AN APPROACH TO OPTIMIZE COSTS DURING ULTRA-LOW HYDRODESULFURIZATION OF A BLEND CONSISTING OF DIFFERENT OIL STREAMS

* E-mail: josesilva@peq.coppe.ufrj.br; arge@peq.coppe.ufrj.br Abstract The presence of contaminants in diesel oil is severely controlled. These components affect the diesel properties, causing impacts on the emissions of pollutants and compromising its commercialization. The Brazilian legislation imposes the use of diesel S10. In this work, a hydrotreatment unit fed with multiple diesel streams was optimized using a phenomenological mathematical model. A three-phase model of a tricked-bed reactor was considered. The optimization of the process was performed with the interior point method considering the hydrodesulfurization reaction of diesel. It was proposed to minimize the operating cost, keeping the amount of sulfur in the final product below the maximum allowed value. The EMSO process simulator was used to model, simulate and optimize the hydrotreatment process. It was observed that the optimization strategy drove the contaminant content into the diesel S10 specification range, as well as reducing the process operating cost by increasing the feed temperature and hydrogen flowrate and adjusting the feed composition blend of the available diesel streams.


INTRODUCTION
The literature is very vast when it comes to the hydrotreatment (HDT) process of petroleum fractions, with many researches addressing the search for the improvement of this process, both in pilot and commercial scale.The diesel hydrotreating process usually occurs in a three-phase heterogeneous reactor, and much effort has been made to improve this operation.But challenges still exist to optimize the HDT process.Trickle-bed reactors (TBR) are widely used in petroleum refineries for hydrotreating processes and for hydrocracking processes (Bhaskar et al., 2004).With the HDT process, impurities such as heteroatoms (sulfur, nitrogen and oxygen), polynuclear aromatics and some metallic compounds, which compromise the diesel quality, can be reduced and even eliminated, meeting the product specifications (Li et al., 2013).
Catalytic hydrotreating is an extremely relevant operation in the petroleum industry, as this process improves a wide variety of products, from direct distillation naphtha to vacuum distillation residues or even in operations with heavy crude oils, gasoil and diesel oil (Alvarez and Ancheyta, 2008a;Ancheyta et al., 2005).
The content of contaminants influences the quality of the diesel oil, generating impacts on its commercialization (Li et al., 2013).The amount of these contaminants present in the diesel such as sulfur and nitrogen must comply with the regulations contained in specific legislation of the fuel sector.In recent years, environmental issues have become an important consideration in discussions around the world, raising the cravings for strong pollution control legislation, especially when it comes to emissions from the use of petroleum products (Ferreira et al., 2013).
The current legislation in Brazil imposes Diesel S10, which contains a maximum of 10 ppm of sulfur in its composition.The production of this fuel requires the intensive use of hydrotreatment units (HDT), with the need for catalysts of high activity and severe operating conditions (Pacheco et al., 2011;Ferreira et al., 2013).One of the most difficult ways to achieve success in diesel hydrotreating is to operate the plant observing different conditions such as product prices and feed that changes constantly (Adetola and Guay, 2010;Jarullah et al., 2011a).
Hydrotreating is a process in which the feed stream, practically any fraction of the oil, reacts with hydrogen at high pressures and temperatures in the presence of a heterogeneous catalyst (Korsten and Hoffmann, 1996;Murali et al., 2007).According to Aye and Zhang (2005) and Ferreira et al. (2013), kinetic models are fundamental for a good performance of the HDT simulation, and the optimization of the hydrotreatment process can benefit from reliable kinetic models of the hydrodesulfurization reactions, among others.
The HDT process, especially deep hydrodesulfurization (HDS) of diesel continues to attract research interest due to environmental regulations which limit sulfur content in several countries (Ali, 2014).Aiming to meet environmental regulations and to reduce diesel engine's harmful emissions, many countries are attempting to produce diesel fuel with ultra low levels of sulfur content (ultra low sulfur diesel, ULSD).Research on the production of ULSD has gained great interest around the world, focusing on deep desulfurization of diesel and on finding cost-effective methodology for ultra low sulfur diesel production.In this way, Stanislaus et al. (2010) discussed advancement in ULSD production from scientific and applied points of view.The authors showed evolution in deep HDS catalysts and advancement in the deep HDS process technologies.
In the literature, few studies were found addressing the optimization of the HDT process of diesel, as well as for the control of the process.Ahmad et al. (2011) studied process integration in the design of a HDT unit, using the simulated annealing algorithm to minimize capital and operating costs.Jarullah et al. (2011a) obtained experimental data for the HDT process in a pilot plant and set up an optimization problem to minimize the total annual cost of the process in the pilot plant, having as optimization variables the inlet and outlet temperatures, subject to system limitations such as the amount of heat involved in the process and the pressure of the system.The authors showed that, with optimization, costs were reduced by approximately 55%.Shokri et al. (2010), aiming to determine the optimal conditions of the hydrodesulfurization process of diesel oil, applied RTO (Real Time Optimization) methodologies in a pilot plant, considering as optimization variables: temperature, pressure, liquid spatial velocity and the amount of sulfur in the product.The authors stated that, initially, the increase in pressure causes the decrease of the amount of sulfur in the product; however, continuing the increase of pressure, this quantity increases.Increasing the feed flowrate and system pressure simultaneously, with constant temperature, the amount of sulfur in the product increases.Zhang et al. (2010) optimized simultaneously materials and energy for a diesel HDT unit aiming to minimize the total costs.The authors showed that, when the material and energy are simultaneously considered, the results of the optimization are more profitable than those obtained from methods that individually optimize the material or energy.Ani et al. (2015) addressed the problem of diesel HDT, considering the reactions of HDS, HDN and HDA.The authors applied the multiobjective optimization based on a genetic algorithm, seeking the best operating conditions of the TBR.The optimization objectives were to minimize the concentration of sulfur and aromatic compounds in the product, with constraints on the TBR feed temperature and reactor pressure.Residence time of the liquid phase and H 2 /oil ratio in the process feed were used as optimization variables.The authors concluded that a very high temperature in the feed stream of hydrogen in the process is not recommended for economic reasons, as well as the fact that this high temperature favors catalyst deactivation, since it accelerates the formation of coke.
In this work, a hydrotreatment unit fed with multiple diesel streams was optimized, using a threephase model for the tricked-bed reactor, considering the HDS process, with the objective to minimize the operating cost, keeping the sulfur concentration in the product below the maximum allowed value by the legislation.
In the next section, the reactor mathematical model and the formulated optimization problem are presented.Then the results are discussed and the main conclusions are stated.

PROBLEM FORMULATION
A multiple feed diesel HDT process was considered in this work, in which a mathematical model of a trickle-bed reactor was implemented in the EMSO (Environment for Modeling, Simulation and Optimization) process simulator.EMSO is an equation-oriented process simulator with a graphical interface for modeling complex dynamic or steadystate processes (Soares and Secchi, 2003).The ALSOC Project (a Portuguese acronym for Free Environment for Simulation, Optimization and Control of Processes) develops, maintains and distributes this objectoriented software.For academic purposes, EMSO is a free software available at <http://www.enq.ufrgs.br/trac/alsoc>.
Fig. 1 shows a scheme of the process that occurs in the presence of a catalytic bed, and the feeds (in which vacuum gas oil, VGO, was considered) are inserted on top of the TBR, which characterize cocurrent operation.Three types of oil (oil A, oil B and oil C) are available to feed the reactor, which can be blended to adjust the feed composition.These feeds are saturated with hydrogen and heated before entering the catalytic bed.At the bottom of the reactor, the treated oil is obtained in the liquid phase, and the removed sulfur leaves the reactor in the gas phase.It was considered that the main difference in the oils A, B and C is the concentration of organic sulfur compounds.
The following assumptions were taken into account to model the HDT reactor:  Three-phase system: gas, liquid and solid phases;  Two interfaces (gas-liquid and liquid-solid) through which mass transfer occurs;  Cocurrent operation with hydrogen saturated feed;  The reactions occur on the surface of the catalyst (in the solid phase);  Stationary process model;  One-dimensional mathematical model;  There are no radial gradients of concentration and temperature;  The velocities of the liquid and gaseous phases are constant along the reactor;  Constant operating pressure;  Pilot scale operation.Model parameters and mathematical correlations were taken from Korsten and Hoffmann (1996), Mederos andAncheyta (2007), Jiménez et al. (2007), Liu et al. (2008), Alvarez and Ancheyta (2008a), Alvarez and Ancheyta (2008b) and Mederos et al. (2012), and are sumarized in Appendix.The input data and the operating conditions prior to the optimization are presented in Table 1.The costs of the oils were based on the current market values (ANP, 2017).The API grade of the oils was considered equal to 22 and the molecular weight equal to 441.9 kg/kmol (Mederos and Ancheyta, 2007).LHSV, (h -1 ) 1 Costs (US$/cm 3 ) 1.3×10 -3 (oil A) 1.4×10 -3 (oil B) 1.5×10 -3 (oil C) 2.0×10 -3 (hydrogen) Costs of heat in the mixer (US$/kJ) 3.0 The hydrocarbon concentrations of the oils A, B and C were kept constant equal to 4.93 (cm 3 mol -1 ), 3.85 (cm 3 mol -1 ) and 2.89 (cm 3 mol -1 ).The inlet concentration of the reactor is obtained through mass balance.
The mathematical modeling of the mixer and the HDT reactor are described in the following sections:

Mass Balance
In the mixer -Overall and component mass balances in the mixer (Figure 1) are given by Equation 1and Equation 2, respectively.
where F total feed (cm 3 s -1 ) is the total feed flowrate of the reactor; F Oil A (cm 3 s -1 ), F Oil B (cm 3 s -1 ) and F Oil C (cm 3 s -1 ) are respectively the feed flowrates of oils A, B and C in the mixer; C total feed (mol cm -3 ) is the inlet sulfur concentration of the reactor; C Oil A (mol cm -3 ), C Oil B (mol cm -3 ) and C Oil C (mol cm -3 ) are the sulfur concentrations of the oils in the mixer.
In the reactor -The following mass balance equations in the TBR were based on the work of Mederos and Ancheyta (2007).
-Gas phase: for the products; r B (g cm -3 ) is the bulk density; x is the volume fraction of the diluted bed; h HDS is the catalytic efficiency for the HDS reaction.
The following boundary conditions were applied to the differential equations: At z = 0, the partial pressures of the gaseous components at the inlet of the reactor are: The concentrations of the components in the liquid phase at the inlet of the reactor (z=0) were based on Danckwerts boundary conditions (Danckwerts, 1995) where p i G (MPa) is the partial pressure of component i; u G (cm s -1 ) is the gas velocity; z (cm) is the spatial variable; R (J mol -1 K -1 ) is the gas constant; T G (K) is the temperature of the gas phase; k i L (cm/s) is the mass transfer coefficient of the component i at the liquid interface; a L (cm -1 ) is the specific area at the liquid interface; (MPa cm 3 mol -1 ) is the constant of Henry's law for component i; C i L (mol cm -3 ) is the concentration of component i in the liquid phase; H 2 is hydrogen gas; H 2 S is the sulfhydric gas.
-Liquid phase: ( ) i = S and HC where e L is the liquid phase holdup; u L (cm s -1 ) is the velocity of the liquid; D a L (cm 2 s -1 ) is the mass dispersion coefficient in the liquid phase; k i S (cm s -1 ) is the mass transfer coefficient of component i at the interface of the solid phase; a S (cm -1 ) is the specific area at the interface of the solid phase; C i S (mol cm -3 ) is the concentration of component i in the solid phase; S in subscript i represents the sulfur compound and HC represents the hydrocarbons.
-Solid phase: and HC in which r HDS (mol g -1 s -1 ) is the rate of the HDS reaction; the "±" sign means "-" for reagents and "+" ( ) where Re liq and Re gas are the Reynolds number of the liquid and gas phases, respectively.

Energy Balance
In the mixer -The energy balance in the mixer (Figure 1) is given by Equation 8.
where h total feed (kJ kmol -1 ) is the enthalpy of the feed stream to the reactor; Q (kW) is the heat source in the mixer; h Oil A (kJ kmol -1 ), h Oil B (kJ kmol -1 ) and h Oil C (kJ kmol -1 ) are respectively the enthalpies of the oils A, B and C in the mixer.
In the reactor -The energy balance equations in the TBR were based on the work of Mederos and Ancheyta (2007).

Numerical Integration
The system of differential equations describing the heat and mass transfers in the reactor was transformed into a set of algebraic equations, using the finite difference method.
The number of discretization points required for the numerical method used to obtain the satisfactory solution was determined using the mesh convergence criterion the absolute difference between the values of the process variables obtained at the discretization points of the refinement mesh k+1 and the values obtained at the discretization points by the refinement mesh k were less than 10 -5 .
The algebraic equations were solved using SUite of Nonlinear and Differential/ALgebraic equation Solvers -sundial algorithms - (Hindmarsh et al., 2005), using EMSO (Environment for Modeling, Simulation and Optimization) software (Soares and Secchi, 2003) as a platform for modelling, simulations and optimization of the process.

Process Optimization
Current Brazilian legislation establishes diesel to present a maximum of 10 ppm of sulfur concentration.An optimization problem was proposed to minimize the operating cost of the HDS process, subject to the maximum allowed sulfur concentration in the final product.EMSO process simulator was used to simulate and optimize the problem, and the IPOPT algorithm (Wächter and Biegler, 2006) was used to solve the optimization problem.
Limitations on variables such as temperature, pressure and LHSV of the reaction mixture should be taken into account, as they influence the performance of hydrotreatment.Many researchers have shown that the reaction temperature can vary greatly depending on the characteristics of the charge.Korsten and Hoffman (1999) studied the HDS reaction at temperatures ranging from 350°C to 400°C, showing that the analyses can be done at higher temperatures depending on the characteristics of the feedstock.These authors also analyzed the effects of pressure on the HDS reaction, showing that the increase in pressure favors the reaction with limits that depend on the nature of the feed and the catalyst.The authors pointed out that the HDS reaction, under the conditions studied, showed good performance between 6 and 10 MPa.The authors analyzed the LHSV between 0.9-4.8(h -1 ) showing that the smaller values favor the HDS reaction.Similar analyzes and conclusions have been reported in the literature (Mederos and Ancheyta, 2007; Al-Daous ( ) where r G (g cm -3 ), r L (g cm -3 ) and r S (g cm -3 ) are respectively the gas, liquid and solid phases densities; C p G (J g -1 K -1 ), C p L (J g -1 K -1 ) and C p S (J g -1 K -1 ) are respectively the specific heat capacities of the gas, liquid and solid; h GL (J s -1 cm -2 K -1 ) and h LS (J s -1 cm -2 K -1 ) are respectively heat transfer coefficients at the gas-liquid and liquid-solid interfaces; T L (K) and T S (K) are respectively the liquid and solid phases temperatures; D R HDS (J mol -1 ) is the heat of the HDS reaction.
The following boundary conditions were applied to the differential equations: the temperatures of each phase at the inlet of the reactor (at z=0) are:

Kinetic Model
We consider that the oil fraction feeding the mixer contains a great amount of organic sulfur compounds and, during reaction, the hydrogen sulfide is adsorbed at the active catalyst sites.In this study, the HDS reaction was considered irreversible and the organic sulfur content and the hydrogen concentration have a positive effect (Korsten and Hoffman, 1999).Usually the overall HDS reaction is represented by the practical and generalized stoichiometric equation.This approach is widely accepted and accumulates the HDS reaction of all sulfur compounds (Dibenzothiophene-DBT and its alkyl-derivates) in a single expression (Korsten and Hoffman, 1999;Bhaskar et al., 2004;Rodríguez and Ancheyta, 2004;Mederos and Ancheyta, 2007;Alvarez and Ancheyta, 2008a).The HDS reaction model is of the Langmuir-Hinshelwood type, which takes into account the inhibitory effects of H 2 S formation by including an adsorption equilibrium constant for H 2 S described by the van't Hoff equation to relate the equilibrium coefficient with temperature on the adsorption of the hydrogen sulphide on the active sites of the catalyst (Korsten and Hoffmann, 1996;Mederos and Ancheyta, 2007;Alvarez and Ancheyta, 2008b;Kallinikos et al., 2010;Alvarez et al., 2011).The reaction rate of HDS occurs according to Equation 12. where r HDS (mol g -1 s -1 ) is the rate of HDS reaction; k HDS (cm 3 g -1 s -1 )(cm 3 mol -1 ) 0.45 is the apparent constant (11) (12) and Ali, 2012;Novaes et al., 2017;Tao et al., 2017).
Based on the literature in the case studies implemented in this work, the limits on the optimization variables were chosen.The Objective Function (OF) given by Equation 13was used to represent the costs of the process.

Model Validation
Operating data from the pilot-scale HDT process were extracted from the work of Mederos and Ancheyta (2007) to validate the model addressed in this work.The authors considered a single feed diesel HDT process and the hypotheses presented in Section 2, with u G = 0.028 cm/s, u L = 1.75×10 -2 cm/s, where u L is the surface velocity of the liquid phase through the TBR, T o = 653 K and P = 5.3 MPa.
The partial pressure profiles of the gaseous compounds, H 2 and H 2 S, and the sulfur concentration in the liquid phase along the reactor can be seen in Fig. 2a, Fig. 2b and Fig. 3, respectively.It is observed that the results obtained in the simulations are similar to the literature, indicating that the reactor model is representative.Mederos and Ancheyta (2007) discussed about some HDT operation conditions and showed that cocurrent operation with H 2 saturated oils is the approach which better fits the experimental data.The model parameters provided by these authors were used to validate the modeling in this work (Fig. 2 and Fig. 3).We observed that the profiles obtained in the simulations of this work were above those predicted in the simulations by Mederos and Ancheyta (2007), this can occur due to the numerical method used, as well as due to the numerical precision of the result of the mathematical model of the process, as shown in Figs. 2 and 3.

Sensitivity Analysis
A sensitivity analysis was carried out within the constraints of the process in order to understand the behavior of the objective function (OF).
Fig. 4 shows that costs are lowered when lower T o values are considered, implying a lower energy supply to heat the oil feed.The objective function is also decreased when the velocity of the hydrogen gas is reduced, so that there is a smaller gas flow feeding the system (Fig. 4b).Then the objective function decreases as T o and u G decrease.In Fig. 4b, the feed flowrate of oil A (F A ) was kept constant and the feed flowrate of oil C (F C ) was varied from 0.01 cm³/s to 0.04 cm³/s, and thus the feed flowrate of oil B (F B ) was obtained from the mass balance.It is observed that the variation in F C does not cause variations in the value of the objective function for the tested operating conditions, showing no sensitivity (for each F C value, surfaces that overlap were generated).These details can be seen in Fig. 4a, where, for each value of T o , values of the objective function are constant with the variations in F A and F C , Subject to: Equality constraints: Equations 1 to 12. Inequality constraints: where OF (US$ h -1 ) is the Objective Function; s Oil A (US$ cm -3 ), s Oil B (US$ cm -3 ), s Oil C (US$ cm -3 ) and s H 2 (US$ cm -3 ) are the costs of the fed compounds, s Q (US$ kJ -1 ) is the cost of supplied heat; F H 2 (cm 3 s -1 ) is the feed flowrate of hydrogen in the reactor; T O (K) is the inlet temperature of the reactor; CS out (ppm) is the sulfur outlet concentration of the reactor.The constraints of the optimization problem were chosen observing the physical conditions of the process.In Table 2, the information about the size of the optimization problem is provided.since the structure of the objective function causes F B to compensate for changes in F A and F C , generating parallel planes to the axes of F A and F C .The highest sensitivities observed were for variations of u G and T o (Fig. 4b).Fig. 5 shows the behavior of the sulfur concentration at the exit of the reactor as function of the feed flowrates of oils in the mixer.It is observed that the sulfur concentration is influenced by the manipulation of the inlet temperature of the reactor.The presence of sulfur compounds decreases with a temperature increase.It is also observed that the flow of oils at the entrance of the system impacts the quantity of sulfur compounds at the exit of the system.In these cases, the highest sensitivities are observed when the temperature is varied.The concentration of 10 ppm of sulfur at the reactor outlet was obtained between T o = 702 K and T o = 703 K, considering u G = 0.4 cm/s (Fig. 5 and Fig. 6).These operating conditions favor the HDS reaction rate.In Fig. 6, the concentration of sulfur at the exit of the reactor is around 10 ppm, indicating that, in this way, the product specification can be achieved.1, and the inlet flow rate of the reactor was kept constant according to Table 1.Between the temperatures of 650 K and 680 K, the sensitivity is greater as to the variation of u G .From 680 K, the response is more sensitive to temperature variation.The conditions for obtaining the product with concentrations around 10 ppm of sulfur are observed from the temperature of 700 K and gas velocity between 0.1 cm/s and 0.5 cm/s.It is observed that the variations in F C cause small differences among the surfaces observed in Fig. 7, since the highest sensitivities are observed in the variations of T o and u G .

Optimization Results
In Table 3, it can be verified that the optimization problem generated a product that meets the specification with a sulfur concentration of 9.84 ppm.
The optimized value of the objective function was 404.09US$/h, which is a minimum value for the desired product specification.As compared to the original value, there was an increase in reactor input temperature and variations in gas velocity and oil flow rates.
Simulations of the optimization problem showed that a feasible region was reached (as seen in Fig. 5 to Fig. 7), in which the specified diesel can be obtained.There was a decrease of 25% in the gas velocity ( ), 40% and 56% decreases in the flow rates of oils A and B (F A and F B ), respectively, a 200% increase in the oil C flow rate (F C ), a 7% increase in the inlet temperature (T o ), increase of 13.3% in the value of the objective function, and obtaining the product with concentration of organic sulfur compounds within the specification (Table 3).The increase in the temperature causes a higher reaction rate, and since the feasible region encompasses a range of possible gas velocity values, the value has been decreased because although higher values favor the reaction, this would cause higher values of the objective function.In this way, the optimization problem is a good tool to adjust the best values of the variables of optimization in order to minimize the operational costs.The flow rates of oils A and B decreased, while the flow rate of oil C increased.As the concentrations of organic sulfur in the oils A and B (400 ppm and 300 ppm, respectively) are higher than oil C (200 ppm), the flow rates of these oils tend to decrease in the optimization problem.The F B , despite having a lower concentration, decreases more than F A , since the original F B was higher than F A .These effects occur to adjust the concentration of organic sulfur at the reactor inlet with the blending of oils A, B and C in the mixer.
Simulations of the optimization problem showed that the decrease in the objective function competes with the constraint of the product at the exit of the reactor, which must have a concentration of at most 10 ppm in the content of organic sulfur compounds.
Process optimization that seeks to minimize the value of the operating cost and meets the product specification is necessary and of great interest.In a possible increase of scale, the costs can be high, and decreases in these costs are appreciated.The mathematical approach discussed in this paper can be used to scale up the HDS process of diesel, due to the fact that the large-scale operation has to consider, in addition to mass balance, the energy balance that considers temperature profiles within the reactor (Mederos and Ancheyta, 2007;Jarullah et al., 2011b).The optimization problem can be used to adjust the kinetic parameters of possible scale up of the reactor in the HDS process of the diesel, in order to have satisfactory answers with larger dimensions of the reactor.The optimization strategies implemented and approached from the HDS process of diesel are fundamental to estimate the operational costs of increasing the scale of production and may reduce possible problems.
Due to changes in feedstock and operating conditions to achieve ultralow sulfur diesel, existing hydrodesulfurization plants have started revamping and need to overcome many challenges such as control and operational safety (Ancheyta et al., 2002).Unknown kinetic parameters can be determined depending on the experimental information.The predicted values from the model employed should match with the experimental data as closely as possible so that errors between experimental and theoretical data are minimized (Reséndiz et al., 2007).Some authors use their experimental information to calculate kinetic parameters of hydrodesulfurization of feedstocks, and others prefer to assume the value of the parameters (Ancheyta et al., 2002).Knowing about kinetic parameters of hydrodesulfurization of feedstocks is required, and the optimization results will be influenced, impacting the products.

CONCLUSIONS
A trickle-bed reactor model was employed in this work to predict the behavior of a pilot hydrotreating reactor and to implement optimization, and the following conclusions can be pointed out: • The blend of oils with specific characteristics in the system feed, seeking to meet the product specification is an appreciable alternative to reduce process difficulties.Thus, the blends combined to the possibility of variations in their flow rates and adjustment of the organic sulfur concentration at the TBR inlet can be used as a tool to optimize the diesel hydrotreatment process.
• The temperature and the hydrogen flowrate at the inlet of the reactor showed the highest sensitivities in the search for the oil quality at the exit of the reactor, being important variables in the adjustment to obtain the product within the specifications.
• The optimization strategy addressed can be useful in the scale up of the diesel HDT process, and the production of Ultra Low Sulfur Diesel (ULSD) can

Figure 1 .
Figure 1.Schematic diagram of the TBR, representing the cocurrent operation of the diesel HDT process.

Figure 2 .
Figure 2. a) Profiles of partial pressures of the H 2 along the reactor: continuous line, data obtained from the simulations; discontinuous line, data obtained from Mederos and Ancheyta (2007).b) Profiles of partial pressures of H 2 S along the reactor: continuous line, results obtained from the simulations; discontinuous line, data obtained from Mederos and Ancheyta (2007).

Figure 3 .
Figure 3. Profile of sulfur concentration in the liquid mixture (CS L ) along the reactor: continuous line, results obtained from the simulations; discontinuous line, data obtained from Mederos and Ancheyta (2007).

Figure 4 Figure 5 .
Figure 4. a) Objective Function (OF) as a function of the oil flow rate at the inlet of the mixer, with the gas surface velocity (u G ) equal to 0.4 cm/s and T o equal to 653 K, 683 K and 703 K.; b) Objective Function (OF) as a function of the gas velocity (u G ) and the reactor inlet temperature (T o ), with the feed flowrate of oil A (F A ) kept constant, and the feed flowrate of oil C (F C ) varying between 0.01 cm 3 /s and 0.04 cm 3 /s.(b) (a)

Fig. 7 Figure 7 .
Figure 7. Sulfur concentration as a function of the gas velocity (u G ) ant the inlet temperature (To) of the reactor, with the flow of oil A (F A ) kept constant equal to 0.03 cm 3 /s, the flow of oil C (F C ) varying between 0.01 cm 3 /s and 0.04 cm 3 /s and the flow rate of oil B is obtained from the mass balance.mass balance by Equation1, and the inlet flow rate of the reactor was kept constant according to Table1.Between the temperatures of 650 K and 680 K, the sensitivity is greater as to the variation of u G .From 680 K, the response is more sensitive to temperature variation.The conditions for obtaining the product with concentrations around 10 ppm of sulfur are observed from the temperature of 700 K and gas velocity between 0.1 cm/s and 0.5 cm/s.It is observed that the variations in F C cause small differences among the surfaces observed in Fig.7, since the highest sensitivities are observed in the variations of T o and u G .

Table 1 .
Information about the system studied.

Table 3 .
Results of the proposed optimization problem.from this methodology, seeking to obtain diesel fuel that complies with restrictive environmental laws. benefit