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Optimization ofAdvancedBiofuelProductionviaFischer-TropschSynthesis

Umesh Pandey1, Koteswara R. Putta1, Ljubisa Gavrilovic1, Kumar R Rout2, Erling Rytter1, Edd A. Blekkan1, ∗Magne Hillestad1

1 Department of Chemical Engineering, NTNU, Sem Saelands Vei 4,7491, Trondheim2 SINTEF Industry, Trondheim

Problem Description

Model Description

Fischer-Tropsch reactions

Paraffin polymerization

CO + U1(α1)H2

r1−−→ H2O + ν1(α1)CH4 + ν2(α1)C2H6 +

ν3(α1)C3H8 + ν4(α1)C4H10 +

ν[5,∞](α1)Cp5+

Olefins polymerization

CO + U2(α2)H2

r2−−→ H2O + ν1(α2)CH4 + ν2(α2)C2H4 +

ν3(α2)C3H6 + ν4(α2)C4H8 +

ν[5,∞](α2)Co5+

• Kinetic model developed by Todic et al. used for mod-eling application.

• A new kinetic model will be proposed and used for fur-ther design application.

The design model

[γI− uMσJ̃]dx

dξ= σuAR̃(x) + uFK(xF − x)− uHE(x− xw)

dγ

dξ= uF − uS

ξ is the dimensionless PATH VARIABLE, ( VVt)

γ is the dimensionless mass flow rate, (W/W0)

x = [wC , θ], θ =T−TrefTref

R(x) is the reaction rate vector in mass basis

σ residence time or space time, (VR/W0)

J̃ is the partial derivative of component reactions

K is a diagonal matrix, K = diag(1, 1, ...,Cp,FCp

)

E is a diagonal matrix of reaction enthalpies

Path Optimizationmax

[σ,u]∈UJ

s.t.dz

dξ= f(z,u), z = [x, γ], z(0) = z0

h(z, u) 6 0

Design variables (u)

FT volume distribution ∆VV

Hydrogen feed distribution uFCoolant temperatures TcCatalyst activity/ dilution uAMixing structure uM

• Optimization solver: MultiStart, global optimizationsolver in MATLAB

• Constraint: Treactor < 230◦

• Vtotal,bed = σ × W0, same for three different reactorsystems

Flow Profiles at Optimal production of Liquid Hydrocarbons (C5+)

Figure 2: Mass fraction, component reaction rate, temperature and H2:CO profiles for single stage (left), two-stage (middle)

and three-stage(right) reactor systems at optimal production of C5+.

Key Findings

Characteristics 1-stage 2-stage 3-stage

CO conversion 74.97% 86.86% 94.60%

Total C5+ production 41117 kg/h 49027 kg/h 53228 kg/h

Extra H2 feed requirement 10379 kg/H 9847 kg/h 10164kg/h

Reactor types Stage-1: PFR Stage-1,2: PFR Stage-1: CSTRStage-2,3: PFR

NPFR (φ = 5cm and L = 8m ) Stage-1: 14170 Stage-1: 8237 Stage-1: —-Stage-2: 5933 Stage-2,3: 2947 and 6273

Cooling temperature Stage-1: 214.7◦C Stage-1: 213.2◦C Stage-1: 213.1◦CStage-2: 214.8◦C Stage-2,3: 234.9◦C, 215.2◦C

Reaction Stoichiometry (φ = ν/2.1) Stage-1: φ < 1 Stage-1: φ < 1 Stage-1,2: φ < 1Stage-2: φ > 1 Stage-3: φ > 1

Conclusion• 29.5% improvement in C5+ production between opti-

mal single stage to 3-stage reactor system.

• Understoichiometric mode of operation for initialstages and overstoichiometric mode for the final stage.

• H2/CO ratio suitable for the bio-syngas (φfeed =1

2.1 << 1) with integration for extra H2 supply.

• Three stage system has highest extra H2 feed to theproduction ratio and corresponds to optimal multi-stage reactor system.

• Results are applicable for conceptual biomass to liquidplant design.

References

[1] Magne Hillestad. Systematic staging in chemical reac-tor design. Chemical Engineering Science, 65(10):3301–3312, 2010.

[2] Branislav Todic, Wenping Ma, Gary Jacobs, Burtron H.Davis, and Dragomir B. Bukur. CO-insertion mechanismbased kinetic model of the Fischer–Tropsch synthesis re-action over Re-promoted Co catalyst. Catalysis Today,228:32–39, jun 2014.

[3] Magne Hillestad. Modeling the Fischer-Tropsch ProductDistribution and Model Implementation. Chemical Prod-uct and Process Modeling, 10(3):147–159, 2015.

[4] Dongsheng Wen and Yulong Ding. Heat transfer of gasflow through a packed bed. Chemical Engineering Sci-ence, 61(11):3532–3542, 2006.

[5] Zsolt Ugray, Leon Lasdon, John Plummer, Fred Glover,James Kelly, and Rafael Martí. Scatter search and localnlp solvers: A multistart framework for global optimiza-tion. INFORMS Journal on Computing, 19(3):328–340,2007.

Optimization Superstructure

Figure 1: A multistage superstructure considered for product optimization basedon path optimization concepts.

Feed characteristics:

• H2/CO ratio: 1:1

• Feed pressure and tempera-ture: 20 bar and 210◦C.

• Flow rate: 133550 kg/h

Process characteristics:

• A fixed bed Reactor, threephase separation, heat ex-changers and mixing units ineach stage

• Main feed to each stage is at210◦C and 20 bar

• Bulk catalyst density: 200kg/m3

• Alternative paths to choose be-tween one big reactor or twoseparate reactor with recycles