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Parametric study and control of a pressure swing adsorption process to separate the water-ethanol mixture under disturbances
Journal Pre-proofs Parametric Study and Control of a Pressure Swing Adsorption Process to Separate the Water-Ethanol Mixture Under Disturbances Jesse Y. Rumbo Morales, Guadalupe López López, Víctor M. Alvarado Martínez, Felipe J. Sorcia Vázquez de, Jorge A. Brizuela Mendoza, Mario Martínez García PII: DOI: Reference:
S1383-5866(19)33496-3 https://doi.org/10.1016/j.seppur.2019.116214 SEPPUR 116214
To appear in:
Separation and Purification Technology
Received Date: Accepted Date:
5 August 2019 14 October 2019
Please cite this article as: J.Y. Rumbo Morales, G.L. López, V.M. Alvarado Martínez, F. J. Sorcia Vázquez de, J.A. Brizuela Mendoza, M.M. García, Parametric Study and Control of a Pressure Swing Adsorption Process to Separate the Water-Ethanol Mixture Under Disturbances, Separation and Purification Technology (2019), doi: https://doi.org/10.1016/j.seppur.2019.116214
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© 2019 Published by Elsevier B.V.
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Molar fraction of ethanol
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1
Molar fraction of ethanol
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0.9895
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0.94 0.92
0.989
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0.88 0.86
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Output data (Ethano purity) Input data (PRBS 55 bits) Input data (PRBS bits) Output data (Ethano purity) 512.2
Flow (kmol h )
Molar fraction of ethanol
0.989
511.7
Time (h)
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55
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139
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194
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0.98 0.975
0.989
0.97
0.988 0.987
0.965
0
27.3
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Molar fraction of ethanol
510 0.985
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0.96
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490
480
470
0.955 0.95
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13.8
27.7
41.6
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55.5
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Time (h)
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Highlights
• The Pressure Swing Adsorption Process produces a bio-ethanol with 99% purity complying with international standards. • The sensitivity analysis allows to identify the possible input and output variables, which gives rise to establishing the primary and secondary control loops. • The Hammerstein-Wiener model allows capturing the important dynamics of the PSA process (rigorous model described by PDE). • The controllers (Optimal MPC and Fuzzy PD + I) attenuate the disturbances that occur at the entrance of the PSA process, allowing to always have a purity that complies with international standards.
S1383-5866(19)33496-3 https://doi.org/10.1016/j.seppur.2019.116214 SEPPUR 116214
To appear in:
Separation and Purification Technology
Received Date: Accepted Date:
5 August 2019 14 October 2019
Please cite this article as: J.Y. Rumbo Morales, G.L. López, V.M. Alvarado Martínez, F. J. Sorcia Vázquez de, J.A. Brizuela Mendoza, M.M. García, Parametric Study and Control of a Pressure Swing Adsorption Process to Separate the Water-Ethanol Mixture Under Disturbances, Separation and Purification Technology (2019), doi: https://doi.org/10.1016/j.seppur.2019.116214
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© 2019 Published by Elsevier B.V.
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" "
" " "
' % ,&& *" -
! %
"$
. ! " . " $ ,&& $ % ! $ . & ! $ $ ,&&
" / 01123
tdes
P roduct ratedes ∗ ye,product,des dt
tads F eed rateads ∗ ye,f eed,ads dt 0
tdes P roduct ratedes ∗ ye,product,des dt Ethanol productivity = 0 tcycle ∗ mass of adsorbent Ethanol recovery =
0
5
4
+
P roduct rate y t t t f eed rate y !" # $ des
e,product
cycle
ads
des
ads
e,f eed
% & 73%" '' P, T, q, c, y" () * + * " ) , & 45% * ) -
#
!"
!
"
! "
! kmol h−1 ! # $ % kmol h−1 ! # $
# $ &''
!
( ( ) ! # $
*+ # $ , %
- . % ! # $ # ( $ ! .
# $ ( # $ / ( ! # $ 0 #*+ 1$ ( 2
! 0 /
±1% ! "#$% "#&% ' S=
!
TF K
t
!
Change in measured variable(%) Change in manipulated variable(%)
$(
e kmol h−1 (wt%)
yw
PF Pa
Pp Pa
!
!
!
! !! ! !
! ! !! !
s
" " " " " " "
) $ * + , - + + . / 0 + 1 2 3 3 3 &$
0.9892
0.989 Purge pressure (positive step)
0.991 Production pressure (positive step)
0.989
0.9905
Molar fraction of ethanol
0.9888
0.9886
0.9888
0.99
0.9886
0.9895
0.9884
0.989
0.9882
0.9885
0.988
0.988
0.9884
0.9882 0
14
27
42
0
55
0.98895
27
55
83
111
0
138
27
55
83
111
0.9905
0.989 Composition (ethanol and water) (positive step)
Purge time (positive step)
0.9889
Temperature (negative step)
0.9889
0.99
0.9888
0.9895
0.9887
0.989
0.98885 0.9888
0.98875 Feed flow (negative step)
0.9887 0.9885
0.9886
0.98865 0
14
27
42
55
69
83
0
14
27
42
55
69
83
0
27
55
83
111
Time (h)
! " #$
" #$
%%
1
Molar fraction of ethanol
0.98 0.96
0.9895
step applied (0.5 %)
0.94 0.92
0.989
0.9 0.9885
0.88 0.86
0.988 67
0.84 0
19
81
38
60
95
130 111
167 167
Time (h)
!"# $% & ' ()*
!" # $ % & % % ' !" % %
( ) * # % % % + , #
- ")". % $ + & % ) /01 % % 2"" 3 4 1
N = 5 !!"#
# NTP RBS TP RBS # # 176 400 s 49 h"# # !! !$" %&$' ( !! # 1 s 8 × 105 ) ±0.5% * Ê + , - Ê #
512.3
0.9889
512.1
0.98885
512
0.9888
511.9
0.98875
511.8
0.9887 0
27
55
83
111
139
167
194
222
-1
0.98895
Output data (Ethano purity) Input data (PRBS 55 bits) Input data (PRBS bits) Output data (Ethano purity) 512.2
Flow (kmol h )
Molar fraction of ethanol
0.989
511.7
Time (h)
+ + + . + + + / 0 + , + # 1 %23'# %22'# %2$'4 # 1
# # 1 0 , , 1 0 + # + 5 +# + + !3" 3&
! "# # YL/UL $ % " UL YL & Ut Yt '() # 1 second * & & # $ " +, ! ⎧ ⎪ ⎪1.4647Ut ⎪ ⎪ ⎨2.1952U t UL = ⎪ 2.1941U t ⎪ ⎪ ⎪ ⎩1.4615U t
− 749.95 − 1123.9 − 1123.4 − 748.26
511.994912644229 511.997394173535 511.999875709115 512.002357241804
< Ut < Ut < Ut < Ut
≤ 511.997394173535 ≤ 511.999875709115 ≤ 512.002357241804 ≤ 512.004838774515
YL (z) B(z) −z(z − 1) = = UL (z) F (z) (z + 0.7243)(z − 0.9645)(z − 1)
⎧ ⎪ 0.003756YL + 1.3038 ⎪ ⎪ ⎪ ⎨5.3121 × 10−5 Y + 0.98882 L Yt = −5 Y + 0.98883 ⎪ 4.3701 × 10 L ⎪ ⎪ ⎪ ⎩−0.0037983Y + 1.3174 L
−170.355568258469 < YL ≤ −85.0649012247007 −85.0649012247007 < YL ≤ 0.461491758658657 0.461491758658657 < YL ≤ 85.5164328428406 85.5164328428406 < YL ≤ 170.807099876609
%
&
# # " # # " " - $ ! # # . " UL Ut " +,& Yt YL # - / 0 " +, " " #
1 .
! " # $%& '()* ! + , -. $ / & ye − Yt F IT = 100 1 − $%& ye − mean(ye ) + 0 12 '* $ / & 3'4
Molar fraction of ethanol
0.989 PSA model Hammerstein-Wiener model
0.98895 0.9889 0.98885 0.9888 0.98875 0.9887
27
55
83
111
139
167
194
222
Time (h)
Ú×
%5
Molar fraction of ethanol
0.991
0.9905 PSA model Hammerstein-Wiener model
0.99
0.9895
0.989
0.9885 0
14
28
42
56
70 Time (h)
83
97
111
125
! " # $ % % & '(() % xRn , uRm, yRp, k * '(() + , * % + "- * % & xk+1 = Axk + Buk
yk = Cxk
'() % xss uss # . # Px Pu % & xss = Px rk uss = Pu rk '(.) uk − uss = −K(xk − xss ),
(
rk
uk+i − uss =
−K(xk+i − xss ) + ck+i i = 0, . . . , nc − 1 , −K(xk+i − xss ) i ≥ nc
ck+i nc ! ck " # " xk+i,k = Φxk+i + Buk+i uk+i = −Kxk+i + Pr rk+i + ck+i ,
$
x k =Pcl xk + Hc − c k + Prx rk − → → y k =Pcly xk + Hcy − c k + Pry rk → → − u k =Pclu xk + Hcu − c k + Pru rk → − →
%
! Φ = A − BK # Pr = KP x + Pu !
" #
Δu u k − Puk−1 uk−1. −→k =PΔu − →
x k ∈ R(n)(n ) y k ∈ R(p)(n ) # − → → − (m)(n ) u n k , Δuk ∈ R y → −→ − & ' ( )* )# # +,$- c k ' − → y
y
y
J = zkT P zk +
n c −1
cTk+i [BP B + R]ck+i
i=0
=
zk 2P
+
.
− c k 2W , →
! zk = xk − xss W = (BPB + R) R > 0 BP B > 0 ⇒ W > 0 zk 2P
. 2 Jc = → −c k W .
.
/
P
ΦT P Φ = P − ΦT QΦ − K T RK.
!
" " # "
x≤− xk ≤x u≤− uk ≤u → → y ≤ y k ≤ y Δu ≤ Δu −→k ≤ Δu. → −
$
% &' $
Mc − c k ≤ qc (xk , uk−1, rk ). → (
Mc
) *
&
+, - "
&. &
/
∗ Jc −c k = argc → k → −
s.t. Mc → −c k ≤ qc (xk , uk−1, rk ).
0 123
4
$5
/ "
2SWLPL]HU ck
rk
Pr
+
+ −
uk
x k +1 = Ax k + Bu k y k = Cx k .
xk
K
"
uk = Kxk + ck + Pr rk &.
6
! " #$ % " %
% & '"() * % * + #$, * #$ -.
* #$ +/ 0 /1 , #$ 2 3 +"4, Un = [f (GE ∗ en , GCE ∗ cen ) + GIE ∗ ien ] ∗ GU
3 +"4,% 3 +".,
+"4,
GCE GIE Un = GE ∗ GU ∗ en + +"., ∗ cen + ien GE GE en % cen ien
*
!
#$ #$ #
GE * +3 +"5,/+"6,, GE ∗ GU = Kp
+"5,
GCE = Td GE
+"(,
"7
GIE 1 = GE Ti
! ""# $!% &
& ' & ( ) (* + ,-& ) (*
. /01 23
44& / ' 5
67
& & 8
⎤ ⎡ ⎤ ⎡ 1 1.24 0.4583 −0.6986 ⎦ B = ⎣0⎦ C = 0 −1 1 0 0 A=⎣ 1 0 0 1 0 k = t = 1 3
#!
. /01 & ( + ," 9 ,
uk = uL ! " # # ! ! ! $
%& ! ! ! ' −150 ≤ uk ≤ 50
( !! ! ! ! 400 (kmol h−1 ) ≤ uk ≤ 590 (kmol h−1 )
) * !! yt yt ≤ 1 yt !! ! %& ! + ,# ! ! ! ! ! ' - ' ! .
! /. !!+ 0 1 (222 - 1 222 1 32 1 42
! ! + & ! ! ! " # ! !! ! * + 5+ ! *!.. 6 7 0 ! # # ! * + (2+ )( 0 ≤ yL ≤ 1.8
!" ##$ %&' ( )*
uk = uL −150 ≤ uk ≤ 50
!
" ## $ % &
"' $ ( ) &
## $ $ )$ *+ , - . $ ##
/ $ 0 1 2 ##
$ $ 3 GE 44 400 (kmol h−1 ) ≤ uk ≤ 590 (kmol h−1 )
GU
GCE
GIE
!! " # $ !%
& " ' & (
)**' +, - " ) #
! "
"
& ' . & ' ' /#012 (' ( ' 3' &'
&. +45
( '
6"67 ' '
'
' 8 ' +45 &
& & &2 3 & 9 & : ' '
7 6+ )**' +, - " +45 ; '
< ' = : : & ) 0 # &' !>
!"" # $ s %"&
$
440 K
'() 409.2 K
$ *
#) $
% 0
() 19 s
s
* %+, #( -.%! * %+, 0 -.%! * %+, ** -.%!
/ * /$ $
( ) #)
'()
# $
1 $ **( 00) $ 00 * * )
2 3 - .%! 44 % + , , 1
- .%! 5
6
7
(/ 0 ) , 44 % + , 5 /
$ ( **) $ ( 8
**)
- - .%! $$$# 44 % + , 7 $$$ /0
6
a) Disturbance at the input (temperature)
0.995
b) Control signal
520
0.99 PSA without control Fuzzy PD+I control Optimal MPC control Reference
0.98 0.975
0.989
0.97
0.988 0.987
0.965
0
27.3
55.5
Flow (kmol h-1)
Molar fraction of ethanol
510 0.985
83.3
0.9881 0.988 0.9879
0.96
Fuzzy PD+I control Optimal MPC control
500
490
480
470
0.955 0.95
460 0
13.8
27.7
41.6
55.5
69.4
83.3
0
13.8
27.7
41.6
55.5
69.4
83.3
Time (h)
Time (h)
a) Disturbance at the input (composition)
0.99
b) Control signal
520
PSA without control Reference Fuzzy PD+I control Optimal MPC control
0.986 0.984 0.989
0.982
0.9885
0.98
0.988 0
27.7
55.5
83.3
0.978 0.98895 0.9889 0.98885 0.9888
0.976 0.974 0.972
510
Flow (kmol h-1)
Molar fraction of ethanol
0.988
500
480
470 0
13.8
27.7
41.6
Time (h)
Fuzzy PD+I control Optimal MPC control
490
55.5
69.4
83.3
0
27.7
55.5
83.3
Time (h)
!" #$ % & ' () *%% )# +
& , & - . !/ " $ & ' () . 0 1 & & ' *%% )# + & . 0 & & 2 a) Disturbance at the input (Purge time)
Molar fraction of ethanol
0.988
PSA without control Reference Optimal MPC control Fuzzy PD+I control
0.986 0.984 0.989
0.982
0.9885
0.98
0.988 0
27.7
0.978
55.5
83.3
0.9888
b) Control signal
520
510
Flow (kmol h-1)
0.99
500
Optimal MPC control Fuzzy PD+I control
490
0.9887
0.976
480
0.9886
0.974 0.972
470 0
13.8
27.7
41.6
55.5
69.4
83.3
0
13.8
27.7
41.6
55.5
69.4
83.3
Time (h)
Time (h)
, & ' () *%% )# + & $ *%% )# + & . 0 , & 3
14 . & )5 & 1 & & 6 & - . , 7 *& !/ , &
7 8 87
440 K 15 s) ! " ! # $% & 440 K ! "
! # ' s $% &
409.2 K 19 s $% 409.2 K 19 s $%
$
( #) "
* ") + ! $%'' &% (( ! " * #)") ( # ) ) ( + $%& , - %' (( ! " * ) ! ( " + #) ) + ( ( ! ) % ) ) ) * ( .( - ) # ) //+ "
( ) # ( ( ( 0" ) ( .( ) ( ) 12
"((* ) #- * ) "
( !
) ( ") ) ( + " " #) ( (% " . .( - ) ) "
( ! ) (" ( .# $ ' ' kmol h−1 * )( ( ." ( ) # ( . "( " ( ) "
- #) ) + ( ) )+ " + #) ( ( (* $%& % (( ! " * ) ) ) * ) //+ "
( ) ( (
) ( #) ( (" ( ! 3 #% 45#(* ) " . ! ( # ( ( . ! " ( ! ) 12
"((* )( . ( # ) ( # + "+" $ ( )+ " ( ) + " + - * ( ( .( - % * ) #- * #) ) "
( # //+ # ( ((. ) +% % . .( - ) "
( ! ) ) ( ) ( . "% 6)( "
( * !
) "+" $ (" ( $$ (* . )( ( ) + " .) - "+" " ( ) 12
"(( ) " . ! # . ( ) ) - 7" ) - . ) +% 8- #) )( (" ( ! ) 12
"(( ) "
( ) +* . ( "5 ) ( 0" + ( ) //+ (* #)") 5#( ( ( ) - ( (" ( ) "
( . ( " + #) ) .0"- ! ) ( +% +* ) " . ! # ( ! # ( ( . ) 12
"((* #) # ( .( - ) #) "
) +
(* ") # + $% , - &% (( ! " *)( # ( . "( ) - ") 7" ) ) + ( ) " . #) ) " ( * ) #- &
b) Control signal
a) Disturbance at the input (composition and temperature) 520 Reference Optimal MPC control Fuzzy PD+I control PSA without control
0.98
0.97
0.989 0.9885 0.988 0.9875
0.96
0
27.7
55.5
0.95 0.9882 0.988 0.9878 0.9876
0.94
0.93
510
Flow (kmol h-1)
Molar fraction of ethanol
0.99
500 Optimal MPC control Fuzzy PD+I control
490
480
470
460 0
13.8
27.7
41.6
55.5
69.4
0
27.7
55.5
Time (h)
Time (h)
! " # $ %
& '(
a) Disturbance at the input (Purge time and composition) 0.99
b) Control signal
520
PSA without control Reference Fuzzy PD+I control Optimal MPC control
0.986 0.984 0.989
0.982
0.9885
0.98 0.988
0.978
0
27.7
55.5
83.3
510
Flow (kmol h-1)
Molar fraction of ethanol
0.988
500
490 Optimal MPC control Fuzzy PD+I control
480
0.989
0.976
0.9888
470
0.974 0.972
460 0
13.8
27.7
41.6
55.5
69.4
83.3
0
13.8
27.7
41.6
55.5
69.4
83.3
Time (h)
Time (h)
kmol s−1 MJkmol−1 kmol kmol kmol−1
! % "# ! $% &' $( ')%*
+ , ( MJkmol−1 ! $$ - ."/$ ."/% ." ! $$ ! $ $, ! $0 $( ( $ ! $ &'1( 2 3"/ 4 %( 2 3"/ 4 "5 6 - - ) * /## ! ( 7 ,&
"
# "##
"
"
#"
"
"
&'%
" # "
#" #
#
#
#"
" " #
"
"
"
"
"
" "
" "
(kmols−1 )
!
(kmol)
$%% (kmol)
$(!!%
(kmolkmol−1 )
&'%
%' $) " −1 (MJkmol )
(kmols−1 )
!
(kmol)
" #
"##
"
"
"
# "
# #
#
#"
""
"
#
#
#
#
"
# #
# #
""
" "
"
"
#
"
$%% (kmol)
&'%
$(!!%
(kmolkmol−1 )
&'%
%' $) (MJkmol−1 )
# " "
' ) ( ' ') (' ' (! !%( ' ! $!)* !% '!( (* ') ) ( * %+
!
, !% - ' !( . ' ) ( / * %+ 0 ('% . ' ( !' % ' ' $!) +$( '% " * ! !( ) -(+ ' ( ' ) ( $(( ' ) ( +% . 1 %! 1* '!' + ( (( .
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!" $% &'(#
! $ ($) (")
*+! *+$ , ! +! - $!& . !" $$" (") $ +$ / -
#!) 0 $ +$ !
+! 1 % " # ! $ - +! +$
!
"#$
%
!
"#$
%
2 -($ &'-!# !# 2 $&) !" 2 ! $ #$) #()
- $ +$
%$
#
! !
!
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! ! !!
!
! " #
$ # # # ! % # # $ & # # '( # ! " )* (++ ,- # ! . / 0 1 " )* 2 (++ , ! " )* # (++ ,-
#
# !
% # # " )*
! " (++ ,-
#
! 3 # " )* ! % # 456 607
kmolh−1
$ & $ #
88!6 9 ! % # # / 88!28 9 : *:; :; 062<5 88!0< 9 =
88!07 9 + > ; 25 ?4<@! % 0AA9 B # ! 3 # # B 42
!
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% ! ! & '()*+, '% , &
'"#$, ' ,
) $ & --. &
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+ , +
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% $%#*' 4&( ) 4"*
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D + 1+ C ; ! - + 5 + !
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Highlights
• The Pressure Swing Adsorption Process produces a bio-ethanol with 99% purity complying with international standards. • The sensitivity analysis allows to identify the possible input and output variables, which gives rise to establishing the primary and secondary control loops. • The Hammerstein-Wiener model allows capturing the important dynamics of the PSA process (rigorous model described by PDE). • The controllers (Optimal MPC and Fuzzy PD + I) attenuate the disturbances that occur at the entrance of the PSA process, allowing to always have a purity that complies with international standards.