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 Reconciliation and Gross Error Detection of Nonlinear Systems, Comput. Chem. Eng.. 15,10,679-690. Received: 3 September 1995; Accepted afier revision: 3 May 1996. 182

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