Bottom-up Modeling of the Steam Consumption in Multipurpose

Ind. Eng. Chem. Res. 2008, 47, 7323–7334

7323

Bottom-up Modeling of the Steam Consumption in Multipurpose Chemical Batch Plants Focusing on Identification of the Optimization Potential Andrej Szïjjarto, Stavros Papadokonstantakis,* Ulrich Fischer, and Konrad Hungerbu¨hler Safety & EnVironmental Technology Group Institute for Chemical- and Bioengineering, Swiss Federal Institute of Technology (ETH), CH-8093 Zu¨rich, Switzerland

A detailed approach for modeling the steam consumption in a multipurpose chemical batch plant was developed, tested, and used for analysis of the energy-efficiency. The main advantage of the approach presented in this paper compared to available modeling approaches is the ability to describe the transient steam consumption. Thus, the new approach can be used for the dynamic optimization of batch operations with respect to the energy efficiency. The bottom-up method was implemented by modeling particular unit operations (UOs) in a case study plant, and validation was accomplished with direct measurements on both UO and building level. The principle of the bottom-up model is a detailed energy balance of each particular UO for which process parameter measurements are necessary as input data. These were extracted from the measurements archive of the case study plant for a period of two months. Process data from almost 1000 sensors installed in ca. 100 UOs were acquired, transformed into a time-series with common time basis, and used as an input data for the model. Special attention was paid to model the losses of the UOs because in earlier studies it was found that these are significant. Loss models were developed in the form of empirical parametric equations considering the losses due to radiation and the internal losses in the heating/cooling system due to inefficient operation. The parameters of the loss models were fitted, based on the developed methodology, to steam measurements of 4 UOs and consequently integrated into the overall bottom-up model for modeling other UOs as well. The energy usage efficiency of the UOs was inferred and the optimization spots were identified. The results in the case study plant have indicated that the energy savings potential for particular UOs with low steam-usage efficiency can be easily identified and serve as a good hint for the overall plant energy auditing and steam consumption optimization. 1. Introduction In the specialty chemicals production energy represents approximately 10% of the overall cost,1 making it an important item in the inter- and intraenterprise competition. This percentage becomes more important if it is considered that 60% of the overall cost is fixed and refers to raw materials cost, leaving in this way 40% for potential cost savings. Moreover, the significant boost of the energy prices in the last years has intensified the efforts of the manufacturers for more energy efficient strategies in plant operation. Although some energy losses during chemical processes are unavoidable according to fundamental laws of physics and thermodynamics, a major part can be viewed as potential for embracing efficient technologies and practices. For example, the losses of the energy utility used for heating in the chemical batch processes can reach more than 50% of the overall heating utility consumption for particular process units.2 Therefore, the energy optimization potential is significantly high in these units. Since the heating energy utility in the chemical industry is mostly steam, this study is focused on the steam as an energy utility with high savings potential. Estimates of practical energy savings available to industry with low effort optimization steps range from 10 to 20%.3,4 The energy consumption of chemical processes can be estimated using nonintensive life cycle inventory methods.5,6 These rely on the “cradle to grave” environmental impact analysis for the whole life cycle of the chemical products. Application of such methods may produce chemical product specific indicators, for example, cumulative energy demand.7 * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +41 44 6334449. Fax: +41 44 6321189.

Then, for a given process the input and output substances can be identified, and using the aforementioned indicators the process energy demand can be estimated. However, for the optimization of the energy utilities consumption, a “gate to gate” process specific approach with high results resolution is necessary. A lot of research effort has been dedicated to optimization of the individual batch unit operations (UO)s, in particular batch reactors,8-11 but not with a focus on energy consumption. Although the rigorous models for the individual UOs are precisely describing the behavior of a specific equipment, the application in plantwise scale is a problem because of necessary extensive modeling and computational effort as well as lack of detailed properties data especially in the case of high molecular organic compounds.12 On the other hand, the energy optimization of the continuous processes has reached the adult stage represented by the pinch analysis and process integration.13 Although these methods were also applied for the batch chemical processes,14,15 they have not been proven as appropriate for continuous processes,16

Figure 1. Scheme of bottom-up modeling.

10.1021/ie071291o CCC: $40.75  2008 American Chemical Society Published on Web 09/06/2008

7324 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008

and specific changes can be proposed on the basis of the analysis of the results. Moreover, the modeling results significantly simplify the identification of the energy saving potential in the observed multipurpose chemical batch plant. Namely, the UOs with highest energy utilization inefficiency can be identified. The rest of the paper is structured into model and case study description sections, focusing mainly on the loss models development. Accuracy and applicability of the models as well as the optimization potential is discussed in the results section followed by the conclusions. 2. Bottom-up Modeling Approach for Steam Consumption

Figure 2. Heating/cooling energy flows in UO (reactor).

mainly because of the necessary installation of the heat storage tanks which increase the costs of the batch process integration.17,18 More suitable tools for the optimization of energy consumption in the batch chemical processes seem to be the models describing particular steps of the batch production. These models allow the study of “what-if” scenarios to minimize the energy consumption of the process. Bieler et al. (2003)19 showed the applicability of the top-down modeling in the monoproduct and multiproduct chemical batch plants of low product mixture variability. The production and energy consumption of these plants can be well correlated on the basis of statistical models; however the level of detail of the model results is relatively low, because it is related to the overall plant energy consumption and can not be traced in the product-line or apparatus level. Bieler et al. (2004)2 presents the bottom-up modeling approach which comprises UO-based energy balances, and their results can be used for targeting the highest energy consumers, tracing in this way the most promising units from an energy-optimization point of view. Their bottom-up model was based on the standard batch data defined in the process step procedure. This restricts the model only to predicting the integral steam consumption of the UOs and the applicability for the optimization is very limited. Moreover the model cannot capture the batch-to-batch variability of the energy utility consumption, which might also be an important indicator for the energy efficiency of the production process. Therefore, in this study a more detailed approach was used for the bottom-up modeling, namely the input data for the model are taken directly from the process data historical database of the case study plant in the form of time-series per batch. This approach requires considerably higher computational power to process the real-plant data and analyze the results. However, compression techniques of the time-series can significantly decrease the amount of the processed data preserving the desirable accuracy.20 Therefore the modeling of the steam consumption can be carried out dynamically which enriches the applicability of the models in the field of steam consumption optimization. Furthermore, by utilizing this kind of data, a variety of models in the form of empirical parametric equations were developed to describe the losses due to radiation and the internal losses in the heating/ cooling system due to inefficient operation. The types of the heating/cooling (H/C) system have significant influence on the UO efficiency.21,22 Therefore, the proposed approach in this study was tested for reactors with different types of H/C system (half-pipe coil, double jacketed vessel, direct steam heating). The particular operations carried out in the UO can be investigated from the transient steam consumption point of view

2.1. General Modeling Approach. The basic principle of the bottom-up model is the energy balance using standard or measured process data (e.g., temperature and reaction mass for reactor as UO), physicochemical data of the substances which are processed in the UO (heat capacity, heat of evaporation, heat of reaction), and the process description (recipe or process step procedure) as input data. The type of the input data for the modeling determines the complexity of the modeling procedure and detail level of the results. As shown in Figure 1, the standard input data acquired from the recipes are describing the standard process and are delivering the average or targeted integral energy utility consumption per batch as a result. As an alternative to the standard data, the real production data can be used as an input for the bottom-up model. This approach provides highly detailed results of utility power consumption (energy per time interval of process data measurement) which can be valuable from optimization point of view. Using process data also allows to model not only the energy consumption of individual batches but also of steps within an individual batch. This is particularly interesting for investigation of energy utilization efficiency of different operations that are carried out during a batch, while it also offers the possibility to analyze the influence of the changes of the batch steps on the overall efficiency of the process. Total steam consumption in infinitesimal time interval dEUO,st tot dt can be expressed by UO,st UO,st dEUO,st dEdiss dEloss dEUO,st tot th ) + (1) dt dt dt dt As seen in eq 1, the theoretical part of the bottom-up model, UO,st Eth , represents the thermodynamically determined steam consumption that has to be supplied to the UO to carry out the desired process. Theoretical energy utility consumption can be calculated rigorously for each UO and the accuracy of the calculation is determined by the accuracy of the input data, mainly the physicochemical data (e.g., heat capacities) of chemical substances being processed. Measurement errors of process parameters can have some influence on the results but, compared to the accuracy of the physicochemical data, is considered as insignificant. UO,st Ediss describes the dissipation of turbulent kinetic energy of the stirrer to the heated media, increasing the internal energy and the temperature inside the UO, therefore decreasing the UO,st Etot . UO,st The loss term, Eloss , represents the losses from the heated system which occur because of radiation and heat loss inside the H/C system (e.g., due to simultaneous heating and cooling and/or inefficient heat transfer from the jacket into the reactor).

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7325

Figure 3. Scheme of bottom-up modeling in the case study plant.

where in the absence of kinetic data the reaction energy is assumed to be uniformly distributed over the whole time interval tR. This approximation is not expected to influence the results significantly in the cases of not strongly endothermic or exothermic reactions; however, if the kinetic data are available, the term can be adjusted with respect to them. ∆Tmaterial,i is the difference of the material been processed in the UO in the time interval i, as compared to time interval i - 1: ∆Tmaterial,i ) Tmaterial,i - Tmaterial,i-1

Figure 4. Direct steam heating.

The loss term can be calculated either rigorously with detailed CFD modeling for a particular UO,23 or with empirical/ semiempirical correlations taking into account the process parameters and apparatus specification. A semiempirical approach was developed and used in this study because of its suitability for complex chemical plants with multiple different UOs, for all of which detailed CFD modeling would be infeasible. The energy flows in the investigated UO are depicted in Figure 2. In the scope of this paper, we focus on the steam consumption, therefore the considerable energy flows are Etherm representing the inflow of the heating utility, Ereaction representing the heat of reaction, Ediss standing for the dissipated heat from the stirrer, and Eloss covering the heat losses from the system. On the basis of these terms, the heat balance can be setup for the UO for the time interval ti: UO,st Etot,i ) (mmaterialcp,material + mappcp,app + mH⁄Ccp,H⁄C)∆Tmaterial,i + ti UO,st UO,st ∆hevap∆mevap + mmaterial∆Hr - Ediss + Eloss,i (2) tR

(3)

2.2. Modeling of the Dissipated Mechanical Energy and Losses. Previous analysis of the steam consumption2 has shown that the losses represent an important part (40%) of the overall consumed steam. Therefore, improvement of the steam usage efficiency provides a big potential for energy saving. On the contrary, the dissipated energy from the stirrer is almost negligible from the steam consumption point of view and represents only 1.5% of the overall steam consumption. Therefore, this study focused on modeling the losses, while the dissipated mechanical energy was calculated using simplification according to following equation: UO,st Ediss,i ) ηγPNti

(4)

where PN is the nominal power of the stirrer, η is the efficiency, and γ is the ratio of the actual to the nominal power of the stirrer, typical values being 60% and 28%, respectively.2 Significant effort has been dedicated to develop and test the loss models in order to track the exact source of the losses (radiation losses from the equipment surface, losses in the heating cooling system etc.). The objective is to describe the UO losses in a precise way, while keeping the amount of the necessary input data in a reasonable level. The latter significantly influence the engineering effort invested into energy modeling; therefore, only significant and easy-acquirable data


Figure 5. Steam heating through jacket with (a) direct condensation; (b) hot water circulation. H/C system boundaries are depicted by dashed line. Table 1. Volumetric Flow Rate for Different H/C Systems of the Reactorsa nominal volume [m3]

material

volumetric flow rate of H/C water [m3 h-1]

6.3 10 16 25 6.3 10 16 25 40

SE SE SE SE SS SS SS SS SS

30 45 65 65 40 40 60 60 80

a

Figure 7. Data management scheme.

Material: SS, stainless steel reactor; SE, glass lined steel reactor.

the overall energy consumption using the standard input data. However, its ability to describe the wide variety of the production scenarios (and batch to batch variability) is questionable. Model B. Considering losses in the H/C system: UO,st b ) a(EUO,st Eloss,i th,i )

(6)

On the basis of empirical knowledge, the model assumes that the losses are only due to H/C system inefficiencies (e.g., simultaneous heating and cooling, losses of the fresh steam from the heating cooling system, fouling for jacket type of H/C system, etc.). Model C. Combining radiation losses and H/C system losses: UO,st b ) a(EUO,st Eloss,i th,i ) + kAapp(Tmaterial,i - Tamb)ti

(7)

Model D. Incorporating the filling degree (FD): UO,st UO,st b ) a(1 - FD)(Eth,i ) + kAapp(Tmaterial,i - Tamb)ti (8) Eloss,i

Figure 6. Scheme of losses-model parameters fitting: solid line, process flow; dashed line, data flow.

were used in this study. The following models were developed and tested in the case study plant: Model A. Considering overall thermal losses from the UO described purely by the radiation loss term, used also by Bieler et al. (2004):2 UO,st Eloss,i ) kAapp(Tmaterial,i - Tamb)ti

(5)

In this model the losses from the reactor are described only by the temperature difference between the temperature of the material being processed in the UO and the ambient temperature. This difference is the driving force for the heat transfer from the UO. It has been demonstrated that this approach can describe

This model is similar to model C, but additionally uses the filling degree of the vessel defined as the ratio of the actual reaction mixture volume in the vessel to its nominal volume. The reaction mixture volume is calculated using reaction mass measurements and mixture density data from the case study plant safety documentation. FD theoretical values are ranging from 0 to 1 with a typical value of 0.7 during the energy consumption relevant operations. FD determines the heat transfer area and therefore has potentially an influence on the heating efficiency. 2.3. Fitting of the Model’s Parameters. The parameters of the loss models have to be fitted for particular types of UO using the direct steam measurement as a target value in the fitting procedure. The direct steam measurement should be carried out in the steam measuring period (SMP) covering several batches in order to test the batchwise performance and


Figure 8. Accuracy of the steam consumption calculated form H/C energy balance vs correlation of H/C steam consumption with valve opening.

Figure 9. Influence of the dead time on the modeled energy utility consumption.

stability of the models for different process parameters that are varying during the batch production in longer time. The variability of the process parameters can arise either as a result of the change in the recipe or from inconsistent quality of the processed input materials which can result, for example, in longer processing time. The fitting of the parameters was done on the overall SMP for each particular UO according to eq 10. The assumption is made,

that the thermal losses of the UOs with the same or similar design characteristics as nominal volume (NV), lining material, and H/C system concept can be described with one set of parameters fitted for the UO, where the measurement was carried out. param ) arg min OF(param) (9) In the case of loss model A, the single loss parameter k was fitted by one-dimensional minimization as described by eq 5


for the overall SMP according to:

Table 2. Time-Lag between Modeled and Measured Steam Consumption for Different H/C System Types H/C system type

time-lag [min]

direct steam heating steam heating via a jacket hot water circulation

1 8 11

RSDSMP ) 1 PMRbatch

Table 3. Specifications of the UOs with Steam Measurement average no. of nominal consumption no. of volume [kg steam/ training validation 3 batch] batches batches UO no. H/C type material [m ] UO1 UO2 UO3 UO4

hot water hot water direct direct

SS SS Sgum Sgraph

40 25 25 40

3014 230 2235 5816

8 2 2 4

14 3 3 7

1 Σ (PMRbatch - PMRbatch)2(13) NbatchSMP - 1 batch

where PMRbatch represents the average PMR of all batches produced during investigated SMP and NbatchSMP stands for the number of complete batches produced during the SMP. (3) The dynamic performance of the transient model was evaluated by the coefficient of determination (CD) as follows: CDbatch ) tot,st tot,st tot,st tot,st - EUO,meas,batch )2 - Σ (EUO,meas,i - EUO,pred,i )2 Σ (EUO,meas,i

batch

batch

Σ

batch

for the overall SMP. The objective function for model A (OFA) was defined as follows: tot,st tot,st - Σ EUO,pred,i OFA ) Σ EUO,meas,i

(

SMP

SMP

2

)

(10)

OFA takes into account only the overall model accuracy, since model A was developed to fit the integral steam consumption during SMP and is used as a reference point that represents the approach used by Bieler et al. (2004).2 Fitting of the parameters vector param for the loss models B, C, and D was done by minimizing the objective function (OFBCD), which takes into account also the dynamic behavior of the models B, C, and D. Therefore, the normalized sum of the squares of errors between the measured and the predicted energy consumption for each time-interval was introduced according to the equation: tot,st tot,st 2 - Σ EUO,pred,i + OFBCD ) Σ EUO,meas,i

(

SMP

)

SMP

1

tot,st 2 Σ (Etot,st - EUO,pred,i )(11) nSMP SMP UO,meas,i

where nSMP represents the number of time-intervals in considered SMP. In eq 11 the first part penalizes deviations from the integral and the second part from the differential measured energy consumption, improving the models performance in the case of transient steam consumption modeling. 2.3.1. Evaluation of the Fitting for Particular Models. The steam consumption models should provide reliable results for all ranges of operating conditions, in order to be applicable for the “what-if” analysis and optimization. The accuracy and stability of the steam consumption models were tested versus measurements for particular UOs focusing on the main desired features of the model, which are (1) overall performance of the modelsability to calculate the total steam consumption for investigated period or batch as close as possible to the real one; (2) dynamic performance of the modelsability to model the transient steam consumption in each particular step of the interval in the modeling grid. On the basis of these features, the following indicators were introduced to evaluate the fit of the particular models: (1) The integral model performance was tested with predicted-tomeasured steam consumption ratio (PMR) for each particular batch according to PMRbatch )

tot,st Σ EUO,pred,i

batch

tot,st Σ EUO,meas,i

(12)

batch

(2) The stability of the approach performance per batch was expressed by the relative standard deviation (RSD) of the PMR

tot,st tot,st (EUO,meas,i - EUO,meas,batch )2

(14)

tot,st j UO,meas,j where E represents the average measured steam consumption during the considered batch.

3. Case Study Plant Description The testing of the modeling approaches was carried out in a multipurpose batch plant producing around 50 different fine chemical products per year. The goal was to model the overall steam consumption of the production building including each relevant UO for the steam consumption. The overview of the plant is given in Figure 3. The steam consumption was directly measured in the case of continuous apparatus and infrastructure using permanently installed steam measurement. The continuous apparatus was represented by solvent regeneration distillation columns and thin film evaporators and the infrastructure included the off-gas scrubbers and space heating. In the case of the apparatus operated in batch mode the steam consumption was modeled using developed models as discussed in section 4.1. The level of modeling detail was divided into two categories on the basis of the importance of modeled UO from the optimization point of view for the specific case study: (1) Approximate modeling, in the case of paddle dryers and heating chambers used for preheating of substances with high viscosity stored in the vessels, where the model A with integral loss term k, was used to describe the steam consumption, developed and fitted by Bieler (2004);2 (2) detailed modeling using the model with the best performance out of models A-D. The majority of the UOs were the reactors and the storage tanks with typical NV ranging from 6.3 to 40 m3, various heating/cooling systems, and lining materials. This equipment is the core of a multipurpose chemical batch plant and together with the continuously operated solvent recycling distillation columns represents the major part of the steam consumption. Therefore, the model parameters fitting and the validation were carried out by direct measurement of the steam consumption of the reactors. A set of reactors was selected, where the steam measurement device (vortex technology) was invasively installed into the steam-supplying pipe, and the steam consumption data were logged in 30 s time steps. 3.1. Types of H/C Systems. The rate of heat transfer to or from agitated liquid mass in a vessel is a function of the physical properties of that liquid and the heating or cooling medium, the vessel geometry, the degree of agitation, and the H/C system, the latter having a significant influence on the losses. Therefore, the losses-models were developed to capture the main features of the H/C systems. The differences of the H/C systems are then depicted in the coefficients of the models. 3.1.1. Direct Steam Heating (Steam Injection). Direct steam injection, depicted in Figure 4, involves the discharge of

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7329 Table 4. Fitted Model Parameters model A UO no. UO1 UO2 UO3 UO4

model B

model C

model D

k [J s-1 m-2 K-1]

a

b

a

b

k [J s-1 m-2 K-1]

a

b

k [J s-1 m-2 K-1]

14.113 3.775 10.303 13.730

6.176 7.963 2.029 1.621

0.641 0.678 0.878 0.946

6.740 5.028 4.999 9.950

0.519 0.530 0.642 0.491

0.168 0.440 0.520 0.225

5.013 5.002 16.520 1.020

0.816 0.538 0.485 0.819

0.233 0.608 0.493 0.307

Table 5. Overview of the Models Accuracy for Different UOs losses model UO no. performance indicator model A model B model C model D UO1 UO2 UO3 UO4

PMRbatch RSDSMP CDbatch PMRbatch RSDSMP CDbatch PMRbatch RSDSMP CDbatch PMRbatch RSDSMP CDbatch

1.003 0.059 0.708 1.022 0.456 0.260 1.003 0.315 0.596 1.069 0.283 0.721

0.936 0.037 0.800 0.909 0.217 0.081 0.977 0.123 0.199 0.958 0.061 0.827

0.996 0.044 0.815 0.948 0.181 0.230 1.034 0.077 0.568 1.000 0.066 0.830

0.980 0.050 0.836 0.927 0.195 0.202 0.989 0.055 0.593 0.971 0.064 0.841

steam at higher pressure into a liquid at lower pressure and temperature, so that the condensation heat from the steam is transferred into the surrounding liquid. This method is only used when the direct contact between steam and liquid is allowed, and the dilution of the reaction mixture does not cause a problem concerning safety and quality of the product. This is mostly the case in water-solution chemistry. The heat transfer rate and the losses are influenced by the following.24 (1) Size of the steam bubble: to ensure the complete condensation of the steam bubbles, their surface area to volume ratio must be as high as possible, favoring in this way smaller bubbles. (2) Temperature of the liquid being heated: the difference between this temperature and steam temperature directly influences the rate of condensation. (3) Filling degree of the vessel heated with direct steam: a higher filling degree increases the steam bubbles residence time and consequently the probability to be condensed. Steam which does not condensate in the heated medium is sucked by the offgas nozzle and there its energy content is lost. 3.1.2. Indirect Steam Heating via a Jacket. This H/C type uses a heating or cooling utility which circulates in the annular

Figure 10. Comparison of the UO models vs measurement for UO1 (see Table 3 for details).

Figure 11. Overall building level model performance on the daily basis, R2 ) 0.78. Table 6. Overall Model Performance number of modeled days overall steam modeled overall steam measured relative overall error relative mean daily error

60 4179 4145 0.81% 9.02%

space between a jacket and the vessel walls, transferring the heat through the wall of the vessel. Considering the steam as heating utility, two possible installations are depicted in the Figure 5a,b. The heat transfer rate and the losses are mainly influenced by (1)fouling in which an additional layer in the heat transfer area will negatively influence the heat transfer from the jacket to the heated medium and increase the losses; (2) steam trap in which the malfunction of the steam trap influences the losses of the fresh steam from the H/C system; (3) length of the pipelines in the H/C system which has an influence especially for hot water circulation because of the radiation losses from the surface. 3.2. Steam Measurements and the Heating Cooling System Energy Balance for the Hot Water Circulation H/ C System. The measurement/knowledge of the actual steam consumption of a particular UO is necessary for fitting the parameters of the loss model. The most reliable way of acquiring the steam consumption data is the direct measurement of the steam. However, the installation of a steam measurement device is problematic in running production facilities and therefore this option can be used to measure the steam consumption only for a limited number of UOs. Hence other possibilities to calculate the steam consumption from the measured process data and tabulated data of the H/C system based on the hot water circulation were investigated, and an approach based on the H/C system energy balance was proposed as an alternative to direct steam measurement. Since the hot water circulation H/C system concept represents around 50% of all H/C systems installations in the case study plant, the steam consumption data calculated by applying this approach significantly enrich the set of the


steam consumption data used for the loss models parameters fitting. A schematic view of the H/C system balance with the system’s boundaries and the material and energy streams is depicted in Figure 5 b. The developed approach takes into account the H/C systems of the reactors on the basis of the hot water circulation concept, where the inlet and outlet temperatures of the H/C water are measured and its volume flow is assumed as constant for a given NV of the reactor and lining material. This assumption is based on the fact that the H/C systems in the case study plant are built according to a well-documented and uniform industrial specification, which defines the standardized parameters for the same reactor type (see Table 1). On the basis of this data, the steam consumption can be calculated using mass balances for the H/C system. Considering steady state in the H/C system (Figure 5b), the mass balance of the H/C system can be described by the following equation: mHCsteam,i ) mHCcondensate,i

3.3. Data Management in the Case Study Plant. The overall data management is presented in Figure 7. The most important part is the process data acquisition from the sensors installed in the case study plant, which comprise the fundamental input information for the modeling approach and allow realistic modeling of the steam consumption in the chemical processes. However, the amount of data is enormous and substantial prehandling is required in order to use them in the model. The process data are stored in compressed format in the form of time series using the swinging door compression mechanism.26 The time series stored in nonuniform time scale for different sensors have to be rescaled to one common time scale before they are used as input in the calculation engine. A common time scale with a 1 min time spacing was used for this purpose. The rescaling from the original time series (j) to common time scale (i) is done for different data as follows. (1) Measured process data (DP) as temperature, mass, pressure: common linear interpolation (first-order hold) according to Singhal et al.20 provides very accurate results.

(15)

The energy balance of the H/C system takes into account as input streams the steam entering the system (mHCsteam,ihsteam) and the circulating hot water leaving the jacket (m ˙ circHChcircHC,iTHCout) and as output streams the condensate leaving the system (mHCsteam,ihcondensate) and the circulating hot water entering the THCin jacket (m ˙ circHChcircHC,i ). On the basis of the energy balance of the H/C system, the steam consumption can be calculated as follows:

DPi ) DPj +

ti - tj (DPj+1 - DPj) tj+1 - tj

(18)

(2) Data from the process control system (DCS) stored at step change.: zero-order hold is used to rescale the compressed data to common time scale by holding the last value from original time series until another sample is received. DCSi )

{

CDj if ti < tj+1 CDj+1 if ti g tj+1

(19)

.

THCin THCout mcircHC(hcircHC,i - hcircHC,i ) mHCsteam ) hsteam - hcondensate

(16)

so in terms of energy consumption: tot,st EUO,predHC,i ) mHCsteam,i(hsteam - hcondensate)

(17)

The thermodynamic properties of water and saturated steam at 6 bar were calculated according to IAPWS-IF97 standard.25 3.2.1. Evaluation of the H/C System Energy Balance Accuracy. The accuracy of the steam consumption calculated from the energy balance in the boundaries of the H/C system is extremely dependent on the accuracy of the data measured by the sensors, especially the temperature of the hot water entering and leaving the H/C system, THCin and THCout respectively. These two process parameters introduce the inaccuracy into the energy balance since their difference is directly influencing the THCin THCout - hcircHC ) term in the steam consumption calculation. (hcircHC Taking into account that the H/C system temperature difference is in the range of 2-10 K, low divergence from the real values caused by malfunction of the sensor will already introduce high inaccuracy into the calculation. The quality of the temperature measurement data is therefore crucial for the energy balance of the H/C system. The testing of the H/C system energy balance results is based on the assumption that there should be a good correlation between the opening of the steam control valve, VO and tot,st EUO,predHC,i . Although the VO does not quantitatively specify the consumption of the steam, it is a good measure to qualitatively describe the steam consumption. Therefore, good correlation between VO and Etot,st UO,predHC,i is expected for the UOs and batches with good quality of measurements. tot,st The H/C system steam consumption EUO,predHC,i can then be used as a target value for loss models according to scheme depicted in Figure 6.

4. Results The application of the modeling approaches was tested in the case study plant in two levels. In the UO level, the steam consumption of individual apparatus was investigated and the model performance was compared with installed steam consumption measurements. On the basis of this evaluation, the most suitable model for the UOs were chosen and used in a second level for the overall case study plant modeling of the steam consumption. 4.1. Applicability of the Detailed Models in the UO Level. 4.1.1. Steam Consumption Calculated from H/C System Energy Balance. The accuracy of the batchwise overall steam consumption calculated from the H/C system energy balance was verified in the case of one reactor with circulating hot water H/C system, where the simultaneous steam consumption measurement and H/C system inlet and outlet temperature data acquisition was carried out. This verification was done to prove the approach using the data from the H/C system as well as the reliability of the measured and tabulated data. The steam consumption calculated according to eq 17 was compared with the measured steam consumption for 14 different batches produced in the particular UO. The influence of the correlation (r2) between the steam consumption calculated from H/C system balance and the valve opening (VO) in the model accuracy expressed as a ratio between the model prediction and the measurement was investigated, and the results are plotted in Figure 8. As it can be seen, there is a dependence between the VO correlation with Etot,st UO,predHC,i and the overall model accuracy. For r2 values below the critical value (0.88), the overestimation of the H/C balance steam consumption for particular batches is as high as 60%. This is due to low quality of the input data for these particular batches which is caused mainly by compression error of the process data, where inconsistent H/C data are stored. For r2 values greater than this critical value, the Etot,st UO,predHC results


Figure 12. Efficiency of the steam usage in particular UOs considering different nominal volume (NV). Material: stainless steel (SS) and glass lined steel (SE). Type of H/C system: half-pipe coil (HP) and double jacket (DJ). Table 7. Comparison of the Efficiency Data Sets for Two UOs: R22 and R54 95% CI for mean UO

mean

high

low

SD

low

high

median

R22 R54

0.432 0.714

0.387 0.685

0.476 0.742

0.110 0.068

0.284 0.434

0.719 0.747

0.407 0.737

are within a range of (10% of the direct steam measurement. Therefore, the results of the H/C system energy balance which fulfill the condition of good correlation (r2 > 0.9) where the steam control valve opening can be considered as a good approximation of the real steam consumption. These results can be then used for the fitting of the losses models parameters. 4.1.2. Investigation of the Time-Lag between the Modeled and Measured Steam Consumption. The response of the temperature, as controlled parameter in the modeled UO to the energy utility consumption represented by valve opening is delayed. Therefore, the theoretical modeled energy utility consumption based on the temperature inside of the UO will be delayed as well, as seen in Figure 9 where the theoretical consumption without losses and related steam measurement are depicted. Hence the dead time was investigated for different H/C systems of measured and modeled UOs and included into the models of all UOs by shifting the modeled steam consumption. The generalization of the lag-times for different H/C systems is summarized in Table 2. 4.1.3. Comparison of the Loss Models Accuracy. The applicability of the loss models was investigated in the case of four different UOs where the steam consumption measurements were carried out. Additional information about the modeled UOs can be found in Table 3, where in each one of the four UOs only one product was produced during the SMP. The loss models parameters were fitted for a set of training batches and they are shown in Table 4. The results of the models evaluation in the batches used for validation are summarized in Table 5. From these tables it can be inferred that the models’ accuracy generally deteriorates in low overall steam consumption per batch, which is more obvious in the case of UO2. The UOs with lower steam consumption use the steam usually to keep a

constant temperature in the vessel. The accuracy deterioration arises from the fact that the response of the temperature (Tmaterial) is not as significant as at the UOs with higher steam consumption. Hence the signal-to-noise ratio decreases which makes the modeling results more inaccurate. Comparing the models performance it can be seen that although model A has relatively good overall accuracy, PMRbatch, the standard deviation RSDSMP of the overall accuracy between different batches is high, especially in the case of UO2 and UO3. This indicates that the dynamic performance of model A is poor. This means that even though model A has average PMRbatch for the evaluation set of batches close to 1, the error within individual batches can be quite high as the RSD values of 0.45 and 0.30 indicate in the cases of UOs with low or high steam consumption per batch (UO2 and UO4 respectively, Table 5). The standard deviation of model B is lower compared to model A, but it has also some significant inaccuracies in the dynamic modeling part and worse performance considering the PMRbatch. Model C shows the best overall performance from both the integral and the dynamical performance point of view. The PMRbatch values are close to 1 for all the UOs, and the RSDSMP being close to 0.05 for high steam consumption UOs and at a maximum of 0.2 in the case of UO2 indicates low model to measurement error for individual batches. Model D did not show any significant improvements in the accuracy by including an additional parameter into the model. Therefore, this model was omitted for further calculations. This can be explained by the structure of the model C, which implicitly includes the filling degree (FD) in the theoretical steam UO,st consumption term (Eth,i ), where the mass of the material in the UO is included. Fitted parameters a and b then incorporate the relation FD ) f(m j material). The reliability of model C is illustrated by plotting the modeled and measured steam consumption in Figure 10. Considering model C, 13 out of 14 modeled batches lie within 10% error range. Therefore, model C was used for modeling the steam consumption of the reactors, which represent the core UOs of the batch chemical production.


Figure 13. Probability plots for normal distribution of the batch efficiencies for UOs R22 and R54; dashed lines refer to the reference lines of the normal distribution.

Figure 14. Detailed analysis of the steam consumption of the UO with efficiency under 50% during a batch.

4.2. Overall Model Application and Accuracy. The overall modeling approach was tested in a 60 day period in the case study plant. The objective was to test the modeling approach as well as the tools applied to the complex industrial database. Historical process data were extracted, preprocessed, and rescaled into a one minute time grid and stored in the database which was an input file for the calculation engine. All UOs relevant from steam consumption point of view were modeled, using the loss models parameters fitted for the UOs of the same type where the steam consumption was measured or derived from the H/C system balance.The overall results were rescaled to the one day time scale and the accuracy analysis was carried out. The overall model accuracy is depicted in Figure 11. Although there is a considerable loss of accuracy in the overall model compared to the UO model, the results are still reliable and most of the calculated overall daily steam consumption lies within the 30% error range.

Figure 15. Control valve opening during batch in UO R22 (VO values above 50%, heating; below 50%, cooling).

The overall results analysis shown in Table 6 indicates much better performance of the model for longer modeling periods, where the relative error between overall and modeled steam consumption during a 60 day period was less than 1%, while the mean relative error of the daily prediction of the steam consumption is stable around 10%. Taking into account the complexity of the system and the engineering effort needed, the overall model of the steam consumption produced reliable results which can be rescaled into the desired time scale and analyzed from optimization point of view. 4.3. Optimization Potential. Optimization of the steam consumption in the multipurpose batch plant should be focused on improving steam usage efficiency of a particular UO. The efficiency is defined as a ratio between theoretically needed energy from steam and overall consumption including the losses. Ranking the UOs according to their efficiency can help to detect optimization potential in the plant. The heating perfor-


mance of 18 UOs was observed batchwise within the modeled period of 60 days. The thermal efficiencies of observed UOs are depicted in Figure 12 The most promising UOs from a steam consumption optimization point of view are those with low mean value and high standard deviation of the efficiency and high average steam consumption per batch,. It can be seen that the average efficiency ranges from 40 to 70%, and it is mainly influenced by the number of products produced in the particular UO. The UOs with higher product variability tend to have lower mean value and higher standard deviation of the efficiency. The low efficiencies compared to the conventional heat exchangers can be due to the lower heat exchange area to volume ratio. Another reason is the batch operation mode of the UOs, where the operations of heating and cooling are ordered accordingly, thus a lot of the supplied energy is used to reheat the media in the H/C system. This part of energy is modeled by loss model and decreases the efficiency of the UO. As an example, two monoproduct UOs with comparable number of produced batches, R22 and R54, were chosen for further statistical analysis. As can be seen in Table 7, both lower mean value and higher standard deviation of R22 efficiency indicate suboptimal operating conditions of this UO compared to R54. In Figure 13 the probability plots for normal distributions of observed UOs are depicted. Despite some outliers, both data sets appear to be consistent with the normal distribution. However, there is a significant difference between the distributions of the data sets. In the case of R22 there seems to be a clustering of the efficiency into two groups revealing probably two efficiency modes. The majority of the batches (84%) were produced in low efficiency mode. In contrast to R22, the majority of the R54 batches were produced with high efficiency, and the probability of occurrence of the low efficiency batch is below 10%. This analysis implies that there is considerable improvement potential regarding heating efficiency of the R22, and further effort should be dedicated to investigate the operation of this UO. In Figure 14, the cumulative steam consumption of the UO R22 is depicted. It can be seen that almost 40% of the overall steam required for the production of this batch is consumed during the waiting step, when the temperature is maintained at 55 °C. During this step the UO R22 is waiting for the end of reaction step in the previous UO. Long duration of the waiting step indicates the problems with the synchronization between 2 UOs. Furthermore, analysis of this reactor in Figure 15 shows the VO and temperature course during the same batch as depicted in Figure 14. It is obvious, that during the waiting step heating of the reaction mass occurs followed by cooling, which indicates a problem with the control valve, which represents the main optimization spot concerning this particular UO. Further optimization can be reached by improved scheduling of the UOs, which would decrease the waiting time of the UO R22 and increase the heating efficiency. 5. Conclusions A reliable modeling approach was developed which allows the modeling of the steam consumption of individual UOs using extensive data of the process measurements in a multipurpose batch plant. The models can describe both total and transient steam consumption of the UOs taking into account the theoretical steam consumption and losses. Several loss models were tested and the one with the best performance was chosen for the overall building scale. The approach was also successfully tested in modeling of the overall steam consumption in the case study plant with a very complex production portfolio. Both on

the UO and overall level, the accuracy of the model was satisfactory, taking into account the system complexity. One main advantage of the proposed approach is the minimum engineering effort which has to be invested into the modeling and data treatment since the developed software tools can handle all the data in a highly automated way. This feature of the approach allows applying it for online steam consumption monitoring, which can lead to prompt energy saving steps in the production to solve the acute problems. On the other hand, application of the model with historical data as input can lead to identification of systematic sources of inefficiencies in both individual UO and its H/C system, which can then be eliminated. The flexibility of the model makes possible to use it for “what-if” analysis of the process parameters and optimize the energy efficiency in the multipurpose chemical batch plants. This optimization has to be done with respect to the safety and quality requirements defined by the plant chemists. These issues have to be reflected in the optimization procedure as boundaries of the optimized parameters. Analysis of the possible optimization of the steam consumption of reactors as main consumers is the main scope of the future work. Nomenclature A ) surface[m2] a ) heat loss coefficient (related to H/C losses) b ) heat loss coefficient (related to H/C losses) cp ) heat capacity [J kg-1 K-1] CD ) coefficient of determination CI ) confidence interval DCS ) data from control system DP ) process data E ) energy utility consumption [J] FD ) filling degree of the unit operation h ) specific enthalpy [J kg-1] k ) heat loss term (related to radiative losses) [J s-1 m-2 K-1] m ) mass [kg] n ) number of time-intervals N batch ) number of produced batches NV ) nominal volume OF ) objective function param ) parameters matrix PMR ) prediction-to-measurement ratio RSD ) relative standard deviation SD ) standard deviation T ) temperature [K] t ) time [s] tR ) reaction time [min] VO ) steam control valve opening [%] Indices amb ) ambient app ) apparatus batch ) batch related diss ) dissipation of mechanical energy evap ) evaporation HC ) heating/cooling system i ) time interval in the rescaled time scale j ) time interval in the original time scale loss ) losses material ) material processed in particular unit operation meas ) measurement no. batch ) number of produced batches in the unit operation pred ) prediction SMP ) steam measuring period related

7334 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 st ) steam th ) theoretical tot ) total UO ) unit operation

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ReceiVed for reView September 26, 2007 ReVised manuscript receiVed April 10, 2008 Accepted July 23, 2008 IE071291O

Bottom-up Modeling of the Steam Consumption in Multipurpose

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