文献翻译-碳酸钙在AISI316管内污垢热阻模型的预测

英语翻译 Fouling resistance model for prediction of CaCO3 scaling in AISI 316 tubes M. Sultan Khan, S. M. Zubair, M. O. Budair, A. K. Sheikh, A. Quddus Abstract： The term fouling is generally used to describe the deposition of unwanted (initially fluid) particles, which increases both resistance to heat transfer and pressure drop through the heat exchanger. CaCO3 which is predominantly present in the cooling water, has inverse solubility characteristics i.e., it is less soluble in warm water, resulting in deposition of scales in heat transfer equipment. An experimental program is described in this paper to study the growth of fouling as a function of tube surface temperature, Reynolds number, tube diameter and the time for which the tube has been subjected to the scale forming solution. The data collected from the experiments are used to develop a fouling resistance model. In addition, the results obtained from the present study are also compared with those discussed earlier by several investigators with regard to CaCO3 fouling. Keywords： scaling， the heat exchanger， CaCO3 1 .Introduction The deposition of unwanted particles on the surfaces of heat exchangers is defined as fouling. The presence of these deposits represents an additional thermal resistance to heat transfer which reduces the thermal-hydraulic performance of the heat transfer equipment. The deposition may be crystalline, biological material, the products of chemical reactions including corrosion, or particulate matter 1. The growth of deposits depends upon a number of parameters such as fluid composition (pH value, concentration, etc.), temperature, geometric dimensions, and Reynolds number (Re) of the flowing fluid. Different aspects of the deposition process and its characterization are discussed in the pioneering paper of Taborek et al. 2. It should be noted that an understanding of the economic penalties associated with fouling is one of the primary reasons for greater interest in the fouling-related research. Pritchard 3 presented cost estimates associated with fouling in Britain. Thackery 4 estimated the overall annual cost of fouling in U.K. to about 0.3 of GNP for the year 1978 (approximately $1 billion). The order of magnitudes of these estimates is confirmed by Van Nostrand et al. 5 while investigating the fouling related costs for the U.S. specificrefinery units. Steinhagen et al. 6 estimated the foulingrelated costs for New Zealand at about $30 to $46 million which is about 0.1-0.17% of the annual GNP for the year 1988. A project has been initiated at the King Fahd University of Petroleum and Minerals, Dhahran to study the impact of fouling in heat exchangers. The objective of this paper, which is partially based on the above mentioned project, is to present a fouling resistance model of CaCO3 scaling in AISI 316 stainless steel tubes. In this regard, a literature survey on precipitation fouling with emphasis on CaCO3 fouling is discussed in the next section which is followed by details of test equipment design and procedure to obtain parametric experimental fouling data. The data thus obtained from the test equipment is presented in the form of a dimensionless regression model. 2 Background of CaCO3 fouling The problem of fouling is encountered in industrial operations and processes with natural water or aqueous solutions containing dissolved inorganic salts. Some of these salts or their combinations have inverse solubility characteristics, so that they are less soluble in the hot fluid adjacent to the heattransfer surface. Examples of such salts are CaCO3 and CaSO4. Figure 1 shows the behavior of normal and inverse solubility salt solutions 1. For normal solubility salt solution, at point A, solution is undersaturated but on cooling to point B it is just saturated. On further cooling, the solution becomes supersaturatedand crystal nucleation occurs at point C. As crystallization and cooling proceeds solution concentration falls and moves in the direction of D. Now for an inverse solubility salt solution it is undersaturated at point A, as it is heated it reaches the solubility limit at point B at temperature 1 and then under continued heating the solution becomes supersaturated reaching point C at temperature 2 where precipitation starts. The formation of scale on heat transfer surfaces is a common phenomenon where aqueous solutions are involved, e.g. the use of natural waters for cooling purposes or evaporative desalination. Unless suitable measures are taken, the problem of scale formation can give rise to serious consequences. In steam boilers, for instance, the presence of scale on water side can give rise to high metal temperatures that may result in mechanical failure of heat-transfer equipment. Hanlon, as mentioned in reference 1, commented on the potential of scale formation in industrial equipment is very high. As an example, he observed that for a 1 million gallon/day desalination plant under normal concentration conditions,a maximum of about 1400 kg of CaCO3 could be precipitated each day. In terms of scale thickness, it would represent a build up of 0.1 mm per day on the total heat exchanger surfaces within a typical plant. Although this may be regarded as an extreme example it does illustrate the magnitude of scaling or crystallization fouling problems in industrial plants. A systematic study of scaling characteristics of cooling tower was conducted by Morse and Knudsen 7. Effect of surface temperature on the scaling behavior was discussed by Story and Knudsen 8. Lee and Knudsen 9 designed an experimental apparatus to simulate the operating conditions of a cooling tower. This is a somewhat extensive investigation to determine the effect of flow velocity, surface temperature and water quality on scaling of exchanger tubes. Coates and Knudsen 10 have discussed results of their experiments conducted for obtaining data regarding CaCO3 scaling. Watkinson and Martinez 11 studied scaling due to CaCO3 in copper tubes under conditions that promote rapid and severe scaling. In this regard, artificially hardened water of high dissolved and suspended solids was circulated through a heated test section. Effects of flow velocity, tube diameter and bulk temperature on asymptotic fouling resistance have been determined. Manzoor 12 conducted fouling related experiments and statistically analysed CaCO3 fouling data. The objective of Manzoors study was to demonstrate that fouling resistance varies from point to point along a horizontal tube and also for the same point it varies from replicate to replicate. The operating parameters were temperature, pressure, solution concentration and velocity which were kept constant during the experiments. Konings 13 on the basis of experimental work with cooling water, treated by different methods to eliminate scaling, presented a table of guide values for the fouling resistance. An experimental study of tube-side fouling resistance in water chilled evaporator was carried out by Haider et al. 14 in which 12.6 ft long evaporator tubes were used and fouling data were taken for four tube geometries. No data were taken at different sections of the tube. The fouling characteristics of cooling water for precipitation and particulate fouling are also discussed by Knudsen 15 where he emphasized serious problems when heat exchangers are over designed due to the use of incorrect design fouling allowance. Practical and fundamental aspects of precipitation fouling(CaCO3 scaling) were reviewed by Hasson 16. He considered the problem of defining precipitation fouling tendency by reviewing principles of solution equilibria and precipitation kinetics for salt systems frequently encountered in heat exchanger applications. Branch and Muller-Steinhagen 17 developed a model for fouling in shell and tube heat exchangers by considering Hassons ionic diffusion model for CaCO3 scaling. Hesselgreaves 18 discussed the effect of system parameters on the fouling performance of heat exchangers. A model for CaCO3 scale formation, which gives reliable prediction of the fouling rate with alteration of feed water chemistry, was developed by Tretyakov et al. 19. It should be noted from the above studies that so far no fouling resistance (f ) model has been developed that may predict f as a function of , tube surface temperature and tube diameter. 3Test equipment design The test apparatus was a double-pipe counter-flow heat exchanger as shown in Fig. 2. The working fluid was passed through the inner tube comprised of six test sections, each 0.1524 m long. To heat up the surface of the inner tube, hot water was circulated in the outer tube using a Constant- Temperature Water-Circultor Bath (CTWCB), which had a provision of variable temperature settings. Three heat exchangers were fabricated with inner tube sizes of 1/4 in (0.00635 m), 3/8 in (0.00952 m) and 1/2 in (0.0127 m). The outer to inner radii ratio of tubes was set at four for all three heat exchangers. All fittings were made of AISI 316. To simulate the conditions encountered in cooling water systems, Na2CO3 and CaCl2 solutions, prepared in de-mineralized (distilled) water were used to produce CaCO3 as a product of chemical reaction. The product solution, when passed through the inner tube resulted in the deposition of CaCO3 scale on the inner side of the tube. The chemical reaction to produce CaCO3 scale is given by 20 OxHNaClCONaxHCal 23322 The chemical solutions were pre-heated, separately, using pre-heaters and heating tapes to achieve a temperature of 50C before the solution entered the heat exchanger. The system is a once through type and a Back Pressure Regulator (BPR) was used to maintain a pressure of 689 kPa at the end of the heat exchanger. Figure 3 shows the scaling apparatus which consists of two high pressure variable stroke pumps, storage tanks for the chemical solutions, pre-heaters, heating tapes, CTWCB, thermocouples, temperature controllers and a BPR. Additional details and description of the test apparatus are presented in reference 21. 4 Experimental procedure The concentration of the product solution was kept constant at 0.0006 mol/l. This required 2.543 and 3.528 g of Na2CO3 and CaCl2, respectively, to be mixed in 40 l of distilled water. The parameters that were varied during the experiments are Reynolds number, surface temperature and diameter of the inner tube. It should be noted that experiments were conducted for all possible combinations of the parameter values as shown in Table 1, in which Reynolds number is based on the inner diameter of the test sections. As already mentioned three heat exchangers were designed and fabricated for the three tube sizes. For a particular size, Reynolds number was fixed and various experiments were conducted by varying the surface temperatures of the inner tube by the help of the CTWCB. Two hours continuous operation of the test is referred to as a test run. One experiment consisted of five 2 h runs for a particular set of parameters. At the end of each run, the heat exchanger was dismantled and the test sections were dried in the oven. Mass gain of the test pieces due to scaling was then measured using an analytical weighing scale which had an accuracy of1 mg. The heat exchanger was then re-assembled for the next experimental run. It was observed that 0.25 in (0.0127 m) tube blocked due to scaling after 10 h of operation thus restricting the duration of the experiments to a maximum of 10 hours. Periodic measurements of the flow rates were carried out to maintain a constant Reynolds number during the entire experiments. For the next set of experiment, new set of tubes were used. Using the mass gain method, fouling resistance (f ) wasdetermined as follows: where 2 is the inside radius of the tube, 1 is the average value of radius krRf12due to the deposit for a particular test section which can be calculated by using the relation lmasginr215 Concluding remarks The fouling resistance data of CaCO3 scaling were presented to study the influence of tube surface temperature, Reynolds number and tube diameter. It was observed that the influence of Reynolds number in the range investigated (9001700) was almost negligible, which was also noticed by Lee and Knudsen 9 who have presented the same conclusion for their experimental data on asymptotic fouling resistance. They had observed that by varying the fluid velocities from 3 to 10 ft/s (0.91 to 3.05 m/s) there was no profound effect on the amount of CaCO3 fouling resistance. However, the influence of tube surface temperature and tube diameter on the fouling growth was found to be appreciable for the range investigated. The reasons for the increased fouling resistance as a function of surface temperature and diameter were explained by considering the inverse solubility characteristics of CaCO3 and tube surface effects. The data obtained from experiments are presented in the form of a dimensionless fouling resistance model for estimation and prediction purpose. In this regard, all the variables in the model are non-dimensionalized with respect to the respective maximum values considered in this study. The model thus developed has been investigated in somewhat more detail by observing the normal probability plot of residuals. In addition, several other statistical checks are also made to assess the suitability of the model. No apparent model defects are noticed. It is thus concluded that the fouling resistance model may be considered as a reliable model within the range of experimental parameters investigated in the present study. References 1. Bott, T.R.: Fouling of Heat Exchangers. Elsevier, Netherlands(1995) 2. Taborek, J.; Aoki, T.; Knudsen, J.G.: Fouling, the major unresolved problem in heat transfer. Chem. Eng. Progress 68-2 (1972) 5967 3. Pritchard, A.M.: Fouling-Science or art. In: E.F.C. Somerscales and J.G. Knudsen (Eds.). Heat Transfer Equipment. Hemisphere, Washington, D.C. (1981) 4. Thackery, P.A.: The cost of fouling in heat exchanger plant. In: A.M. Pritcard (Ed.), Fouling-Science or Art.Guildford, United Kingdom (1979) 5. Van Nostrand, W.L.; Leach, S.H.; Haluska, J.L.: Economic penalties associated with the fouling of refinery heat transfer equipment. In: E.F.C. Somerscales and J.G. Knudsen, (Eds.),Fouling of Heat Transfer Equipment, Hemisphere, Washington,DC (1981) 6. Steinhagen, R.; Steinhagen, H.M.; Maagni, K.: Problems and costs due to heat exchanger fouling in New Zealand Industries. Heat Transfer Eng. 11-7 (1993) 1930 7. Morse, R.W.; Knudsen, J.G.: Effect of alkalanity on the scaling of simulated cooling tower water. Canad J. Chem. Eng. 55 (1977)272278 8. Story, M.; Knudsen, J.G.: The effect of heat transfer surface temperature on the scaling behaviour of simulated cooling tower water. AIChE Symp. Ser. 74-1124 (1978) 2530 9. Lee, S.H.; Knudsen, J.G.: Scaling characteristics of cooling tower water. ASHRAE Trans. 85-1 (1979) 281302 10. Coates, K.E.; Knudsen, J.G.: Calcium carbonate scaling characteristics of cooling tower water. ASHRAE Trans. 86-2 (1980) 6891 11. Watkinson, A.P.; Martinez, O.: Scaling of heat exchanger tubes by calcium carbonate. J Heat Transfer 97 (1975) 504508 12. Haq, M.U.: Reliability-based maintenance stratigies for heatexchangers subject to fouling. Masters Thesis, King Fahd University of Petroleum and Minerals, Saudi Arabia (1995) 13. Konings, A.M.: Guide Values for the fouling resistances of cooling water with different types of treatment for design of shell-andtube heat exchangers. Heat Transfer Eng. 10-4 (1989) 5461 14. Haider, S.I.; Meitz, A.K.; Webb, R.L.: An experimental study of tube-side fouling resistance in water-chiller-flooded evaporators. ASHRAE Trans. 98-2 (1992) 86103. 15. Knudsen, J.G.: Coping with cooling water fouling in tubular heat exchangers. AIChE Symp. Ser. 85-267 (1989) 112 16. Hasson, D.: Precipitation fouling. In: E.F.C. Somerscales ad J.G. Knudsen, (Eds), Fouling of Heat Transfer Equipment. Hemisphere, Washington, DC (1981) 17. Branch, C.A.; Steinhagen, H.M.M.: Influence of scaling on the performance of shell-and-tube heat exchangers. Heat Transfer Eng. 12-2 (1991) 3785 18. Hesselgreaves, J.E.: The effect of system parameters on the fouling performance of heat exchangers. ICHEME Symp. Ser. 129 (1992) 9951006 19. Tretyakov, O.V.; Kristskiy, V.G.; Styazhkin, P.S.: Improved prediction of the formation of calcium carbonate scale in heat exchangers of secondary loops of conventional thermal and nuclear power plants. Heat Transfer - Sov. Res. 23 (1991) 532538 20. Masterten, W.L.; Hurley, C.N.: Chemistry, Principles and Reactions. Saunders, Philadelphia (1989) 21. Khan, M.S.: Effect of thermal-hydraulic parameters on CaCO scaling in heat exchangers. Masters Thesis, King Fahd Univer3sity of Petroleum and Minerals, Saudi Arabia (1996) 22. Parry, D.J.; Hawthorn, D.; Rantell, A.: Fouling of Power Station Condensers within the Midlands Region of the C.E.G.B., In: Somerscales, E.F.C. and Knudsen, J.G. (Eds.) Fouling of Heat .Transfer Equipment. Hemisphere, Washington, DC (1979) 23. Montgomery, D.C.; Peck, E.A.: Introduction to Linear Regression Analysis. Wiley, New York (1985) . 碳酸钙在 AISI316 管内污垢热阻模型的预测 摘要 ： 结垢此术语常常用来描述不期望的会加大热交换器的压力降和热阻的颗粒 (最早在液体中 )的沉降。可知，碳酸钙主要存于冷却水当中，有难溶的特点，因为其难溶于热水，导致它在热交换设备中的结垢沉降。此篇论文目的在于研究有关管子表面的溶液，雷诺数，温度和在管子中结垢时间和污垢增长关系，将描述一个的实验项目。从当今研究中得到的结果也被用来与早些时候部分调研人员关于碳酸钙结垢的讨论进行比较。另外，来自实验中的数据被用来建立一个污垢热阻模型 关键词： 结垢，热交换设备，碳酸钙 1.绪论 这些沉积的存在会表现出附加的热阻，将会降低热交换设备的水传热性能。沉积的增加取决与包括液体成分（ pH 值，浓度等），温度，几何尺寸和流体雷诺数在内的一系列参数。结垢是指非期望颗粒在热交换器表面的沉积这些沉降物可能是包括腐蚀、颗粒物质在内的化学反应产物或者结晶生物物质。在Taborek 等人早期的论文中对沉积过程的不同方面及其特性进行了讨论。应该注意到结垢所造成的经济损失是结垢相关研究的一个主要原因。 Pritchard 提出了英国在结垢方面的大概成本。 Van Nostrand 等人在调查了美国精炼厂之后确认了这些估计。 Steinhagen 在 1985 年在新西兰，污垢造成的损失约占当年国民生产总值的 0.1-0.17%，约为 3000-4600 万美元。 Thackery 在 1973 年英国污垢所造成的全部损失大约是当年国民生产总值的 0.3（大约为