1. A DISTILLATE COMPOSITION ESTIMATOR
FOR AN INDUSTRIAL MULTICOMPONENT
SPLITTER WITH EXPERIMENTAL
TEMPERATURE MEASUREMENTS
Marcella Porru1, Roberto Baratti1, Jesus Alvarez2
(1) UNIVERSITA’ DEGLI STUDI DI CAGLIARI
Dipartimento di Ingegneria meccanica, chimica e dei materiali
(ITALIA)
(2) UNIVERSIDAD AUTÓNOMA METROPOLITANA UNIDAD IZTAPALAPA
Departamento de Ingeniería de procesos e hidráulica
(MESSICO)
2. INTRODUCTION (1)
Industrial distillation column are frequently undergone to changes in operating
conditions.
Key impurities need to be controlled for achieving the desired separation.
Online composition analysis would be needed in order to monitor control
performance and immediately act when the concentration of interest in the
effluent is different from the desired one.
Composition analyzers present high costs of purchase and maintenance,
reliability problems and measurement delays, implying the impossibility of direct
online composition analysis
3. INTRODUCTION (2)
Compositions can be estimated through a simple model driven by temperature
measurements.
Differently from the binary case, in a multicomponent column the composition in
a tray is not uniquely related to the temperature, meaning that the use of
temperatures does not always allow adequate composition estimation.
A crucial point is therefore the selection of the number and the locations of
temperature sensors along the column, in order to obtain good performance.
4. THE IC4-NC4 SPLITTER
7 component;
56 stages;
PI temperature controller with temperature measurement at 49 stage;
Control target: NC4 in the distillate between 0.01 and 0.06 [molfrac];
ESTIMATION TASK: TO ONLINE INFER THE CONCENTRATION OF
THE NC4 IN THE DISTILLATE.
Feed composition
[molar fraction]
Normal boiling
point
[K]
Propane C3 0.008 231.1
I-butane IC4 0.394 261.4
I-butene IC4- 0.032 266.2
N-butene NC4- 0.031 266.9
N-butane NC4 0.467 272.7
2-butene trans C4-T 0.039 274.0
2-butene cis C4-C 0.029 276.9
Hydrocarbons and their nominal compositions and normal
boiling points in the splitter feed.
5. CONTROL (AND ESTIMATION) OVER ANY PROCESS IS MOST
SUCCESSFULLY ACHIEVED BY THOSE WHO UNDERSTAND THAT
PROCESS.
),,( dxfx PPP u Composition Dynamics: Material Balances
)( Pp xhy Temperatures: Bubble Point Function.
6. FULL ORDER AND PASSIVE INNOVATION
The estimation TASK: on-line estimation of the NC4 composition in the distillate
with temperature measurements.
The most employed estimator in process engineering is the EXTENDED KALMAN
FILTER (EKF).
DISADVANTAGES OF FULL ORDER OBSERVERS FOR MULTICOMPONENT
DISTILLATION COLUMNS:
High number of ODEs to be on-line integrated (e.g. EKF will need of about
60,000 ODEs for our case study);
The high order is detrimental for the robustness of the observer.
7. FULL ORDER AND PASSIVE INNOVATION
The estimation TASK: on-line estimation of the NC4 composition in the distillate
with temperature measurements.
The most employed estimator in process engineering is the EXTENDED KALMAN
FILTER (EKF).
THE CHOICE OF A PASSIVE OBSERVER IS MOTIVATED BECAUSE
Temperature in a stage is the expression of changes in some states.
Magnitude of the number of ODEs equal to the number of the modeled states.
8. DETECTABILITY CONDITION
))(( j
ii cabs c
Detectability condition (DC) for
multicomponent distillation column.
If DC is adequately met for a component:
),(1
yx i
c
The bubble point function can be robustly
solved for the innovated component.
The dynamics of the other states are given
by the material balances:
),,,),(( 1
dxcfx uyh i
Practically speaking, the passive observer will have a single innovation
per temperature measurement, while the other dynamics will be inferred
with the simplify model of the process.
9. THE ESTIMATOR STRUCTURE
Design the Estimator Structure means:
Find the stage and the component for which the DC is adequately met.
Develop a simplified model.
Design the Estimator Structure with:
Per-Component temperature gradient diagram
i
C
j
j
TT
i
1
j
j
j
j
i
i
i
i
c
c
c
T
)(
10. THE PER-COMPONENT TEMPERATURE
GRADIENTS (1) – SENSITIVE INDEX
KTS T
j
iR 1*
*
j
i
Ci
j TCi
j,
maxarg*)*,(
If a pair sensitive stage and component exists, they are the sensor location
and the innovated component.
i* = [44-49]
Cι* = IC4
11. THE PER-COMPONENT TEMPERATURE
GRADIENTS (2) – RELATIVE SENSITIVE
INDEX
The set of modeled components must give a contribution to the global
gradient higher than the 90 % at the sensitive stage.
9.0
)(
1
,
TC
j
j
i
i
R q
T
Tabs
Q
QR
44=0.94
μ=[IC4,NC4]
QR
49=0.94
μ=[IC4,NC4,NC4-]
12. THE PER-COMPONENT TEMPERATURE
GRADIENTS (3) – INFORMATION
CAPABILITY INDEX
The sensitive stage and component must be located sufficiently near to the
effluent.
IR ≤ ½, IR = (N – iR*)/(N – nf)
IR
44 = 0.5
IR
49 = 0.3
13. SENSITIVE STRUCTURES COMPARISON-
SIMULATION RESULTS
1 ={ ir = 44, Cj = IC4, },
= {IC4, NC4}
(SR, QR, IR) ≈
(1.35, 0.94, 0.5)
Faster transient
behavior
2 ={ ir = 49, Cj = IC4, },
= {IC4,NC4,NC4-}
(SR, QR, IR) ≈
(1.21,0.94,0.3).
Lower asymptotic off-
set
o Higher SR , faster estimation dynamic.
o Lower IR , less the off-set
17. SENSITIVE STRUCTURES COMPARISON-
RESULTS WITH PLAN DATA (2)
2 ={ ir = 49, Cj = IC4, },
= {IC4,NC4,NC4-}
(SR, QR, IR) ≈ (1.21,0.94,0.3).
o The ternary structure allows to obtain good performance in case of
changes in operating conditions.
o The ternary model-based observer supplies the lacks in hardware
analyzers reliability.
18. CONCLUSIONS (1)
Composition estimators are on-line software that allow to control and monitor
the distillation units instead of hardware analyzers (high costs, reliability
problems, delay times).
Passive observers must be preferred in case of systems with high number of
states (full order observers need the integration if a number of ODEs that grows
quadratically with the number of the states that cannot be on line integrated).
The structure design (modelled and innovated component, and sensor location)
is a key step to obtain the best performance.
19. CONCLUSIONS (2)
The per-component temperature gradient diagram allow to identify the
contribution of each component to the global gradient.
Sensitive measures on the per-component temperature gradient diagram help
in the structure design.
A ternary model driven by temperature measurement at 49 stage guarantees
good performance over all tested column operating condition.
A closely similar behavior can be attained using a binary model with sensor at
the most sensitive stage with an unacceptable cost of behavior with sensor
location changes.
