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Data Reconciliation Using AspenPlus.

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Data Reconciliation Using Aspenplus
M. Piccolo, P.L.Douglas*
Department of Chemical Engineering, University of Waterloo
Waterloo, Ontario, Canada
and
P.L. Lee
School of Physical Sciences, Engineering & Technology
Murdoch University, Perth, Western Australia
Process measurements ma& in chemical plants generally do not satisfy
material and energy balance constraints due to random or possibly gross errors
in the measuring device readings. Data reconciliation is a method of adjusting
random errors in the measurements in a weighted least squares sense in order to
satisfy the process constraints. Linear data reconciliation involves solving a
linear system of mass and energy balances as well as inequality constraints.
Non-linear data reconciliation, involving non-linear mass and energy balances
and constraints, is substantially more complex and requires a significant amount
of work in developing the model andlor solution strategy.
Steady state simulation packages equipped with optimization routines can be
used to perform data reconciliation and parameter estimation with existing
models which automatically satisfy mass and energy balance constraints. The
time required to develop a data reconciliation problem can be shortened by
using these packages without sacrificing the quality of the results. Five
examples are presented to illustrate this technique using the AspenPlus
flowsheet simulation and Optimizationsystem. Thefirst four are simple problems
*Authorfor correspondence(pdouglas@cape.uwaterloo.ca).
157
M.Piccolo, P.L. Douglas and P.L Lee
takenfrom literature and are included to validate the method. The fifth example
involves a nonlinear industrial distillation example included to illustrate the
scope of the technique.
In the f i s t four cases, the solution to the data reconciliation problem war
easily developed and quickly solved. Thefifth example involved somewhat more
work but was still relatively quickly developed and solved. Steady state process
simulation systems can be used to peqonn non-linear data reconciliation. The
reduction in development time increases dramatically with the problem
complexity involving staged separation and multiple units.
Introduction
Determination of process performance makes use of measured process
information. Errors in these measurements could result in misleading or
inaccurate conclusions. Crowe (1983) states These raw measured data are in fact
subject to random and possibly gross errors so that they may not be consistent
with the conservation of mass and energy. The data must be adjusted so that the
adjusted values obey the conservation laws and some weighted measure of the
total amount of the adjustment is minimized.' Much research has be devoted to
the development of various techniques designed to achieve this end. The work
summarized here will introduce the use of commercial process simulation
software systems to solve various data reconciliation problems.
Data reconciliation problems are either linear or nonlinear. The linear case is
based on the assumption that any stream which has its concentration or
temperature measured also has its total flow measured (Crowe, 1983). The
nonlinear case involves the omission of this assumption thereby placing products
of unmeasured variables in the balance equations, making them nonlinear
(&we,
1986). In both cases, data reconciliation involves the creation of a
matrix that is representative of the process flowsheet Crowe (1986) proposed a
matrix projection algorithm to remove all unmeasured variables from this
Data reconciliationusing AspenPlus
process matrix. The resultant solution procedures for both cases involve the
reduced process matrix and Lagrange multipliers to handle the conservation law
equality constraints. The nonlinear case required an iterative solution. Recently,
other methods for the solution of the nonlinear case (mainly involving the
developmentof a detailed process model) have been proposed by Takiyama et al.
(1991), MacDonald and Howat (1988), Liebman et al. (1992) and Tjoa and
Biegler (1991).
The data reconciliation method presented here can be applied to linear and
nonlinear problems without the need to develop complex process models and
inmcate iterative solution procedures. This approach takes advantage of existing
simulation software capable of optimizing a user defined objective function. The
package chosen for the development and demonstration of this scheme is
AspenPlus, Aspen Technology (1993). AspenPlus is a sequential modular or
closed form simulator in which the unit operation system models are solved one
process unit at a time. If recycles exist, the solution becomes iterative and a
convergence promotion method, Wegstein’s Method for example, is used to
make the appropriate adjustments in order to satisfy mass and energy balances.
Another approach used by some simulators is to solve the process equations
simultaneously, e.g. Speedup, MassBal. In this case, the model equations are all
written in a general form i.e. f(x) = 0, is the so called open equation form. The
resulting process matrix is subsequently solved using an equation solving
method. This approach has proven to be more flexible and powerful than the
sequential modular approach. However, at the present time, sequential modular
simulators are the most widely used simulators in industry.
It should be noted that although AspenPlus is used to demonstrate this
approach to data reconcillation other simulation systems with similar capabilities
(i.e. steady state process simulation models and process optimization) such as
Speed Up, Pro-Vision, Hysim,MassBal could also be used.
The following sections will describe the approach used to perform data
reconciliation and parameter estimation using AspenPlus and summarize the
results from five example problems. Four examples used were taken from the
159
M.Piccolo, P.L. Douglas and P . L Lee
literature for purposes of illustration and one industrial example was developed
to show the scope of the procedure.
Problem Formulation
The general linear data reconciliation problem can be written as the following
constrained weighted least squares problem :
choose x
to min[(y - x ) ~ Q - '(y - x ) = aTQ-'a]
such that: Ax = 0
y is the vector of measured values
where:
x is the vector of reconciled values
Q is a weighting mamx, usually the inverse of the variance of the
measured variables
A is an incidence mamx representativeof the system
a is a vector of adjustments made to the measured values, a = (y-x)
The solution to Equation (1) is given by the following equation (Crowe, 1983)
as:
x=y-QA
T (AQA T )-1
Ay
(2)
The nonlinear data reconciliation problem is formulated in much the same way:
choose x
to min
l(Y-x)T Q '(Y-41
such that h(x) = 0 and g(x) 2 0
where:
h(x) are the set of equality constraintsrepresenting the model
g(x) are any inequality constraintspresent in the process
160
Data reconciliation using Aspenplus
In the case of nonlinear data reconciliation both h(x) and g(x) are generally
nonlinear functions. h(x), representing the process model, could, in general, be
a very complex nonlinear function involving heat and material balance
equations, equilibrium, reaction equations and thermodynamics for a process
involving multiple components, multiple phases, multiple units with recycle
streams. The advantage of using a process simulator is that the simulator already
has a library of process modules already available and satisfies the equality
constraints, h(x) = 0, automatically to a specified tolerance. Commercial
simulation packages allow one to formulate a data reconciliation problem with
relative ease because the models (unit operation, thermodynamic, optimization
and convergence) are already available in the simulation system. The user is,
however, limited by the diversity of the models contained in the package and the
quality of the optimization algorithm. AspenPlus, like all commercial
simulators,possesses a wide variety of different process models and optimization
routines.
When solving a data reconciliation problem using a simulator it is
recommended that the user follow a step-wise approach. The first step involves
developing a model of the process using the simulator to represent the equality
constraints h(x)= 0. Once this is accomplished, an optimization loop to perform
the data reconciliation subject to any inequality constraints g(x) 2 0 may be
added. A more detailed discussion of these steps follows.
Step 1
The development of the process model is generally a straightforward
procedure, and will not be discussed in detail. The user must describe the
flowsheet, define the process units, provide values for the input stream variables
(i.e. flow rates, composition, temperatures, pressures, etc.) select the
thermodynamic package and supply any additional models needed in the
process. The required information is problem specific and the format of the
161
M. Piccolo, P.L. D o u g h and P.L. Lee
required information is simulator specific. Simulator manuals and on-line help
are generally sufficientreference.
Step 2
Once the simulation has been developed the data reconciliation problem, in
the form of an optimization problem, must be defined. The optimization step is
not always straightforward. The user must specify the decision variables to be
adjusted in order to achieve the optimum. Not all variables can be adjusted in a
sequential modular simulator. For example, output stream variables cannot be
directly adjusted. To adjust an outlet stream variable one must adjust an
appropriate input stream variable or unit operation parameter which will then
affect the output variable. A general rule of thumb to remember when using any
sequential modular system is that only inlet stream properties and process unit
variables can act as manipulated variables. Unit variables are those variables
affecting the performance of a process unit. For example. unit variables for a
distillation column include reflux ratio, reboiler duty, product flowrate, stage
efficiency, or pressure, among others. This selection of the appropriate adjusted
variables is highly problem specific. Problems may not have a unique set of
manipulated variables and the user should try to use as few as possible to keep
computation times low. Inlet flow rates should always be chosen as manipulated
variables when flow rates are being reconciled. This will allow for the proper
amount of material to be in the system. The unit variables to be chosen as
manipulated variables should be those with the greatest effect on the variables
being reconciled. Those unit variables being adjusted can be considered as
parameters being estimated simultaneously with the data reconciliation. The
user will also have to specify upper and lower limits for the manipulated
variables. Determination of these limits will be based on several considerations
including process knowledge and equipment restrictions. It is important that the
final values of the manipulated variables do not lie on the bounds. If they do one
should widen the bounds to allow the optimizer to find the unbounded optimum.
162
Data reconciliation using Aspenplus
If the final values continue to lie on one of the bounds, the likely cause is an
error in the objective function
Step 3
Once the user has determined the adjusted variables the objective function
must be formulated. In the optimization procedure, the objective function can be
formulated in a Fortran block using process variables defined by the user. For
example, the user can define the Fortran variable ‘FEED’ as the total flow rate of
the feed stream. Virtually all process variables, can be accessed and defined.
This is extremely beneficial since all measured variables can be evaluated by the
simulator and are therefore available for use in the objective function. Once the
user has defined the appropriate process variables, the objective function can be
written as the weighted sum of squares of the adjustments of the measured
variables. The adjustment is defined as the difference between the adjusted and
measured values of the variables. The weights are normally the inverse of the
corresponding variances evaluated as the sample variances of a set of
measurements over a certain period of time at a steady state. Variables whose
accuracy is crucial can have their weights increased simply by multiplying the
corresponding objective function term by some constant greater than 1.
Generally, factors of 1, 2, and 3 are quite sufficient in providing priority to
chosen measurements.
Once these steps are completed, the user must indicate to the program to
minimize the objective function. The optimization routine also allows the user to
adjust certain optimization parameters such as convergence tolerances,
manipulated variable ranges, maximum number of iterations, etc. The
Aspenplus default values were found to be adequate for simple problems.
However, in complex cases where the system is very sensitive or highly nonlinear, certain problem specific adjustments may have to be made. These
adjustments are usually found through experience and trial and error.
163
M. Piccolo, P.L Douglas and P.L. Lee
By following these steps, the user will have set up an optimization routine to
minimize the weighted sum of squares of the adjustments of the measured
variables. This definition is equivalent to the classical data reconciliation
problem formulation stated in Equation (2).
Assumptions
There are several noteworthy assumptions made in the development of this
approach.
1) the process is at steady state
2) the measurementscontain no gross emrs; if gross errors are present they
should not be included in the objective function
3) the variance of each measured variable is known
4) the random errors are independent
Examples and Results
Four examples have been taken from the literature to illustrate details of the
method and compare the results. In each case the problem was solved using
Aspenplus with an SQP algorithm and Gams (an open-form optimization
program) with a MINOS5 algorithm Gams (1994). The time required to develop
and solve these problems was typically less than 1 hour. A fifth example
involving a large distillation system is illustrated in which stage temperatures,
product compositions and flow rates are reconciled. This last example shows
how this approach can be used for data reconciliation and parameter estimation
of a complex nonlinear system.
Example 1
This recycle example is taken from a set of course notes prepared by Crowe
(1992). A simulation diagram is illustrated in Figure 1. The process data is
contained in Table 1. The split fraction in unit 2 is given as a = F3/F4 = 0.50.
164
Data reconciliation using Aspenplus
Table 1 - Example 1 - Measured Flows and Standard Deviations
Figure 1. Simulation Flowsheet for Example 1
It is desired to reconcile the measured flows F1 and F3 to satisfy the mass
balance. The data reconciliation problem can be stated as the classical
optimization problem as follows:
choose F1, F2,F3,F4, F5
tomino,=(
F1- 105
) +(
F3-95
2
).
(3)
165
M.Piccolo, P.L. Douglas and P.L. Lee
such that h(x) = 0
where:
F1= flow rate of stream 1
F3= flow rate of stream 3
h(x)= process model equations
The model equations h(x) are solved by AspenPlus to a specified tolerance.
The flows in the system are not independent of each other. For example, if you
spec@ F1, the simulator will use the model equations to solve for all other
streams which are dependent on F1. Therefore, the problem statement when
using a sequentialmodular simulatorlike AspenF'lus is as follows:
choose Fl
to minimize equation (3)
such that h(x) = 0
The solution of the problem using Gams involved writing a system of linear
mass balance equations around each unit and an overall mass balance to be used
as equality constraints when minimizing the objective function, Equation (3).
The results, presented in Table 2, are essentially identical. The AspenPlus
results could have been made more exact by decreasing the convergence
tolerance of the optimization block. The time required to develop the solution to
this problem in AspenPlus was approximately 30 minutes.
Table 2 - Example 1 - Reconciliation Results
166
Data reconciliation using Aspenplus
Example 2
This example is taken from Crowe (1983). It is designed to show how data
reconciliation can be performed in the face of a previously detected gross error
and an unmeasured process I&.
The process flow diagram is shown in Figure
2. The measured variables to be reconciled are the flowrates of streams 1 to 4
respectively, shown in Table 3.
Table 3 - Example 2 - Measured Flow Rates
I
I
Leak
Figure 2. Simulation Flowsheetfor Example 2.
167
M. Piccolo,P.L. Douglas and P.L.Lee
The stream flowrate measurements were assumed to have equal variances,
therefore the weighting factors were all set equal to 1.
The classical
optimization problem is stated as follows:
choose F1,F2,F3, F4
to min.
OF = (F1 - 98.5)2 + (F2 - 101.0)2 + (F3 - 96.5)2 + (F4- 96.5)2 (4)
such that h(x) = 0
where : F1= flow rate of stream 1
F2 = flow rate of stream 2
F3 =flow rate of stream 3
F4 = flow rate of stream 4
One cannot adjust F2,F3,or F4 independently of F1. Therefore the only
way to adjust all four flows is to adjust only F1 and let AspenPlus calculate the
subsequent adjustment to F2,F3, and F4 while satisfying the models equality
constraints. The solution to the problem using AspenPlus is, therefore, as
follows:
choose F l
to minimize Equation (4)
such that h(x) = 0
The reconciliation results are shown in Table 4. In Run 1, it was assumed
that there were no gross errors and therefore no measurements were deleted
from the objective functions. In runs 2 and 3 the measured flows of streams 2
and 4 respectively were deleted from the objective functions because it was
suspected that they contained a gross error. These results show that this
technique can be altered to account for gross errors once they have been
detected. If the variable with the gross error is a manipulated variable, it should
Data reconciliation using AspenPlus
Run 1
Var.
Cmwe
Run 2
ASPEN+
Guns
Crime
Run 3
ASPEN
Gams
Crowe
ASPEN+
CnmS
98.61
+
F1
I?
97.88
91.86
97.88
%.83
96.82
96.83
98.67
98.65
97.88
91.86
97.88
(%.83)
(%.82)
(96.83)
98.61
98.65
98.61
F3
91.88
97.86
91.88
%.83
96.82
%.83
98.61
98.65
98.67
91.88
97.86
97.88
%.83
%.82
96.83
(98.67)
(98.65)
Q8.67)
17.688
17.688
17.681
4.661
4.667
4.667
10.167
10.168
10.167
OF
'
remain a manipulated variable, otherwise, it should remain a dependent variable.
Crowe also reconciles the measured flows assuming that an unmeasured leak
exists in unit 2. To account for this, the AspenPlus model for unit 2 becomes a
splitter whose split hction is varied along with the feed flow rate to minimize
the objective function. The results are summarized in Table 5. Again, the
AspenPlus results agree with previous work.
Table 5 - Example 2 - Process Leak Results
Variable
I Crowe
........F l......i.....gg;7....
...................... .......-............
OF
3.625
...............................................
ASpenPlUS
..................................
99.73
GamS
............................
99.75
99.73
99.75
95.98
96.00
95.98
96.00
............................
3.625
3.626
Example 3
This separator problem is taken from Crowe (1983) and the process
flowsheet is illustrated in Figure 3. In this problem the compositions of the three
components of the feed streams and products are assumed to be known exactly.
The errors are assumed to occur only in the flowrates. The concentrations of
components A,B and C are presented in Table 6.
169
M. Piccolo, P.L. Douglas and P.L. Lee
Figure 3. Simulation Flowsheetfor Example 3.
Table 6 - Example 3 - Separation Unit Stream Compositions
1 Component 1
stream Compositions
1
2
3
4
The measured flowrates and their respective variances are contained in Table 7.
Table 7 - Example 3 - Measured Flow Rates and Variances
Variance
4
170
0.1858
0.000289
4.7935
0.0025
1.2295
0.000576
3.88
0.04
Data reconciliation using AspenPlus
The classical optimization problem in this case is:
choose Fl,F2,F3, F4
to min. OF =
(F1- 0.1858)2 (F2- 4.7935)2 (F3- 1.229a2 (F4- 3.88)2 ( 5)
+
+
+
0.04
0.000289
0.0025
0.000576
such that h(x) = 0
Again in this case the flows F3 and F4 are a function of F1, F2 and the
operation of the splitter. Therefore in AspenPlus one must only adjust the inlet
flows and operate the splitter such that the outlet compositions remain as
specified in Table 6. Therefore, the solution to the problem using AspenPlus is:
choose Fl,F2
to minimize Equation (5)
such that h(x) = 0
The data reconciliation results are shown in Table 8. The Gams and
AspenPlus results compare well with Crowe’s results.
Table 8 - Example 3 - Separation Unit Reconciliation Results
171
M.Piccolo, P.L. Douglas and P.L. Lee
Example 4
This ammonia plant example is also taken from Crowe (1983). The process
flow sheet is shown in Figure 4. The measured component flows in streams
1,23 and 5 can be found in Table 9.
Figure 4. Simulation Flowsheetfor Example 4.
Table 9 - Example 4 - Ammonia Plant Measured Flow Rates
MeaSured
ROWrate
33
89
0.4
101
20.2
69
62
205
172
Data reconciliation using Aspenplus
Since some component flow measurements are from the Same stream,
covariance's must now be included in the objective function. As in Equation 1,
the covariance matrix is inverted to obtain the objective function weighting
factors. The covariance matrix is given by Crowe as:
0.82
1.14 5.1%-3
0.0142
1.14
6.34
5.1% - 3 0.0142 1.28e-4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.816 0
0
0
0.816 0.326 0
0
0
0
3.81 0
0
0
0
0
0 3.08 0
0
0
0
0 32.0
0
0
0
8.16
-
The solution is obtained by varying the feed stream component flow rates, the
reaction conversion in the reactor, and the split fraction in the stream splitter
(unit 4). The objective function is the weighted sum of squares of the
adjustments from the measured values detailed in Table 8 weighted by the
elements of the inverse covariance mamx.
The optimization problem is
therefore written as:
choose Hz('),
N2(l), Ar('), Nz@),
NJ3),NHt4),
Hi5), reaction conversion,
purge split fraction
173
M.Piccolo, P.L. Douglas and P.L Lee
-0.0574
-2444
such that Mx) = 0
The solution to the problem using AspenPlus is:
choose Nil’, Hi’’, A/” ,reactor conversion,purge split paction
to minimize Equation (6)
such that h(x) = 0
The results, summarized in Table 10 indicate that the solution using
AspenPlus and Gams agree well with Crowe (1983). Run 1 refers to the solution
with no measurements deleted. Run 2 refers to the case where, HZ(’).
H2in
stream 1.
is deleted from the objective function because it was assumed to
contain a gross error. This was also performed using Gams and AspenPlus.
I74
Data reconciliation using Aspenplus
Table 10 - Example 4 - Ammonia Plant Reconciliation Results With and
Without Gross Errors .
Run 1
Run 2
Crowe
Aspenplus
GamS
Crowe
Aspenplus
GamS
31.68
31.68
31.68
32.70
32.76
32.74
94.94
94.98
94.94
(98.04)
(98.30)
(98.17)
0.40
0.40
0.40
0.40
0.40
0.40
100.05
99.63
100.05
100.56
99.59
100.58
20.12
20.06
20.12
20.15
20.03
20.15
69.76
69.32
69.76
69.23
68.19
69.20
60.57
60.60
60.57
62.66
62.80
62.74
203.95
204.38
203.95
205.00
205.19
205.00
0.729
0.336
=
15.927
15.970
15.927
0.344
The previous examples illustrated the use of a commercial steady state
simulator to solve several data reconciliation problems taken from the literature.
In each case the problems were relatively simple in that they involved simple
models and only reconciled process flowrates. In the final example we extend
the technique to a much more complex system to illustrate the power of the
approach.
Example 5
The following example was constructed using plant data collected from a
pemleum refinery operation of the gas separation system located downstream
from a fluidized catalytic cracking unit. Figure 5 shows a flowsheet of the
proc=.
I 75
M.Piccolo,P.L.Douglas and P.L Lee
to fuel
r
1
product
+
C!k
Fractionator
overhead feed
De-ethanizer
L
Debutanizer
Figure 5. Process Flowsheetfor Example 5.
The feed to the system is a gaseous overhead stream from a large fractionator
containing a wide slate of petroleum fraction components. The first column in
the process is a de-ethanizer with 50 trays and is used to remove components
lighter than propylene. The second column is a debutanizer with 47 trays and is
used to remove components lighter that the gasoline product which exits from
the bottom of the unit. It is desired to develop a simulation of the process which
can be used to obtain better estimates of the measure plant variables.
Variables which represent product properties (mainly flow rate and
composition) should be considered more important than most intermediate
stream properties.
This will serve to concentrate the model mismatch in
variables other than those related to the products. The product properties are
obviously important for performance and economic evaluations. The variables
deemed important in this system are:
176
Data reconciliation using Aspen Plus
- column overhead compositions
- major product flows (gasoline)
- top and bottom temperatures for each column
Other variables to be reconciled are:
- debutanizer overhead product flow
- de-ethanizer bottoms flow
The standard deviations were assumed to be 5% of the value of the
corresponding measured variables; variances are the squares of the standard
deviations. The overall objective function is a sum of the squares of the variable
mismatches divided by their variances and multiplied by a factor denoting the
importance of the particular variable. The factor becomes larger as the variable
becomes more important to match closely.
Five manipulated variables were chosen to minimize the objective function.
The feed rate was adjusted to affect the system’s many flow measurements. The
reboiler duty of each column was chosen
to try and match the column
temperature profiles. The Murphree efficiency of each column was chosen to try
and match the separation achieved in each unit. More manipulated variables
could have been used.
However, the AspenPlus optimization procedure
calculates the objective function derivatives by perturbing the manipulated
variables and subsequently solving the flowsheet. Therefore, the addition of
more manipulated variables could result in significantly increased run times.
The solution to the problem using AspenPlus can be written:
choose: feed rate from the fractwnator
de-ethanizer bottomsflow rate
de-ethanizer overall Murphree efficiency
debutanizer bottomsflow rate
debutanizer overall Mwphree efficiency
debutanizer reboiler duty
I77
M.Piccolo, P.L. Douglas and P.L. Lee
to minimize OF =
I
+3
+3
+I
+I
+2
+3
*
*
*
*
*
*
*
((fractionator refluxflow - 8258.4)I 412.92)2
-
(( de-eth top temp. 61-35)I 3.07f
(( de-eth top propylene molfrac - 0.0108)10.00054y
(( de-eth top propane mol frac - 0.0024) I 0.00012f
-
(( de-eth top recycle rate 5095.18) I 254.74y
(( de-eth bottom temp - 195.69)l9.785y
(( gasoline product jlow - 10767.76) I 538.39,’
+2
* (( de-but top i-pentane molfrac - 0.02075) I O.OOOlO4f
* (( de-but top ethylene molfrac - 0.01984) /0.000992?
* (( de-but overhead product jlow rate - 5269.79) I 263.49)2
* I( de-but top temp - 136.76) 16.383f
* (( de-but bottom temp - 350.11) I I7J06f
+I
*
(( de-eth bottomflow rate - 19150.33)1957.52f
+25
*
*
((de-eth eficiency - previous value) * 200,’
*
*
((debutanizerreflux ratio - 2.0) *
+2
+2
+I
+3
+2s
+4
+4
((debutanizereficiency - previous value) * 200,’
((debutanizerreboiler duty - previous value) * I f
The results obtained using Aspenplus are shown in Table 11 indicate that
the reconciled values match the measured values quite well. The reconcilation is
quite substantial as indicated by the reduction in the objective function from
27,463to 378.0.
178
Data reconciliation using Aspenplus
Table 11- Example 5 - Distillation System Measurment and Remodelled ValuesBefore Shutdown
P
Measured Value
Reconciled Value
OF Contribution
8691.65 bpd
7967.36 bpd
5.55
deahtoptempelawe
6585°F
70.03"F
4.83
de-eth toppro~lenefraction
&-ah top propane frauion
1.5wo
1.02%
121.20
0.29%
0.36%
20.35
de-uh top stage feed flow rate
4768.35 bpd
4479.0 bpd
1.47
&& boaom temperature
187.03'F
189.59'F
0.15
gasoline product flow rate
10107.29 bpd
9493.96 bpd
4.42
0.3wo
0.27%
4.02
debut top i-penme fraction
debut top ethylenefraction
1.51%
1.12%
8.99
4965.96 bpd
w
53.39
debuttoptRnw
138.15"F
127.02"F
0.37
debutbonomtean~
34582°F
321.31 OF
5.20
18959.01 bpd
19045.74 bpd
0.008
-
95.1%
-
debut ovehead product flow
&cth bottoms flow rate
dGerh Murphree&ciency
debut M u p h efficiency
debutrefluxratio
-
40.4%
-
1.50
1.84
46.25
-
15.482 MMBtuhr
-
27463
378.0
Process data for Example 5 was also collected for a period of time
immediately after a plant shut down. It was suspected that the column was
fouled or that some mys had suffered significant damage. The column's poor
performance was evident when analyzing its overhead product composition.
Table 12 shows that the reconciled values match the measured values quite well.
The reconciliation is quite substantial as indicated by the large reduction in the
value of the objective function from 535,800 to 199.5. The most significant
result of this reconciliation is an overall debutanizer efficiency. An efficiency of
21.9%is very ow and indicative of severe fouling or nonstandard operation such
as flooding.
179
M.Piccolo, P.L. Douglas and P.L. Lee
Table 12 - Example 5 - Distillation System Measured and Reconciled ValuesAfter Shutdown
OFcontribution
7005.3 bpd
18.41
61.35"F
65.01"F
4.27
1.08%
5293
0.24%
0.85%
0.30%
5095.18 bpd
4527.74 bpd
4.96
195.69"
189.42"F
0.82
10767.76 bpd
9658.57 bpi
14.88
208%
213%
0.91
1.98%
1.91%
1.27
5269.79 bpd
5692.06 bpd
5.14
136.76OF
124.9"F
6.90
8528.4 bpd
objectivefuuction value
.
i
Remncilcd Value
Measund Value
22.79
350.1 1oF
330.86"F
2.42
19150.33bpd
19788.37 bpd
0.44
-
21.9%
-
2.0
2.34
0.46
-
19.81 MIvlBtulhr
535880
149.5
91.6%
The key result is the drastic drop in Murphree efficiency in the debutanizing
column. These results further support the conclusion that this method (with
proper selection of manipulated variable and reasonable objective functions) is a
valid tool in estimating process conditions, operating parameters. Development
of a problem of this scale without a commercial simulator would be a very
laborious and time consuming endeavor. The time total required to develop and
solve this particular problem was approximately 40 hours to obtain an initial
AspenPlus input file. The time required by AspenPlus to solve the problem was
about 2 hours on an IBM RISC6OOO computer that was being fully utilized by
about 10 other users.
The optimization results can be entered into the original flowsheet model of
the plant (i.e. without optimization code) and the response of the plant to
changes in certain operating variables can now be examined by simply changing
Data reconciliation using AspenPlus
the desired variable in the AspenPlus input file. It is important to remember that
there will always be some degree of model mismatch.
However, when
examining plant responses, this mismatch should remain constant. Thus, the
magnitude of the changes observed in the model variables should be fairly close
to the changes that would be seen in the plant given the same changes (assuming
the change is not sufficiently large to discredit the model results).
Conclusions and Notes
1.
Steady state simulation packages equipped with optimization routines can be
used to perform data reconciliation and obtain accurate results. This
approach can be used to reconcile linear and nonlinear problems via the
minimization of a weighted least squares objective function by varying
appropriateflowsheet variables.
2. Example 5 illustrates how this approach can be used to construct and solve a
data reconciliation and parameter estimation problem involving different
types of process variables for a complex nonlinear process.
3. The time required to solve a complex data reconciliation problem is greatly
reduced through the use of this approach since the model and solution
strategy can be constructed using existing software.
4. The use of sequential modular simulation system such as AspenPlus
necessitates the selection of surrogate decision variables to affect a change in
the primary decision variables. This requires some additional insight and
understanding of the use of the simulation system. This limitation would be
obviated by the use of an equation oriented system.
5. Model mismatch will always exist. However, the agreement of the absolute
values of the variables is not nearly as important as matching the
magnitudes of the changes seen in the variables values given some change
in input.
181
M.Piccolo, P.L. Douglas and P L Lee
References
Aspen Technology. 1993. AspenPlus Users Manual, AspenTech Ltd.,
Cambridge, Mass., USA.
Crowe, C.M., 1992. "Short Course on Real-Time Optimization".
C.M. Crowe, Y.A. Garcia Compos and A. Hrymak, 1983, Reconciliation of
procesS Flow Rates by M a m x Projection Part I : Linear Case, AIChE J.,
29,6,881-888.
C.M.Crowe, 1986, Reconciliation of Process Flow Rates by Matrix Projection
Pan II :The Nonlinear Case, AIChE J., 32,4,616-623.
C.M.Crowe, W. Holly and R. Cook, 1989, Reconciliation of Mass Flow Rate
Measurements in a Chemical Extraction Plant, Can. J. Chem. Eng., 67,595601.
Gams 1994, Release 2.25 GAMS. A User's Guide, The Scientific Press, South
San Fransisco, California, USA.
J.Y. Keller, M. Zasadzinski and M. Darouach, 1992, Analytical Estimator of
Measurement Error Variances in Data Reconciliation, Comput. Chem. Eng.,
16,3, 185-188.
M.J. Liebman, T.F. Edgar and L.S.Lasdon, 1992, Efficient Data Reconciliation
and Estimation for Dynamic Processes using Nonlinear Programming
Techniques, Comput. Chem. Eng., 16,10/11,963-986.
R.J. McDonald and C.S. Howat, 1988, Data Reconciliation and Parameter
Estimation in Plant Perfomance Analysis, AIChE J., 34,1,1-8.
G.R.Stephenson and C.F.Shewchuk, 1986, Reconciliation of Process Data with
Process Simulation, AIChE J., 32,2,247-254.
H. Takiyama, Y. Naka and E. Oshima, 1991, Sensor Based Data Reconciliation
Method and Application to the Pilot Plant, J. Chem. Eng. Japan, 24, 3,339345.
I.B. Tjoa and L.T. Biegler, 1991, Simultaneous Strategies for Data
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Received: 3 September 1995; Accepted afier revision: 3 May 1996.
182
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