Virtual sensing method and system for controlling a composition variable in a urea production process

Abstract

The invention relates to a virtual sensing method and system for controlling at least one composition variable in a urea production process, based on a plurality of online measured process variables and a model, wherein the model is used to estimate, during the urea production process, the at least one composition variable indicative of a urea content on the basis of the plurality of online measured process variables, and modifying at least one of the plurality of online measured process variables for ensuring that a value of the at least one composition variable is within a predetermined range. The invention also relates to determining the model.

Claims

1. A virtual sensing method for controlling at least one composition variable in a urea production process, exclusively based on a plurality of online measured process variables and a model, wherein the model is used to estimate, during the urea production process, the at least one composition variable, on a basis of the plurality of online measured process variables, wherein the composition variable is selected from a group of a N/C ratio defined as a ratio between a total equivalent NH.sub.3 and a total equivalent CO.sub.2, a H/C ratio defined as a ratio between a total equivalent H.sub.2O and a total equivalent CO.sub.2, and/or an extent of reaction defined as a ratio between urea and total equivalent CO.sub.2, wherein the method includes modifying at least one of the plurality of online measured process variables for ensuring that a value of the at least one composition variable is within a predetermined range, wherein the model is obtainable by: retrieving, over a first period of time during the urea production process, a plurality of online measurement data relating to a plurality of predetermined process variables by means of a plurality of sensors arranged in a urea synthesis plant, the plurality of predetermined process variables comprising at least one of a group consisting of a flow rate, a liquid level, a temperature, and a pressure; retrieving, at time points within the first period of time, a plurality of offline measurement data of the at least one composition variable; and processing the plurality of online and offline measurement data and performing a statistical analysis for identifying the model, wherein the statistical analysis comprises an algorithm for performing a principal component analysis or a partial least squares analysis, wherein the process variables are selected from a group comprising a CO.sub.2 feed flow, CO.sub.2 flow to CO.sub.2 stripper, a passivation air flow to reactor, a passivation air flow to any stripper, a carbamate recycle flow to carbamate condenser, a carbamate recycle flow to HP scrubber, a steam flow from carbamate condenser, a total flow of NH.sub.3, a flow of NH.sub.3 to carbamate condenser, a flow of NH.sub.3 to carbamate ejector, a flow of NH.sub.3 to reactor, a steam consumption of thermal stripper, a steam consumption to CO.sub.2 stripper, steam to (any) strippers pressure, synthesis pressure at reactor top, carbamate condenser steam pressure, pressure of NH.sub.3 feed, CO.sub.2 stripper vapor exit temperature, CO.sub.2 stripper liquid exit temperature, temperature of NH.sub.3 feed, temperature carbamate, temperature at reactor top, temperature of middle of reactor, temperature of urea solution from reactor, temperature of bottom of reactor, thermal stripper vapor exit temperature, thermal stripper liquid exit temperature, pressure difference in urea reactor outlet valve, liquid level in reactor, liquid level in HP Scrubber, liquid level in HP Separator, wherein the plurality of online measured process variables obtained by means of online measurements over a second period of time different from the first period of time are provided as inputs to the identified model, wherein the model provides as an output at least one predicted composition variable, which is being controlled.

2. The method according to claim 1, wherein gathered sensor data from online measurements are stored in a data store, wherein a reduced data set is obtained from the data store, wherein the model is identified based on the reduced data set, the model providing a correlation between the reduced data set and the at least one composition variable.

3. The method according to claim 1, wherein a set of 2 to 6 process variables is used.

4. The method according to claim 1, wherein a set of process variables is used including at least one or more reactor temperatures and a steam flow to a thermal stripper.

5. The method according to claim 1, wherein a set of process variables is used including at least three of a group consisting of a steam consumption of a first NH.sub.3 stripper, a temperature of the urea solution from a reactor, a temperature of a gas outlet of a second NH.sub.3 stripper, a temperature of a NH.sub.3 feed, a temperature in the middle of the reactor, and a temperature at the reactor top.

6. The method according to claim 1, wherein the urea production process is a CO.sub.2 stripping process and/or thermal stripping process.

7. The method according to claim 1, wherein the urea production process is an isobaric double recycle process.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) The invention will further be elucidated on the basis of exemplary embodiments which are represented in a drawing. The exemplary embodiments are given by way of non-limitative illustration. It is noted that the figures are only schematic representations of embodiments of the invention that are given by way of non-limiting example.

(2) In the drawing:

(3) FIGS. 1a-1d show schematic diagrams of embodiments of a urea synthesis plants;

(4) FIGS. 2a-2d show schematic diagrams of embodiments of a urea synthesis plants;

(5) FIG. 3 shows a schematic diagram of an embodiment of a correlation matrix of a model;

(6) FIG. 4 shows a plot comparing model prediction data with offline measurement data;

(7) FIG. 5 shows a plot comparing model prediction data with offline measurement data;

(8) FIG. 6 shows a plot comparing model prediction data with offline measurement data;

(9) FIG. 7 shows a time plot with online and offline measurements;

(10) FIG. 8 shows a schematic diagram of a method; and

(11) FIG. 9 shows a schematic diagram of a method.

DETAILED DESCRIPTION

(12) FIG. 1a shows a schematic diagram of an example of a urea synthesis plant 100. In the example of FIG. 1a, it concerns a plant 100 implementing a conventional urea synthesis plant. In this example, the plant 100 includes a CO.sub.2 compressor 20, a High-pressure ammonia pump 34, a urea reactor 22, a medium-pressure decomposer 27b, an ammonia-carbamate separation column 37, a Low-pressure decomposer 27c, an evaporation section 30, a finishing Section 49 (in the schematic a prilling section is shown, but as alternative other finishing sections can be installed, such as granulation section, spherodizer section, crystallization section, blending with ammonium nitrate solution to produce liquid urea ammonium nitrate), a waste water treatment 50 (in the schematic a desorber 50 (wastewater stripper) is shown, but as alternative a section including a hydrolizer, to remove traces of urea from water, can be installed) and a vacuum condensation section 31.

(13) FIG. 1b shows a schematic diagram of an alternative example of a urea synthesis is plant 100. In the example of FIG. 1b it concerns a plant 100 implementing the Stamicarbon CO.sub.2-stripping urea process. In this example, the plant 100 includes a CO.sub.2 compressor 20, a hydrogen removal reactor 21, a urea reactor 22, a high-pressure stripper 23, a high-pressure carbamate condenser 24 (high pressure carbamate condenser can be alternatively a falling film type as in the schematic or a pool condenser type), a high-pressure scrubber 25, a high pressure carbamate ejector (XX), a low-pressure absorber 26, a low-pressure decomposer and rectifier 27, a pre-evaporator 28, a low-pressure carbamate condenser 29, an evaporation section 30 (alternatively made by one or two evaporators, according if the finishing section is a prilling section, granulation section, spherodizer section, crystallization section, or UAN section), a vacuum condensation section 31, and a process condensate treatment section 32. In FIG. 1b CW indicates cooling water, and TCW indicates tempered cooling water.

(14) FIG. 1c shows a schematic diagram of an alternative example of a urea synthesis plant 100. In the example of FIG. 1c it concerns a plant 100 implementing the Snamprogetti self-stripping process. In this example, the plant 100 includes a CO.sub.2 compressor 20, a urea reactor 22, an high pressure ejector 33, a high-pressure ammonia pump 34, a carbamate separator 35, a high-pressure carbamate condenser 24, a high-pressure carbamate pump 36, a high-pressure stripper 23, a medium-pressure decomposer and rectifier 27a, an ammonia-carbamate separation column 37, an ammonia condenser 38, an ammonia receiver 39, a low-pressure ammonia pump 40, an ammonia scrubber 41, a low-pressure decomposer and rectifier 27, a low-pressure carbamate condenser 29, a low-pressure carbamate receiver 42, a low-pressure off-gas scrubber 43, a first evaporation heater 44, a first evaporation separator 45, a second evaporation heater 46, a second evaporation separator 47, a wastewater treatment section 48, and a vacuum condensation section 31. In FIG. 1c CW indicates cooling water.

(15) The urea synthesis process performed in the plants 100 of FIGS. 1a, 1b 1c and 1d is well known to the person skilled in the art and need not be further elucidated here.

(16) FIG. 1d shows a schematic diagram of an alternative example of a urea synthesis plant 100. The urea synthesis plant 100 may for example be an isobaric double recycle (IDR) process, which can be particularly integrated. In this example, the plant 100 includes a urea rector 22, a thermal stripper 23a, a CO.sub.2 stripper 23b, a carbamate condenser 24, a carbamate separator 35

(17) Disturbances in the process generally give composition variations in a part of the synthesis process, and damping these variations via active control can be important for stabilizing the operation of the urea synthesis process at optimal or near-optimal conditions.

(18) The composition of flows in the synthesis process is mainly characterized by the content of CO.sub.2, NH.sub.3, H.sub.2O and urea in the reactor 22. For convenience, one defines the N/C ratio as the ratio between total equivalent NH.sub.3 and total equivalent CO.sub.2 and the H/C ratio as the ratio between total equivalent H.sub.2O and total equivalent CO.sub.2. The urea content can be stated in terms of weight fraction or extent of reaction, that is the ratio between urea and total CO.sub.2. These composition figures are not directly measured. Typically, the costs involved for direct measurement of these composition variables, for example by means of a dedicated measurement unit, are very high. Also integration of such units in existing plants may be challenging.

(19) Online measurements of flows, temperatures, levels and pressures can be analyzed by means of statistical methods to estimate the unknown compositions or composition variables. The predicted composition variables, such as the N/C ratios, can be correlated to the energy consumption of the plant. Combining physical modelling with statistical analysis may provide a model which is not yet sufficiently robust to handle measurement uncertainty.

(20) Moreover, both CO.sub.2 and parts of the NH.sub.3 may not enter the reactor 22 directly, but e.g. via stripper 23 (23a, 23b), and/or carbamate condenser 24. Additionally, vapors from thermal stripping of reactor effluent may be recycled into the reactor. In such a case, a physical model may be hard to establish, and may not provide sufficient accurate results for establishing a predictive unit operation model of the stripper. On the other hand, often in urea production plants, laboratory analysis samples of the reactor effluent are taken on a regular, e.g. daily, basis. Hence, sufficient plant data may be available. This fact allows to collect a reasonable amount of plant data as a basis for a statistical/empirical model.

(21) In FIGS. 1a, 1b, 1c and 1d an overview of urea production processes in a urea synthesis plant 100 is illustrated. It is appreciated that the method and system according to the invention can also be used with other types of a urea synthesis plant.

(22) For both an empirical model and physical model, the scope of the system plays an important role. A too narrow scope does not capture sufficient process characteristics as a basis for a reliable model for providing accurate estimations or predictions of a composition variable. A too wide scope includes more process noise and dynamics, but also requires a higher number of independent variables, i.e. degrees of freedom, to identify a suitable model.

(23) FIGS. 2a, 2b,2c and 2d show schematic diagrams of examples of a urea synthesis plant 100. In this figure, potentially relevant instrumentation/sensors for providing online process variable measurements are provided for the exemplary urea synthesis plant 100. It will be appreciated that other types of a urea synthesis plant 100 can also be employed. The sensors can provide online measurements. The table below describes tags linked to the sensors.

(24) TABLE-US-00001 Tag Process Variable Unit F1 CO.sub.2 feed flow t/h F2 CO.sub.2 flow to reactor t/h F3 CO.sub.2 flow to CO.sub.2 stripper t/h F4 Passivation air to reactor kg/h F5 Passivation air to (any) stripper kg/h F6 Total carbamate recycle flow t/h F7 Steam flow from carbamate condenser t/h F8 Total flow of NH.sub.3 t/h F9 Flow of NH.sub.3 to high pressure t/h carb. condenser F10 Flow of NH.sub.3 to high pressure t/h carb. ejector F11 Flow of NH.sub.3 to reactor t/h F12 Steam consumption of thermal stripper t/h F13 Steam consumption of the CO.sub.2 stripper t/h P1 Pressure of steam to (any) stripper barg P2 Synthesis pressure at reactor top barg P3 Pressure of steam from carbamate barg condenser P4 Pressure of NH.sub.3 feed barg P5 Pressure of CO.sub.2 feed barg T1 CO.sub.2 stripper vapor exit temperature ° C. T2 CO.sub.2 stripper liquid exit temperature ° C. T3 Temperature of NH.sub.3 feed ° C. T4 Temperature of CO.sub.2 feed ° C. T5 Temperature at reactor top ° C. T6 Temperature in middle of reactor ° C. T7 Temperature of urea solution ° C. from reactor T8 Temperature in bottom of reactor ° C. T9 Temperature of vapors from reactor ° C. T10 Thermal stripper vapor exit ° C. temperature T11 Thermal stripper liquid exit ° C. temperature T12 Temperature of carbamate to high ° C. pressure carbamate ejector T13 Temperature of carbamate to ° C. high pressure condenser T14 Temperature of carbamate to ° C. high pressure Scrubber T15 Temperature of carbamate to reactor ° C. DP1 Pressure difference in valve mbar outlet from reactor L1 Liquid level in reactor % L2 Liquid level in high pressure scrubber % L3 Liquid level in high pressure Separator % V1 Valve position for reactor level % control

(25) Data analysis may be performed on the obtained laboratory data relating to the offline measured at least one composition variable. The laboratory data may for instance be obtained in a format containing time stamp and molar concentration of NH.sub.3, CO.sub.2, Urea and/or H.sub.2O. For example, the samples may be taken at a time within an interval of approximately 30 minutes of the reported sampling time.

(26) Online measurements, by means of sensors, of the plurality of process variables can be received as event-based raw data having a relatively high time resolution, e.g. down to one sample per second (i.e. 1 Hz). Other sampling frequencies can also be employed. Data can be averaged over, e.g. fixed time, intervals, e.g. before storage. The data can e.g. be averaged over five minute intervals. Online data can be collected for a period of time (e.g. two-hour period) around the nominal analysis sample times (e.g. −90 minutes to +30 minutes). For each offline measurement or laboratory analysis sample, the data may be rejected if a. the laboratory analysis does not sum to a value between 97 and 103%; b. the online data indicates abnormal operation; and/or c. the variation in online data indicates dominating transitional behavior.

(27) As a result, a data-set of validated samples can be obtained, containing both offline measurements (i.e. laboratory measurements) and, e.g. averaged, online measurements (here online-data).

(28) The above steps can be carried out if necessary. Additional steps may be added, or some steps may be omitted. Many of the provided exemplary steps can be considered as optional.

(29) In a next step, the raw laboratory analysis values of the offline measurements can be converted to the desired and algebraic independent mole ratios N/C, H/C and X, here defined as

(30) $N/C=\frac{x_{{\mathrm{NH}}_3}+2x_{\mathrm{Urea}}}{x_{{\mathrm{CO}}_2}+x_{\mathrm{Urea}}}$$H/C=\frac{x_{H_{2}O}-x_{\mathrm{Urea}}}{x_{{\mathrm{CO}}_2}+x_{\mathrm{Urea}}}\mathrm{and}$$x=\frac{x_{\mathrm{Urea}}}{x_{{\mathrm{CO}}_2}+x_{\mathrm{Urea}}}$

(31) The laboratory analyses are giving weight fractions w.sub.i, and these are converted to mole fractions x.sub.i by using molecular weights M.sub.i via

(32) $x_i=\frac{w_i}{M_i}{\left(\underset{j}{.Math.}\frac{w_j}{M_j}\right)}^{-1}$

(33) Furthermore, a mass feed ratio FR is introduced, relating total NH.sub.3 feed to total CO.sub.2 feed:

(34) $\mathrm{FR}={\left(\frac{{\stackrel{.}{m}}_{{\mathrm{NH}}_3}}{{\stackrel{.}{m}}_{{\mathrm{CO}}_2}}\right)}_{\mathrm{feed}}=\frac{\mathrm{Value}\mathrm{of}F8}{\mathrm{Value}\mathrm{of}F1}$

(35) FIG. 3 shows a schematic diagram of an embodiment of a correlation matrix of a model. In this example, a categorical variable OC has been introduced in the data set, defined as zero for all samples before a certain date, and one for all samples beyond that date, to account for a major change in operation conditions were implemented on that certain date. FIG. 3 shows the correlation coefficient matrix for the obtained dataset, wherein the column headers are identical to the row headers. The correlation matrix includes mole ratios from laboratory analysis (see rows 0-2 of the matrix), online measurements (see rows 3-30 of the matrix), and derived variables FR (see row 31 of the matrix) and OC (see row 32 of the matrix). Correlation coefficients (corr) are shown as integers, i.e. floor(10.Math.corr), e.g. +2 means a positive correlation between 0.20 and 0.29. All coefficients with absolute value less than 0.2 are omitted in this example.

(36) In this example, the N/C ratio is well correlated to the reactor temperatures (see rows 12-20, being encircled in the matrix). Moreover, here a pressure drop over a valve between reactor and stripper is found to be an important variable (see rows 28-30, being encircled in the matrix), as it indirectly measures the density of the reactor content. Due to natural circulation with the total head and density as driving force, the liquid level and the pressure drop are coupled via the flow, which is primarily given by other process constraints.

(37) The change of operation conditions (OC) reveals that many process variables were significantly changed, such as synthesis pressure, carbamate recycle flow and steam flow to the CO.sub.2 stripper. The analyzed urea content also significantly increased. A most predictive linear model is obtained by fitting a parameter vector p and constant offset p.sub.0 to minimize the residuals of the equation:
(N/C).sub.i=p.Math.x.sub.i+p.sub.0

(38) for all samples i. Here, x.sub.i is a complete set of available online measurements of the predetermined process variables, as from index 3 to 27 in the exemplary correlation matrix, see FIG. 3. In this example, the resulting model accounts for 78% of the observed variance in N/C. With the given online data, this can be considered as a theoretical limit. The remaining 22% of variance is not correlated to any of the observable process variables, and a major part of it might be measurement noise, uncertainties of laboratory measurements or the like.

(39) To get an understanding of this limit, the variance of laboratory analysis error: σ.sup.2.sub.lab is considered. The observed R.sup.2 value (=0.78) is defined based on variances as

(40) $R^2=1-\frac{\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{lab}}-{\left(N/C\right)}_{\mathrm{calc}}\right]}{\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{lab}}\right]}=1-\frac{\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{true}}-{\left(N/C\right)}_{\mathrm{calc}}\right]+{\sigma }_{\mathrm{lab}}^2}{\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{lab}}\right]}$

(41) Even with a perfect model, i.e. (N/C).sub.calc=(N/C).sub.true, the limiting condition can be given as

(42) $R^2<1-\frac{{\sigma }_{\mathrm{lab}}^2}{\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{lab}}\right]}\iff {\sigma }_{\mathrm{lab}}^2<\mathrm{var}\left[{\left(N/C\right)}_{\mathrm{lab}}\right]\left(1-R^2\right)$

(43) For the given exemplary data set, var[(N/C).sub.lab ]=0.0094, hence σ.sub.lab<0.045.

(44) A laboratory analysis error in N/C ratio of approximately 0.045 is more than reasonable, as it relates to an error in the individual species analysis of approximate approximately 0.5%.

(45) Hence, for the given exemplary data set, it may not be expected that an identified model reaches a R.sup.2 value larger than 0.78, and this value will due to the limited number of samples include false correlations between offline measurement (i.e. laboratory measurement) error and online measurement of process variables.

(46) Furthermore, when utilizing all available online and offline measurements, the regressed model may not be robust against measurement errors and process noise. For instance, the process variable tag P1 receives the coefficient 0.8, hence a realistic pressure variation by approximately 0.5 bar would generate extreme predictions of N/C ratios, that is approximately 0.4.

(47) Advantageously, the total set of independent variables can be reduced to those which are really correlated to the N/C ratio. According to FIG. 3, these are for instance the reactor temperatures and the steam flow to the thermal stripper 22. The reactor temperatures can be strongly correlated to each other. Including all of reactor temperatures as independent variables may trigger the same issues as described above. The following equation represents a reasonable model with three independent variables:
=3.4774+0.0120(T−185° C.)−0.071(T.sub.6−185° C.)++0.0289({dot over (F)}.sub.12−25t/h) with T=¼(T.sub.5+T.sub.6+T.sub.7+T.sub.8)

(48) This model in this example, however, only explains 44% of the actual variance of N/C(R.sup.2=0.44). By including the pressure drop and level measurements, the results of this approach can be further improved. However, generally, with the given set of online measurements of the process variables, a compromise can be found between robustness and the predictive properties.

(49) In an advantageous embodiment, a steady-state limitation is implemented for identifying the model. However, alternatively, a dynamic model can be identified based on step response experiments or on reliable physical modelling of process dynamics. The step-test approach may require frequent sampling of synthesis fluid (cf. composition variable) by means of offline measurements, which need to be analyzed in the laboratory. Frequent sampling may not be required when employing a steady-state approach.

(50) With physical modelling, time constants could possibly be estimated to supplement dynamics information to the steady-state gain model obtained by data regression. That is, knowing the steady-state effect of a measured process variable on the N/C ratio by steady-state data analysis, the physical model needs to supply the transient information. Such model could be implemented either by means of for example a state filter (Kalman filter) or as individual delays of measurements using a quasi-steady state model.

(51) A steady-state model can be time-efficient, and more easy to obtain than a dynamic model. This is especially advantageous, since the urea processing plant may comprise numerous recycle flows and therefore very integrated process dynamics. A predictive steady-state model can be provided which does not suffer from the negative effect of transients, which may become amplified, on the predictions of the at least one composition variable, such as for example the N/C ratios.

(52) When the predictive steady-state is implemented into the distributed control system DCS, a steady-state detector could be realized as well, which can be configured to calculate a standard deviation of key measurements over a real-time moving time interval. If this standard deviation is above a certain threshold, defined for each input variable, the predicted N/C ratio values may be flagged or disregarded, since these values may not be accurate (i.e. limited usability of the provided values).

(53) Partial least squares modelling may be employed for obtaining the model. As seen above, a selection of only a few independent variables can result in a significant reduction in R.sup.2, while utilizing all measurements can yield a model which is far too sensitive to disturbances. In an advantageous approach not all the selected process variables are treated as independent variables. For instance, it may be beneficial to utilize many of the online tags for the process variables (see above table), but not treat each of the online tags independently. For example, as already indicated in the equation above, the average temperature can be used.

(54) A systematic approach can be provided by means of an (orthogonal) partial least square method (OPLS). The OPLS method transforms the predetermined input variables to maximize correlation with the output variable (N/C). In this way, only the most correlated transformed input variables can be included into the model. An order parameter k can determine how many of these so-called directions are to be included into the model. Therefore, the OPLS method can help obtaining a predictive model without the risk of over-parameterization.

(55) Since for a urea production process, such as for example shown in FIG. 2d, there may be strong correlation among the available online measurements, an input process variable set can be drastically reduced without significant loss of a predictive quality of the model. Additionally or alternatively, in this way, the robustness of the model against failure of measurement signals of the process variables can be improved.

(56) The OPLS method can be used for identifying an initial order of the model, necessary for capturing a significant correlation between the online measured process variables (cf. online measurements) and the offline measured compositions variable(s) (cf. laboratory analyzed N/C ratio). Subsequently, successively one sensor at a time can be removed, selected by its minimal negative impact on model quality. The OPLS data fit can be repeated in each step. This gives an indication on the model quality in reach for a limited number of sensors involved.

(57) Finally, a (direct sampling) Monte Carlo regression sequence on any combination of sensors can be performed, seeking the maximum R.sup.2 value for a model with limited number of sensors used. Other similar techniques may also be employed. Due to strong correlation of online measurements, it can be seen that multiple distinct sets of sensors give very similar results.

(58) The following table gives coefficients of four exemplary models, obtained by running OPLS with k=4 on 8 random sets of measurements as input for the Monte Carlo regression with 10.sup.5 iterations each.

(59) TABLE-US-00002 Coefficients c_i: (N/C) = C + sum (c_i*x_i) Tag × i Model 1 Model 2 Model 3 Model 4 F1 −0.02450 −0.02230 −0.02603 −0.02641 F13 0.01716 0.01429 0.01625 0.01532 P2 −0.01044 −0.01117 −0.01004 −0.00987 T15 0.04584 0.04624 0.04486 0.04625 T6 −0.06798 −0.03831 −0.07175 −0.07397 T1 0.04859 0.03295 0.04808 0.04590 V1 0.02942 0.02834 0.02799 DP1 −0.00533 T10B −0.00432 T7 −0.02562 P1 0.00017 F12 −0.00285 Constant C 0.73233 4.26689 0.94003 1.63320 R2 [%] 70.6 70.6 70.6 70.7

(60) All these models are of similar quality, i.e. within 70.6%≤R.sup.2≤70.7%. The table contains the four best models for an exemplary urea processing plant 100. It can be seen that all models have similar prediction properties.

(61) FIG. 4(a), (b) shows a plot comparing model prediction data with offline measurement data. It can be seen in FIG. 4(a) that indeed the four different alternative models using online measurement data of a first time period provide similar predictions, closely resembling the offline measurements (N/C lab analyses).

(62) The obtained model can be validated and/or improved, if necessary. In order to validate and/or improve the identified model(s), a second data set can be obtained from the plant, spanning a second time period. The selected set of process variables for building the model can be limited to the most promising candidates of input variables. The periods with available data with regarding offline measurement data (laboratory analysis values) can be combined to obtain a new data set. As can be seen in FIG. 4(b). In this example, due to technical issues, the CO.sub.2 feed flow data was not available in some periods, and no predictions could be made within these time intervals, as all identified models rely on this process variable. While the model still predicts the general trends, a clear deterioration is observed, visible as a bias towards higher N/C predictions. Still, the predictions of all four models remain very similar.

(63) An observed deviation (as e.g. shown in FIG. 4(a), (b)) can for example be caused by: (a) over-parameterization of the models, (b) changes in the urea process (c) significant changes in operation, causing non-linear effects, and/or (d) utilization of operational handles that have not been used equally much in the calibration period.

(64) Option (a) may be rather unlikely, as only four principle components are used, and many different models (depending on the set of selected input variables) give very similar results. Option (b) cannot be ruled out, but such process changes would normally be less dynamic. Both option (c) and (d) can apply, not least caused by significant changes in ambient conditions especially during the second half of the calibration period. The mitigating action for both latter cases is to improve the models by including the new data samples into the calibration. In this example data, several operational changes were implemented since the start date of the second time period.

(65) FIG. 4(b) shows a plot comparing model prediction data with offline measurement data. This figure provides a model validation with more recent data.

(66) Remodeling can be carried out based on a complete data set. A wider data basis yields a model that is more robust against similar effects in the future, a hypothesis that naturally has to be validated over time. In order to obtain new models, a different approach can be followed than to (only) maximize the R.sup.2 value. Due to the lack of calibration data, the priority can be on the predictions of new data, not guaranteed by just maximizing R.sup.2. A statistical tool to quantify this property is the calculation of Q.sup.2, defined as follows:

(67) 1. For all samples (i) in the data set:

(68) a. Exclude the sample (i) and generate a model using all remaining samples in the data set, in this case using the orthogonal partial least squares method. b. Add the deviation of the i.sup.th sample (y.sub.i,calc−y.sub.i,meas).sup.2 to a sum denoted as PRESS. c. Add the deviation of the i.sup.th sample to the mean value (y.sub.i,meas−y.sub.mean).sup.2 to a sum denoted as TSS.
2. Calculate Q.sup.2=1−PRESS/TSS, wherein TSS=total sum of squares

(69) For over-parameterized models, Q.sup.2 rapidly decreases and even becomes negative, that is, the model becomes worse than stating that N/C is constant at its mean value. Maximizing Q.sup.2 gives confidence in the predictive properties of the model, but is expensive to calculate, and the Monte Carlo method to find the best set of processing variables (see tags) may no longer yield the optimal solution in reasonable calculation time. Optionally, the optimization method of simulated annealing can be applied to identify the optimal set of tags.

(70) Using six input processing variables (cf. tags), the highest Q.sup.2 value for a model can be obtained with e.g. four principal components. The operational changes implemented in the second data set promote use of a different set of input variables. The following table shows the coefficients of an advantageous model for the exemplary embodiment of the urea processing plant 100 of FIG. 2d.

(71) TABLE-US-00003 Tag Model 5 F12 −0.009475 T7 −0.001033 T1 0.060801 T3 0.008454 T6 −0.114106 T5 0.031956 Constant 6.022045 Q.sup.2 0.713018 R.sup.2 0.0734279

(72) Exemplary model 5 is configured to predict N/C ratio, based on the complete set of data.

(73) Clearly, the detected model 5 has a Q.sup.2 value very close to R.sup.2, meaning that the model will perform predictions just as good as description of calibration data, if the process and/or its operation does not substantially change. This is expected as the model is an empirical model.

(74) FIG. 5 shows a plot comparing model prediction data with offline measurement data. The plot is for the identified predictive model 5 for the first data set (FIG. 5(a)) and the second data set (FIG. 5(b)). As can be seen in FIG. 5(a), the identified model gives very similar predictions compared to the previously developed models for the first data set, of the first time period. FIG. 5(b) shows the same comparison for the second data set, this is the second time period. Here, the final model succeeds to eliminate the bias that has been observed using the initial models.

(75) FIG. 6 shows a plot comparing model prediction data with offline measurement data, more particularly N/C ratio values as the composition variable). In this figure, the model fit is visualized in a direct comparison plot, showing no significant indications of deviation from a linear relationship.

(76) Optionally, the identified (empirical) models can be extended with an additional data set, for example from an original three months of data to six months of data. Further monitoring and validation against laboratory data is highly recommended. The determined model can be optimal with regard to predictive properties, given the set of available data. Model deterioration can still occur for instance with changing ambient conditions (towards summer) or operational changes. As a consequence of revamp activities, a recalibration of the model may be required.

(77) Such a recalibration can be carried out manually or may be at least partially automatized. Such automation can be achieved by a computer program product configured to read in plant data (either directly from the plant or via data files), and perform the necessary steps for generating a new set of coefficients for the model. The computer program product may be configured to maintain a (file-based) database of historical data that can be reused in the calibration and validation process.

(78) Furthermore, the concept of model-based N/C predicting can be extended to model-based predicting other composition variables, such as for instance a H/C ratio and/or an extent of reaction. An advantage of the N/C ratio as the selected composition variable is that it may be rather easy to predict from online measured process variable data.

(79) The method and system, with or without physical modelling, greatly helps optimizing urea production in urea production plants.

(80) FIG. 7 shows a time plot 200 with online measurements 201 and offline measurements 202. In this example, a plurality of online measurements 201 are carried out at subsequent time steps or time points. Furthermore, a plurality of offline measurements 202 are carried out at subsequent time steps. The model can be constructed on the basis of measurement data obtained in a first time period 203. It is appreciated that a different time period can also be used, for instance including a different time frame and/or other data. It is also envisaged that within a time period 203 particular online and/or offline measurement data is not taken into account for identifying the model. For instance, measurement data at certain time steps can be omitted (e.g. outliers).

(81) The online measured process variables may be sampled at regular intervals. The time interval between subsequent offline measurements is typically larger compared to the time interval between online measured process variables. This can for instance be due to the fact that measurements of online process variables are rather easy to obtain compared to the offline measurements of the at least one composition variable (involving lab test).

(82) The plurality of offline measurement data 202 can be obtained by sampling the at least one composition variable at different time points. The results of the offline measurements can be obtained for the time step at which an offline sample was taken for determining the at least one composition variable. However, the results of the offline measurement, for instance obtained by means of a lab test, can be obtained at a later time. The lab tests may take for example several hours, while the online measurements can be carried out frequently, or in real-time (or quasi real-time).

(83) FIG. 8 shows a schematic diagram of a method 1000 for controlling a urea production process based on a plurality of online measured process variables and a model. In a first step 1001, the model is used to estimate, during the urea production process, at least one composition variable indicative of a urea content on the basis of the plurality of online measured process variables. In a second step 1002, at least one of the plurality of online measured process variables is modified for ensuring that a value of the at least one composition variable is within a predetermined range. The model is obtainable by retrieving, over a first period of time during the urea production process, a plurality of online measurement data relating to a plurality of predetermined process variables by means of a plurality of sensors arranged in the urea synthesis plant, the plurality of predetermined process variables comprising at least one of the group comprising a flow rate, a liquid level, a temperature, and a pressure; retrieving, at different time steps within the first period of time, a plurality of offline measurement data of at least one composition variable; and processing the plurality of online and offline measurement data and performing a statistical analysis for identifying the model for predicting the at least one composition variable on the basis of the plurality of predetermined process variables.

(84) FIG. 9 shows a schematic diagram of a method 2000 for obtaining a model for a urea production process. In a first step 2001, over a first period of time during the urea production process, a plurality of online measurement data relating to a plurality of predetermined process variables are retrieved by means of a plurality of sensors arranged in the urea synthesis plant, the plurality of predetermined process variables comprising at least one of the group comprising a flow rate, a liquid level, a temperature, and a pressure. In a second step 2002, at different time steps within the first period of time, a plurality of offline measurement data of at least one composition variable are retrieved. In a third step 2003, the plurality of online and offline measurement data are processed and a statistical analysis is performed for identifying the model for predicting the at least one composition variable on the basis of the plurality of predetermined process variables.

(85) The orthogonal partial least squares algorithm can be implemented in different ways. As already indicated above, the data from measurements can be collection, (re-)arranged and/or down-sampled in various ways, if necessary.

(86) It will be appreciated that the method may include computer implemented steps. All above mentioned steps can be computer implemented steps. Embodiments may comprise computer apparatus, wherein processes performed in computer apparatus. The invention also extends to computer programs, particularly computer programs on or in a carrier, adapted for putting the invention into practice. The program may be in the form of source or object code or in any other form suitable for use in the implementation of the processes according to the invention. The carrier may be any entity or device capable of carrying the program. For example, the carrier may comprise a storage medium, such as a ROM, for example a semiconductor ROM or hard disk. Further, the carrier may be a transmissible carrier such as an electrical or optical signal which may be conveyed via electrical or optical cable or by radio or other means, e.g. via the internet or cloud.

(87) Some embodiments may be implemented, for example, using a machine or tangible computer-readable medium or article which may store an instruction or a set of instructions that, if executed by a machine, may cause the machine to perform a method and/or operations in accordance with the embodiments.

(88) Various embodiments may be implemented using hardware elements, software elements, or a combination of both. Examples of hardware elements may include processors, microprocessors, circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), logic gates, registers, semiconductor device, microchips, chip sets, et cetera. Examples of software may include software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, mobile apps, middleware, firmware, software modules, routines, subroutines, functions, computer implemented methods, procedures, software interfaces, application program interfaces (API), methods, instruction sets, computing code, computer code, et cetera.

(89) Herein, the invention is described with reference to specific examples of embodiments of the invention. It will, however, be evident that various modifications, variations, alternatives and changes may be made therein, without departing from the essence of the invention. For the purpose of clarity and a concise description features are described herein as part of the same or separate embodiments, however, alternative embodiments having combinations of all or some of the features described in these separate embodiments are also envisaged and understood to fall within the framework of the invention as outlined by the claims. The specifications, figures and examples are, accordingly, to be regarded in an illustrative sense rather than in a restrictive sense. The invention is intended to embrace all alternatives, modifications and variations which fall within the spirit and scope of the appended claims. Further, many of the elements that are described are functional entities that may be implemented as discrete or distributed components or in conjunction with other components, in any suitable combination and location.

(90) In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word ‘comprising’ does not exclude the presence of other features or steps than those listed in a claim. Furthermore, the words ‘a’ and ‘an’ shall not be construed as limited to ‘only one’, but instead are used to mean ‘at least one’, and do not exclude a plurality. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to an advantage.