Controlling cooling tower water quality by hydrodynamic cavitation

ASHRAE Transactions, July, 2007 by W.A. Gaines, B.R. Kim, A.R. Drews, C. Bailey, T. Loch, S. Frenette

Calculation Methods

The LSI was calculated as follows (Snoeyink and Jenkins 1980; Benefield et al. 1982):

LSI = p[H.sub.actual] - p[H.sub.s]

where

[pH.sub.actual] = actual, measured pH

[pH.sub.s] = pH of water if in equilibrium with [CaCO.sub.3] at the solution concentrations of [HCO.3.sup.-] and [Ca.sub.2 ], = [pK.sub.2] - [pK.sub.so] p{[Ca.sup.2 ]} p{[HCO.sub.3.sup.-]}

[K.sub.2] = {[H.sup. ]} {[CO.sub.3.sup.=]}/{[HCO.sub.3.sup.-]}

[K.sub.so] = the solubility product constant of [CaCO.sub.3]

The procedures described by Snoeyink and Jenkins (1980) and Benefield et al. (1982) were used to correct the above equilibrium constants and activities for ionic strength and temperature.

The overall heat-transfer coefficient [U.sub.o] for each heat exchanger was calculated as follows:

[U.sub.0] = Q/([A.sub.0][DELTA][T.sub.lm])

where

[U.sub.o] = overall heat-transfer coefficient (Btu/h.[ft.sup.2].[degrees]F)

Q = heat-transfer rate (Btu/h)

[A.sub.o] = heat-transfer area ([ft.sup.2])

[DELTA][T.sub.lm] = log mean temperature difference ([degrees]F) = ([DELTA][T.sub.2] - [DELTA][T.sub.1]) / ln ([DELTA][T.sub.2] / [DELTA][T.sub.1])

[DELTA][T.sub.2] = cold-fluid temperature difference, [T.sub.2in] - [T.sub.2out], ([degrees]F)

[T.sub.2in] = heat exchanger process water inlet temperature ([degrees]F)

[T.sub.2out] = heat exchanger tower water outlet temperature ([degrees]F)

[DELTA][T.sub.1] = hot-fluid temperature difference, [T.sub.lin] - [T.sub.1out], ([degrees]F)

[T.sub.lin] = heat exchanger process water outlet temperature ([degrees]F)

[T.sub.1out] = heat exchanger tower water inlet temperature ([degrees]F)

Changes in the overall heat transfer efficiency during operation of the HCD unit were determined from the fouling factor ([R.sub.f]), which is a measure of the resistance to heat transfer due to fouling. The higher the fouling factor, the poorer the heat transfer. The overall heat transfer coefficient data were used to calculate the change in fouling factor using by the following formula:

[R.sub.f] = 1/[U.sub.0,initial] - 1/[U.sub.0,final]

The concentration of dissolved substances in the system water is a balance between their concentrations in the makeup water and the loss of system water through blowdown, drift losses, and evaporation losses. The cycles of concentration (CoC) were calculated by two methods: (1) by taking the ratio of the concentration of a conservative substance (in this case calcium) in the system water to its concentration in the makeup water (Metcalf and Eddy 1991),

CoC = (Concentration of Ca in recirculating water)/(Concentration of Ca in makeup water),

and (2) by taking the ratio of the rate of the total water loss to the estimated rate of loss due to evaporation and drift as shown below (Mortensen 2003):

CoC = (E D B)/(D B)

where

E = evaporation loss (gal/min) = recirculation flow rate (gal/ min) x temperature drop ([degrees]F) x 0.0008

D = drift loss (gal/min) = recirculation flow rate (gal/min) x 0.00005

B = blowdown (gal/min)

Because the evaporative and drift losses are difficult to measure directly, they were estimated as shown above.