Analysis of Multi-Loop Control Structures of Dividing-Wall Distillation Columns Using a Fundamental Model
Abstract
:1. Introduction
2. Design and Modeling of DWCs
2.1. Design of DWCs
2.2. Model Equations
3. Investigated Column and Controller Design
Mixture | Components (A,B,C) | ESI |
---|---|---|
M1 | n-pentane, n-hexane, n-heptane | 1.04 |
M2 | n-butane, i-pentane, n-pentane | 1.86 |
M3 | i-pentane, n-pentane, n-hexane | 0.47 |
M4 | benzene, toluene, ethylbenzene | 0.98 |
3.1. RGA Analysis and PI Controller Tuning
L1 | S | QR | βL | |
---|---|---|---|---|
xA | ||||
xB | ||||
xc | ||||
yp11 |
L1 | S | QR | βL | |
---|---|---|---|---|
xA | 1.1938 | −0.0015 | −0.1880 | −0.0043 |
xB | 0.2409 | 0.8407 | −0.0688 | −0.0127 |
xc | −0.3074 | 0.1629 | 1.3019 | −0.1574 |
yp11 | −0.1273 | −0.0021 | −0.0449 | 1.1743 |
Control structure-Controlled variable | Manipulated variable | τc (min) | Kc (%/%) | τI(min) |
---|---|---|---|---|
DB-LSV | ||||
xD(nC5) | L1 | 13.65 | 2.778 | 46.77 |
xS(nC6) | S | 14.68 | 8.613 | 73.43 |
xB(nC7) | QR | 7.72 | 3.553 | 41.38 |
yp11(nC7) | βL | 16.57 | 0.3851 | 83.38 |
DV-LSB | ||||
xD(nC5) | L1 | 15.87 | 2.938 | 39.68 |
xS(nC6) | S | 10.01 | 65.98 | 33.35 |
xB(nC7) | B | 6.77 | 13.83 | 45.14 |
yp11(nC7) | βL | 16.56 | 0.3825 | 82.83 |
LB-DSV | ||||
xD(nC5) | D | 29.50 | 3.855 | 59.01 |
xS(nC6) | S | 39.76 | 54.88 | 79.52 |
xB(nC7) | QR | 7.88 | 4.983 | 52.57 |
yp11(nC7) | βL | 16.59 | 0.3885 | 83.02 |
LV-DSB | ||||
xD(nC5) | D | 28.38 | 4.44 | 56.77 |
xS(nC6) | S | 13.86 | 176.3 | 27.72 |
xB(nC7) | B | 18.18 | 14.9 | 90.94 |
yp11(nC7) | βL | 16.59 | 0.3873 | 82.24 |
3.2. Results and Discussion
4. Effect of Mixture Properties on Control Structure Selection
Mixture | RR | Nmain | Nprefrac | NL | NV | NS | QR/[KW] | βL | βV |
---|---|---|---|---|---|---|---|---|---|
M1F1 | 2.44 | 36 | 17 | 11 | 28 | 18 | 481.09 | 0.3849 | 0.6571 |
M1F2 | 10.19 | 37 | 37 | 11 | 28 | 17 | 576.23 | 0.3611 | 0.6947 |
M2F1 | 16.62 | 93 | 21 | 11 | 60 | 21 | 1839.67 | 0.1497 | 0.1893 |
M2F2 | 43.72 | 99 | 21 | 11 | 66 | 21 | 1732.19 | 0.1251 | 0.1619 |
M3F1 | 8.48 | 80 | 62 | 33 | 73 | 63 | 1147.89 | 0.1680 | 0.3035 |
M3F2 | 29.18 | 80 | 59 | 33 | 72 | 62 | 1243.35 | 0.1457 | 0.2733 |
M4F1 | 2.05 | 37 | 18 | 10 | 27 | 17 | 526.23 | 0.4960 | 0.7548 |
M4F2 | 9.16 | 42 | 16 | 9 | 31 | 17 | 634.77 | 0.2268 | 0.5570 |
Mixture | Components (A,B,C) | ESI | BEST CONTROL STRUCTURE | |
---|---|---|---|---|
F1 | F2 | |||
M1 | n-pentane, n-hexane, n-heptane | 1.04 | DB-LSV | LB-DSV |
M2 | n-butane, i-pentane, n-pentane | 1.86 | LB-DSV | LB-DSV |
M3 | i-pentane, n-pentane, n-hexane | 0.47 | DB-LSV | DV-LSB |
M4 | benzene, toluene, ethylbenzene | 0.98 | DB-LSV | DV-LSB |
Mixture/Feed Composition | Controlled variable | Flow Rate Disturbance | Composition Disturbance | ||||||
---|---|---|---|---|---|---|---|---|---|
Structure | DB-LSV | DV-LSB | LB-DSV | LV-DSB | DB-LSV | DV-LSB | LB-DSV | LV-DSB | |
M1F1 | xA | 0.01077 | 0.01107 | 0.03661 | 0.04963 | 0.00355 | 0.00507 | 0.01595 | 0.02560 |
xB | 0.00050 | 0.00053 | 0.00218 | 0.00144 | 0.00039 | 0.00039 | 0.00041 | 0.00043 | |
xC | 0.00328 | 0.00376 | 0.01931 | 0.00433 | 0.00094 | 0.00358 | 0.00199 | 0.00357 | |
Overall | 0.01455 | 0.01536 | 0.05811 | 0.05541 | 0.00488 | 0.00903 | 0.01835 | 0.02960 | |
M1F2 | xA | 0.02701 | 0.01982 | 0.00449 | 0.06340 | 0.00331 | 0.00259 | 0.00202 | 0.02894 |
xB | 0.00231 | 0.00207 | 0.00231 | 0.00247 | 0.00027 | 0.00029 | 0.00029 | 0.00050 | |
xC | 0.00658 | 0.00239 | 0.00692 | 0.00337 | 0.00050 | 0.00263 | 0.00056 | 0.00274 | |
Overall | 0.03590 | 0.02428 | 0.01372 | 0.06924 | 0.00409 | 0.00551 | 0.00287 | 0.03219 | |
M2F1 | xA | 0.14802 | 0.14760 | 0.00293 | 0.00264 | 0.20397 | * | 0.00172 | 0.00162 |
xB | 0.10982 | 0.10965 | 0.00187 | 0.00181 | 9.84515 | * | 0.00083 | 0.00083 | |
xC | 0.00269 | 0.00088 | 0.00080 | 0.00251 | 0.00374 | * | 0.00019 | 0.00091 | |
Overall | 0.26053 | 0.25813 | 0.00559 | 0.00697 | 10.05287 | * | 0.00274 | 0.00335 | |
M2F2 | xA | 0.28814 | * | 0.01153 | * | 0.32005 | * | 0.00568 | * |
xB | 0.00764 | * | 0.00268 | * | 0.01081 | * | 0.00094 | * | |
xC | 0.02220 | * | 0.00569 | * | 0.02285 | * | 0.00153 | * | |
Overall | 0.31799 | * | 0.01989 | * | 0.35371 | * | 0.00815 | * | |
M3F1 | xA | 0.00852 | 0.00454 | 0.02430 | 0.02424 | 0.00037 | * | 0.02763 | 0.02796 |
xB | 0.02075 | 0.01146 | 0.06875 | 0.06074 | 0.00037 | * | 0.01832 | 0.01832 | |
xC | 0.01375 | 0.02858 | 0.01960 | 0.01686 | 0.00139 | * | 0.00625 | 0.00348 | |
Overall | 0.04303 | 0.04458 | 0.11264 | 0.10185 | 0.00213 | * | 0.05219 | 0.04976 | |
M3F2 | xA | 0.02714 | 0.00742 | * | * | 0.00857 | 0.00283 | * | * |
xB | 0.01551 | 0.00813 | * | * | 0.00310 | 0.00141 | * | * | |
xC | 0.06955 | 0.00859 | * | * | 0.02707 | 0.00280 | * | * | |
Overall | 0.11220 | 0.02414 | * | * | 0.03873 | 0.00705 | * | * | |
M4F1 | xA | 0.04206 | 0.04084 | 0.06167 | 0.05524 | 0.01631 | 0.01211 | 0.02310 | 0.02050 |
xB | 0.01527 | 0.04995 | 0.07069 | 0.07444 | 0.00200 | 0.00146 | 0.00099 | 0.00132 | |
xC | 0.02281 | 0.02386 | 0.02678 | 0.02353 | 0.00268 | 0.00225 | 0.00204 | 0.00225 | |
Overall | 0.08014 | 0.11465 | 0.15914 | 0.15321 | 0.02099 | 0.01582 | 0.02613 | 0.02407 | |
M4F2 | xA | 0.05396 | 0.02353 | 0.01004 | 0.00978 | 0.01836 | 0.00759 | 0.01831 | 0.01031 |
xB | 0.00362 | 0.00444 | 0.00183 | 0.00303 | 0.00062 | 0.00117 | 0.00043 | 0.00054 | |
xC | 0.02957 | 0.00875 | 0.01705 | 0.00621 | 0.00453 | 0.00423 | 0.00261 | 0.00258 | |
Overall | 0.08715 | 0.03672 | 0.02893 | 0.01901 | 0.02351 | 0.01300 | 0.02135 | 0.01343 |
5. Conclusions
Nomenclature
Aholes | total area of all active holes |
Atray | tray active area |
B | bottoms flow rate |
D | distillate flow rate |
F | feed flow rate |
g | Gravity |
H | enthalpy of vapor |
h | enthalpy of liquid |
hweir | liquid height on weir |
L | liquid flow rate |
L1 | reflux flow rate |
Lp | liquid flow rate fed to the prefractionator |
LR | total liquid leaving the bottom tray in the rectifying section |
K | vapor-liquid equilibrium constant |
Kc | proportional gain |
S | side product |
Lweir | weir length |
Nc | number of components in the mixture |
Nmain | number of stages in the Main Column |
Nprefrac | number of stages in the Prefractionator |
NL | liquid interconnecting stage |
NV | vapor interconnecting stage |
NS | side stream stage |
M | moles of liquid retained |
MD | moles of liquid retained in the reflux drum |
MNT | moles of liquid retained in the base of the column |
Q | heat transferred |
QC | condenser heat duty |
QR | reboiler heat duty |
RR | reflux ratio |
U | liquid sidestream |
V | vapor flow rate fed to the prefractionator |
Vp | vapor flow rate |
VS | total vapor leaving the top tray in the stripping section |
W | vapor sidestream |
x | liquid mole fraction |
xA | mole fraction of A in the top product |
xB | mole fraction of B in the sidestream product |
xC | mole fraction of C in the bottoms product |
y | vapor mole fraction |
yp11 | mole fraction of the heavy component on stage 11 at the top of the prefractionator |
z | mole fraction of the feed |
Greek Symbols
α | dry-hole pressure drop coefficient |
βL | liquid split |
βV | vapor split |
β | aeration factor |
ρ | molar density |
φL | liquid fugacity coefficient |
φV | vapor fugacity coefficient |
γ | liquid molar volume |
τc | filter parameter |
τp | time constant |
τI | integral time |
θ | dead time |
Subscripts and Superscripts
L | liquid phase |
V | vapor phase |
i | component |
NT | total number of stages |
j | stage number |
Acknowledgments
Conflicts of Interest
Appendix
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Tututi-Avila, S.; Jiménez-Gutiérrez, A.; Hahn, J. Analysis of Multi-Loop Control Structures of Dividing-Wall Distillation Columns Using a Fundamental Model. Processes 2014, 2, 180-199. https://doi.org/10.3390/pr2010180
Tututi-Avila S, Jiménez-Gutiérrez A, Hahn J. Analysis of Multi-Loop Control Structures of Dividing-Wall Distillation Columns Using a Fundamental Model. Processes. 2014; 2(1):180-199. https://doi.org/10.3390/pr2010180
Chicago/Turabian StyleTututi-Avila, Salvador, Arturo Jiménez-Gutiérrez, and Juergen Hahn. 2014. "Analysis of Multi-Loop Control Structures of Dividing-Wall Distillation Columns Using a Fundamental Model" Processes 2, no. 1: 180-199. https://doi.org/10.3390/pr2010180