Model for Gasification of Residual Fuels from Petroleum Refineries

ARTICLE pubs.acs.org/IECR

Model for Gasification of Residual Fuels from Petroleum Refineries Using the Equation Oriented (EO) Approach Jorge E. Marin-Sanchez* and Miguel A. Rodriguez-Toral Instituto Mexicano del Petroleo, Eje Central Lazaro Cardenas No. 152, C.P. 07730, D.F., Mexico ABSTRACT: An attractive way to use residual fuels from petroleum refineries (vacuum residue and petcoke) is their gasification to produce syngas, which contains mainly H2, CO and small quantities of CH4, CO2, as well as nitrogen and sulfur compounds. Syngas has a large range of possibilities to be used, as fuel in IGCC plants, or as raw material for other chemical manufacturing processes An equilibrium based model for entrained-flow gasification of petroleum refinery residual fuels is here proposed. Using an equation oriented (EO) approach where the process model is set up as a Non Linear Algebraic Equations System and simultaneously solved, the model gives the syngas composition, with CO, H2, CO2, CH4, H2S, HCN, NH3, N2, O2, COS, and H2O, as well as the slag composition, with NiS, FeS, V2O3, ashes, and no reacted hydrocarbon. The slag mass flow and composition calculation is an important feature not considered by previously published models. A sensitivity analysis was made in order to show the effect of input variables. Model predictions were compared to published industrial and experimental data. The results are in good agreement between both the simulated and published data.

1. INTRODUCTION Gasification is a partial oxidation of fuel with an oxidizing agent (air or oxygen) and steam, where synthesis gas (or syngas) is produced, its main components are CO and H2. A solid residue (slag) is also produced. Syngas is easier both for handling and cleaning than the original fuel. It can be used as fuel for power generation in IGCC plants, or as a raw material in many applications, including ammonia or petrochemicals production. Because of this, gasification has turned into an excellent alternative for the use of fuels, instead of just burning them. Vacuum residue and petroleum coke (petcoke) are, respectively, heavy liquid and solid byproducts from crude oil refining, they are often used as fuel in boilers for power production, natural gas has been more commonly used in the past few years in power generation; reducing the market for both vacuum residue and petcoke. Thus, gasification presents an attractive alternative for the use of these residual fuels. The syngas composition determines its treatment and use, and the slag composition must be considered in the materials selection of the gasifier and in the maintenance schedule, so it is of utmost importance to know the properties of the input and output streams, to predict the performance and the products of the gasifier. Three kinds of reactions occur inside the reactor: pyrolysis, which is the thermal decomposition of fuel in volatiles and a solid residue called char; oxidation of char; and reduction reactions, which are reactions within the char with some of the present gases or gas-gas reactions. The gasifier operating conditions depend on the fuel properties, and the type of gasifier. In order to predict syngas and slag composition both kinetic and equilibrium based models have been published. Regarding petroleum refinery residuals Uson et al.1 developed a model for cogasification of coal, petcoke and biomass, based on reaction kinetics. They considered the fuel as composed of C, H, O, N, S, and ashes, the r 2010 American Chemical Society

char has the same elements with a reduced composition, and the gas products are CO, CO2, H2, CH4, H2S, N2, COS, and H2O. Watanabe et al.2 proposed a CFD gasification model for extra heavy oil, once volatiles are produced char is considered just carbon, this assumption can be good enough for coal gasification, but for other fuels, mainly petroleum derived, depends on the fuel chemical components. In this model2 products are CO, CO2, H2, CH4, and H2O. Both models consider the solid residue (slag) as the inorganic matter and not reacted char. Trommer and Steinfield3 developed a kinetic model for gasification of petcoke from flexicoking and delayed coking with steam (without oxygen) in a solar chemical reactor. Fuel is considered to be composed of C, H, O, N, and S, and the main gasification products are H2, CO, CO2, and H2S, char is considered to be composed by carbon only. Regarding chemical equilibrium based models, in the work from Chern et al.,4 they presented an overall gasifier and a flaming pyrolysis zone model5 for downdraft gasification of biomass, with air as the oxidizing agent. They considered the biomass composed by C, H, O, and N, and the char only as carbon. Zainal et al.,6 also presented a model for a downdraft gasifier for biomass,composed by C, H, O, and N, and was focused both in the prediction of syngas composition and its calorific value. Zaporowski7 developed an equilibrium model for coal composed by C, H, O, N, S, and Ar, and do consider nitrogen compounds among 25 gaseous products. Research works have been recently published for coal and biomass,8 biomass,9-12 and municipal solid waste.13 These Special Issue: IMCCRE 2010 Received: March 17, 2010 Accepted: July 12, 2010 Revised: June 29, 2010 Published: July 29, 2010 2628

dx.doi.org/10.1021/ie100663w | Ind. Eng. Chem. Res. 2011, 50, 2628–2640

Industrial & Engineering Chemistry Research

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works considered the fuel composed by C, H, and O;8,9 C, H, O, and N13; and C, H, O, N, and S.10-12 Sharma10 explains that in order to improve the results, it is sometimes needed to fix the char yield as zero, and drop heterogeneous reactions from the equilibrium calculations. Jarungthammachote and Dutta13 improved the accuracy of their model by multiplying two equilibrium constants with two coefficients respectively, to fit the model’s data with experimental data. Regarding gasification of petroleum derived fuels it must be mentioned that the models so far, do not consider the presence of metals in fuel, such as nickel, iron or vanadium that are present in significant amounts in some crude oils, and may have some impact in the gasifier materials selection.14 Only few reported models consider nitrogen in fuel reacting toward other compounds different from N2. For petroleum derived fuels gasification, this is not considered in previous research from open literature. The model here presented is based on chemical equilibrium, and it is focused on gasification of vacuum residue, and petcoke, so it is developed to find the syngas and slag composition, taking into account not only the effect of sulfur, but also nitrogen and metals (Ni, Fe, and V) not presented in previous reported models. Our model supplies information that can be used for other stages; like syngas cleanup and materials selection. In addition, the equation oriented (EO) modeling approach used allows the evaluation of different scenarios, by selecting a variety of fixed and free variables. In the EO approach the process model is represented by an equation system like, f ðxÞ ¼ 0

2. EO MODELING The EO model describes the gasification process consisting of input process streams; gasification model; and output process streams The main variables involved for process streams are T, P, F, H, h, s, and composition. The equations relating these variables are as follows: enthalpy flow: ð2Þ

h-h ð T;PÞ ¼ 0

ð3Þ

s-s ð T;PÞ ¼ 0

ð4Þ

specific enthalpy:

specific entropy:

The equations used for the calculation of specific enthalpy and specific entropy for the process streams modeled are explained in Appendix A. A basis for mole calculations is added for convenience Mass Flow: F-F mol MW ¼ 0

ð5Þ

and the restriction for composition in multi component streams, with n compounds: n X

ð1Þ

Where f(x) is a residual functions vector, and x is the vector of process variables, the main characteristic of this representation is the fact that the residual function does not aim to compute any particular variable, and all equations are solved simultaneously;15 thus, against the traditional sequential modular approach, the advantage of the EO approach is that, as long as there are no redundant equations, and the degrees of freedom remain zero, any variable may be set or calculated as an input, output, or parameter. All process variables are treated the same way in EO models, and are simultaneously modified toward the convergence. In addition we use the EO flowsheeting concept,15,16 so we split the model in modules, representing the process streams, and the gasifier. All equations are still solved simultaneously in EO flowsheeting; the model is better structured and the code can be reused. A bounded Newton’s method17 is used to solve the model developed, this is specially suited for sparse systems like the proposed EO model represented by a nonlinear algebraic equations (NLAE) system. By using the equation oriented (EO) approach a model for entrained flow gasification is presented, developing independent models for process streams, and the gasification process, and they can be solved stand alone or within a whole gasification model. In this paper the EO modeling approach is presented first, then the equilibrium based model for the gasifier is developed, and some considerations for the solution of the model are explained, followed by the sensitivity analysis of the main values assigned to some input variables, afterward the results of some industrial and experimental cases of study are shown, as compared to model predictions, and the conclusions of this work are finally discussed.

H-hF ¼ 0

yi ¼ 0

ð6Þ

i

Then we have 7 þ n variables and five equations relating them, so we have 3 þ (n - 1) free variables, which must be fixed to solve the process stream model. For each stream we need to know or compute other properties that depend on the specific stream, for example for fuel we need HHV or LHV. In order to solve the model it must be assured that the additional variables and equations keep zero free variables (degrees of freedom), otherwise it will be necessary to know the variable values, to satisfy this condition The gasification model, as any unit operation model, must contain the following parts. Material balance: The mass flow for the process streams in the gasifier is given by X X Fin Fout ¼ 0 ð7Þ in

out

Energy balance: The enthalpy for the process streams and the enthalpy produced in the gasifier are related by X X Hin þ ΔHgassif ier Hout -Q ¼ 0 ð8Þ in

out

Momentum/pressure relationships: the inlet and outlet pressure are related by Pinlet -ΔP-Poutlet ¼ 0

ð9Þ

Performance equations: They define the composition and temperature for the output streams, in our case; they are the chemical equilibrium reactions and the stoichiometric balance equations. 2629

dx.doi.org/10.1021/ie100663w |Ind. Eng. Chem. Res. 2011, 50, 2628–2640


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Figure 1. EO model for gasification.

Figure 1 presents a simplified EO model for gasification. The model developed consists of input process stream models, gasifier model, and output process stream models. To solve the model it is necessary to know, for all the input streams, the independent variables T, P, as well as their flow and composition. For the gasifier model the parameters for performance equations (stoichiometric coefficients, thermodynamic constants, etc.) must be known. By solving the EO model we obtain all the variables for the output streams (e.g., T, P, H, h, s, composition, etc.), and the gasification temperature (or Fsteam or Q if gasifier temperature is chosen as a fixed variable). Refineries often process a blend of two or more different crude oils, so their products are dependent on the processed blend characteristics. The EO model developed allows flexibility for the assessment of the impact of different fuel properties as well as several gasifier operating conditions. The model has a feasible solution when there are zero redundant equations, and zero free variables. The EO model was set up by using the flexible modeling system (FMS) described by Mitchell.18 This is an equationoriented modeling environment for simulation, optimization and synthesis, leading to the creation of individual units and linking them in a larger model. The selection of fixed variables can change as long as the system keeps zero degrees of freedom. This can be used to analyze different model responses. The set of equations defined by the process streams and gasifier model was evaluated in an equation analyzer,19 which performs structural analysis of a system of equations, detecting redundant equations and free or unspecified variables, and performs a numerical check on the equations in order to detect singular linear or nonlinear subsets of equations. The equation analyzer allows the identification of an undetermined model by assessing the number of free variables and redundant equations in the NLAE system formed by the equations used in the process model.

3. GASIFIER MODELING The chosen model for this study is the gasification in an entrained-flow gasifier. There are many gasifier types, it has been reported though that only the entrained-flow gasifier can be used for either solid or liquid hydrocarbons,20 this is a reactor where oxidizer, fuel, and steam go in cocurrent flow (Figure 2), they can go upflow or downflow. The syngas outflows in the opposite side

Figure 2. Entrained-flow gasification.

of the feed streams into the gasifier, whereas the slag is withdrawn at the bottom. Developed after 1950, these gasifiers are able to handle successfully almost all kinds of fuels. The operation temperature (up to 1500 °C for coal) is the highest of all gasifiers.13 Also, as stated by Higman and van der Burgt14 it is considered that for almost all gasifiers (except the moving bed gasifier) the reaction rates are high enough to suppose that chemical equilibrium is reached. The advantages of using entrained flow gasifier come with the penalty of high oxygen demand, the oxygen used is approximately 0.45 kgmol O2/kg atom of carbon in fuel. The steam is used for temperature control, by providing a reductive environment and for controlling the H2/CO ratio. The steam flow (plus water flow, when the fuel is fed as a slurry) depends on the fuel used. It can take values from zero to 0.5 kg-mol H2O/kg-atom C in fuel, here values between 0.27 (for vacuum residue) and 0.49 (for petcoke) kgmol H2O/kg-atom of C are used in fuel according to the case of study. In the entrained-flow gasifier, fuel reacts with the steam and oxidizer moving in the same direction, with a few seconds residence time.14 Due to a lower density of char and fuel than that of slag, this goes down to the bottom of the reactor while the fuel and char remain reacting with the gases a little longer. Since all the reactants go in the same direction, and the chemical equilibrium is reached, the output stream properties can be computed in a model where all reactions take place in a single stage where they finally come to chemical equilibrium. However, it is considered that pyrolysis and oxidation can take place first in the gasifier, and after that, the remaining reactions occur. Thus, a second model is proposed where the gasifier is divided into two stages (Figure 3), where pyrolysis and oxidation take place in the first stage, at the entrance of the reactor, and at the second stage the remaining reactions (reduction reactions) take place. The EO approach becomes very useful for the two stages model because the second stage only implies reusing the modules already defined. The output streams of the first stage are introduced as the input streams for the second stage of the gasifier, supplying the slag and syngas as the final output streams of the model (see Figure 3). The composition and temperature are the result of the enthalpy change of pyrolysis/oxidation reactions for stage 1 and for reduction reactions regarding stage 2. The proposed model 2630



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3.1.2. Oxidation. It is the reaction of char with oxygen, extended from the model of Uson et al.1 as: Ccc Hhc Ooc Nnc Ssc V vc Z þ o2 O2 f a2 CO þ b2 CO2 þ e2 H2 S þ n2 N2 þ i2 V 2 O3 þ w2 H2 O þ Z

ðR.2Þ

3.1.3. Reduction. These kind of reactions are Char with CO2, known as Boudouard reaction, Ccc Hhc Ooc Nnc Ssc V vc Z þ b3 CO2 f a3 CO þ e3 H2 S þ h3 H2 þ n3 N2 þ i3 V 2 O3 þ w3 H2 O þ Z

ðR.3Þ

Char with H2O, or the water-gas reaction, Ccc Hhc Ooc Nnc Ssc V vc Z þ w4 H2 O f a4 CO þ e4 H2 S þ h4 H2 þ n4 N2 þ i4 V 2 O3 Z

ðR.4Þ

Char with H2, or the methanation reaction, Ccc Hhc Ooc Nnc Ssc V vc Z þ h5 H2 f d5 CH4 þ e5 H2 S þ n5 N2 þ i 5 V 2 O3 þ w 5 H 2 O þ Z

ðR.5Þ

CO-shift reaction, CO þ H2 O S CO2 þ H2

Figure 3. Streams used for the gasifier model with two stages.

was tested with both one stage and two stage options to show the best approach for gasifier performance assessment. 3.1. Chemical Reactions Involved. Gasification is a partial oxidation of fuel in a reductive atmosphere, which is generated by controlling the oxygen rate, added in substoichiometric amount, and adding steam, this reduces the formation of undesired compounds as NOx or SOx. Three kinds of chemical reactions can occur: 3.1.1. Pyrolysis. Is the thermal decomposition of fuel, products are volatiles and a solid residue called char. In the work from Uson et al.1 this reaction is defined as:

steam-methane reaction, CH4 þ H2 O S CO þ 3H2

Ccf Hhf Oof Nnf Ssf Ninif Fefef V vf Z f Ccc Hhc Ooc Nnc Ssc V vc Z þ a1 CO þ b1 CO2 þ d1 CH4 þ e1 H2 S þ f1 HCN þ g1 NH3 þ h1 H2 þ j1 NiS þ k1 FeS þ w1 H2 O

ðR.1Þ

Where CcfHhfOofNnfSsfNinifFefefVvfZ is the condensed formula of a refinery residual fuel and CccHhcOocNncSscVvcZ is the condensed formula of char (look up the nomenclature section for variable names). CO, CO2, CH4, H2S, HCN, NH3, H2, and H2O are considered to be the most representative volatiles from pyrolysis. NiS and FeS, are not volatiles but they are considered as product from pyrolysis.13 They are included because iron and nickel are present in crude oil in significant amounts, together with vanadium, which reacts with oxygen and produces V2O3 which can build up deposits in the reactor.21 This is important in materials selection and maintenance scheduling. Iron and nickel only react with sulfur present in fuel, and nonreacting Ni and Fe are assumed to be negligible, or trapped in ashes.

ðR.7Þ

Also, in the gas phase the ammonia and hydrocyanic acid produced in pyrolysis can participate in a chemical reaction according to Phillips,22 HCN þ H2 O S NH3 þ CO

ðR.8Þ

And COS can be produced according to Uson et al1 by CO2 þ H2 S S cos þ H2 O

CHhf Oof Nnf Ssf ðH2 OÞZ f CHh Oo Nn Ss Z þ Volatiles þ wH2 O Residual fuels from heavy crude oils contain other pollutants than S, like Ni, Fe, and V, thus this reaction can be extended to,

ðR.6Þ

ðR.9Þ

Reactions R.1-R.9 above presented are those considered in the gasification model, reaction R.8 is not taken into account in previous published models found in open literature, but it must be considered here as in this case, petroleum refining residuals are the fuels involved, often containing nitrogen which reacts toward NH3 or HCN; additionally we considered the presence of metals in the fuel’s composition, whereas previous models did not. Compounds like NOx and SOx are not present for both practical and simulation purposes because the reductive atmosphere in the gasifier avoids their formation.14 Stoichiometric coefficients ai, bi, ..., wi, etc. in reactions R.1-R.5 and the atom numbers in the condensed formula of char (cc, hc, oc, nc, sc, and vc) are constants in this model. They are computed in a separated linear model, but they can be included in the gasifier model. According to Chern et al.4 reactions R.3 and R.4 (boudouard and water-gas) can be combined to give the CO-Shift R.6 reaction, also reaction R.4 and R.5 (water-gas and methanation) can be combined to give steam-methane R.7 reaction. Then it is possible to eliminate two reactions (R.6 and R.7), or three (R.3, R.4, and R.5) depending on the selected chemical reactions. Reactions R.6 and R.7 remain for equilibrium calculation 2631



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An independent system of linear equations is built by an elemental component balance, represented by X X xcompound welement xcompound welement ¼ 0 ð10Þ reactants

w1 H2 O ¼ γ8 ¼ H2 pyrolysis h1

ð19Þ

a2 CO ¼ CO2 oxidation b2

ð20Þ

products

where xcompound represents the stoichiometric coefficient and welement represents the atom number of the element being balanced. The atom numbers for fuel are known from the fuel stream model, so only the unknown atom numbers are those for char (since its stoichiometric coefficient equals one). The unknown stoichiometric coefficients are for known compounds, thus the elemental balance described by eq 10 is a linear equation system of 32 equations and 50 variables. Since the fuel composition is known, the 8 molecular coefficients of fuel plus the 32 equations give 10 degrees of freedom. In order to reduce them, 10 constants are added, which are relations among some of the variables. Watanabe et al.2 used an auxiliary constant, defining a ratio between two produced compounds, specifically CO and CO2, or γ¼

CO CO2

ð11Þ

The creation of this constant is based on an experimental analysis performed by Arthur,23 which brings out this relationship defined as a function of temperature. Since the temperature of gasification in the model does not change, all of the new variables this kind are constants. These constants are defined by choosing compounds sharing two of their elements (CO and CO2 are an example) and because of that, the mole balance for the reaction is underdetermined (there are less equations than variables), therefore, more information is needed to compute the reaction coefficients. The constants added are: γ1 ¼

hc hydrogen in char ¼ hf hydrogen in f uel

ð12Þ

oc oxygen in char ¼ of oxygen in f uel

ð13Þ

γ2 ¼

γ9 ¼

w3 H2 O γ10 ¼ ¼ H2 Boudouard h3

γ1-γ4 are relationships between char and fuel components (except carbon, which is computed from its elemental mole balance), γ5 and γ9 are defined by choosing compounds sharing in the same reaction two of their elements, γ6, γ7, γ8, and γ10 they were mainly used to close the hydrogen balance. The values for these constants can be set by using information about the fuel, for example γ6 can be estimated by knowing if the nitrogen in fuel is bound to aromatic rings or if it is present as amine.14 They can also be fixed by using some system insights (for example, γ1 must be close to zero) or by using other relationships presented in the literature as the one mentioned by Arthur23 for γ9, and several correlations for pyrolysis compiled by Song et al.24 A sensitivity analysis for these parameters is presented in the Section 4, where the impact of the γi values in the results is explained. The γi relationships were validated with the equation analyzer,19 so they match our requirements of zero degrees of freedom adding no dependencies, nor redundant equations. For modeling purposes reactions R.1-R.9 are carried out simultaneously, or in stages, as stated before, and the extent of each reaction is estimated by chemical equilibrium among gasgas reactions. 3.2. Material Balance. For each chemical reaction, we define an equation for the extent of reaction (molar), εj so the material balance for the ith component is " # " # X X X Fk xik þ νij εj Fl xil ¼0 ð22Þ k

nc nitrogen in char ¼ nf nitrogen in f uel

ð14Þ

sc sulf ur in char ¼ sf sulf ur in f uel

ð15Þ

a1 CO γ5 ¼ ¼ CO2 pyrolysis b1

ð16Þ

γ3 ¼

γ4 ¼

j

in

γ7 ¼

d1 CH4 ¼ h1 H2 pyrolysis

ð17Þ

l

out

For n - 1 components and the total mass balance Ff uel þ Foxidant þ Fsteam -Fsyngas -Fslag ¼ 0

ð23Þ

3.3. Energy Balance. The energy balance involves the enthalpy of the input and output streams, and the global reaction enthalpy change, being more convenient in this case, since the fuel is a blend of hydrocarbons. The energy balance is defined as ! X X Hl Hk þ ΔHglobal -Q ¼ 0 ð24Þ l

f1 HCN γ6 ¼ ¼ NH3 pyrolysis g1

ð21Þ

k

Where ΔHglobal is the global reaction enthalpy changes. The global reaction enthalpy change can be defined as combustion ΔHglobal -Ff uel ΔHfuel þ

þ

ð18Þ

X

X

Fsyngas ΔHicombustion

i

Fslag xj ΔHjcombustion ¼ 0

ð25Þ

j

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combustion for fuels is expressed as the lower heating value ΔH obtained in the fuel stream model, for syngas components we use LHV data reported in literature. Equation 25 is set up on the basis that the enthalpy change of the process reactions can be obtained by subtracting the total heat produced from fuel minus the heat still available in the products of the process.25 Within the EO model the energy balance allows to know the reactor temperature or, if necessary, it can be used to compute the steam needed or Q for a reactor where a fixed temperature is used. 3.4. Momentum/Pressure Relationships. The inlet and outlet pressure is related by

Pinlet -ΔP-Poutlet ¼ 0

Where the reactor pressure P is considered constant for this study. νi,j is the stoichiometric coefficient for the component i in the jth reaction, it is considered positive if compound i is a product, and negative if it is a reactant. In the heterogeneous reaction case, when one component is present as solid or liquid, and its vapor pressure does not change, its composition is not present in the equilibrium equation, since its chemical activity is defined as the unity.30 Kj is related to temperature by the equation, ΔGj RT

ð27Þ

Where ΔGj is defined by ΔGj ¼ ΔHj -TΔSj

ð28Þ

ΔHj, ΔSj, are computed, respectively, from the equations ZT X X ΔHj ¼ νi, j ΔHi,T0 þ νi, j CpdT ð29Þ T0

i

and ΔSj ¼

X i

Z νi, j ΔSi,T0 þ

i

P T T0

i

CGE-

ð9aÞ

Some documents like that from the Shelton and Lyons26 present a difference of 1.2% between the inlet and outlet streams pressure for the Texaco Gasifier27 or near 1% and for the Lurgi gasifier.28 In addition some experimental studies29 report small pressure drop values (less than 1%) for entrained flow gasifiers. ΔP is considered negligible for the model here presented the sensitivity analysis (Section 4) shows that setting ΔP a value of up to 10% of the inlet pressure has no effect on the simulation results. 3.4. Chemical Equilibrium. The pyrolysis and oxidation reactions are considered complete. For the gas-gas chemical reactions presented in Section 3.1, equilibrium was computed by using the general equilibrium equation Y ν P νj ð26Þ Kj ¼ ðyi Þ i, j P0 i

ln Kj ¼ -

For heterogeneous reactions the effect of the solid or liquid compounds is present in the Gibbs free energy calculation, although it does not appear explicitly in eq 30. The syngas composition is a function of temperature and pressure ruled by chemical equilibrium inside the reactor. Within performance equations of the model, eq 30 is used for the reactions considered in equilibrium. Two more equations are used in order to evaluate the gasifier performance, • The cold gas efficiency (CGE), which is the heating value of syngas compared to the heating value of fuel

νi, j Cp T

dT

From eq 27, in order to compute the gas composition inside the gasifier for reaction j, we have, X X P νi, j ln yi þ νi, j ln -ln Kj ¼ 0 ð30Þ P 0 i i

low heating value of syngas ¼0 low heating value of f uel

ð31Þ

• And the carbon conversion (CC), that is the amount of carbon reacted compared to the carbon in fuel CC-1 þ

carbon in syngas ¼0 carbon in f uel

ð32Þ

These two additional variables are used in the sensitivity analysis presented in Section 4. The equations for material balance (eqs 22 and 23), energy balance (eqs 24 and 25), momentum balance (eq 9), and performance equations (eqs 30 to 32) represent the EO model for gasification, given by a NLAE system that has a feasible solution when there are zero redundant equations and zero free variables. 3.5. Model Solving. Through simple identification of the number of variables and equations, the model seems to be complete, when the system was checked with the equation analyzer19 two equations were identified as redundant though. As explained in Section 3.1, reactions R.3 and R.4 (boudouard and water-gas), and reactions R.4 and R.5 (water-gas and methanation) can be combined to give the CO-Shift R.6, and steam-methane R.7 reactions. Even if this statement is used when char is only carbon, it remains valid because we consider in our system that the compounds produced additionally to the reactions with carbon (H2S, N2, V2O3, and Z) are present as products in all the mentioned reactions. In addition they are produced in the same proportion with respect to the char reacted (e.g., e3 = e4 = e5, for H2S). Then it is possible to eliminate two reactions (R.6 and R.7), or three (R.3, R.4, and R.5). For equilibrium calculation we keep eqs R.6 and R.7. Thus, we have now six chemical reactions (R.1, R.2, and R.6-R.9), producing six equilibrium equations, since the number of unknown extents of reaction are also reduced to six; the model is still a complete NLAE system. This time, the equation analyzer identified zero degrees of freedom and zero redundant equations. For the reactions involving fuel and char the equilibrium constants Kj are too large (ln Kj > 100, at temperatures close to the gasifier temperature) meaning that those reactions are complete (i.e., the limiting reactants are totally consumed) and the composition cannot be obtained through equilibrium relationships because when the molar reactant fractions are nearly zero, the equilibrium equation (which involves logarithms) becomes undetermined. In this case, basic thermodynamics books like that of Smith et al.,31 outline that a reformulation of the problem must be performed by means of a combination of the reactions leading to a system, where reactions with large equilibrium constants are not involved. In fact this has been 2633



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Table 1. Sensitivity of γi Constants Used for the Calculation of Stoichiometric Coefficients As They Modify Gasification Temperature (See Section 3.1) senstitivity value (μ*) interval of tested values

variable

definition

γ1

hydrogen in char hydrogen in fuel

504.2

γ2

oxygen in char oxygen in fuel

116.4

γ3

nitrogen in char nitrogen in fuel

γ4

sulfur in char sulfur in fuel

γ5

γ6

γ7

γ8

γ9

γ10

CO CO2

Table 2. Sensitivity of γi Constants Used for Calculation of Stoichiometric Coefficients As They Modify Cold Gas Efficiency (See Section 3.1)

0-1

γ1

hydrogen in char hydrogen in fuel

0.58

0-1

0-1

γ2

oxygen in char oxygen in fuel

0.08

0-1

1.42

0-1

γ3

nitrogen in char nitrogen in fuel

0.0015

0-1

18.16

0-1

γ4

sulfur in char sulfur in fuel

0.15

0-1

0-100

γ5

1.1 10-6

0-100

HCN NH3 pyrolysis

0.0003

0-100

CH4 H2 pyrolysis

0.0031

0-100

H2 O H2 pyrolysis

0.001

0-50

0.0026

0-100

0

0-100

0.001

CO CO2

pyrolysis

0.25

0-100

γ6

CH4 H2 pyrolysis

3.61

0-100

γ7

H2 O H2 pyrolysis

1.46

0-50

γ8

2.96

0-100

γ9

CO CO2

CO CO2

oxidation

H2 O H2 Boudouard

interval of tested values

definition

HCN NH3 pyrolysis

μ*

variable

0

already done by eliminating reactions R.3-R.5 from the model, nonetheless we still have reactions R.1 and R.2, with large equilibrium constant values. Reaction R.1 only involves fuel as reactant. Oxygen is present only in reaction R.2, since O2 is fed in a substoichiometric amount, and the fuel pyrolysis is normally complete, to eliminate equilibrium equations for R.1 and R.2 we considered a fixed value (very close to zero, or 10-10) for the oxygen molar fractions in syngas (yO2) and for the fuel molar fraction in slag (mfuel). Thus, instead of six equilibrium equations we only have four equilibrium equations, but six extents of reaction yet, so we still have a NLAE system with a feasible solution.

4. SENSITIVITY ANALYSIS In order to review the impact of the values assigned to the parameters used in the model, a sensitivity analysis using the “Elementary Effect Test” described by Saltelli et al.32 was

pyrolysis

oxidation

H2 O H2 Boudouard

γ10

0-100

performed. The elementary effect is an average of derivatives over the space of the parameters. From a chosen “state” of our model (defined as Y(x1,x2, ..., xi, ..., xk), which is the result of the simulation evaluated for the parameters of study) the ith input factor for the elemental effect is defined as EEi ¼

Y ðx1 ,x2 ,:::,xi þ Δ,:::,xk Þ-Y ðx1 ,x2 ,:::,xi ,:::,xk Þ Δ

ð33Þ

And the sensitivity value is the obtained mean, defined as μi ¼

r 1X j jEEi j r j¼1

ð34Þ

Where r is the number of elemental effects For the gasification model here presented, the test was performed over the parameters used for the calculation of the 2634



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Table 3. Fuel Data Used for Gasification Model Validation Case 1 vacuum residue (Choi et al.)

petcoke (Wabash River)

C, wt %

81.85

87.86

H, wt %

10.03

fuel

vacuum residue (Lurgi)

Case 2

specific gravity (15 °C)

1.05

C/H ratio, kg/kg

8.72

petcoke (Lurgi)

22.37

O, wt %

3.17 1.0

N, wt % S, wt %

4.1

6.2

V wt ppm Ni, wt ppm

210 70

1000 230

Fe, wt ppm

0

0

ash wt %

0.07

0.05

HHV MJ/kg

39.82

38.63

0.2

0.89

5.72

6.93

V and Ni ppm

1900

stoichiometric coefficients (constants γ1-γ10), and for the pressure inside the gasifier. The “states” chosen for the model were the temperature of syngas and the cold gas efficiency, CGE (eq 31) for the cases of study as shown in the Results section. The results of the sensitivity analysis for gasification temperature are presented in Table 1, and in Table 2 for CGE. For γ1 to γ4 the values are from 0 to 1 and, for the rest of the constants the interval of tested values is that in which the variable (T or CGE) has a significant change. The global effect is computed as the mean (μ*) times the size of the interval. A special case is γ10 (see eq 21 and reaction R.3), as in order to evaluate its sensitivity, ɛ3 must be greater than zero. As explained in the model solving (Section 3.5), we first set ɛ3 as zero, and the carbon conversion is computed by only considering pyrolysis and oxidation reactions. For the sensitivity analysis the carbon conversion is fixed with a greater value than that obtained considering pyrolysis and oxidation only, ɛ3 is now a free variable in the model and the elemental effects of γ10 are analyzed. From Tables 1 and 2 it can be seen that the variables with the biggest global effects on temperature and cold gas efficiency are γ1, γ7, and γ9, the rest of the constants do not have a significant effect on those “states”. For constants with the highest impact it is recommended to use a function already tested, γ9 is computed by means of the function presented by Arthur,22 γ7 can be computed using some of the relationships presented by Song et al.,23 for γ1, it is considered that almost all the hydrogen is converted in pyrolysis, so γ1 is set as almost zero, but keeping the linear system feasible (i.e., all the stoichiometric constants are greater than zero). The value of the remaining constants can be set as an average inside the interval tested or an approximate value given from the process insights. Pressure was perturbed in an interval of (10% of the inlet value, the maximum variation in the calculated temperature was 1 °C, and of 0.0006 for CGE, thus confirming the assumption that ΔP does not have any effect in the model results. There are other types of gasifiers where the pressure drop is bigger so, attention to this variable must be enhanced. The model predictions for a few cases of study are shown in the next section considering our findings in the sensitivity analysis.

0.14 41.88

34.53

5. RESULTS The model was tested using data from Lurgi33 for gasification of vacuum residue and petcoke in an industrial entrained-flow gasifier (“Case 1”); also for a 1 ton/day vacuum residue entrained-flow gasifier from Choi et al.20 (“Case 2” for vacuum residue), and from the Wabash River gasification repowering project, sub task 1.5b from the report by Becthel, Global Energy and Nexant34 (“Case 2” for petcoke). This is a 1977 ton/day (dry basis plus 40 ton/day of fluxant) for petcoke IGCC plant. The vacuum residue gasifiers process the fuel together with oxygen and steam. The petcoke plant from Lurgi uses a 70/30% petcoke slurry and a small quantity of steam. The petcoke gasifier for Case 2 process a slurry of petcoke, fluxant (ashes), and water, which is gasified with oxygen at 95% purity. The gasification model was solved by using the information available from the mentioned sources, as basis for input data, simulations were made in the single stage and two stage models. The model predictions were compared to the experimental or industrial information as appropiate. The fuel data used for simulations is shown in Table 3. Other streams and gasifier properties used as input information are listed in Table 4. It must be mentioned that not all the input information was found in the industrial or the experimental data extracted from literature, then practical assumptions were taken from data marked with a with “a” in Table 4. For vacuum residue, petcoke, oxygen, and water, the supply temperature was assumed as the temperature of the product stream coming out from the respective process plant in a typical refinery (vacuum distiller, delayed coking, air separation unit, and water demineralizer). Mass flow for water in Case 2 of petcoke, was assumed as that required for petcoke slurry like in Case 1 (0.428 kg-mol H2O/kg-atom C in fuel). Also as explained in the sensitivity analysis, the carbon conversion can be set as an independent variable if one of ε3, ε4, or ε5 is released. Since the ashes flow is given in the document for Case 2 of petcoke,34 slag flow is set at 70 ton/day, ε4 is computed as a free variable, and the syngas composition is compared to the industrial data. Results from the gasifier model for dry gas composition are listed in Table 5 for Case 1 and in Table 6 for Case 2, compared to values from the mentioned sources. The predictions of syngas and slag composition, and gasifier output temperature between 2635



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Table 4. Feed Streams Data Case 1 fuel

vacuum residue (Lurgi)

Case 2 petcoke (Lurgi)

vacuum residue (Choi et al.)

petcoke (Wabash River)

hydrocarbon: flow rate (kg/h)

360

467

41.67

82375

temperature (°C)

110a

30a

200

30a

oxygen: % oxygen (mol)

99

99

99

93.6

flow rate (kg/h)

378

480

33.67

89292

temperature (°C) steam:

100a

100a

100a

100a

flow rate (kg/h)

126

60

25

0

temperature (°C)

380

380

280a

0

200

0

added water (for slurry): flow rate (kg/h)

a

46792

30a

temperature (°C)

30a

gasifier operating temperature (°C)

1200-1450

1200-1450

1300

gasifier operating pressure (MPa)

6

6

0.55

2

Assumed values based on industrial practice.

Table 5. Results from the Gasification Model, Case 1 vacuum residue fuel

petcoke

simulation

reported (Lurgi)

simulation

reported (Lurgi)

1447 1255

1200-1450

1961 1631

1200-1450

972

1000

1044

1000

reactor temperature (°C) oxidation zone (two stages as in Figure 3) output syngas flow rate (Nm3/h of COþH2) composition % mol (dry) H2

43.14

45.4

30.8

32.1

CO

50.8

49.1

59.6

53.2

CO2

4.5

3.9

7.5

11.7

CH4 N2

0.37 0.27

0.3 0.2

0.01 0.31

0.2 0.4

H2S

0.97

1.0

1.65

2.3

COS

0.05

0.1

0.14

0.1

slag flow rate (kg/h)

20.3

29.50

composition (% wt) char

98.1

96.2

V2O3 NiS

0.5 0.2

2.28 0.57

ashes

1.2

0.94

the one stage and two stages model show no significant differences in the results, so only the temperature of the pyrolysis/ reduction stage is shown in these tables. For vacuum residue the syngas composition and flow rate show a good agreement with those reported, while the model performance for petcoke presents more deviations regarding reported information. For vacuum residue the main compounds, CO and H2 show a difference of 8.6% at most, and temperature is considered in an acceptable range of values

since the difference is of 4%. There is a bigger difference between the model predictions and the reported information for petcoke, especially for H2 which could be of almost 20% (for Case 2, where the errors can be attributed to the water flow, being just assumed because the data is not available), but the order of magnitude is still considered acceptable. One significant difference is the molar fraction of CH4 (especially for petcoke), the equilibrium for reaction R.7 predicts that, at high temperatures almost all the CH4 is converted into CO, 2636



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Table 6. Results for Gasification Model, Case 2 petcokea

vacuum residue fuel

simulation

reported (Choi et al.)

simulation

reported (Wabash River)

reactor temperature (°c) oxidation zone (two stages as in Figure 3)

1591

output

1258

1300

1909

carbon conversion (%)

88.4

65-92

116

50-110

1709

syngas flow rate (Nm3/h) flow rate (clean kg/h)

183,757

193,531

46.6

27.3

27.2

41

61.3

59.6

4.5

10.3

8.6

9.0

CH4

0.01

2.1

0.01

1.6

N2

0.22

2.21

2.6

HCN

0.01

0.15

NH3

0.05

H2S COS

1.27 0.05

composition % mol (dry)a H2

50.4

CO

43.5

CO2

0.45 0.5

slag flow rate (kg/h)

5.12

2,917

char

84.8

98.0

ashes

15.2

2.0

2,917

composition (% wt)

a

For petcoke results are for clean and dry syngas.

even so the molar fraction is small compared to that of CO or H2. Based on the results (see Tables 5 and 6) it is considered that the model for one stage is the best option for predicticting both products and gasifier operating conditions. It is also considered that for vacuum residue the model performs better than that of petcoke, but it can be used successfully if applied for both fuels. As stated before, the equation oriented approach allows to change the choice of variables to compute, and since the used industrial data for the model validation did not report temperature of feed streams, (except for steam in Case 1), nor the heat losses in the reactor, these variables can be fixed as well as the gasification temperature to analyze their effect in chemical equilibrium. As for the performance of the used solver, the local search method used brings up the necessity of providing an acceptable initial guess. This is due to the nonlinearity of some equations (like equilibrium, enthalpy and entropy). The initial values can be obtained by fixing a reactor temperature, after that, the solver performs in the worst cases approximately 200 iterations, (in fact, if after this number of iterations the system does not converge, it is better to find different initial values). For the sensitivity analysis through which several cases were solved, using the last converged results as initial guess for following simulation it took a maximum of 40 iterations, in near one second in a 2.2 GHz Pentium processor.

5. CONCLUSIONS An EO model for the gasification of residual fuels from petroleum refineries has been developed, where syngas composition and reactor temperature was computed using chemical

equilibrium. Syngas composition only depends on chemical reactions in equilibrium, and those reactions only involve gaseous components (all known). So, the syngas composition can be predicted only with the basic information of the inlet streams used in gasification. The slag composition is also important the results show that the slag is mainly composed of non reacted char and a small quantity of the metal compounds formed in pyrolysis. These metal compounds can melt and build up deposits in the reactor walls, so the results can provide a guide to operation, maintenance scheduling, and gasifier materials selection, and for further use of slag. The model presented here is intended to be used for vacuum residue and petcoke, and its predictions for syngas composition are considered suitable for these fuels based on the comparison of the predicted results, against the industrial and experimental data used for model validation. The EO approach used for solving the model gives flexibility for other variable analysis, and the equation analyzer allows avoiding redundant equations or a lack of information, giving robustness to our model.

’ APPENDIX Appendix: Equations Used for Enthalpy and Entropy of Process Streams

For a full description of the streams present in the gasification model, three variables (T, P, and F) must be fixed, the other variables are computed by the equations presented in Section 2 (eqs 2-345). The specific enthalpy and specific entropy for fuel, steam, slag and the gaseous streams are computed in a different way depending on the nature of its components, the equations used here are described afterward. 2637



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A.1. Fuel (Vacuum Residue or Petcoke). The specific enthalpy and entropy are computed by the following equations: Specific Enthalpy: ZT CpdT ¼ 0 ð35Þ hT0

Specific Entropy:

Z s-

T

Cp dT ¼ 0 T0 T

ð36Þ

A.4. Slag Stream. Although the slag is a single stream, it is a mixture of the non reacted fuel, char, NiS, FeS, V2O3, and Z (the ashes from fuel), that means six components, and their molar fractions mi (for i = 1, ..., 6, in the same order). The fuel is considered completely consumed in pirolysis, so its fraction is zero in slag composition, but it is included as part of what can go as a residual from gasification. For fuel and char the specific enthalpy and specific entropy (hf and sf for fuel, and hchar and schar for char) are computed as in Section A.1, while the slag stream properties are obtained by Specific Enthalpy:

h ¼ m1 hf þ m2 hchar þ RT ðm3 CpNiS þ m4 CpFeS þ m5 CpV 2 O3 þ m6 CpZ ÞdT T0

The heat capacity (Cp) is defined depending on the type of fuel, for liquid fuels. It is obtained by using the specific gravity (Sg)35 in the formula Cp ¼

0:388 0:00045T þ Sg Sg

Cp ¼ 10:89cf þ 7:56hf þ 13:42of þ 18:74nf þ 12:36sf þ 25:46nif þ 29:08fef þ 29:36vf þ 26:63

ð38Þ

A.2. Steam (or Water). The functions used for water or steam are Specific Enthalpy:

h-½jhV ðT, PÞ þ ð1-jÞhL ðT, PÞ ¼ 0

ð39Þ

Specific Entropy: s-½jsV ðT, PÞ þ ð1-jÞsL ðT, PÞ ¼ 0

ð40Þ

Where j is the vapor fraction, hV and hL are the specific enthalpy for vapor and liquid, respectively and sV and sL are the specific entropy of vapor and liquid, in that order. These functions are physical correlations explained in detail by Rodriguez-Toral.37 A.3. Gaseous Streams (Oxidizer and Syngas). The equations for specific enthalpy and entropy of gas streams are explained in detail by Rodriguez-Toral;37 they are Specific Enthalpy: n Z T X yi Cpi dT ¼ 0 ð41Þ hi¼1

T¼

Specific Entropy: s-

n Z X yi i¼1

n X Cpi P dT - Rln -R yi ln yi ¼ 0 P0 T¼ T i¼1 T

ð42Þ

And Cp for the ith component is expressed as Cpi ¼ a1 þ a2 T þ a3 T 2 þ ::: þ a7 T 6

Specific Entropy:

ð37Þ

Where T is expressed in °F and Cp is in BTU/lb °F. For solid fuels as petcoke and char (present in slag) Cp is computed using the mole number in the condensed molecular formula (in kJ/kgmol K), by the Koop-Harrison rule:36

ð43Þ

Where a1, a2, ..., a7 are constants reported in several sources, those presented by Liley et al.38 are used here.

ð44Þ

s ¼ m1 sf þ m2 schar þ m3 CpNiS þ m4 CpFeS þ m5 CpV 2 O3 þ m6 CpZ R T dT T0 T

ð45Þ

Where CpZ used is 26.63 kJ/kgmol K (from eq 38).

’ NOMENCLATURE a1, moles of CO2 produced in reaction R.1 b1, moles of CO produced in reaction R.1 cc, atoms of carbon in char cf, atoms of carbon in fuel d1, moles of CH4 produced in reaction R.1 e1, moles of H2S produced in reaction R.1 f1, moles of HCN produced in reaction R.1 fef, atoms of iron in fuel g1, moles of NH3 produced in reaction R.1 h, specific enthalpy h1, moles of H2 produced in reaction R.1 hc, atoms of hydrogen in char hf, atoms of hydrogen in fuel hL, specific enthalpy for liquid (for water stream) hV, specific enthalpy for vapor (for water stream) i1, moles of V2O3 produced in reaction R.1 j1, moles of NiS produced in reaction R.1 k1, moles of FeS produced in reaction R.1 mi, molar fraction of ith component in slag nc, atoms of nitrogen in char nf, atoms of nitrogen in fuel n1, moles of nitrogen produced in reaction R.1 oc, atoms of oxygen in char of, atoms of oxygen in fuel o2, moles of oxygen consumed in reaction R.2 s, specific entropy sc, atoms of sulfur in char sf, atoms of sulfur in fuel sL, specific entropy for liquid (for water stream) sV, specific entropy for vapor (for water stream) vc, atoms of vanadium in char vf, atoms of vanadium in fuel w1, moles of water produced in reaction R.1 welement, atom number of a given element xcompound, stoichiometric coefficient of a given compound yi, molar fraction of ith compound 2638


Industrial & Engineering Chemistry Research Z, ashes CC, carbon conversion CGE, cold gas efficiency (defined in eq 31) Cpi, heat capacity of component i F, mass flow Fmol, molar flow H, enthalpy flow Kj, equilibrium constant for reaction R.j MW, molar weight Sg, specific gravity (for vacuum residue) T, temperature T0, temperature of reference (298.15 K) P, pressure P0, standard pressure (1 atm) Q, heat losses or additions to gasifier R, gas constant Greek Symbols ΔHglobal, global enthalpy change of gasification , enthalpy of combustion of component i ΔHcombustion i ΔHj, enthalpy change of reaction R.j ΔGj, Gibbs energy of reaction R.j ΔP, pressure change ΔSj, entropy of reaction R.j εj, molar extent of reaction R.j j, vapor fraction (for water stream) μi*, mean of elemental effects of variable i γi, auxiliary constant for stoichiometric calculation νij, stoichiometric coefficient of ith component in reaction R.j νj, global stoichiometric balance for reaction R.j

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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Model for Gasification of Residual Fuels from Petroleum Refineries

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