along an HDT reactor due to the volatility of light oil compounds. Excellent agreement was found between the results predicted and pilot- plant results.
Chowdhury et al. (2002) investigated the desulfurization and dearomatiza-tion of diesel oil in an experimental isothermal trickle- bed reactor. A one-dimensional reactor model based on Korsten’ s model was developed for a two – phase flow reactor considering both mass transfer and chemical reaction, and the kinetics for HDS and hydrogenation of three types of aromatics were established. Nonactive zones packed with inert particles, which are located before and after the catalytic bed (the active zone), were also modeled in order to simulate the hydrogen mass transfer from gas to liquid. The correlation between experimental and predicted data was higher than 0.9.
Pedernera et al. (2003) studied the influence of oil fraction composition on the conversion of sulfur compounds in laboratory-scale TBR. The reactor model was used to evaluate various configurations of the desulfurization process with straight- run gas oil as feed, as no advantage was found when separated treatments of individual oil fractions were used. Hydrogen consumption was ascribed to the conversion of sulfur and nitrogen, hydrogenation of aromatics, and hydrocracking. Additionally, liquid distribution and wetting efficiency were determined using a magnetic resonance imaging technique. The model used by these authors was an extension of that presented by Chowdhury et al. (2002) – which includes modeling of the heat balance in an adiabatic industrial reactor. This paper illustrated the use of new techniques for flow pattern characterization, which highlight the trends for hydrodynamic studies in the future.
Bhaskar et al. (2004) developed a one-dimensional heterogeneous reactor model to simulate the performance of pilot-plant and industrial TBRs applied to the HDS of diesel fractions. It employed a three-phase heterogeneous model based on two-film theory. The major HDT reactions were modeled: HDS, HDN, HDA, HGO, and HCR. The kinetic parameters were obtained from pilot-plant experiments. The authors reported that the model was capable of successfully reproducing industrial profiles of temperature and the concentration of impurities. This work is one of the first that simulates most HDT reactions.
Cheng et al. (2004) investigated the performance of a fixed – bed reactor in co-current and countercurrent flows to remove sulfur and aromatics in diesel fuel. The model presented by this group is one-dimensional heterogeneous and accounts for HDS and HDA reactions to simulate the concentration profiles of the reactants and products in the gas, liquid, and solid phases. Superior performance for removing sulfur was observed when an experimental reactor was operated in countercurrent mode with respect to co-current mode. These authors have expressed adequate HDA reaction rates, compared with Chowdhury et al. (2002) and Bhaskar et al. (2004).
Froment (2004) illustrated a fundamental approach for kinetic modeling of HDS, accounting to the maximum extent for the information provided by the physical-chemical characterization. This structural contribution approach considers detailed feedstock compositions but also transfer limitations inside the catalyst. To validate this approach, an adiabatic commercial reactor for the HDS of a synthetic diesel mixture was simulated using a heterogeneous plug-flow model. Rate equations were considered for the conversion of thiophene, (substituted) benzothiophene, and (substituted) DBT. The results of simulations showed an improvement in the removal of the majority of refractory sulfur components by intermediate flashing of H2S.
They employed an isothermal heterogeneous reactor model, which was validated with experimental information obtained from a small HDS reactor using straight-run gas oil as feed. This study provides a series of formulas for calculating characteristic factors of the catalytic bed involved in the development of the reactor model.
The HDS reaction was described by kinetic equations of the Langmuir-Hinshelwood type; HDN was modeled as a consecutive reaction scheme in which nonbasic compounds are hydrogenated first to basic nitrogen compounds (HDNNB), which undergo further reactions to eliminate the nitrogen atom from the molecule (HDNB); and HDA was represented by a first-order reversible reaction. The model was validated with experimental information obtained during the HDT of VGO in a pilot-plant reactor operated under isothermal conditions. The commercial reactor was simulated and temperature and concentration profiles were obtained.
Yamada and Goto (2004) also used the model proposed by Korsten and Hoffmann (1996) to simulate and compare the HDS of VGO in a TBR for both modes of operation, cocurrent and counter-current. Pilot and industrial scales were simulated with both modes of operation. The hydrogen velocity was also varied in both reactor scales to observe its effect on the outlet sulfur concentration. They assumed almost no resistance between the gas and liquid phases. It was recognized that more research is necessary for correct simulation of the countercurrent mode of operation because it could involve significant axial dispersion.
To optimize a cost function representing the essential economical parameter of the HDT process, Al-Adwani et al. (2005) employed a reactor model described by Lababidi et al. (1998), including a deactivation model. The model was time dependent, which means that all operating variables were time variant. However, since catalyst deactivation is a slow process, the mathematical model was considered a quasi- steady-state model. Heavy residuum was used as a feedstock. This study was focused on conversion, throughput, and catalyst life. An industrial-scale atmospheric residue HDS process was selected as a typical HDT unit to demonstrate the capabilities of the optimization model. This study showed that the optimum cost is affected strongly by the catalyst cost and the monetary benefit of lower-sulfur products.
Jimenez et al. (2005, 2006, 2007a,b) illustrated the use of a steady-state one-dimensional heterogeneous TBR model with both gas and liquid phases in plug flow and upflow, based on data obtained at a pilot-plant scale to predict the quality of products during the HDT of VGO and demetallized oil (DMO) over commercial CoMo/7-Al2O3 and NiMo/Al2O3 catalysts.The model involved HDS, HDN, and HDA (mono-, di-, and triaromatic) reactions, and combined the Froment et al. (1994) and Korsten and Hoffmann (1996) models. The HDS reaction was described by the kinetic model of Broderick and Gates (1981) for DBT, while HDN and HDA reactions used the kinetic models proposed by Avraam and Vasalos (2003). Two types of sequential design of experiments were used: for optimal model discrimination and for optimal parameters estimation during kinetic investigation. In most recent papers (Jimenez et al., 2007a,b), the HDS process was simulated using the mathematical model developed in previous work (Jimenez et al., 2005, 2006) and several kinetic models were reported in the literature. The best kinetic model and its optimal parameters estimation were selected by means of sequential design of experiments (SDE). They also reported that water markedly enhanced the capacity to remove sulfur and nitrogen compounds during the HDT of the heaviest fractions of VGOs (Jimenez et al., 2007a).
Mostoufi et al. (2005) developed a one- dimensional plug- flow heterogeneous model in order to simulate the two-stage pyrolysis gasoline hydrogena-tion process to obtain a C6- C8 cut suitable for extraction of aromatics. The first hydrogenation stage was performed in the liquid phase in an adiabatic TBR over a Pd/Al-O3 catalyst in which hydrogenation of diolefins was the main reaction. The second hydrogenation stage took place in a two-compartment adiabatic fixed-bed reactor in series loaded with NiMo/Al2O3 and CoMo/ Al2O3 catalysts, and operating in the vapor phase. Hydrogenation of monoole-fins took place in the first compartment, and sulfur was removed in the second compartment. Simulations for HGO and HDS reactions in the second-stage reactor were carried out considering model compounds such as cyclohexene and thiophene, respectively. The model proposed considered hydrodynamic parameters: pressure drop, liquid holdup, and catalyst wetting efficiency.
Stefanidis et al. (2005) presented a study on the improvement of representative operating temperature from temperature profiles of an industrial adia-batic reactor, which is used to simulate reactor performance by laboratory-scale isothermal reactors. To validate the temperature estimated, a steady-state pseudohomogeneous plug – flow model with no resistance to mass and heat transfer was developed to describe mass balances of sulfur, hydrogen sulfide, hydrogen consumption, and hydrogen, as well as the heat balance in the adia-batic HDT reactor, with feeds ranging from heavy gas oil to diesel. The main disadvantage of this technique is the need of three experimental points: inlet, middle, and outlet, while the main advantage is its reliable prediction when deep desulfurization is performed.
Nguyen et al. (2006) developed a one-dimensional heterogeneous model at a steady-state regime with axial dispersion to analyze the influence of fluid dynamic nonidealities on the HDS performance of gas oils in isothermal bench-scale reactors. A Langmuir-Hinshelwood type of rate model was used to represent the HDS rate of reaction. Recently, Shokri and Zarrinpashne (2006) developed a two-phase (liquid-solid) heterogeneous model for the effectiveness factor of an HDS reaction with DBT as representative of sulfur compounds in gas oil. The mathematical model is at particle-scale conditions because it was based only on the mass balance equations inside a catalyst particle. However, more recently, Shokri et al. (2007) reported a hybrid model, the previous model with a plug-flow one-dimensional heterogeneous model that was validated with gas oil HDS pilot data. The model was implemented in Hysys commercial software through Fortran codes. The rate of chemical reactions was described by kinetics of the Langmuir-Hinshelwood-Hougen-Watson type, with DBT representing all the sulfur compounds in the feedstock.
Murali et al. (2007) developed a one-dimensional heterogeneous model in order to simulate the performance of bench- and commercial-scale HDT reactors. The HDS, HDA, and HGO reactions were taken into account in the model. The HDS reaction kinetics were described by a single lumped model for total sulfur similar to the Langmuir-Hinshelwood-type rate equation used by Korsten and Hoffmann (1996)- whereas the kinetic model for HDA reactions was taken from Chowdhury et al. (2002). In the simulations, a significant amount of feed vaporization (20 to 50%) was found under normal operating conditions of HDT, which suggested that partial-feed vaporization during simulations needs to be considered. The model was validated with pilot-plant data obtained from an upflow operating mode, near ULS levels, to account properly for feed vaporization in heat balance equations. It was mentioned that diesel vaporization is very important in heat balance equations for adia-batic plant simulation because it consumes a significant amount of energy, but it is normally neglected in models reported in the literature. Therefore, the most important contribution of this work in the simulation of HDT reactors was a consideration of whether diesel vaporization and the temperature-H2/ oil ratio were dependent on the liquid specific heat capacity.
A one – dimensional heterogeneous plug – flow model, which accounts for intraparticle transport of the compounds by Fickian diffusion inside the catalyst pellets, was developed by Verstraete et al. (2007) to predict the performance of fixed-bed hydrotreating units. The feedstock of this study was vacuum residue, and experimental data were obtained from an isothermal fixed – bed reactor unit. The model predicts the evolution of concentration profiles of gas, saturates, aromatics, resins, and asphaltenes, their atomic composition in terms of C, H, S, N, O, Ni, and V, and the hydrotreating performances throughout the reactor. It was remarked that it is necessary to take intraparticle diffusion into account when modeling residue hydrotreating processes.
The HDS, HDN, and HDA were modeled and an energy balance procedure was performed in order to predict profiles of temperature along the reactor bed when quenching was employed.
Liu et al. (2008) proposed a novel methodology to understand the dynamic behavior of an HDT process. The new methodology, known as the system dynamics (SD) model, can predict the influence of operating conditions on the conversion efficiencies of HDS, HDN, HDA, and consumption of H– In this work, the SD methodology was applied for the first time in HDT process modeling with the intention of simulating individual sulfur, nitrogen, and aromatics compounds separately and achieving successful simulation. The methodology was validated with experimental LCO HDT data. The methodology consists of two steps; in the first step it is necessary to develop a dynamic loop diagram showing how a change in one variable modifies other variables, which in turn affects the original variable, and so on. The second step consists of developing a mathematical model, usually shown as a stock-flow diagram, which captures the model structure and the interrelationships between variables. This last diagram is translated to a system of ordinary differential equations, which in this case represented a steady-state one-dimensional heterogeneous model. Liu et al. (2008) also reported a similar study using the SD methodology to simulate the HDS process of LCO, including the nitrogen and aromatic compound inhibition effects on HDS activity.
2. computational fluid dynamics models Although great effort has been made to incorporate hydrodynamics in modeling trickle- bed reactors through correlations derived from empiricism, more fundamental approximations must be made to account for suitable predictive models. The fundamental approximation in modeling, from a rigorous point of view, must be performed by solving conservation equations called Navier-Stokes equations- a set of nonlinear partial differential equations, whose solution is possible only for a few simple flows in simple geometries; however, the analysis of fluid dynamics is mathematically complex for actual packed beds. Additionally, constitutive relations that govern a material’s internal response to external effects must be introduced into the conservation laws. Constitutive relations are derived from correlations; therefore, appropriate selection and validation of those relations are extremely important. Since constitutive equations are established by experimental data, experiments are fundamental in the study of fluid mechanics.
Realistic problems in fluid mechanics can be solved quite effectively by using both computational methods, called CFD models, which solve conservation equations, and experimental information. Some assumptions must be made to reduce the complexity of conservation equations, such as a consideration of the lack of effect of viscosity.
The CFD models can be employed as both a competitor and a natural complement to experimentation. For many problems, computational fluid dynamics provide a cost-effective alternative to experimental fluid mechanics. Various physical effects can be turned off, thus providing the opportunity to partially study the phenomena. The simulation of fluid dynamics can help us to understand the hydrodynamics of trickle-bed reactors and hence to perform scale – up and scale – down properly.
Dudukovic et al. (1999) have reported the use of CFD models for hydrodynamics, highlighting the two approaches commonly employed: Euler-Euler formulation and the Euler-Lagrange approach. Although the second approach seems to be more fundamental, it contains the tuning of parameters, which in turn must be validated with experimental information. Moreover, no clear advantages of one over the other formulation has been documented. An application of CFD was reported by Gunjal and Ranade (2007), who simulated the fluid dynamics of trickle-bed reactors in order to understand its interaction with chemical reactions in laboratory- and commercial-scale reactors. The model was employed to understand the influence of porosity distribution, particle characteristics, and scale on the overall reactor performance. The CFD model for TBR consisted of two main parts: (1) implementation of porosity distribution in the bed, and (2) flow equations for each phase (mass and momentum equations), which are based on Eulerian-Eulerian multifluids models. The model was applied to the HDS and HDA of diesel oil, and configuration and operating conditions were similar to those reported by Chowdhury et al. (2002) – It was pointed out that CFD-based models with appropriate validation can be helpful in reducing the gap that exists on prediction between laboratory scales and commercial reactors. It was also reported that CFD models overpredicted conversions because they use apparent kinetic parameters reported in the literature, which have previously lumped hydrodynamics and intrinsic kinetic parameters together. Therefore, when those apparent kinetics parameters are used again in the CFD model, which takes into account the prediction of hydrodynamic parameters, the hydrodynamic effects are being estimated twice (i.e., liquid holdup effects). However, the authors mentioned that the CFD model was used only to understand the influence of reactor scales on its performance. The CFD simulations indicated that porosity distribution is an important parameter when estimating hydrody-namic variables (i.e., pressure drop, liquid holdup, wetting efficiency, etc.), which needs to be taken into account for proper prediction of reactor performance (Dudukovic et al., 1999- Gunjal and Ranade, 2007). The authors also recognized that H2 S solubility in oil fractions is not predicted correctly by empirical correlation at different operating conditions; hence it is advisable to use an equation of state (EoS) in order to improve the estimation. The use of an EoS makes it possible to include the effects of both temperature and pressure; however, suitable interaction parameters could be the limiting factor.
3. discrete models Instead of employing the continuum theory (i.e., modeling a TBR with a set of differential equations), some relaxations have been proposed, such as the supposition that the system can be treated as a number of connected cells. This assumption allows for simplifying the problem of complex reactor system modeling and also favors the use of commercial simulators which accurately predict the results of light petroleum fractions.
a. Cell Models Atrickle-bed reactor was modeled by Sanchezetal. (1995) as a group of consecutive cells, consisting of a CSTR reactor coupled with a separator, in order to take into account vapor-liquid equilibrium existing in the reactor. The flash calculations were performed using a commercial simulator, while proper correlations were taken from the literature for simulating pressure drop and catalyst wetting fraction. The pseudo component evaluations were calculated by lumping a set of 500 different molecules into three compound types: paraffins, naphthenes, and aromatics. The reactions of hydro-genation and hydrocracking were selected and a low conversion level was maintained. First- order irreversible reactions were assumed. The plug- flow model was reached by using 25 cells. It was observed that increasing the number of cells had minor effects on product- distribution simulations. The main conclusion was that using proper thermodynamic properties and compound class lumping can be an effective method of trickle-bed reactor modeling and kinetic parameter estimation of a complex reaction network. This work shows how available tools such as commercial simulators (Aspen, PRO/II, Hysys, etc.) can be used to save time and effort when simulating multiphase catalytic reactors.
Guo et al. (2008) developed one – and two - dimensional mixing – cell reaction network models to simulate the steady-state behavior of TBRs using the highly exothermic benzene HDT reaction to validate the model. The model was based on a network of CSTRs. Each cell was designed to consider the contribution of interphase mass transfer, reaction kinetics, heat transfer, and vaporization effects. This model was developed with the intention of handling multiphase flow and reaction rates, as well as external wetting efficiency, liquid holdup, and temperature change due to both phase transition and flow maldistribution for a TBR. The model was shown to be suitable and efficient to predict temperature runaway in a catalyst bed, and it could also be applied in the scale-up of FBRs.
b. Stage Models Jakobsson et al. (2004) modeled the co-current and countercurrent operations of an HDS reactor using a mixture consisting of DBT, 4,6-dimethyldibenzothiophene (4,6-DMDBT), H2, H2S, and n-eicosane as a solvent. Previous models were used for simulation of the co-current (Toppinen et al., 1996) and countercurrent (Taylor et al., 1994) modes of operation. Countercurrent operation was studied to demonstrate the separation of H-S during the HDS process. Since H2S inhibits the HDS reaction, the countercur-rent operation was proposed to be used to protect high-performance catalysts. The modeling of countercurrent operation used a rate-based stage model, in which the reactor is modeled as a series of rate-based segments (or stages) and each rate-based segment can be indentified as a segment of a packed bed, with direct consideration of diffusion, heat transfer, and multicomponent interaction effects on the calculated segment. These segments are connected by means of mass and heat balance equations to form the reactor model.
To demonstrate the benefits of countercurrent contacting of gas oil with H2 over conventional co-current contact in a TBR for HDS, Ojeda and Krishna (2004) used the equilibrium-stage model of Taylor and Krishna (1993) in HDS reactions in the liquid phase. DBT was selected to represent the most refractory sulfur compounds in a liquid feed of n-hexadecane, which represented a diesel fraction. The reaction rate for DBT was described as a Langmuir-Hinshelwood type, and a plug-flow pattern for both gas and liquid phase flow was assumed. It was observed that increasing BT concentration in the feed leads to a lower sulfur concentration in the reactor effluent. That finding was attributed to a higher heat of reaction liberated, which provoked higher temperatures and hence larger conversions. Therefore, and in addition to the fact that the countercurrent gas phase cools down the liquid phase, accurate modeling of thermal effects in the reactor during HDS process must be carried out. However, it was observed that profiles of sulfur content in the liquid phase along the reactor do not match those from continuous models.
Dynamic Heterogeneous Models Reliable three-phase reactor modeling and simulation should be based on true dynamic heterogeneous models, which can be used not only for scale-up, startup, shutdown, and operability studies, but also to obtain a meaningful continuity path to the steady state of the reactor and to investigate the existence of exotic phenomena such as oscillations and steady-state multiplicity, since dynamic models provide a realistic description of the transient states of three-phase reactors. Study of the dynamic behavior of the three -phase reactor also makes it possible to design the best system control in order to obtain a safe, efficient, and profitable operation. Dynamic models, although more complicated to formulate and solve, should be preferred over steady- state models because the numerical solution strategy of dynamic models is more robust than the solution of steady-state models (Warna and Salmi, 1996; Salmi et al., 2000). Some important reports using such models are described in the following sections.
1. continuous models The hydrogenation reaction of toluene to methyl-cyclohexane, which occurs in a three-phase trickle-bed reactor with counter-current and co-current gas and liquid flow, was simulated by Warna and Salmi (1996) by means of a dynamic three-phase reactor model. The model equations for the gas, liquid, and catalytic phases consisted of ODEs and parabolic PDEs, which were solved using numerical methods. The reactor was assumed to operate adiabatically and nonisothermally. The reaction rate for toluene hydrogenation was of first order and kinetic parameters were obtained in an isothermal laboratory-scale co-current trickle-bed reactor at total pressure of 4 MPa and temperature ranging from 65 to 125°C. It was observed that coun-tercurrent operation gave slightly higher toluene conversion than did co-current operation. This work showed that the dynamic approach provides a meaningful path to the steady state of the reactor and gives valuable information on reaction dynamics. Because no mass transfer resistances inside the catalyst were considered, the model is applicable only for nonporous particles.
The dynamic modeling principles for fixed (trickle) beds were described by Salmi et al. (2000) – An axial dynamic heterogeneous model was applied for the hydrogenation of aromatics simulation. The kinetics was conveniently measured in a laboratory-scale autoclave. It was proposed that dynamic models should be preferred to steady-state models, since the former provide a realistic description of the transient states of three-phase reactors and the numerical solutions of dynamic models are more robust than those of steady-state models. The case studies revealed the importance of internal mass transfer resistance in catalyst particles as well as the dynamics of various phases in three-phase reactors. This study confirmed the disadvantages of the Warna and Salmi (1996) model, where intraparticle mass transfer resistances were not considered. A two-dimensional model for temperature and concentration was applied by Hastaoglu and Jibril (2003) to simulate gas-solid reactions in a desulfuriza-tion fixed-bed reactor. Three levels of process space were used: bed, pellet, and grain. Steady- state experimental naphtha HDS data of a fixed – bed reactor were used to validate the bed model for concentration, whereas thermal behavior was validated transiently. The model was tested by generating the transient concentration of each component, and profiles of system parameters were obtained, giving good insight into the behavior of the system variables. However, since the model was developed for a gas-solid system, it does not include all the mass and energy transfer terms that should be present in a three-phase reactor model to simulate a TBR.
Vogelaar et al. (2006) derived a plug-flow model to describe coke formation and metal deposition profiles in catalyst pellets found in hydroprocessing as a function of position in the isothermal reactor and to predict catalyst deactiva-tion behavior due to pore blocking at the reactor level. A lab-scale HDM experiment was simulated as a case study. The model is based on three levels of scale: the reactor level, the catalyst particle level, and its active phase. The modeling of this process provides a better insight into the deactivation mechanism of hydroprocessing catalysts and can be used to predict their deactivation behavior in industrial reactors. At the particle level, the effective Fickian dif-fusivity (Df) of a molecule inside a porous structure was estimated assuming friction between the solute and pore walls by a restrictive factor due to that friction with the pore wall.
The deposition process of fine particles under chemical reaction conditions in a high-pressure, high-temperature TBR was analyzed theoretically by Iliuta et al. (2006) using a dynamic multiphase flow deep-bed filtration model coupled with heat and mass species balance equations in the liquid, gas, and solid (catalyst + solid deposit) phases. This deep-bed filtration model incorporated the physical effects of porosity and effective specific surface area changes due to fines deposition and detachment, gas and suspension inertial effects, and coupling effects between the filtration parameters and interfacial momentum exchange force terms. The three-phase heterogeneous model developed in this work to simulate TBR performance incorporated the intraparticle mass transfer resistance and solid deposits by fine particles that lead to porosity reduction and bed plugging. It was found that fine particle deposition does not influence TBR performance appreciably. The only undesirable consequence of the fine particle deposition process was reflected in an almost exclusive hydraulic effect of bed plugging and the increase in resistance to gas-liquid flow.
Ho and Nguyen (2006) developed a four-parameter plug-flow one-dimensional heterogeneous model that gave more quantitative insight into how sulfur, nitrogen, and the catalyst surface interact on many widely dissimilar time scales. The theory on which the model is based is applicable to reaction systems where catalyst poisoning dynamics is driven by nonequilibrium adsorption. Modeling of nitrogen-competitive adsorption phenomenon effects in the HDS of oil fractions at the catalyst surface level was addressed with special attention to the design of robust catalyst-deactivation-compensation operating strategies in the deep HDS of middle oil fractions. The experiments were carried out in a co-current fixed-bed reactor operated isothermally in the upflow mode. The model was capable of reproducing the observed inhibiting effect of nitrogen species on the HDS of hindered heterocyclic sulfur compounds.
Mederos et al. (2006) developed a dynamic heterogeneous one-dimensional model to simulate the behavior of TBRs used for catalytic HDT of oil fractions on the pilot and commercial scales. It considered the main reactions present in the HDT process of oil fractions: HDS, HDN, and HDA (total aromatics). The model was validated with experimental data obtained in an isothermal pilot reactor during the HDT of VGO over a commercial NiMo catalyst. After validation of the dynamic model with pilot- plant data, it was employed to predict the dynamic behavior of a commercial HDT reactor. The start- run simulation of the commercial HDT reactor showed the "wrong-way" behavior in the temperature axial profiles before steady state was reached, a phenomenon reported in earlier papers. The combining of heterogeneous mass balance and pseudohomogeneous heat mass balance, as reported by Rodr-guez (2004) – seems to be inconvenient; however, Mederos et al. (2006) demonstrated that this assumption is correct only if predictions of concentration and temperature profiles at steady state are necessary. In other contributions by the same authors,the effects of co-current downflow and countercurrent flow operation modes on HDS, HDN, and HDA were analyzed by employing the same model (Mederos et al., 2006). An important finding was that higher HDT conversion in the countercurrent mode of operation is obtained with respect to the co-current flow mode, which justifies the development of new reactor internals to improve the performance of TBR operating in a countercurrent mode.
2. cross-flow models The cross-flow model seems to be more realistic than others because it assumes a stagnant zone and a dynamic zone, which is a reasonable supposition for trickle-bed reactors. Only one work dedicated to the HDT process with this assumption is available in the literature.
Tsamatsoulis and Papayannakos (1995) employed a cross- flow model to investigate the nonideal behavior of the liquid flow in a dynamic regime in a bench-scale TBR under HDT operating conditions. The development consists of two first-order partial differential equations to model the static and dynamic regions, which were solved analytically. This study provides information on how a catalyst bed should be diluted with inert particles so that the plug-flow pattern describes the liquid flow in an experimental trickle-flow hydrotreater in order to derive kinetics. The main disadvantage of this model was the use of nonporous grains.
Learning Models An artificial neural network (ANN) builds an internal model of the governing relationships embedded in the database used for training. The basic method of neural networking refers to implementing in the computer, by software or by the special hardware of processing nodes, neurons, which are linked to each other by variable-strength connection weights. Causal relations between each model input and output may be calculated from an analysis of the trained ANN structure.
The ANN must learn about the problem under study, and this learning stage is commonly called the -raining process- Once an ANN is trained, it can be used for proper simulation of an HDT unit, the effect of the type of catalysts evaluated, and feedstocks on unit performance, for control of an operation, for unit optimization, and so on. Since the ANN approach presents user friendliness and simplicity, suppressing the difficulties and complexities associated with first-principle models, it is not necessary to have sufficient mathematical and programming expertise to formulate complex objective functions and constraints.
ANNs was used by Berger et al. (1996) to model hydrodesulfurization of atmospheric gas oil in a mini-pilot-plant trickle-bed reactor as a function of temperature, pressure, LHSV, inlet sulfur concentration, and staging. The hidden layer contained three neurons. Inputs were normalized to give equal importance to each input and to reduce the effect of outliers in the database. The database, which contained 25 examples, was randomly divided into learn and test sets containing 17 and 8 examples, respectively. The results calculated by the ANN model were compared with the experimental data and an average relative error of 10% was observed. The causal index (CI), which determines the relative effect of each input variable on the model outputs, was applied to the five variables tested in the HDS system and the relative significance of LHSV and temperature over HDS was observed. Almost linear dependence was observed for the sulfur outlet as a function of LHSV; however, this behavior does not correspond to experimental data trends. It is probably necessary to input more data to the model in order to do better learning at low space velocities.
Lopez et al. (2001) proposed different structured and trained models based on process data and laboratory analysis obtained from a commercial VGO hydrotreater unit. The authors showed the power of a three-l ayered percep-tron ANN used as an analysis tool for the optimization of several existing functions between important process variables controlling continuous operation of a VGO unit. Those different ANN models were used to predict the following operating conditions: feedstock composition (paraffins, naphthenes, total aromatics, and mono-, di-, tri-, and tetraaromatic compounds), feedstock and liquid product quality properties (sulfur and metals content, API gravity, TBP at 50 vol%, and refractive index), and process operating variables (product flow rate and average reactor temperature). After comparison of results predicted from correlation modeling and ANN, better data fitting was observed for the last approach. This feature could be attributed to the fact that the ANN model globally takes all effects occurring in the reactor, while correlations only allow for predicting specific parameters, ignoring some effects, such as transport problems within the reactor.
Commercial data were used by Bollas et al. (2004) to develop predictive models for the integration of two units, HDS and FCC, and to examine the economical benefits of their optimization. The 350 data series were randomly split into training and validation sets, consisting of 225 and 125 data series, respectively. The HDS kinetics derived from pilot-plant studies was first simulated by a predictive model and then operation of the commercial unit. Vacuum gas oil was considered as a feed to the HDS and the liquid product obtained from this process was fed to an FCC unit. The main product, a gasoline fraction, was subject to maximization and restrictions. The neural network was a multilayer perception (MLP) consisting of three layers: an input layer with as many nodes as the input variables, a hidden layer with the number of nodes varying from 1 to 5, and an output layer with as many nodes as output variables. Simulated trends agreed well with the existing experience, although the model performance deteriorated for predictions of sulfur in gasoline fractions.
A hybrid neural network model, a deterministic pseudohomogeneous mathematical code coupled with a neural network, was presented by Bellos et al. (2005). This model was used to predict the catalyst deactivation rate and the dependence of catalyst activity on the liquid feed quality. The reactions taken into account to validate the industrial HDT reactor model were HDS and HCON. Part of the kinetic parameters was obtained from industrial reactor operation data and also from experiments carried out in a small-scale reactor using industrial catalyst size and representative feeds.
Salvatore et al. (2005) used a hybrid approach based on ANNs together with a postprocessing classification algorithm to detect faults in a simulated HDT unit. An HDT model to represent the real unit was also developed. The modeling equations were chosen so that the process showed a dynamic similar to that of existing units, by means of concentration and temperature profiles through the catalytic beds. The model of the reactor was built assuming that the reactor is composed of n CSTR cells (12 stages) in series with equations describing mass and energy balances in each stage.
Zahedi et al. (2006) presented an ANN model for the simulation of an industrial HDT unit based on measured plant data. The model proposed predicts hydrogen demand for HDS, outlet API, and sulfur content as a function of inlet API and sulfur content in weight percent for seven different feedstocks: kerosene, furnace oil, diesel, coker gas oil, cat cycle oil, thermal cycle oil, and virgin gas oil. Eighty-three data sets were used for training, and then 40 data sets were predicted and compared with those collected from operating plants. Optimum ANN architecture was determined to achieve good generalization. The ANN model results were compared with those predicted by a conventional simulator, and it was observed that the ANN model accuracy outperforms the traditional simulator.
Recently, Lukec et al. (2008) developed ANN models to determine the sulfur content in the hydrotreating product of LGO and VGO. The models were trained using the process and laboratory data of routine refinery production. As the models were shown to be simple and easy to use, with good predictability they were used in practice for accurate continuous process monitoring, continuous online predictions, process fault detection, estimation of unmeasured states and parameters, to point out a measurement error to the hardware analyzer, and for process regulation, adaptive control, real-time optimization, and efficient product quality control. This work emphasizes the main advantage of the neural network models because they can estimate the kinetic parameters for different feedstocks, which depends primarily on the number of data sets used during the training process.
Advantages and Disadvantages of Reactor Models A kinetic model based on a detailed description can only be described by a large system of deferential and algebraic equations, implying a huge number of physical and physico-chemical parameters. Due to this feature, some simplifications have been proposed. Among the different approaches in the kinetics of petroleum fractions employed during the last two decades, the most common formulation is that based on a single lump by employing a power law or Langmuir-Hinshelwood expression, although it seems that it is most appropriate to divide the reactant mixture into two lumps: easy to convert and refractory. This approach has been employed because of its easy numerical implementation and its dependence on global parameters, which in turn can easily be measured. However, a single lump is not valid for high conversions because it does not take into account variations in the composition of different feedstocks; moreover, due to future requirements of lower impurities contents in fuels, the power-law model is no longer reliable. Other approaches have been proposed following different criteria. As main contributions, the widely cited structural approach of Froments’ work is a novel way of lumping more rationally the huge number of sulfur species contained in a real feedstock, although considerable analytical work must be performed to obtain the parameters involved. Recently, Froment et al. (2008) have reported the application of this theory to different feedstocks for which the parameters are available by taking almost the same catalyst system and performing a few experiments. Thus, data obtained together with the numerical parameters from previous work were employed for reproducing the overall conversion of some compounds. It has highlighted the necessity of establishing a catalog of invariant feed elements for different commercial catalyst to apply this approach to routine analysis. Another approach cited by Te et al. (2003) is based on computational quantum chemistry, supposing a linear relationship between the reaction rate and the equilibrium constant. Few reports using this approach in real systems are available; however, with the accelerated development of more efficient computers and friendly-use quantum chemical software, this approach could be, in the next years, an important trend in exploring the kinetics of real feedstocks.
It seems that although accurate, these approaches are not used for exploratory studies, because they demand considerable analytical work; they must be worked extensively in the future to account for more fundamentals and feedstock invariants. The most recent promissory approach employed is continuum kinetic lumping. This theory assumes the mixture as a continuum, where reactants are distributed over the entire mixture and reactivity of agglomerates of molecules decreases monotonically with molecular weight or another index. In this same direction, a novel gamma function distribution has been proposed to predict accurately the deep desulfurization of diesel (Inoue et al., 2000). The continuous kinetic approach appears accurate and involves only a few parameters. Moreover, it has been applied to real feedstocks with close agreement between predictions and experimental data (Sau et al., 1997). It seems that a continuum kinetic model is enough to describe an industrial process because it is possible to predict the apparent order of reaction accurately and provides a tool for the prediction of physical properties through the length of the reactor, which can be used for the prediction of transport and thermodynamic properties. Easy adaptation of a power-law or Langmuir-Hinshelwood expression can be incorporated in a continuous theory of mixtures. One disadvantage of the continuum approach observed by Mejdell et al. (2001) was the fact that some components have large deviations from the general TBP-reactivity tendency, such as substituted benzothiophenes. Due to that, these authors recommend modeling these compounds separately from the rest of spectrum, especially for high-conversion kinetics. The same observation, but employing discrete lumping, has been pointed out by Hu et al. (2002): using multiple lumps based on types of sulfur compounds for explaining desul-furization kinetics at ultralow sulfur levels. This observation is in agreement with Murali et al. (2007) – who have pointed out that at low LHSV, a better match could be obtained if sulfur speciation is considered. However, such approaches require the support of advanced analytical tools to identify the various sulfur compounds present in the feedstock.
Recent trends in the production of heavy crude oils and the need to refine them and their distillates create the need to develop suitable reactor models in order to make preliminary calculations in the process design of new refining units. Currently, due to the continuous changes in feedstock composition, only average properties can be obtained, and kinetic studies are only carried out by employing the simplest expression (i.e., the power-law or Langmuir-Hinshelwood approach with adjustable parameters and a single lump). A better kinetic approach is not usual because of the unavailability of characterization techniques for heavy crude oils and residua. The same happens for the reactor system, since no correlations are available to evaluate all the parameters of a detailed model. For such cases it has been better and more convenient to employ simple kinetic and reactor models. However, these models cannot be used for modeling the complex hydrodynamics existing in an HDT reactor. Recently, Guo et al. (2008) have proposed a sequential approach for reducing the gap between CFD simulation and a complex reaction system based on the cell network model. Even if one employs a simplistic reactor model, detailed kinetics coupled with such a reactor model is not well suited for online analysis or optimization and control. Again, depending on the purpose of the study, one could sacrifice the chemistry in order to study more realistic systems such as those of a simple (lumped) reaction sustained in a reactor in order to analyze the fluid dynamics by means of CFD models instead of performing cold-flow experiments. Even with the powerful computers now available, modeling hydrodynamics of complex systems can only be performed for simple kinetic models (Ho, 2008).
A deep discussion of kinetic model selection is beyond the scope of this review. More detailed treatment of these kinetic approaches is summarized elsewhere (Te et al., 2003). More comprehensive details and limitations of continuum lumping have been revised by Ho (2008).
Regarding phase equilibria calculations, two different approaches have been proposed: One involves measurement of bulk properties employing EoS, considering the phases as a single compound, and the other one is based on continuous thermodynamics, which is rarely used in real systems such as petroleum distillation.
Akgerman et al. (1985) reported the influence of feed volatility on conversion in TBRs, arriving at the conclusion that a very different level of conversion is predicted if volatility is included with respect to the case when it is not included. Frye and Mosby (1967) correlated the level of HDS for light catalytic cycle oil with the liquid vaporization at the entrance of reactor, supposing that appropriate reaction rate constants are provided. The effect of species volatility on deep desulfurization of diesel has been explained by Hoekstra (2007) -arguing that light compounds are striped from the liquid and the remaining sulfur compounds increase its concentration, favoring reaction rates. Avraam and Vasalos (2003) have showed the effect of volatilization through the length of reactor by plotting the variations of liquid and gas holdup as a function of dimensionless position through the reactor and emphasized the importance of volatilization on energy balances. The same conclusion was brought out by Murali et al. (2007) – who only calculated the vaporization at the entrance of reactor, however. These authors have also recognized the need for an accurate kinetic model coupled with vaporization effects to predict the performance of a reactor for deep desulfurization. Chen et al. (2009) conducted a VLE study with LCO to investigate the influence of vaporization of feedstock on the operating regime of a pilot-plant hydrotreater, although they remark that results observed at this small scale cannot be extrapolated directly to a commercial plant.
More research in this area is necessary, particularly for HDT of light fractions of petroleum. It is also necessary to incorporate the continuous thermodynamic approach since it permits the description of realistic systems, such as petroleum fractions, which could be considered as a mixture of an infinite number of components (Cotterman and Prausnitz, 1985; Cotterman et al., 1985). As can be inferred, the continuous descriptions, together with separate modeling of some identifiable compounds, can provide an accurate explanation of either kinetics or thermodynamics, although a system described by these approaches could be too complex.
It is not strictly necessary to take into account vaporization effects for the modeling of hydroteatment of heavy crude oils and residua, because almost all reactive compounds remain in the liquid phase even at the high temperatures employed for these processes, as observed in a recent study (i.e., less than 1% of the mole fraction of VGO in the gas phase at typical reaction conditions).This simplification can contribute to reducing the complexity of such a model and favors the exploration of other features, such as the chemistry or related phenomena.
Some researchers have established that probabilistic models can be fitted to the experimental data for TBRs more flexibly than deterministic models, which suggests that a probabilistic description of TBRs corresponds more closely to reality than does a deterministic description (Hofmann, 1977). However, still further research is required to reach a final conclusion: for example, the usefulness of such complex models. The advantages and disadvantages of the various models reported in the literature to simulate HDT reactors are described below.
