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1. The presence of carbonate ions in the tap water leads to a reaction with the dissolved calcium ions to form a white calcium carbonate precipitate which coats the lime particles and inhibits further dissolution. Calcium carbonate, with a Ksp of 4.8 x 10 ^-9, is far less soluble than calcium hydroxide, which has a Ksp of 4.7 x 10 ^-6, so we would expect it to precipitate first when there is a high concentration of calcium ions in solution. The reaction would be

{latex}
\small
$$
Ca^{ - 2} (aq) + CO_3^{ + 2} (aq) = CaCO_3 (s)
$$
{latex}

This may also be thought of in terms of a replacement reaction in which hydroxide is exchanged for carbonate on the surface of the solid lime, as in figure 1. Then the surface of the particles becomes much less soluble and the lime contained within them is effectively lost. The team is unsure of the specific chemical mechanism at work here.

2. Upflow velocity is the vertical component of the flow velocity. The settling velocity of the particles must be balanced with the upflow velocity in order for particles to remain in suspension. If the fluidized bed is not well-maintained by the upflow velocity in the vertical column, the lime settles into a dense bed at the bottom of the apparatus where preferential flow paths lead to insufficient contact time for full dissolution.

3. Also related to kinetics, the concentration of solid lime particles in the fluidized bed (that is, the volume of solid lime per volume of water) may decline as solid lime is lost with the effluent, so that there is not enough available solid lime surface area for the solution to become saturated within the reactor's residence time.

4. There is a minimum contact between solid lime and water that is required for the water to approach equilibrium. This required contact time is related to depth of the fluidized bed, flow rate, solids concentration in the bed, and particle size distribution.

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A shift in the particle size distribution leading to insufficient surface area for dissolution is likely some combination of these three phenomena.

Particle Coalescence

In the "Particle Size" section above it was noted that flocculation of the particles in the fluidized bed was observed. This phenomenon of lime particles sticking together was seen again with the particles sliding down the bottom of the tube settler. The team observed a large solid buildup in the smaller reactor which plugged the branched pipe segment except for some small flow paths. It was thought that the initial buildup occurred on the rim in the pipe connection and that additional settling lime added to the formation of the aggregate solid. This behavior has only been seen when the lime is broken up with a blender prior to the experiment, so the tendency of the particles to stick together seems to be related to some extent to particle size. Other surface properties and chemistry may also play a role, but this is not well understood. Clearly, just as the formation of flocs decreases the surface area available for dissolution, the formation of a solid block of lime is detrimental to the performance of the reactor.

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Preferential flow paths through the "clearest" water in the reactor may also be a mechanism which contributes to the reactor's failure. For example, when the large apparatus is loaded with 200 grams of lime with a flow rate of 120 ml/min, a significant amount of lime remains suspended in the upper slanted segment, but it settles to the lower side of the tube while a clean stream of water flows up the upper side, avoiding further lime dissolution, as in figure 3. This failure mode indicates that the tube settler should not contain settled lime. If more contact time is needed the vertical tube should be made longer.

Chemistry

The carbonate replacement reaction on the surface of the lime particles, mentioned above in the "Beginning of the Semester" section, is the primary chemical mechanism believed to be related to the reactor's failure. Further controlled testing with distilled water should provide further insight into the importance of this phenomenon. In a supplemental test, it was found that even in an effluent sample well below saturation concentration with significant suspended solids the pH decreases over time. The results are shown in figure 4. The steady drop in pH may be due to the effect of carbon dioxide dissolving in the open system and precipitating the calcium. In any case, the fact that the pH decreases rather than increases indicates that the solids remaining in suspension are not calcium hydroxide, which would dissolve over time and raise the pH. This suggests that the leftover solids may be primarily calcium carbonate.