Ind. Eng. Chem. Res. 1998, 37, 439-448
439
Calcium Carbonate Scaling Kinetics Determined from Radiotracer Experiments with Calcium-47 Carl W. Turner* and David W. Smith Chalk River Laboratories, Chalk River, Ontario, Canada K0J 1J0
The deposition rate of calcium carbonate on a heat-transfer surface has been measured using a calcium-47 radiotracer and compared to the measured rate of thermal fouling. The crystalline phase of calcium carbonate that precipitates depends on the degree of supersaturation at the heat-transfer surface, with aragonite precipitating at higher supersaturations and calcite precipitating at lower supersaturations. Whereas the mass deposition rates were constant with time, the thermal fouling rates decreased throughout the course of each experiment as a result of densification of the deposit. It is proposed that the densification was driven by the temperature gradient across the deposit together with the retrograde solubility of calcium carbonate. The temperature dependence of the deposition rate yielded an activation energy of 79 ( 4 kJ/mol for the precipitation of calcium carbonate on a heat-transfer surface. Introduction The deposition of calcium carbonate is one of the principal modes of fouling of the heat-transfer surface of a fresh-water-cooled heat exchanger. Fouling of the heat exchanger leads to a deterioration of its thermal performance, causes an increase in pressure drop across the exchanger for a given flow rate, and produces regions on the heat-transfer surface that are ultimately susceptible to localized corrosion. Hasson (1981) has reviewed the literature on precipitation fouling and published a model to predict the rate of calcium carbonate deposition on a heat-transfer surface (Hasson et al., 1968). The model is based on the eddy diffusion of calcium bicarbonate to the surface followed by the precipitation of calcium carbonate. Hasson et al. (1968) found that for fairly aggressive scaling conditions (i.e., a supersaturation ratio of 17 at the heat-transfer surface and a surface temperature of 75 °C) and forced-convective heat transfer, the deposition rate of calcium carbonate was controlled by the rate of mass transfer to the surface. Watkinson measured scaling rates (Watkinson, 1986) from hard water under very aggressive scaling conditions (i.e., supersaturation ratio of up to 44 at an inlet temperature of 37 °C) that were generally much higher than the rates predicted by Hasson’s model. Watkinson attributed the discrepancy to particulate fouling by suspended particles of calcium carbonate that had precipitated in the bulk fluid. In tests where the suspended material was removed by filtration the agreement between the model and the measured rates was improved, but the measured rates were still significantly higher than those predicted by the model. In experimental investigations of fouling, the kinetics of the fouling process are generally determined by measuring either the deterioration of the total heattransfer coefficient or the increase in pressure drop produced by deposition on a heat-transfer surface (Knudsen, 1981). Alternatively, the deposit mass or deposit thickness can be measured after fouling has * Author to whom correspondence is addressed. E-mail:
[email protected].
taken place for a fixed period of time and the rate determined with the assumption that the deposit buildup had a linear time dependence. Radiotracers, however, permit a direct measurement of the deposit mass as a function of time throughout the fouling experiment and thus provide additional insights into the kinetics of the fouling process. We report here the results of an experimental investigation of the kinetics of calcium carbonate deposition on a heat-transfer surface measured using radioactive calcium-47. Both mass deposition and thermal fouling rates were measured in each experiment. A comparison between the two provided insights into the process of deposit aging on a heattransfer surface. The mass deposition rate data were analyzed using a diffusion/precipitation model to yield rate constants for calcium carbonate precipitation for surface temperatures from 57 to 89 °C. Experimental Methods and Analyses Heat-Exchanger Fouling Loop. A schematic of the loop used to measure the kinetics of calcium carbonate scaling under forced-convective heat transfer is shown in Figure 1. All components of the loop, including the test section, are constructed from stainless steel. Water containing the scaling solution is pumped around the loop with a centrifugal pump. The flow rate is measured with a magnetic flowmeter. A process signal is sent from the flowmeter to a controller that operates an airactuated valve to regulate the loop flow rate to within ( 1% of the set point. Scaling takes place on the inside surface of a test section that is heated electrically with alternating current. A controller maintains the power delivered to the test section to within ( 1% of the set point. The test sections were 0.60 m lengths of 3/8 in. stainless steel tubing with an inside diameter of 7.75 mm. Data from the first 0.15 m (≈20 hydraulic diameters) were excluded from the analysis to allow for boundary layer formation. Thermocouples were spot welded onto the outside of each test section at three locations to measure the wall temperature. Additional thermocouples were located in thermowells within the main flow to monitor the fluid temperature at the inlet and outlet of the test section. Cooling coils in the 200
S0888-5885(97)00309-6 CCC: $15.00 Published 1998 by the American Chemical Society Published on Web 01/14/1998
440 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998
Figure 1. Schematic of the heat-exchanger fouling loop.
L tank maintained the inlet temperature to within (0.2 °C of the set point. The total power to the test section was calculated from a heat balance based on the inlet and outlet temperatures of the heated test section and the flow rate. The bulk fluid temperature was assumed to increase linearly along the length of the test section. The surface temperature at any location along the test section (for x > 20 hydraulic diameters) was calculated from
Q ) h(Ts - Tb)
(1)
h ) 0.027(κf/D)Re0.8Pr0.33(µb/µs)0.14
(2)
where
Since h depends on Ts through µs, Ts was calculated by an iterative process. Ts was considered exact when its value changed by less than 0.2 °C on successive iterations. Before the onset of scaling, the outside wall temperature of the heated test section, Tw, could be calculated from
Tw ) Ts + Qδ/κw
(3)
Estimates of Tw using eq 3 were within (1 °C of the measured wall temperatures, which is a good check on both the consistency of the methods used to determine Q and Ts and the accuracy of the measurements of wall temperature and flow rate. The loop conditions pertaining to the experiments are shown in Table 1. Ts is listed for the midpoint of the test section only. The thermal resistance of the calcium carbonate deposit was calculated as a function of time from
Rd(t) ) (Twf(t) - Twc)/Q
(4)
Chemicals and Chemical Analyses. The scaling solutions were prepared by mixing Fisher reagent-grade calcium chloride and calcium oxide in distilled water in the 200 L stainless steel vessel that serves as the loop chemistry control tank. The calcium oxide was dissolved by purging the distilled water in the tank with a flow of carbon dioxide. Dissolution occurred within 2 h once the pH of the tank had been reduced to ap-
Table 1. Thermal Hydraulic Conditions for the Calcium Carbonate Scaling Experimentsa exp.
U (m/s)
Q (kW/m2)
Re
Tin (°C)
Ts (°C)
1 2 3 4 5 6 8 9 10 11 12 13 14 15
1.06 1.06 1.06 1.06 2.12 1.06 2.12 0.88 0.88 1.06 1.06 1.06 2.12 1.06
53.4 53.4 296 296 255 255 259 296 209 142 142 142 163 288
11 000 11 000 13 440 13 440 14 400 26 100 25 800 12 580 11 730 13 000 13 000 13 000 25 860 14 460
31 31 31 31 31 36 35 35 35 35 35 35 35 35
41 41 80 80 63 61 61 91 76 60 60 60 61 82
a
Ts is listed for the midpoint of the heated test section.
proximately 5. After the calcium oxide was dissolved, the pH was raised to its target value by sparging the tank water with a mixture of 1% carbon dioxide in air and argon gas. The gas flow rates were regulated using Tylon mass-flow controllers to maintain constant pH. The gas flow was continued at a reduced rate throughout the experiment. Filtered samples of the loop water taken during the test period showed no evidence for particulate formation, so all of the calcium was assumed to have remained in solution after the final adjustment of the pH and application of the heat flux to the test section. The concentration of dissolved calcium was determined by titration with the disodium salt of ethylenediaminetetraacetic acid (EDTA) using a well-established technique (Kolthoff et al., 1969). A spike of standard magnesium carbonate solution (Fisher standard grade) was added to sharpen the end point, and fresh solutions of Eriochrome Black T indicator were prepared biweekly. EDTA dried at 70 °C for 16 h and cooled in a dessicator was weighed to five significant figures and dissolved in distilled, deionized water. This solution was diluted to approximately 0.001 M in a volumetric flask and standardized with a calcium carbonate standard solution (Fisher standard grade). The chloride concentrations were measured with an Orion chloride selective electrode. Potassium chloride dried for 16 h at 70 °C and cooled in a desiccator was
Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 441 Table 2. Chemistry Conditions at the Midpoint of the Heated Test Section for the Calcium Carbonate Scaling Experiments S
exp.
pH
[Ca] × 103 (mol/kg)
[Cl] × 103 (mol/kg)
[HCO3-] × 103 (mol/kg)
[CO32-] × 106 (mol/kg)
Tb
Ts
1 2 3 4 5 6 8 9 10 11 12 13 14 15
7.33 7.45 7.45 7.50 7.55 7.80 7.61 7.60 7.60 7.78 8.00 8.00 8.00 8.00
2.60 2.60 2.60 2.60 2.53 2.53 2.50 2.45 2.38 2.38 2.10 2.38 2.28 2.13
2.73 2.73 2.87 2.82 2.82 2.90 2.93 2.93 2.80 2.93 2.93 3.01 2.96 2.90
2.46 2.46 2.32 2.38 2.23 2.08 2.05 1.95 1.95 1.81 1.25 1.72 1.57 1.33
3.85 5.07 5.24 6.03 7.51 10.6 6.97 6.65 6.41 8.64 7.73 13.6 5.89 11.0
1.8 2.3 2.7 3.2 3.0 5.5 3.9 3.9 3.4 4.2 3.5 6.7 5.9 5.5
2.4 3.1 9.6 11.0 6.8 10.9 6.7 14.9 9.3 8.1 6.6 12.8 11.6 17.0
weighed to five significant figures and dissolved in distilled, deionized water. This solution was used to prepare a calibration curve for the chloride-sensitive electrode. The electrode was recalibrated for each measurement of chloride in the tank water. The pH of the tank water was measured with an Orion pH probe. The probe was calibrated regularly using standard buffers at pH 4, 7, and 10. Water samples for the pH measurements were collected in a 250 mL Erlenmeyer flask that was immediately sealed with a rubber stopper to prevent the escape of dissolved carbon dioxide to the atmosphere. The pH probe was fitted with a rubber stopper to prevent the escape of gas during the measurement. Before measuring the pH, the ionic strength of the sample was increased by the addition of a spike of a concentrated potassium chloride solution to quicken the response of the pH probe. The propensity for the water to scale under heattransfer conditions was determined by calculating the supersaturation ratio, S, of the solution, which can be defined as
S ) [Ca2+][CO32-]fD2/Ks
(5)
The Langelier saturation index for calcium carbonate (Langelier, 1936) is equal to the common (base 10) logarithm of the supersaturation as defined in eq 5. The mathematical expressions used to calculate the supersaturation are given in Appendix A. The chemistry conditions for each experiment along with the calculated S at Tb and Ts (at the midpoint of the heated test section only) are shown in Table 2. Radiotracing and Data Reduction. The deposition of calcium carbonate on the heated test section was monitored using a radiotracing method. A sample of calcium oxide that was irradiated in the NRU reactor at Chalk River Laboratories to produce calcium-47 (halflife ) 4.54 days) was dissolved along with inactive calcium oxide in the 200 L loop tank. The activity of calcium-47 (both in solution and deposited in the form of calcium carbonate on the test section) was determined from the intensity of the γ ray at 1297 keV, which signifies the decay of calcium-47 to scandium-47, using an on-line high-purity germanium crystal γ-ray detector. Lead shielding was placed around the detector to ensure that only those γ-rays that originated from an effective length “L” (≈0.12 m) of the test section (centered at the detector) were measured. The mass per unit area of calcium carbonate that deposited onto the heated test section was calculated
from both on-line and off-line radiotracing data. The activity of calcium-47 in solution measured by the online detector is related to the concentration of calcium in solution by
Ab ) 0.100GFf[CaCO3]bAspπD2L/4
(6)
Similarly, the activity of calcium-47 in the deposit measured by the on-line detector is related to the deposit mass per unit area by
Ad ) GMdAspπDL
(7)
The factor 0.100 in eq 6 accounts for the conversion from kilograms to moles of calcium carbonate. From eqs 6 and 7, the deposited mass of calcium carbonate per unit area is given by
Md ) 0.025AdDFf[CaCO3]/Ab
(8)
The mass calculated from eq 8 is called the “on-line” deposit mass. Samples were withdrawn from the loop periodically throughout each experiment to determine both the concentration and the activity of calcium carbonate per unit volume of the test solution. These data were used to calculate the specific activity of calcium carbonate. At the end of each experiment, the test section was cut into a series of 30 mm lengths and the activity per unit area was measured on each of these lengths using an off-line γ counting system. From the specific activity, the measurements of deposit activity per unit area were converted to a deposit mass per unit area. The deposit mass determined using this method is called the “off-line” deposit mass. Since Ts increases along the length of the test section in a well-defined way, the measurements of off-line deposit mass versus position along the length of the test section provide data on the temperature dependence of the deposition rate of calcium carbonate. There was generally good agreement between the on-line deposit mass and the off-line deposit mass averaged over the midregion of the test section. The deposit on the heated test section was also examined using X-ray diffraction (XRD) and scanning electron microscopy (SEM) to determine the crystalline phase and the deposit morphology, respectively. Results Calcium carbonate precipitated onto the heat-transfer surface in one of two crystalline phases: calcite or
442 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998
Figure 2. Deposit mass versus time for experiment 2. The figure shows the kinetics of calcium carbonate deposition during the induction stage.
aragonite. Calcite crystals were observed when the supersaturation ratio at the temperature of the heattransfer surface was relatively moderate (i.e., 8 < S < 10), whereas aragonite was observed when the supersaturation was relatively high (i.e., 9 < S < 22). There was no sharp boundary between the regimes where calcite and aragonite were the dominant crystalline phases. In both cases, the precipitation of calcium carbonate on the heat-transfer surface was preceded by a period where the rate of deposition was relatively low. Some investigators have called this the induction period. The time spent in this preliminary stage of deposition was observed to decrease with both increasing supersaturation at a given surface temperature and increasing surface temperature at a given supersaturation. For experiments where S < 7, the precipitation of calcium carbonate remained in this preliminary, or induction, stage for the duration of the test (i.e., generally
