Investigation of Initial Fouling Rates of Calcium Sulfate Solutions under Non-Boiling Conditions (Work-in-Progress)

Transcription

1 eereed Proceedings Heat Exchanger Fouling and Cleaning: Fundamentals and Applications Engineering Conerences International Year 23 Investigation o Initial Fouling ates o Calcium Sulate Solutions under Non-Boiling Conditions (Work-in-Progress) Feridoun Fahiminia A. Paul Watkinson Norman Epstein The University o British Columbia The University o British Columbia The University o British Columbia This paper is posted at ECI Digital Archives.

2 Fahiminia et al.: Initial Fouling ates o Calcium Sulate Investigation o Initial Fouling ates o Calcium Sulate Solutions under Non-boiling Conditions (Work-in-Progress) Feridoun Fahiminia, A. Paul Watkinson and Norman Epstein Department o Chemical and Biological Engineering The University o British Columbia, 2216 Main Mall, Vancouver, BC, Canada, V6T 1Z4 ABSTACT This study initiates an experimental investigation o how process variables such as temperature and velocity aect the initial precipitation ouling rate o the inverse solubility salt, calcium sulate, under sensible heating conditions. The eect o luid velocity and temperature on the delay time is also being measured. Introduction Motivation or this work stems rom the development o a mathematical model or the initial ouling rate in chemical-reaction, particulate and precipitation ouling (Epstein, 1994). In this study, the model will be tested using experimental data or calcium sulate scaling under non-boiling conditions. According to the model, the attachment o the ouling deposit to the heat transer surace is treated as a rate process in series with mass transer under turbulent low conditions. As shown in the model development, or a given solution and a ixed surace temperature, the attachment or surace integration coeicient (which is assumed to bear the Arrhenius relationship to the surace temperature and to be proportional to the luid residence time near the surace) is inversely proportional to the square o the riction velocity, and the mass transer coeicient is directly proportional to this velocity. Thereore, there is a maximum initial ouling rate at a given surace temperature or a range o luid velocities, demonstrating a shit rom mass transer to attachment control. The model also predicts that this maximum rate (and its bracketing rates) and the luid velocity at which it occurs both increase as the surace temperature is increased. Experimental The apparatus consists o a low loop in which the calcium sulate in iltered aqueous solution is continuously recirculated rom a holding tank through the heated test section (d i = 9.17 mm), a series o double pipe coolers and back to the holding tank. The test section itsel is a 1.83 m long 34L stainless steel tube with an outside diameter o mm, a wall thickness o.254 mm and a heated length o.771 m, which is subjected to electrical resistance heating at a constant and uniorm heat lux. Bulk inlet and outlet temperatures were measured by thermocouples. The bulk inlet temperature was maintained at 55 C, while clean tube surace temperatures were varied rom 8 to 11 C, as measured by ten thermocouples spaced longitudinally on the outside o the vertical tube. The rate o rise in surace temperature gives a measure o the local ouling resistance at that temperature. This Tube Fouling Unit (TFU) (Wilson and Watkinson, 1996; ose et al., 2) is conigured such that test sections are used only once, and then sectioned to allow in situ deposit examination and urther analysis o the nature o the deposit material, either by optical microscopy, scanning electron microscopy, elemental analysis or deposit coverage studies. Due to the longitudinal temperature gradient at the surace o the tube, it was the highest temperature thermocouples that exhibited the highest rates o ouling, and thus limited the duration o an experiment. Because clean surace temperatures were as high as 11 C, it was necessary to maintain some over-pressure on the test section to prevent the onset o boiling as the surace temperature rose due to ouling. Because o the high temperature restriction, most o the data rom the low temperature regions o the tube gave barely measurable initial ouling rates, so they were neglected in the data analysis. eynolds numbers based on local luid properties were varied rom 7 to 21 to provide adequate data or a complete study o the velocity eect on initial ouling rates. Batches o calcium sulate solution were prepared in saturated solutions (21 ppm) rom its powder. Ater ensuring the saturated condition by using EDTA titration, the solution was added to the holding tank. Prior to the addition o heat to the test section, the solution was circulated or one hour to ensure a thoroughly well mixed chemical system. The power to the test section was then applied to achieve the operating conditions required. Heating up the test section to steady state took approximately 3 minutes. Published by ECI Digital Archives, 23 1

3 Heat Exchanger Fouling and Cleaning: Fundamentals and Applications, Art. 5 [23] esults Fouling in this system was thus ar measured only thermally, although mass deposition and pressure drop measurements could also be made. The local heat transer coeicient at a given thermocouple location along the length o the test section was determined rom the ollowing equation, where Q was evaluated rom the voltage and current applied to the test section, T b rom the bulk inlet and outlet luid temperatures and T w calculated rom the measured thermocouple temperature (T o ) : Q U = ( T w Tb) The ouling resistance was determined rom 1 1 = U U C (2) and the initial ouling rate rom 1 (3) ( U ) dt o = d / dt t d / = = assuming that the convective heat transer coeicient does not change with respect to time or with surace roughness eects. The low rate and hence velocity o the luid through the TFU was measured using a calibrated rotameter. The reported bulk velocity is the time averaged value over the duration o the experiment at any given level. For each experiment, the thermal ouling results were measured rom up to 1 thermocouples located at various axial positions, but ouling was observed only at the top thermocouples. For most o the experiments, the top thermocouples showed a linear increase in wall temperature with time ater a delay time ( t d ). This made the analysis or the initial ouling rate straightorward. In the region where the temperature is irst increasing at a constant rate, the corresponding plot o reciprocal heat transer coeicient versus time is linearly regressed and rom equation (3) the slope is equal to the initial ouling rate. 1/U (m 2 K/kW) T w,c =99.5 C Figure 1. eciprocal heat transer coeicient or TFU 51 (V =.62 m/s) (1) Time (s) T w,c = 98 C Figure 1 shows a plot o reciprocal heat transer coeicient versus time (un 51) or temperatures T w,c = 99.5 C and T w,c = 98 C. Figure 2 shows a ouling Arrhenius plot (ln o = ln A E Tw,c ) or a given experiment, where individual thermocouple results were utilized to determine the surace temperature at a velocity o.62 m/s. The ouling activation energy Initial Fouling ate (m 2 K/kJ) (*1 6 ) y = -646x =.999 Figure 2. Arrhenius plot or TFU 51 (V=.62 m/s) E /T W,c (K -1 ) or this experiment was determined as 53 kj/mol, a value which characterizes the entire ouling process at the given velocity and not just the attachment process as described by the attachment-kinetics activation energy in the model. The results or all runs perormed to date are presented in Table 1. A kinetic compensation eect is evident where both the ouling activation energy, E, and the pre-exponential term, A, increase very strongly with velocity. At a velocity o.62 m/s, or example, the itted rate is a product o one term o magnitude (A), and another o magnitude 1-71 (e E / T w, c ). Thereore, the ouling activation energy values o Table 1 are considered unreasonable. A moderate increase in E with mass lux is expected rom the mathematical model. For small luid velocities (mass transer control) the ouling activation energy will approach a low value, while or high luid velocities (surace attachment control) the ouling activation energy will approach the purely attachment-kinetics activation energy (ose et al., 2). To date, only a narrow range o temperature has been covered. The surace temperature range o C includes the critical value o 98 C where gypsum is transormed into hemi-hydrate, as discussed by Mwaba et al. (21). To obtain reasonable results or the ouling activation energy, more experiments should be carried out over a wide range o temperatures below 98 C. From Table 1 it is however possible to use the Arrhenius expression to determine at a given value o 2

4 Fahiminia et al.: Initial Fouling ates o Calcium Sulate o T w,c or each experiment and hence to tentatively isolate the eect o velocity on initial ouling rate. Thus Initial Fouling ate (m 2 K/kJ) Figure 3. Eect o velocity on initial ouling rate or calcium sulate solution 1/U (m 2 K/kW) (*1 6 ) t d = 5.22 hr Velocity (m/s) T =11 C T =99 C Time (s) Figure 3 shows two sets o results at surace temperatures where the initial ouling rate is strongly dependent upon the velocity. In both cases we can see the presence o a maximum deposition rate at a critical velocity as predicted by the previously discussed model. The two plots indicate how strong a dependence the ouling rate has on surace temperature, with appreciable dierences observed or only a 2 C temperature change. Delay Time The period o time that elapses between the achievement o supersaturation and the irst detection o a ouling deposit has been given dierent names and will be denoted here as the delay time. The duration o the delay time or a given system is aected by the degree o supersaturation, the temperature level, the velocity and the presence o impurities. The occurrence o a delay time is undoubtedly related to the kinetics o nucleation but its signiicance is diicult to analyse. It has been shown that CaSO 4 nucleation on the heat transer surace o a nonboiling low exchanger is a transient nucleation phenomenon (Hasson and Zahavi, 197). Also, Branch (1991) correlated the reciprocal o the delay time as i it were independent o solute concentration but with an Arrhenius dependence on wall temperature, but Najibi et al. (1997) showed that the delay time is a strong unction o the degree o supersaturation and, thereore, cannot be expressed by a zero-order model. Figure 4 shows how the line representing the reciprocal heat transer coeicient prior to ouling buildup (horizontal) intersects with the regressed straight line (the region with a constant ouling rate) and thus determines the delay time or each thermocouple. In all o the ouling runs or the present investigation, delay times were observed and measured using this method and then it was possible to see how the delay time varies with velocity and temperature. Figure 4. Delay time or T w,c = 98 C (un 51) Table 1. Fouling activation energies or calcium sulate experiments un T w,c ( C) T b,x ( C) V (m/s) E (kj/mol) A (m 2 K/kJ) E E E E E+169 Published by ECI Digital Archives, 23 3

5 Heat Exchanger Fouling and Cleaning: Fundamentals and Applications, Art. 5 [23] Figure 5 shows the eect o surace temperature on the delay time or TFU 56. It shows that the delay time is a strong unction o surace temperature. Figure 5. Eect o surace temperature on the delay time at V =.44 m/s Figure 6 shows the eect o velocity on the delay time. It is seen that as the velocity increases, the delay time irst decreases and then remains approximately constant. Delay time (hr) Delay time (hr) T w,c ( C) Velocity (m/s) T = 98 C T = 99.6 C Figure 6. Eect o velocity on the delay time at two dierent wall temperatures Conclusions A systematic study o calcium sulate scaling in turbulent low under sensible heating conditions has been initiated. The results obtained thus ar show, with some scatter, a maximum initial ouling rate at a given surace temperature over a range o luid velocities, and an Arrhenius dependence on surace temperature at any given velocity. Overall activation energies are inordinately large and thereore require urther investigation. Delay times were ound to decrease with increasing surace temperature and luid velocity below about.5 m/s, but to remain approximately constant at higher velocities. This study will be continued over a wider temperature range, with deposit analysis. ACKNOWLEDGMENTS The authors are grateul to the Natural Sciences and Engineering esearch Council o Canada or inancial support. NOMENCLATUE A = pre-exponential actor, m 2 K/kJ d i = inside tube diameter, mm or m E = ouling process activation energy, J/mol Q = heat lux, kw/m 2 = universal gas constant,.8314 k J/mol K = ouling resistance, m 2 K/kW o = initial ouling rate, m 2 K/kJ T = temperature, ºC or K T b T o T = bulk luid temperature, ºC or K = outside tube wall temperature, ºC or K w = inside tube wall temperature, ºC or K t = time, s U = overall heat transer coeicient, kw/m 2 K V = bulk luid velocity, m/s t d Subscripts c = clean = delay time, s EFEENCES Branch, C. A. Heat transer and heat transer ouling in evaporators with krat pulp black liquor,. Ph.D. thesis, University o Auckland, New Zealand (1991). Epstein, N., A Model o the Initial Chemical eaction Fouling ates or Flow within a Heated Tube, and its Veriication, Heat Transer 1994, Proceedings o The Tenth International Heat Transer Conerence, Brighton, UK, 4, (1994). Hasson, D., Zahavi, J., Mechanism o Calcium Sulate Deposition on Heat-Transer Suraces, I&EC Fundamentals 9, 1-1 (197). 4

6 Fahiminia et al.: Initial Fouling ates o Calcium Sulate Mwaba, M. G., indt, C. C. M., Vorstman, M. A. G., Van Steenhoven, A. A., Calcium Sulate Deposition and emoval Characteristics on a Heated Plate, Proceedings o an Engineering Foundation Conerence on Heat Exchanger Fouling: Fundamental Approaches & Technical Solutions, Davos, Switzerland, July, 21. Najibi, S. H., Muller-Steinhagen, H., Jamialahmadi, M., Calcium Sulphate Scale Formation During Subcooled Flow Boiling, Chemical Engineering Science 52, (1997). ose, I. C., Watkinson, A.P., Epstein, N., Testing a Mathematical Model or Initial Chemical eaction Fouling using a Dilute Protein Solution, Canadian Journal o Chemical Engineering 78, 5-11 (2). Wilson, D.I., Watkinson, A. P., A Study o Autoxidation eaction Fouling Heat Exchangers, Canadian Journal o Chemical Engineering 74, (1996). Published by ECI Digital Archives, 23 5