Particulate Fouling and its Effect on U-Tube Steam

Particulate Fouling and its Effect on U-Tube Steam Generator Thermal Performance Xuedong Huang, B.R. Upadhyaya, and J.W. Hines The University of Tennessee Nuclear Engineering Department Knoxville, TN 37996-2300 E-mail: [email protected]

Abstract A multiple-node SIMULINK model of a U-tube steam generator (UTSG) has been developed so as to simulate the UTSG dynamics or responses to various defects, including fouling. UTSG responses to different events, such as reduced heat transfer area, change in heat transfer coefficient at different axial nodes, change in tube material conductivity, and the change of steam valve coefficients have been studied using the SIMULINK model. Then a mathematical model is established and implemented on MATLAB based on a systematic literature review on steam generator and heat exchanger fouling. Finally, the fouling model and the UTSG-SIMULINK model are both used to study the progress of tube fouling and the effects on UTSG thermal performance. The simulation results show the validity of the developed models. The developed models can be used to predict the degradation of UTSG thermal performance and hence provide guidance for plant maintenance planning. They can also be used to generate data for UTSG fault diagnosis. The results of these studies on the various defects and their effect on steam generator thermal performance are described.

1. Introduction In order to monitor and diagnose the structural faults or degradation in a UTSG, it is necessary to develop a high-fidelity dynamic model so as to simulate the changes in the heat transfer characteristics of the UTSG and to generate a database representing normal and degraded process conditions. In general there are two types of models, namely first-principle model and data-driven model. In this research, a first-principle UTSG model with moving-boundary and multi-nodes is developed based on related thermal-hydraulics laws. Although there are various mathematical models and computer codes, such as RETRAN or RELAP, most of them are commercial software and are also quite complex in their implementation. Hence they are also often quite expensive to run on a computer for UTSG simulation. Therefore, based on a simpler model by Naghedolfeizi and Upadhyaya1, we have developed our own multi-nodal UTSG model and implemented the model using the MATLAB-Simulink platform. In order to study the effect of UTSG tube particulate fouling on the overall thermal performance, a good mathematical model is needed to simulate the progress of tube fouling process. These models are generally based on the deposition and removal mechanisms of suspended particles in the bulk flow. However, most of the models are focused on fouling in a single tube. Only a few models are available for steam generators. In this study we use the model developed by Liner et al 2, 3 to study the fouling in UTSGs. A MATLAB-Simulink code is developed for this model. The final simulation results are indicative of the high fidelity of the developed models. The simulation results also show that the models can simulate the fouling problem at different axial locations. The effect of fouling on UTSG thermal performance may be studied using the previously developed multi-node SIMULINK model if the fouling process can be appropriately simulated using a proper model. The simulation results can be used for the prediction of UTSG thermal performance and for application in scheduling its maintenance activities.

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2. UTSG Simulation Model The simulation model has been developed based on Ref [1]. The Mathematical model is derived from the conservation equations (mass, energy, and momentum) and the associated constitutive relations. The heat exchanger tubes are divided into four axial nodes and the moving-boundary method is used to consider the change of the starting point of saturated boiling during the dynamic process. As in Ref [1], the following assumptions are made in the model development. • • • • •

Both water and steam are considered to be saturated. Density and specific heat capacity of the feed water, sub-cooled region, and the primary side are assumed to be constant. Heat transfer coefficients are constant. Steam leaving the steam generator is 100% saturated. Heat transfer between the downcomer and the tube bundle regions is negligible.

The thermodynamic properties of the saturated water and steam are assumed to be linear functions of the steam pressure for a range of ± 100 psi from the normal operating point. The steam flow leaving the UTSG is considered to be a critical flow. The flow is defined in terms of steam pressure and steam valve coefficient as Ws = ClP Where, Ws = steam flow rate, Cl = steam valve coefficient, P = steam pressure. Figure 1 shows the schematic of the multi-nodal model representation. The steam generator water level is controlled by a three-element controller that uses the measurements of the SG water level, steam flow rate, and feed water flow rate. The forcing functions of the isolated UTSG model are: primary inlet temperature, steam valve coefficient, feed water temperature, and SG level set point. After the entire set of mathematical equations are developed, they are implemented under MATLABSimulink. The Simulink model is then used to simulate the dynamic behavior of thermal and hydraulic processes in a typical 1,300 MWe four-loop Westinghouse nuclear plant UTSG system. Here the simulation results of the UTSG responses to normal condition and the following tube degradation mechanisms are presented: • • • •

Tube plugging by changing the heat transfer area. Tube fouling on the primary side (inner tube) by introducing an additional heat transfer resistance at different axial locations. Tube fouling on the secondary side (outer tube) by introducing an additional heat transfer resistance at different axial locations. Tube metal heat conductivity.

Figures 2 through 10 show the results of simulation for normal condition and for the cases of tube degradation. The latter include decreased heat transfer area (tube plugging), decreased heat transfer coefficients (fouling), etc. In all these cases the steam pressure decreased from its nominal value. Figures 11 and 12 show the process dynamics during normal transients. These results are indicative of the high fidelity of the model. The simulation results also show that the new model can simulate the UTSG response to the fouling problem at different axial locations. The following observations are made from the simulation results: (1) When we introduce an additional heat transfer resistance so as to decrease the overall heat transfer coefficient by 50% in the metal-to-secondary side sub-cooled heat transfer nodes (MTL1 and MTL8) or the primary-to-metal side sub-cooled heat transfer nodes (PRL1 and PRL8), the steam pressure decreases from 874.9 psia to 868 psia and 868.6 psia, respectively. (2) When we introduce an additional heat transfer resistance so as to decrease the overall heat transfer coefficient by 50% in the metal-to-secondary side boiling heat transfer nodes or the

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primary-to-metal side boiling heat transfer nodes, the steam pressure decrease from 874.9 psia to about 863.8 psia and 860.1 psia, respectively, and there is not much difference in the pressure difference caused by fouling at different axial locations within the boiling region. These results show that we can differentiate and thus diagnose the fouling in sub-cooled region and the boiling region. However, it seems difficult to diagnose the fouling at different axial locations within a specific heat transfer region.

3. Steam Generator Particulate Fouling Model According to Ref [5], fouling is generally defined as the accumulation of unwanted materials on the surfaces of processing equipment. Fouling is the most troublesome problem commonly occurring to thermal components, such as steam generators, heat exchangers, and condensers. It can affect the thermal performance of the equipment in at least two manners: (1) Generally the fouling deposition layer has a low thermal conductivity, which increases the thermal resistance to heat transfer and reduces the heat transfer efficiency of the heat exchangers or steam generators. (2) As the particulate deposition layer increases, the cross-sectional area of the flow path is reduced, which will lead to an increase in pressure drop across the component. Heat exchangers and SGs are designed for counteracting the effect of fouling by providing excess heat transfer capacity in order to offset the losses in efficiency caused by fouling. That is, the thermal resistance due to fouling, R f, is included in the equation for the overall heat transfer coefficient as follows:

(1) Uo= overall heat transfer coefficient based on outside area of tube wall A = tube wall area A w = mean wall area R f = thermal resistance due to fouling R w = thermal resistance of wall α = convective heat transfer coefficient. As deposit thickness or Rf increases with time, the overall heat transfer coefficient decreases, thus the thermal performance is degraded. The thermal fouling resistance, R f, is defined as: Rf = 1/Udirty - 1/Uclean

(2)

The overall heat transfer coefficient determines how much heat can be transferred between the hot and the cold fluid in a given heat exchanger. When the overall heat transfer coefficient becomes less than a predetermined tolerable value, measures must be taken to improve the heat exchanger thermal performance. According to the fouling mechanism, fouling has been classified into crystallization fouling, particulate fouling, chemical reaction fouling, corrosion fouling, and biological fouling (bio-fouling). In this study, we focus on the study of particulate fouling. Particulate fouling is the accumulation of solid particles suspended in a fluid onto a heat transfer surface. Suspended particles can be ambient pollutants (sand, silt, clay), upstream corrosion products, or products of chemical reactions occurring within the fluid. Depending on the process parameters and the dominant fouling mechanism, the fouling rate is either constant or decreases with time, as shown in Figure 13.

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• • • •

Linear rate: Rf increases with time or the growth rate of deposit is constant. This is the result of hard and adherent deposit where removal and aging can be ignored. Falling rate: Rf increases with time, but with a progressively falling rate or the removal rate increases with time. Asymptotic rate: After a period of time, Rf reaches a constant value or the growth rate of deposit approaches zero. Saw-tooth fouling: Part of the deposit is detached after a critical residence time or once a critical deposit thickness has been reached. The fouling layer then builds up and breaks off again.

Based on the above understanding and the particulate deposition and removal mechanisms, various models6 have been proposed for simulation of fouling in simple tubing. However, very few models for steam generator fouling have been developed. Liner et al2, 3 developed a model for simulation of magnetite particulate fouling in nuclear steam generators. In our study we use this model to simulate the particulate fouling progress in the UTSG. For details of this model, see Ref [2, 3]. As experience has shown, the secondary side SG fouling is of a major concern. Hence we have mainly simulated the secondary side SG tube surface fouling using the Liner’s mathematical model and related constants. The model has been implemented using MATLAB and simulations have been performed to study the progress of the secondary side SG tube particulate fouling. Results are given in Figures 14 and 15. Comparing the results with those from Liner et al 2,3 and the general magnitude of heat exchanger fouling factor 4, we see that the results are reasonable.

4. Results Now we can study the effect of secondary side tube fouling on UTSG thermal performance. We use the previously developed multi-node UTSG SIMULINK model for the UTSG thermal-hydraulics simulation and use the above results for fouling simulation as part of the inputs. Finally, the UTSG thermal performance variations versus time are obtained. The following important assumptions are made in the study: • • •

Only secondary side tube fouling on UTSG tubes is simulated The distribution of fouling deposit along UTSG tube is uniform The increase in pressure drop across the UTSG tube due to cross-sectional area reduction caused by fouling deposition layer is not considered. This is reasonable since the flow area on the secondary side is relatively larger than on the primary side of UTSG.

Figure 16 shows the steam pressure variation versus time. Figure 17 presents the average heat flux (on outer tube surface) variation versus time. From the figures, we can see that as the UTSG secondary side tube fouling progresses and the thermal resistance due to fouling increases, both UTSG steam pressure and the average heat flux decrease until the fouling process reaches an equilibrium, that is, the fouling factor, the steam pressure and heat flux all asymptotically remain constant. From Figures 16 and 17, we see that as the fouling factor increases and reaches the balanced value of about 1.4 s•ft2•°F/Btu (1) The steam pressure decreases from 875 Psia to 798 Psia, which means a percentage decrease of steam pressure by about 11.4% (2) The average heat flux on outer tube surface decreases from 30.3 Btu/(ft2•s) to about 27.7 Btu/(ft2•s), which means a percentage decrease of average heat flux by about 11.7%. These results show that both the steam pressure and average heat flux have been changed by about the same percentage, more than 11%, due to the secondary side tube fouling. This steam pressure decrease is too large in practical plant operation, indicating that the plant performance is degraded and cannot produce the required steam for power generation. Hence, necessary measures, such as

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UTSG cleaning or washing, or improvement of the water chemistry, must be made to recover the plant performance.

5. Concluding Remarks From the above study on simulation of UTSG secondary side fouling and the effects on thermal performance, we can reach the following conclusions: (1) A first-principle multi-nodal UTSG model has been successfully developed and implemented using Simulink. An existing fouling model has been used to simulate the fouling progress in UTSG and its output is used as the input to the previous UTSG Simulink model so as to study the effect of fouling on UTSG thermal performance. Reasonable simulation results have been obtained. These results show that the models can be used to simulate both the normal operation and faulty conditions. (2) The effect of fouling on UTSG thermal performance can be studied using the previously developed multi-node SIMULINK model if the fouling process can be appropriately simulated using a proper model. The simulation results can be used for the prediction of UTSG thermal performance and scheduling of the USTG maintenance activities.

The fouling model used in this study has not been validated by experimental results. Effort is underway to develop an experimental facility to help verify the model behavior.

Acknowledgments This research is sponsored by the U.S. Department of Energy NEER Program, under a grant (DEFG07-01ID14114) with The University of Tennessee.

References 1. M. Naghedolfeizi and B.R. Upadhyaya, “Dynamic Modeling of a Pressurized Water Reactor Plant for Diagnostics and Control,” Research Report, DOE/NE/88ER12824-02, June 1991. 2. Y. Liner, et al, “Simulation of Magnetite Particulate Fouling in Nuclear Steam Generators,” Chalk River Laboratories, AECL Research, Ontario, Canada, 1992. 3. C.W. Turner et al, “Modeling Magnetite Particle Deposition in Nuclear Steam Generators and Comparisons with Plant Data,” Presented at the Second International Steam Generator and Heat Exchanger Conference, Toronto, Canada, 1994. 4. http://www.tranterphe.com/phe/PDFs/SC-TD-017.pdf 5. http://www.cpe.surrey.ac.uk/dptri/hms/fouling.htm 6. E.F.C. Somerscales et al, “Fouling of Heat Transfer Equipment,” Hemisphere Publishing, 1979. 7. B.R. Upadhyaya, J.W. Hines, X. Huang, N.A. Johansen, A.V. Gribok, and S.R. Perillo, "Automated Monitoring and Diagnostics of the Integrity of Nuclear Plant Steam generators, Transactions of the American Nuclear Society Annual Meeting, June 2002. 8. B.R. Upadhyaya, J.W. Hines, et al, “On-Line Monitoring and Diagnostics of the Integrity of Nuclear Plant Steam Generators and Heat Exchangers”, Semi-Annual Report, Report No. DE-FG07-01ID14114/UTNE-01, December 2001.

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9. B.R. Upadhyaya, J.W. Hines, et al, “On-Line Monitoring and Diagnostics of the Integrity of Nuclear Plant Steam Generators and Heat Exchangers,” Annual Report, Report No. DEFG07-01ID14114/UTNE-02, June 2002. 10. B.R. Upadhyaya, J.W. Hines, et al, “On-Line Monitoring and Diagnostics of the Integrity of Nuclear Plant Steam Generators and Heat Exchangers,” Semi-Annual Report, Report No. DE-FG07-01ID14114/UTNE-03, December 2002.

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Figure 1. Schematic of the U-Tube Steam Generator model with four axial tube nodes.

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Figure 2. Steam pressure change for the case of 5% decrease in the number of tubes.

Figure 3. Steam pressure change when decreasing by 50% the overall heat transfer coefficient in the metal-to-secondary side sub-cooled heat transfer nodes (MTL1 and MTL8).

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Figure 4. Steam pressure change when decreasing by 50% the overall heat transfer coefficient in the primary-to-metal side sub-cooled heat transfer nodes (PRL1 and PRL8).

Figure 5. Steam pressure change when decreasing by 50% the overall heat transfer coefficient in the metal-to-secondary side boiling heat transfer nodes (MTL2 and MTL7).

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Figure 6. Steam pressure change when decreasing by 50% the overall heat transfer coefficient in the primary-to-metal side boiling heat transfer nodes (PRL2 and PRL7).


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Figure 11. Steam pressure variation for a 10% decrease in the steam valve coefficient (decreased steam flow rate).

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Figure 12. SG water level variation for a 10% decrease in the steam valve coefficient

Figure 13. Different cases of fouling rate (from Ref [5]).

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Figure 14. Fouling Deposit Mass Variation versus Time.

Figure 15. Fouling Thermal Resistance versus Time.

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Figure 16. Steam Pressure Variation versus Time.

Figure 17. Average Heat Flux (on Outer SG Tube Surface) Variation versus Time.

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