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Frontiers of Chemical Science and Engineering

ISSN 2095-0179

ISSN 2095-0187(Online)

CN 11-5981/TQ

Postal Subscription Code 80-969

2018 Impact Factor: 2.809

Front. Chem. Sci. Eng.    2022, Vol. 16 Issue (2) : 251-273    https://doi.org/10.1007/s11705-021-2071-9
RESEARCH ARTICLE
Synergistic optimization framework for the process synthesis and design of biorefineries
Nikolaus I. Vollmer1, Resul Al2, Krist V. Gernaey1, Gürkan Sin1()
1. Process and Systems Engineering (PROSYS) Research Center, Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
2. Novo Nordisk A/S, 2880 Bagsværd, Denmark
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Abstract

The conceptual process design of novel bioprocesses in biorefinery setups is an important task, which remains yet challenging due to several limitations. We propose a novel framework incorporating superstructure optimization and simulation-based optimization synergistically. In this context, several approaches for superstructure optimization based on different surrogate models can be deployed. By means of a case study, the framework is introduced and validated, and the different superstructure optimization approaches are benchmarked. The results indicate that even though surrogate-based optimization approaches alleviate the underlying computational issues, there remains a potential issue regarding their validation. The development of appropriate surrogate models, comprising the selection of surrogate type, sampling type, and size for training and cross-validation sets, are essential factors. Regarding this aspect, satisfactory validation metrics do not ensure a successful outcome from its embedded use in an optimization problem. Furthermore, the framework’s synergistic effects by sequentially performing superstructure optimization to determine candidate process topologies and simulation-based optimization to consolidate the process design under uncertainty offer an alternative and promising approach. These findings invite for a critical assessment of surrogate-based optimization approaches and point out the necessity of benchmarking to ensure consistency and quality of optimized solutions.

Keywords biotechnology      surrogate modelling      superstructure optimization      simulation-based optimization      process design     
Corresponding Author(s): Gürkan Sin   
Online First Date: 22 July 2021    Issue Date: 10 January 2022
 Cite this article:   
Nikolaus I. Vollmer,Resul Al,Krist V. Gernaey, et al. Synergistic optimization framework for the process synthesis and design of biorefineries[J]. Front. Chem. Sci. Eng., 2022, 16(2): 251-273.
 URL:  
https://academic.hep.com.cn/fcse/EN/10.1007/s11705-021-2071-9
https://academic.hep.com.cn/fcse/EN/Y2022/V16/I2/251
Fig.1  
Fig.2  
Fig.3  
Fig.4  Illustration of the proposed framework S3O with its three stages: (1) selection of products and models, (2) SSO, and (3) SBO, as well as the employed software and toolboxes.
Fig.5  Workflow of the proposed framework S3O indicating the tasks in the three stages and its intermediate and the final results.
Fig.6  Illustration of the entire initial bottom-up composed superstructure for the base-case process design of the introduced case study with a hemicellulose, a cellulose, and a lignin process train; the reduced superstructure which will serve as the base case in this study is marked in bold.
cID Flowsheet
1 PT-UCH-FX-EX-CX1-CX2
2 PT-UCH-FX-EX-CX1
3 PT-UCH-FX-CX1-CX2
4 PT-UCH-FX-CX1
5 PT-FX-EX-CX1-CX2
6 PT-FX-EX-CX1
7 PT-FX-CX1-CX2
8 PT-FX-CX1
Tab.1  Overview of all flowsheet options with their respective cID and the units composing the flowsheet.
Fig.7  Violin plots of the results from the design space exploration of flowsheets (a) cID 1, (b) cID 2, (c) cID 5, and (d) cID 6 with the outputs: the mass of produced xylitol (upper left), the concentration of 5-hydroymethylfurfural in the final stage (upper right), the concentration of acetic acid in the final stage (lower left) and the CO2 ratio (lower right).
Fig.8  Heatmap of the total sensitivity indices ( STi) calculated with the easyGSA toolbox by using ANN surrogates for all flowsheet options and all operational variables.
Fig.9  Parity plots of the ALAMO, the GPR, and the ANN surrogate models for all flowsheets (ALAMO: (a) cID 1, (d) cID 2, (g) cID 5, and (j) cID 6; GPR: (b) cID 1, (e) cID 2, (h) cID 5, and (k) cID 6; ANN: (c) cID 1, (f) cID 2, (i) cID 5, and (l) cID 6) indicating the predicted outputs over the simulated outputs for N = 500 (dark blue, blue, turquoise) and N = 1000 samples (green, bright green, yellow).
Model ALAMO DTR GPR ANN
N = 500 N = 1000 N = 500 N = 1000 N = 500 N = 1000 N = 500 N = 1000
R2 0.822 0.765 1 1 1 1 0.997 0.994
RMSE 5.27 6.29 0 0 0.007 0.017 0.597 0.922
R2train 0.817 0.762 1 1 0.997 1 0.997 0.994
R2test 0.722 0.724 0.487 0.642 0.933 0.952 0.895 0.956
RMSEtrain 5.35 6.31 0 0 0.423 0.121 0.674 0.944
RMSEtest 6.54 6.99 8.802 7.677 2.945 2.66 4.002 2.535
Tab.2  Cross-validation metrics of all surrogate models for flowsheet option cID 1 for both N = 500 and N = 1000 samples for the output variable being the amount of produced xylitol
cID 1-500 ub lb ALAMO/BARON DTR/Gurobi GPR/fmincon ANN/fmincon
opt val opt val opt val opt val
TPT 173 195 179.581 184.31 187.74 177.24
Acid 0.5 2 0.672 1.456 1.337 2.000
Inoc 0.5 3 3.000 1.523 1.497 1.191
tFX 8 16 47.938 43.207 42.656 47.727
vEX 0.99 0.998 0.995 0.996 0.998 0.998
MXyo 59.852 0.000 49.094 48.964 54.083 43.410 85.240 45.682
CHmf 0.5 0.000 0.028 0.058 0.060 0.034 0.006 0.020 0.007
CAac 0.5 0.002 0.004 0.002 0.002 0.001 0.000 0.001 0.000
ϕ 0.1 0.140 0.000 0.118 0.117 0.116 0.100 0.100 0.114
Tab.3  Results from the SSO of flowsheet cID 1 with N = 500 samples with all surrogate models and their respective solvers.
cID 2-500 ub lb ALAMO/BARON DTR/Gurobi GPR/fmincon ANN/fmincon
opt val opt val opt val opt val
Acid 0.5 2 0.685 0.762 0.874 2.000
Inoc 0.5 3 2.998 1.493 0.500 2.736
tFX 12 48 47.999 46.427 40.493 12.490
vEX 0.99 0.998 0.996 0.997 0.990 0.998
vUCH 0.4 0.6 0.512 0.520 0.585 0.423
MXyo 53.004 0.000 50.017 51.123 13.315 0.078 4.410 11.938
CHmf 0.5 0.500 3.935 0.500 0.451 1.830 0.779 1.467 0.136
CAac 0.5 0.000 0.289 0.022 0.021 0.082 0.048 0.057 0.008
ϕ 0.1 0.123 0.000 0.117 0.120 0.028 0.000 0.037 0.028
Tab.4  Results from the SSO of flowsheet cID 2 with N = 500 samples with all surrogate models and their respective solvers.
cID 5-500 ub lb ALAMO/BARON DTR/Gurobi GPR/fmincon ANN/fmincon
opt opt val opt val
TPT 173 195 193.69 185.50 186.6
Acid 0.5 2 0.776 1.188 1.127
inoc 0.5 3 2.315 0.963 0.782
tFX 8 16 28.415 45.079 48.000
vEX 0.99 0.998 0.993 0.998 0.998
MXyo Infeasible 47.915 47.86 54.829 48.12 67.400 46.86
CHmf 0.5 0.152 0.152 0.057 0.038 0.044 0.022
CAac 0.5 0.012 0.126 0.003 0.002 0.002 0.001
φ 0.1 0.118 0.118 0.132 0.123 0.168 0.117
Tab.5  Results from the SSO of flowsheet cID 5 with N = 500 samples with all surrogate models and their respective solvers.
cID 6-500 ub lb ALAMO/BARON DTR/Gurobi GPR/fmincon ANN/fmincon
opt val opt val opt val opt val
TPT 173 195 184.00 184.00 191.04
Acid 0.5 2 0.960 1.265 1.609
inoc 0.5 3 2.536 2.507 0.976
tFX 8 16 23.221 22.465 45.041
vEX 0.99 0.998 0.998 0.998 0.997
MXyo Infeasible 43.688 43.95 47.727 43.58 0.016 26.35
CHmf 0.5 0.373 0.347 0.500 0.322 11.321 4.627
CAac 0.5 0.022 0.021 0.014 0.018 0.243 0.134
φ 0.1 0.112 0.112 0.101 0.111 0.000 0.066
Tab.6  Results from the SSO of flowsheet cID 6 with N = 500 samples with all surrogate models and their respective solvers.
Fig.10  Bubble plot for the visualization of the consistency metrics of the different superstructure modeling approaches, the center of each sphere indicating the predicted value in the optimization problem, the radius of the sphere being the RMSE of the testing dataset in the cross-validation, and the cross/saltire indicating the respective validation simulation for (a) cID 1, (b) cID 2, (c) cID 5 and (d) cID 6 for respectively N = 500 samples (blue, cross) and N = 1000 samples (yellow, saltire).
Item ub lb cID 1 cID 2 cID 5
opt val opt val opt val
TPT 173 195 195.000 195
Acid 0.5 2 0.715 0.984 0.879
Inoc 0.5 3 1.611 3.000 3
tFX 8 16 44.994 30.367 24.271
vEX 0.99 0.998 0.997 0.998 0.998
vUCH 0.4 0.6 0.400
MXyo 56.310 56.736 53.760 54.224 53.96 54.17
CHmf 0.5 0.045 0.032 0.492 0.471 0.062 0.061
CAac 0.5 0.001 0.001 0.019 0.020 0.002 0.002
ϕ 0.1 0.119 0.125 0.127 0.129 0.128 0.128
Tab.7  Results from the SBO for all candidate process topologies with the MOSKopt solver, using 25 initial sampling points, 75 iterations, the mean value as hedge against uncertainty, and the multi-constraint FEI criterion
Fig.11  Visualization of the improvement of the objective function value over the iterations in the SBO with the MOSKopt solver for flowsheet (a) cID 1, (b) cID 2, and (c) cID 5.
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