model-based optimization of reactors involved in the

MODEL-BASED OPTIMIZATION OF REACTORS INVOLVED IN THE STEAM REFORMING OF BIOETHANOL J.A. Francesconi1, M.C. Mussati1, E.E. Miró2, R.O. Mato1, P.A. Aguirre1*. 1

2

Instituto de Desarrollo y Diseño, INGAR (CONICET) Instituto de Investigaciones en Catálisis y Petroquímica, INCAPE (FIQ, UNL-CONICET)

Abstract. Fuel cell power systems for transportation applications have received increased attention in last years because of their potential for high fuel efficiency and lower emissions. The operation conditions of automotive vehicles require short times of start-up, compact and lightweight equipment and efficient operation at different conditions. The reformer, the water gas shift (WGS) reactor and the preferential oxidation reactor (CO-PROX) constitute the nucleus of the processor, and are a significant fraction of the system volume and weight. In this work we approach the synthesis and design of a system processor of ethanol using conventional reactors. A model-based reactor optimization permits to obtain both designs for reducing volumes and optimal operation conditions as temperature and pressure profiles. These results can be useful for estimating the minimum and relative sizes of the component reactors that allows this technology. The reforming process is endothermic and requires an external heat supply from hydrocarbon combustion. Then, a design for improving the heat transfer and satisfying the production levels required and the restrictions of admissible pressure drop is needed. By modeling the combustion chamber coupled to the reformer allowed optimizing the design variables to reduce the total equipment volume. The model computes the exigencies required for the constructive materials, such as maximum operation temperature for steel, refractory and insulating materials. The heterogeneous model used allows computing the optimal WGS reactor length and diameter and the optimal catalyst particle diameter. The CO-PROX reactor requires catalysts with high CO selectivity to reduce the oxidation of H2. According to the CO levels fed to the COPROX, a series arrangement of two reaction units with intermediate cooling is required for the case study analyzed.

Keywords: steam reforming; bioethanol; reformer, WGS, COPROX; optimization

1. Introduction Fuel cell power systems for transportation and stationary applications have received increased attention in last years because of their potential for high fuel efficiency and lower emissions. The operation conditions of automotive vehicles require short times of start-up, compact and lightweight equipment and efficient operation at different conditions (Zalc and Löffler, 2002). Over the past two decades considerable efforts have been expended to develop the conversion of the abundant primary sources of energy into secondary ones that are less polluting, e.g., hydrogen, which may become an important fuel in the future for use as an energy carrier for electric vehicles and electric power plants. There exist several routes for hydrogen production from the primary fuels. A promising route involves the steam reforming of alcohols, primarily methanol and ethanol. The possibility of using alcohol steam reformer to generate hydrogen for a fuel cell engine has resulted in an increased interest in the study of the alcohol-steam reforming process. Ethanol presents several advantages related to natural availability, storage and handling safety, ethanol can be produced renewably from several biomass sources, including energy plants, waste materials from agro-industries or forestry residue materials, organic fraction of municipal solid waste, etc. Besides the bioethanol-to-hydrogen system has the significant advantage of being nearly CO2 neutral, since the produced carbon dioxide is consumed for biomass growth, thus offering a nearly closed carbon loop.

*

To whom all correspondence should be addressed. Address: Instituto de Desarrollo y Diseño - INGAR, Avellaneda 3657, (CP) S3000GJC, Santa Fe - Argentina E-mail: [email protected]

In conclusion, among the various process and primary fuels that have been proposed in the production of hydrogen for fuel cell applications, steam reforming of ethanol is very attractive. For fuel cell applications, a compact, efficient and reliable fuel processor is highly desirable. The synthesis and design tasks are similar to other industrial reforming processes; nevertheless, the productive capacity required by the processor installed in vehicles or other devices are of very low levels compared with the industrial ones. Thus, small size process units and specific designs are required. The reformer, the water gas shift (WGS) reactor and the preferential oxidation reactor (CO-PROX) constitute the nucleus of the processor, and are a significant fraction of the system volume and weight. It is the goal of this communication to investigate the primary components of a fuel processor for PEM fuel cells and show how a model-based reactor optimization permits to obtain both designs for reducing volumes and optimal operation conditions. The results can be useful for estimating the minimum and relative sizes of the component reactors and, more importantly, understanding the sources of performance limitations. This knowledge can suggest a means of process enhancement (lower weight and cost, higher overall efficiency) from the perspective of reactor configurations, catalyst formulations, and process integration.

H2

H2

C 2 H5OH H 2O

Reformer Unit

CO

CO2

WGS Shift

PROX

CO2

PEM Fuel Cell

H 2O

H 2O

O2 or Air

Combustion Gases Reformer Unit C 2 H 5OH ↔ C 2 H 4 O + H 2 C 2 H 4O ↔ CH 4 + CO CH 4 + H 2 O ↔ CO + 3H 2 CO + H 2 O ↔ CO2 + H 2

Water Gas Shift

Reactor

o 298

o 298

= 71 kJ/mol rx#1 CO + H2O ↔ H2 + CO2 ∆H = −41.1 kJ/mol rx#5 rx#2 ∆H o298 = -21.9 kJ/mol ∆H o298 = 206.14 kJ/mol rx#3 Preferencial Oxidation Reactor ∆H o298 = −41.1 kJ/mol rx#4 CO + 1 O → CO ∆Ho298 = −283 kJ/mol rx #6 2 2 2 ∆H

H2 + 12 O2 ↔ H2O

∆Ho298 = −242 kJ/mol

rx #7

CO + H2O ↔ H2 + CO2 ∆Ho298 = −41.1 kJ/mol rx# 8

Fig. 1. Schematic drawing of fuel processing system and listing of relevant chemical reactions.

2. Overall Description of a Fuel Processor In order to generate a hydrogen-rich stream from a fuel processor, bioethanol is converted in a reforming unit that involves steam reforming (feed is composed of fuel and steam). In Fig. 1, a schematic drawing of the overall process is shown for the case of steam reforming, which is a mature technology for hydrogen, ammonia and synthesis gas production facilities that are large, steady-state operations. In conventional tubular steam reforming, the energy to drive the endothermic reforming reactions ((1) and (3)) is supplied by external heating through the tube wall, generally through combustion of a portion of the fuel. Because CO is a poison to the fuel cell electrocatalyst, its presence in the product stream must be reduced to less than 10 ppmv. This task is partially accomplished by a water–gas shift (WGS) reactor (reaction (5)).

Chemical equilibrium limits the conversion achieved in the WGS reactor, thus, final CO cleanup occurs in a preferential oxidation (PROX) unit in which the desired reaction is the oxidation of carbon monoxide (reaction (6)); however, life is complicated by the presence of the undesirable combustion of hydrogen (reaction (7)). Selectivity is a serious issue in the PROX unit, because the oxidation of hydrogen leads to diminished process efficiency and increased water management issues. The reforming, water–gas shift, and preferential oxidation reactors represent a large fraction of the system volume and cost, and pose the greatest technical challenges.

3. Mathematical Modeling In this work, a one-dimensional heterogeneous model has been used as a general model for all reactors. The heterogeneous reactor model offers higher accuracy for the design of the reactor. Eqs. (1)-(8) are applied off the mass and energy balances of the fluid phase, internal an external catalyst phases. 3.1. Reactor Model For the bulk/fluid phase: Mass balance

−

dFi = Ar k g av (Ci − Css,i ) dz

0

(1)

BC:

z = 0; T f = T f0

(2)

BC:

z = 0; P = P 0

(3)

BC: z = 0; Fi = Fi

Energy balance

G ×Cp

∂T f ∂z

= h f × av (Tss − T f ) − q rx

Pressure drop thought the bed

−

dP G 2 (1 − ε )  (1 − ε )  = 1.75 + 4.2 Re5 / 6 3  dz ρ d p ε Re   For the fluid/particle interface: Mass balance

(

)

k g C SS,i − Ci = Deff ,i

dCS ,i dξ

(4)

dp 2

Energy balance

h f (TSS − T )= λeff

dTS dξ

(5)

For the catalyst particle (spherical pellet): Mass balance

dC  1 d   Deff ,i ξ 2 S ,i  − ρ p ∑α ij rj (CS , TS ) = 0 2  ξ dξ  dξ  j =1

ξ = 0;

Nrx

BC:

ξ=

dp 2

dCS ,i dξ

=0

; Cs ,i = C

(6) S S ,i

Energy balance

ξ = 0;

1 d  dT   λeff ξ 2  + ρ p ∑ (− ∆H ) j rj (CS , TS ) = 0 2 dξ  ξ dξ  j =1 Nrx

BC:

dp

ξ=

2

dTS =0 dξ

(7)

s s

; Ts = T

rx

In Eq. (2) the term q , correspond to the heat flux incoming or outgoing to the reactor. For the reforming unit this expression evaluates the heat transfer from combustion gases of the furnace, while for the WGS and COPROX units evaluates the heat loss to environment. An insulation model is incorporated to the WGS and COPROX model. Following, the equations for furnace and insulation are shown

T amb q rins , amb

q cvins , amb

T exins

q cins , amb

Insulation

q cref ,ins

Refractory wall

T exref = Tinins ref T wall

Gases Chamber

q rg , ref q cvg , ref Combustion Products

Tg

q rref , rx

q rg , rx q cvg , rx

rx T wall

Reactor Bed Fig.2 Schematic diagram of the combustion chamber coupled to the reactor.

3.2. Combustion Chamber Model (Plug Flow Furnace) Conservation of heat in furnace

Gg × Cpg ×

4d rx ∂Tg =− q g ,rx + qrg ,rx + qcvg ,ref + qrg ,ref ) 2 2 ( cv ∂z d − d ( f rx )

BC:

z = 0;Tg = Tg0 ;

(8)

Fig. 2 shows a schematic of the heat fluxes considered in the model. The heat flux terms in Eq. (8) represent the energy transfer from combustion gases to the reactor bed and refractory wall. Convective and radiative fluxes are considered. The net energy supply to the reactor is given by q transport to the refractory wall q

ref

rx

= qcvg ,rx + qrg ,rx + qrref ,rx , and the net energy

= qcvg , ref + qrg , ref − qrref , rx . The term qrref ,rx computes energy transport by

radiation from refractory to the bed. The radiation and convective fluxes are given by

Energy transport from combustion gases to fixed bed (radiative and convective fluxes)

1 rx rx 4 qrg , rx = (ε wall + 1) × σ × (ε gTg 4 − α gwTwall ) 2

(9)

rx qcvg ,rx = ho × (Tg − Twall )

(10)

Energy transport from combustion gases to refractory wall (radiative and convective fluxes)

qrg ,ref =

1 ref ref 4 (ε wall + 1) × σ × (ε g Tg 4 − α gwTwall ) 2

(11)

ref qcvg ,ref = ho × (Tg − Twall )

(12)

Energy transport from refractory wall to reactor bed

(

4

ref ref ref rx qrref , rx = F × σ × ε wall Twall − ε wall Twall

4

)

(13)

3.3. Insulation Model In the reformer unit, a heat loss towards the outside is considered modeling the energy transfer by conduction through refractory and insulation materials. The conductivity of the intervening materials was considered temperature depending by means of a quadratic expression k ( T )

= ak + bk T + ck T 2 . To evaluate the heat loss

to environment, radiative and convective flows, Eqs. (16) and (17) respectively, were considered using expressions suggest by A.R. Koenig (1980). Heat flow by conduction through the refractory wall and insulation

qcref ,ins =

2  df ln  d f  d ref

  aref ref 3 bref ref 2  Tex − Tinref 3 ) + Tex − Tinref 2 ) + cref (Texref − Tinref )    ( ( 2   3

(14)

qcins ,amb =

b 2  d f   ains ins 3  ln  Tex − Tinins 3 ) + ins (Texins 2 − Tinins 2 ) + cref (Texins − Tinins )  (  d f  dins   3 2 

(15)

Heat loss from insulation to environment ins ,amb cv

q

= 2.3613 × 10

−4

 1     d ins 

0.2

  1    (Tamb + Texins ) 0.9 − 459.67   

0.181

(T

ins ex

1.266

− Tamb )

(16)

qrins ,amb = σε ins (Texins 4 − Tamb 4 )

(17)

Correlations for C p , µ f , and λ f were obtained from Reid et al. (1987) . Correlations for k g and Deff ,i were obtained from Satterfield (1970). The gas mixture was assumed to be ideal for computing

ρf

.The average

molecular weight and molar flow rate at the reactor inlet were used to compute G. Correlations for gas emissivities were obtained from Mehrotra et al. (1995). The heat transfer coefficient expression was obtained from Froment and Bischoff (1990).

Summarizing, F f , i , T f , P are solved from the differential equations along the reactor axis (Eqs. (1)-(7)). Equations (8)-(13) solve

Tg along the furnace. Insulation between furnace wall and environment for reformer

case, and between reactor wall and environment for WGS and COPROX cases, are modeling by Eqs. (14)-(17). 3.4. Optimization Model The optimization problem was formulated in goal to obtain operative and design variables that minimize the system volume. The problem formulation with objective function, decision variables and constrains are summarized in Table 1. Te objective function was to minimize the total volume of the system. In the reformer unit, volume is computed considering reactor bed ( Vrx ), gases chamber ( Vgc ), refractory material ( Vref ) and insulation ( Vins ). For the other cases, only volume of reactor and insulations are considered.

Table 1. Summary of the optimization problem formulation

Objective Function to minimizing Decision Variables

Reformer Unit

WGS

COPROX

Vtotal = Vrx + Vgc + Vref + Vins

Vtotal = Vrx + Vins

Vtotal = Vrx + Vins

LRx , d t , d p , d f , d rw , d ins1 , d ins 2

Tin , LRx , d t , d p , d ins

Tin , LRx , d t , d p , d ins

Interior Point Constrains Reactor wall temperature

Twall ≤ 1250 º K

Catalyst Temperature

930 º K ≤ Ts ≤ 1350 º K

Insulation temperature

333 º K ≤ Texref ≤ 820 º K

330 º K ≤

Texins

≤ 340 º K

Plug Flow Conditions

448 º K ≤ Ts ≤ 523 º K

450 º K ≤ Ts ≤ 500 º K

330 º K ≤ Texins ≤ 340 º K 330 º K ≤ Texins ≤ 340 º K Lrx / d p > 30 ; d rx / d p > 10

End Point Constrains Allowable Pressure Drop Hydrogen Flow

( Pin − Pout ) / Pin ≤ 0.3 FH ≥ 33 gmol / h 2

CO molar fraction

yco ≤ 0.003

yco ≤ 1.0 × 10 −5

The DAEs system represented by Eqs. (1)-(17), was implemented within gPROMS (2004) software, it is a general process modeling system with proven capabilities for the simulation and optimization. The solver used in gPROMS is bases on variable time step/variable order Backward Differentiation Formulae (BDF). The composition and thermal profile within the pellet, Eqs. (6)-(7), were solved using orthogonal collocation on finite elements method. The mathematical solver used for optimization in gPROMS was the “CVP_MS”, this solver implements a “single-shooting” optimization algorithm.

3. Results and Discussions 3.1. Reforming Unit The target power for the fuel processor was the 1 kW, for this power the required amount of hydrogen is 33.3 gmol/h (Choi and Stenger,2003). For the reforming unit, the feed gas stream was based on a water/ethanol molar ratio of 4, the water molar flow was 40 gmol/h and for ethanol 10 gmol/h. Input temperature to the reactor was fixed at 973 K, and input combustion gases temperature was fixed at 1600 ºK. Table 2 summarizes the results obtained. The optimization problem determine the optimal value for reactor length ( LRx ,) reactor diameter ( d t ), catalyst particle diameter ( d p ), furnace diameter ( d f ), refractory diameter ( d ref ) and insulation diameter ( d ins ). Table 2. Decision variable values for de optimization problem

Reformer Unit - Vtotal= 265 cm3

WGS - Vtotal= 1051.2 cm3

COPROX - Vtotal= 51.5 cm3

LRx =8 cm

d f =3.9 cm

T0 =446.6 K

d t =2.7 cm

d ref =6.18 cm

LRx =30.9 cm

LRx =1.5 cm

d p =0.05cm

dins =6.38 cm

d t =5.06 cm

d t =3.67 cm

d p =0.05 cm

d p =0.05 cm

d ins =6.56 cm

T0 =478.6 K

d ins =6.61 cm

Fig. 3 shows simulation results, for the reformer unit, based in the results obtained. Fig. 3a shows molar fraction composition varying along the reactor. Ethanol decomposition became almost instantly at the reactor entry. The ethanol decomposition is endothermic and requires an external heat supply, so, the mayor temperature drop occurs when the reactive gases come into the reactor. As these compounds diminish, the reactor temperature is stabilized in a smooth profile. Fig. 3b shows temperature profile along de reactor axis. The results obtained for the decision variables, using the model-based optimization, improve the heat transfer satisfying the production levels required and the restrictions of admissible pressure drop and temperature.

Fig. 3. Profiles along de reforming reactor axis a) Molar Fraction b) Temperature

3.2. WGS Unit The WGS reactor was optimized considering those conditions most likely in the WGS reaction for a medium scale ethanol reformer using a Cu/ZnO/Al2O3 commercial catalyst (Choi and Stenger, 2003). The WGS reactor

is the biggest and heaviest component because the reaction is relatively slow compared to the other reactions and is inhibited at higher temperatures by thermodynamics. In our study, was considered as design objective reduce the CO concentration until a 0,3 %. Reforming output flows are considering as input flows to the WGS unit. The heterogeneous model used allows computing the optimal reactor length and diameter and the optimal catalyst particle diameter (Table 2). Due to exothermic reaction is desirable to maintain the temperature within a certain rank. An upper temperature bound is given to avoid sintering of the catalyst, besides, as low temperatures reduce the reaction rate and kinetic expression loses validity, is necessary to impose a lower bound. Input temperature is considered as decision variable, and their optimum value arises as the model's resolution. The thickness used in insulation is an important variable that affect the size of the equipment. If the insulation wall temperature is restricted to stay between 340