SEARCH

SEARCH BY CITATION

Keywords:

  • CO2;
  • carbon dioxide;
  • stripping;
  • modeling;
  • cooling water

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

A simplified mathematical model has been developed to evaluate the effect of CO2 stripping on pH of recirculating cooling water in power plant cooling systems. Experimental data from three pilot-scale cooling towers using treated municipal wastewater as makeup water were used to determine the CO2 mass transfer coefficients in the gas phase kg and aqueous phase kw. The optimum values of the gas film mass transfer coefficient and water film mass transfer coefficient were determined by regression to be kg = 8.4 × 10−6 m/s and kw=8.4 × 10−8m/s, respectively. The results also indicate that the model is capable of predicting the pH of the cooling loop as a function of makeup water alkalinity and cooling loop alkalinity (in case of salt formation) as well as the operating parameters of the cooling system. © 2013 American Institute of Chemical Engineers Environ Prog, 33: 275–282, 2014


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

Recirculating cooling water system pH together with other water quality parameters can significantly affect the scaling and corrosion potential of the water. Traditional approaches for cooling water scaling and corrosion potential evaluation rely on various saturation indices, such as the Langelier saturation index and the Ryznar stability index, that require knowledge of cooling system pH [1]. Thus, cooling water pH prediction is of great interest for scaling and corrosion control evaluation.

Several empirical equations have been proposed that express cooling water pH as different functions of cooling water alkalinity. These empirical equations include Kunz's equation [2], Puckorius' equation [3], and Caplan's equation [4]. However, because the makeup water quality and cooling system operating conditions (i.e., cycles of concentration, temperature, etc.) also affect the pH of the cooling loop, these empirical equations cannot accurately predict the pH of the cooling loop over a broad range of operating conditions.

Other traditional approaches for prediction of cooling water quality are generally based on the cooling water thermodynamic equilibria, which assume that the carbonate species in the cooling water is at equilibrium with the atmosphere. However, cooling water pH and alkalinity monitoring data collected from more than 40 cooling towers have shown that thermodynamic equilibrium is not achieved in most open-recirculating cooling systems [5].

Although comprehensive rate-based models have been developed to estimate CO2 and/or NH3 evaporations in cooling towers [e.g., [6], these models require detailed information on the properties of the water entering the cooling tower which is not usually available. To predict CO2 evaporation in cooling towers using readily available information such as makeup water flow rate and alkalinity, cycles of concentrations, and loop water alkalinity requires an integrated approach that combines the cooling tower with the rest of the cooling system.

Ballard and Matson [7] developed a cooling tower carbonate equilibrium model (CTCE) that considers makeup water pH and alkalinity as input parameters to predict cooling water pH based on the carbonate species mass balance in the cooling system. This model is based on the assumption that the “cooling tower is 100% efficient in achieving equilibrium between dissolved CO2 in the cooling water and CO2 in the atmosphere” [7]. They also showed that a simplified version of CTCE (i.e., SCTCE) predicts results similar to those in their study, indicating that the simplification was reasonable. The cooling loop water pH in the SCTCE model is determined from the following equation:

  • display math(1)

In a cooling system Qx is usually two orders of magnitude higher than Qm and Qb, and Cm and Cyb/KH are usually in the same order of magnitude, thus Eq. (1) can be further simplified:

  • display math(2)

Equation (2) describes the relationship of pH with alkalinity under the condition of aqueous phase equilibrium with the atmosphere when alkalinity is dominated by the bicarbonate species (pH <9). In general, Eq. (2) leads to overestimation of CO2 stripping in the cooling tower resulting in overestimation of the cooling loop pH.

Three pilot-scale cooling towers were used to obtain experimental data to relate the pH of the cooling loop to cooling water alkalinity and makeup water quality using a particular makeup water source. The makeup water source was a treated municipal wastewater. The information regarding the specifications of the towers and the operating procedure has been presented elsewhere [8].

Figure 1 shows the monitoring results of the cooling water pH-alkalinity relationship during a 2-month period of pilot testing, along with the results obtained by Eq. (2) (i.e., equilibrium calculations) as well as those predicted by the SCTCE model and various empirical equations including Kunz's equation, the Pukorious' equation, and Caplan's equation. The results in Figure 1 indicate that none of these models can accurately predict the pH of the cooling loop, suggesting that an improved model is needed that can take into account other important variables that significantly affect the loop pH. These include the mass transfer limitations for evaporation of CO2 in the cooling tower, the salt formation in the cooling system, and the extent of NH3 stripping when degraded waters such as municipal wastewaters are utilized for cooling.

image

Figure 1. pH-alkalinity relationship (1) derived from actual pilot testing data, (2) predicted with SCTCE model, (3) described using equilibrium equation, and (4) described using previous proposed empirical equations (5) No mass transfer (k = 0).

Download figure to PowerPoint

This article focuses on the effect of CO2 stripping in the cooling loop using a similar approach that has been published by the authors in an earlier publication on estimating ammonia stripping [9]. The objectives of this study were to: (1) develop a simplified mathematical model that can be used to predict the cooling water pH as a function of readily available information such as makeup water alkalinity and cooling system operating conditions, (2) determine the mass transfer coefficients for CO2 stripping in the cooling tower using the water quality monitoring results obtained from field testing in pilot-scale cooling towers.

Modeling Approach

Figure 2 shows the schematic diagram of a cooling tower. Air with flow rate Qy (m3/s) and total CO2 concentration Cyb (mol/m3) enters the bottom of the tower and leaves at the top with total CO2 concentration Cya (mol/m3). Makeup water with flow rate Qm (m3/s) and total inorganic carbon (TIC) concentration Cm (mol/m3) enters into the basin of the cooling tower. Blowdown leaves the basin with flow rate Qb (m3/s) and TIC concentration Cxa (mol/m3). Cooling water leaves the basin and enters the top of the tower with flow rate Qx (m3/s) and TIC concentration Cxa. Evaporation rate in the cooling system is Qe (m3/s). Cooling water leaves the tower at the bottom and enters into the basin with flow rate of (Qx-Qe) and total TIC Cxb (mol/m3). For this derivation, activity coefficients are considered unity for all chemical species. Usually Qe is less than 3% of Qx and it is reasonable to assume that Qe is negligible when compared to Qx (i.e., (Qx-Qe) is approximately Qx). Vertical distance above the bottom of the packing is Z (m).

image

Figure 2. Carbon dioxide mass flow diagram for a recirculating cooling tower (Source: Hsieh et al., 2012).

Download figure to PowerPoint

Using the two-film theory [10], the CO2 mass transfer rate across the air-water interface at any vertical section dZ of the packing can be expressed as follows:

  • display math(3)

where CTx is the TIC concentration in the cooling water at a vertical distance Z in the packing (mol/m3) and Cy is the CO2 concentration in the air at a vertical distance Z in the packing (mol/m3). Since H2CO3* dissociation is expected to be significantly faster than its mass transfer rate across the water-air interface [11], the overall mass transfer coefficient in the two film theory with fast dissociation reaction can be expressed by the equation [12]:

  • display math(4)
  • display math(5)
  • display math(6)

In the above equations the coefficient “α” accounts for the influence of CO2/HCO3 speciation and co-diffusion through the water film. Rg is the resistance in the air film (s/m) and is defined as 1/(kgKH), Rw is the resistance in water film (s/m) and is defined as 1/(kwα), and Rg/Rw represents the ratio of the gas to liquid phase resistances. Equation (6) shows that the gas to liquid phase resistance increases as the pH of the aqueous phase increases (increase in α).

The CO2 concentration in the water (Cx) and the total inorganic carbon concentration (CTX) are related through the following equation:

  • display math(7)

In the pH range of interest (i.e., pH of 6–9), alkalinity is typically dominated by bicarbonate, that is

  • display math(8)

and therefore, TIC concentration is related to CO2 through the alkalinity:

  • display math(9)

Since the evaporation rate is significantly lower than the recirculating water flow rate (Qe << Qx), the TIC mass balance in the packing section of the vertical distance from 0 to Z can be expressed as:

  • display math(10)

By substituting CTx from Eq. (9) and Cy from Eq. (10) into Eq. (3), and assuming that alkalinity is conserved in the system (i.e., ALKxa=ALKxb=ALKx and QmALKm=QbALKx), Eq. (3) can be integrated over the ranges of Cx from Cxb to Cxa and Z from 0 to ZT [packing total height, (m)], to obtain the following equation:

  • display math(11)

In Eq. (11), k and KH can be assumed to be constant over the height of the tower (due to near isothermal tower operation), A is the effective total packing surface area (AbaZT), and E is calculated from the following equation:

  • display math(12)

Since QyKH>>Qx, E becomes:

  • display math(13)

and TIC mass balance in the basin can be expressed as:

  • display math(14)

Applying Eq. (9) and alkalinity conservation (i.e., ALKxa=ALKxb=ALKx and QmALKm=QbALKx), Eq. (14) becomes:

  • display math(15)

By substituting Cxa from Eq. (9) into Eq. (13) and after rearrangement, the CO2 concentration in the blowdown as a function of the flow rates and cooling tower properties can be obtained by Eq. (16), while the pH of the cooling water in the basin is given by Eq. (17):

  • display math(16)
  • display math(17)

In Eq. (17), Cxa is [H2CO3*]xa, and Ka1 is the equilibrium constant for the dissociation reaction of [H2CO3*]:

  • display math(18)

Since k and therefore E are functions of pH, pHxa can be calculated by solving Eqs. (16) and (17) using an iterative scheme.

As indicated above, Eqs. (16) and (17) are obtained based on the assumption that the alkalinity is conserved in the system. However, if alkalinity is not conserved in the cooling system due to salt formation, acid addition, or ammonia stripping, Eqs. (16) and (17) cannot be applied. If carbonate salts are precipitating in the basin at a rate of S (mol/s) and alkalinity is also consumed by acid addition at a rate of R (equivalent/s−1), Eqs. (16) and (17) become:

  • display math(19)
  • display math(20)

where S and R are the sink terms, representing alkalinity consumption in the cooling system due to the carbonate salts precipitation and acid addition, respectively. Equations (19) and (20) indicate that the cooling water pH can be estimated using the makeup water properties, the makeup and the blowdown flow rates (Qm and Qb), and the overall mass transfer constant (k).

EXPERIMENTAL METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

The carbon dioxide stripping model represented by Eqs. (19) and (20) was applied to the experimental data to determine the optimum CO2 mass transfer coefficients. The experimental data was obtained from two-month tests with pilot-scale cooling towers using a nitrified secondary treated municipal wastewater (MWW-N) as makeup water. The water chemistry parameters needed for the model were monitored on a regular basis during the pilot testing.

Pilot-Scale Cooling Towers

Three identical pilot-scale cooling towers (CTA, CTB, CTC) were used in this study. Each pilot-scale cooling tower had an evaporative cooling system, a heating system, a makeup water control system, a blowdown flow control system, and a power control system. The detailed specifications of the towers have been presented elsewhere [8, 9, 13, 14].

Tertiary-Treated Municipal Wastewater as Makeup Water

MWW-N from the Franklin Township Municipal Sanitary Authority (FTMSA, Murrysville, PA) was used as makeup water for pilot testing. The facility employs a series of treatment processes including primary clarification, secondary treatment by trickling filter, secondary clarification, nitrification, sand filtration, and UV disinfection. MWW-N used for this study included waters obtained both before and after, but before UV disinfection. During a typical test, MWW-N was pumped into the makeup water storage tanks on a daily basis before being injected into the pilot tower basins. The MWW-N in this study had alkalinity concentration ranging from 11 to 60 mg/L as CaCO3 from 36 samples. The pH value of the MWW-N during the testing period ranged from 6.0 to 7.8 and its ammonia content was less than 0.05 mg/L. Other characteristics of the MWW-N effluent were reported previously [15].

Pilot-Scale Tower Testing and Data Analysis

Pilot-scale cooling towers were operated at FTMSA in 2010. ALKm, ALKxa, pHm, pHxa, and cycles of concentration (N) were monitored regularly. Using the maintained temperature drop of 5°C, Qx = 11.35 L/m (3 gpm), and the recorded N, Qm, and Qb can be calculated. The towers were operated with input water in the temperature range of 35–40°C and with input air at the flow rate of Qy = 4250 (L/m). Values of Ka1 and KH were determined using an average temperature of 37.5°C. pKa1 and KH were calculated to be 6.3 and 1.615 (m3w/m3g), respectively. Ab, a, ZT of pilot towers were 0.093 m2 (1 ft2), 147.5 m2/m3 (45 ft2/ft3) and 0.915 m (3 ft), respectively.

RESULTS AND DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

Pilot-Scale Cooling Tower Test Monitoring Results

Monitoring results for makeup and loop water alkalinity, pH, and cycles of concentrations for the nitrified wastewater (MWW-N) are presented in Table 1. The makeup water alkalinity and the pH variation were due to the variation in the quality of the MWW-N effluent. The experimental data in Table 1 suggest that the pH of the cooling loop generally increases with the alkalinity of the makeup water, and that the pH of the loop does not appear to be dependent on the cycles of concentration N. The data also indicate that, in some cases, alkalinity was lost in the cooling system, which can be attributed to the formation of salts in the system. The lost alkalinity was calculated from the experimental date and used in the model as an input parameter (Eqs. (19) and (20)). Measurements of alkalinity, cooling water pH, and flow rates were used in Eqs. (19) and (20) to determine the overall mass transfer coefficient, k, through regression.

Table 1. Monitoring results for alkalinity in makeup and cooling water, pH of cooling water, and cycles of concentration in pilot testing with FTMSA MWW-N.
Cooling Tower A (CTA)Cooling Tower B (CTB)Cooling Tower C (CTC)
pHmALKmpHxaNALKxapHmALKmpHxaNALKxapHmALKmpHxaNALKxa
  1. Units for ALKm and ALKxa are mg/L as CaCO3.

7.8459.68.384.9126.47.8347.08.415.797.57.7652.48.545.8106.6
7.5639.78.324.3121.07.3636.18.34.6108.47.3928.98.383.9117.4
7.0927.18.024.472.26.9621.77.954.763.26.8827.17.974.277.7
6.5318.17.674.345.26.4518.17.544.447.06.4121.77.723.945.2
6.6623.57.734.449.36.5118.17.274.239.06.5318.17.683.646.2
7.2948.68.574.7185.67.2450.88.595.1216.67.1450.88.584.9187.9
7.0119.88.154.990.26.9622.08.095.390.27.0622.08.145.190.2
6.7922.07.694.341.86.7424.27.684.346.26.7524.27.694.452.8
6.8135.27.944.055.06.6735.27.924.270.46.7335.27.874.066.0
6.5622.07.713.950.66.5926.47.724.264.96.724.27.753.963.8
6.0913.26.894.235.26.0111.06.984.739.66.0611.06.963.937.4
7.1914.47.654.157.86.326.47.134.542.96.3625.37.114.341.8

Mass Transfer Analyses

The overall mass transfer coefficient is a function of the mass transfer coefficient in the aqueous phase, the mass transfer coefficient in the gas phase, and the pH of the aqueous phase (see Eq. (4)). Figure 3 shows the effect of the pH in the range of the cooling tower operation (i.e, pH = 6–9) on the gas-to-liquid resistance ratio Rg/Rw for the mass transfer coefficient ratio kg/kw ranging from 0.01 to 100, indicating that, for the selected ranges of kg/kw and the pH in the cooling tower, both the gas phase and the liquid phase resistances should be considered in the overall mass transfer coefficient. Furthermore, the results in Figure 3 indicate that the ratio of (Rg/Rw) to [(1/kg)/(1/kw)] is very close to one at the low end of the pH range (i.e., pH ≈ 6) and increases by more than two orders of magnitude at the high end of the pH range (i.e., pH ≈ 9).

image

Figure 3. Ratio of carbon dioxide mass transfer air film resistance (Rg) to water film resistance (Rw) with respect to pHxa, in the ranges of pHxa 6–9 and kg/kw 0.01, 1, and 100.

Download figure to PowerPoint

Contreras [16] investigated CO2 stripping in a bubbled column and found that, in the operating range of their column, both the gas and the liquid phase resistances were significant. However, earlier studies on the CO2 mass transfer coefficient in packed towers have been found to be contradictory. While Drane [17] reported a large effect of gas velocity and no effect of water flow rate on the overall mass transfer coefficient, Sherwood et al. [18] found that in the operating range of their packed tower, the water phase resistance was dominant and the gas phase resistance could be neglected. These discrepancies may be attributed to the magnitude of individual mass transfer coefficients in the gas and the water phases dictated by the respective flow rate in the gas and the water phases as well as the differences in the water pH.

Given the uncertainty surrounding the gas-to-liquid (kg/kw) mass transfer coefficient ratio reported in the literature, the experimental data for the cooling loop pH were compared with simulations made with Eqs. (19) and (20) using wide ranges of kg/kw and kg. The average error of the pH (EpHxa) and the standard deviation of the pH (σpHxa) were calculated for each data set using Eqs. (21) and (22).

  • display math(21)
  • display math(22)

where pHxa,exp and pHxa,cal represent the experimental and calculated loop pH, respectively.

The results are presented in Figure 4 and indicate that, as expected, at the low and high end of kg (e.g., kg<1 × 10−8 m/s and kg>1 × 10−4 m/s) the average error approaches asymptotic values representing conditions with zero CO2 stripping and maximum CO2 stripping (thermodynamic equilibrium in the tower), respectively. Furthermore, the results in Figures 4a and 4b show that the best fit of the data is obtained when the average error of the pH is zero (no bias condition), indicating that the model appropriately represents the experimental data.

image

Figure 4. a-The average error and b-standard deviation on pHxa as a function of gas phase mass transfer coefficient kg and mass transfer coefficient ratio kg/kw.

Download figure to PowerPoint

Figure 5 shows the standard deviation of the best fit (minimum σpHxa) obtained from the model (i.e., Eqs. (19) and (20)) and the corresponding kg over a wide range of kg/kw (10−4 to 104). The results indicate that the overall best fit is achieved at kg/kw = 100 with the corresponding kg = 8.4 × 10−6 m/s.

image

Figure 5. The standard deviation of the pHxa predicted by the model as a function of mass transfer ratio (kg/kw)

Download figure to PowerPoint

The experimental data were compared with model simulations at the optimum kg and kg/kw obtained in this study with the parameter S (salt precipitation) determined from the experimental data. Figure 6 shows the pH of the cooling loop obtained from the model for two limiting cases when CO2 stripping in the tower is dictated by either thermodynamic equilibrium or total lack of mass transfer (i.e., k = 0), confirming that the CO2 mass transfer coefficient plays a significant role in determination of the pH of the cooling loop.

image

Figure 6. Simulated pHxa as a function of cycles of concentration (N) for CO2 in the operation of a recirculating cooling system.

Download figure to PowerPoint

The product of the overall mass transfer coefficient and specific area of the packing (k.a) was calculated to be 0.11 to 5.20 h−1 in the pH range of 6.5–9.0, which is consistent with the k.a of 1.3 h−1 measured by Cabassud et al. [19] for CO2 stripping from spring water in a bubbling reactor with the water pH ranging from 7.0 to 8.1. This k.a value is smaller than those reported by others for CO2 stripping in stirred tanks and bubbled bed columns (i.e., 18–120 h−1) [16, 20-22]. This is mainly due to the higher mixing properties in those experiments compared to the cooling tower packing. Sherwood et al. [18] reported k.a of 12 h−1 in a packed column. However, since they have not reported the operating range of the pH in their experiment, this value k.a cannot be directly compared with the values obtained in our study.

Effect of Alkalinity Loss

Figure 7 presents the experimental data (N = 3.6–5.9) along with the simulation results for cycles of concentration N ranging from 3 to 6. The simulations were performed for two cases: in the first case no alkalinity was lost; and in the second case, a cooling loop alkalinity loss of 70% was assumed due to salt precipitation, which corresponds to the maximum alkalinity loss observed in the pilot-scale field test data. The results indicate that, compared to the experimental data, higher values of pH are predicted assuming no alkalinity loss, while lower values are predicted when the maximum value of the observed alkalinity loss is considered. The effect of 70% loss of alkalinity due to salt formation on the cooling loop pH can be as high as two pH units in the makeup alkalinity range of 20–80 mg/L CaCO3. Therefore, to predict accurately the recirculating cooling water pH, experimental data on the extent of salt formation is needed to develop a comprehensive model that combines detailed water chemistry with kinetic models of the chemical reactions contributing to salt formation.

image

Figure 7. Simulated and actual pHxa with respect to makeup water alkalinity for pilot cooling tower operation at cycles of concentration N in the range of 3–6.

Download figure to PowerPoint

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

It was shown that the existing equilibrium models as well as the empirical equations available in the literature are not capable of accurately predicting the pH of the cooling loop, suggesting that an improved model is needed that can take into account other important variables such as CO2 mass transfer limitations and salt formation in the cooling system.

A model was developed in this study that can predict the pH of recirculating cooling water as a function of cooling system water quality and operating parameters, when CO2 evaporation in the cooling tower is controlled by mass transfer resistances. The optimum values of the gas film mass transfer coefficient and water film mass transfer coefficient were determined to be 8.4 × 10−6 m/s and 8.4 × 10−8 m/s, respectively. The results also indicate that loss of alkalinity due to salt formation can significantly affect the cooling loop pH (i.e., as high as two pH units) in the makeup alkalinity range of 20–80 mg/L CaCO3, suggesting that to predict accurately the recirculating cooling water pH, experimental data on the extent of salt formation is needed to develop detailed kinetic models of chemical reactions contributing to salt formation.

ACKNOWLEDGMENTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

This work was supported by the U.S. Department of Energy, National Energy Technology Laboratory, under award numbers DE-FC26-06NT42722 and DE-NT0006550 to Carnegie Mellon University and the University of Pittsburgh. The work was also partially in support of the National Energy Technology Laboratory contract RES1000025 with Carnegie Mellon University. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

APPENDIX

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED

DERIVATION OF EQS. 16 AND 19

CO2 transfer rate across the air-water interface at any vertical section dZ of the packing can be expressed as follows:

  • display math(A1)

The overall mass transfer coefficient is generally calculated based on the resistances in both liquid and gas films:

  • display math(A2)

in Equation A

  • display math(A3)

Mass balance of TIC at any Z:

  • display math(A4)

Neglecting the Qe:

  • display math(A5)

Substitute Eq. (A3) in (A5):

  • display math(A6)

Alkalinity conservation assumption (i.e., ALKxa=ALKxb=ALKx) leads to:

  • display math(A7)
  • display math(A8)

Substitute Eqs. (A3) and (A8) into Eq. (A1):

  • display math(A9)
  • display math(A10)
  • display math(A11)

Assuming k and KH are constant in the packing and integrating both sides of Eq. (A11), Cx from Cxb to Cxa, and Z from 0 to ZT

  • display math(A12)

where A is AbaZT and E is inline image

After rearrangement, Cxb can be expressed as:

  • display math(A13)

TIC mass balance in the basin:

  • display math(A14)

Neglect the Qe, substitute Eq. (A3) into Eq. (A14) and apply alkalinity conservation (i.e., QmALKm=QbALKx):

  • display math(A15)

Substitute Eq. (A13) into Eq. (A15):

  • display math(A16)

After rearrangement

  • display math(A17)

For general cooling tower operation, QyKHE >> Qx therefore Eq. (A17) becomes:

  • display math(A18)

which is Eq. (16).

If carbonate salts are precipitating in the basin at a rate of S (mol/s) Eq. (A14) becomes:

  • display math(A19)

Since alkalinity is not conserved, QmALKm=QbALKxa+ 2S+R, where R represents alkalinity loss due to acid addition. Thus Eq. (A15) becomes:

  • display math(A20)

Equation (19) is obtained by substituting Eq. (A13) into A20 and some rearrangement.

NOMENCLATURE

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED
A

volumetric surface area of packing (m2/m3)

A

the effective total packing surface area AbaZT (m2)

Ab

base area of packing (m2)

ALKm

alkalinity of makeup water (equivalent mol/m3)

ALKx

alkalinity of water in the cooling tower (equivalent mol/m3)

ALKxa

alkalinity of water in the basin of the cooling tower (equivalent mol/m3)

ALKxb

alkalinity of water leaving the cooling tower (equivalent mol/m3)

CTm

total inorganic carbon concentration in makeup water (mol/m3)

CTx

total inorganic carbon concentration in water in the cooling tower (mol/m3)

CTxa

total inorganic carbon concentration in the basin of the cooling tower (mol/m3)

CTxb

total inorganic carbon concentration in water leaving the tower (mol/m3)

Cm

CO2 concentration in makeup water (mol/m3)

Cx

CO2 concentration in water in the cooling tower (mol/m3)

Cxa

CO2 concentration in the basin of the cooling tower (mol/m3)

Cxb

CO2 concentration in water leaving the cooling tower (mol/m3)

Cy

CO2 concentration in air in the cooling tower (mol/m3)

Cya

CO2 concentration in air leaving the cooling tower (mol/m3)

Cyb

CO2 concentration in air entering the cooling tower (mol/m3)

E

defined by Eq. (12)

k

CO2 overall mass transfer coefficient for CO2 based on water film (m/s)

kg

CO2 mass transfer coefficient in air film (m/s)

kw

CO2 mass transfer coefficient in water film (m/s)

Ka1

first dissociation constant of carbonic acid

KH

Henry's Law constant for CO2 (m3 water/m3 air)

N

cycles of concentration

pHxa

cooling loop water pH at the basin of the tower

pHm

makeup water pH

Qb

blowdown flow rate (m3/s)

Qe

cooling water evaporation rate (m3/s)

Qm

makeup water flow rate (m3/s)

Qx

cooling water flow rate entering the tower (m3/s)

Qy

air flow rate entering the tower (m3/s)

R

rate of alkalinity loss in the basin of the tower due to acid addition (Equivalent/s)

Rg

CO2 mass transfer resistance in air film (s/m) and is defined as 1/(kgKH)

Rw

CO2 mass transfer resistance in water film (s/m) and is defined as 1/(kwα)

S

rate of carbonate salts precipitation (mol/s)

Z

vertical distance above the bottom of packing (m)

ZT

packing height (m)

α

defined as (1+ Ka1/[H+])

LITERATURE CITED

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. ACKNOWLEDGMENTS
  8. APPENDIX
  9. NOMENCLATURE
  10. LITERATURE CITED
  • 1
    Asano, T., Burton, F., Leverenz, H., Tsuchihashi, R., & Tchobanoglous, G. (2007). Water reuse: Issues, technologies, and applications, New York: McGraw-Hill.
  • 2
    Kunz, R.G. (2009). Environmental calculations: A multimedia approach. Wiley-AIChE: p.570.
  • 3
    Puckorius, P. (1983). Get a better reading on scaling tendency of cooling water, Power, issue of September, 7981.
  • 4
    Caplan, G. (1990). Cooling Water Computer Calculations: Do They Compare? Paper No. 100, National Association of Corrosion Engineers (NACE) Meeting Corrosion 90, Las vegas, NV, April 23–27.
  • 5
    Kunz, R.G., Yen, A.F., & Hess, T.C. (1977). Cooling-water calculations, Chemical Engineering, 84, 6171.
  • 6
    Budzianowski, W., & Kozol, A. (2005). Stripping of ammonia from aqueous solutions in the presence of carbon dioxide effect of negative enhancement of mass transfer, Chemical Engineering Research and Design 83(A2), 196204.
  • 7
    Ballard, C.W., & Matson, J.V. (1991). Precise prediction of cooling water pH, CTI Journal, 13, 1654.
  • 8
    Chien, S.H., Hsieh, M.K., Li, H., Monnell, J.D., Dzombak, D.A., & Vidic, R.D. (2012). Pilot-scale cooling tower to evaluate corrosion, scaling, and biofouling control strategies for cooling system makeup water, Review of Scientific Instruments, 83, 024101024101-10.
  • 9
    Hsieh, M.K., Walker, M.E., Safari, I., Chien, S.H. Abbasian J., Vidic, R.D., & Dzombak, D.A. (2012). Ammonia stripping in open-recirculating cooling water systems, Environmental Progress and Sustainable Energy. doi:10.1002/ep.11648.
  • 10
    Whitman W.G. (1923). The two-film theory of gas absorption, Chemical and Metallurgical Engineering, 29, 146148.
  • 11
    Stumm W., & Morgan J.J. (1996), Aquatic Chemistry (3rd Edition), New York: Wiley.
  • 12
    Schwarzenbach, R.P., Gschwend P.M., & Imboden D.M. (1993). Environmental organic chemistry, New York: Wiley, p. 929.
  • 13
    Li, H., Hsieh, M.K., Chien, S.H., Monnell, J.D., Dzombak, D.A., & Vidic, R.D. (2011). Control of mineral scale deposition in cooling systems using secondary-treated municipal wastewater, Water Research, 45, 748760.
  • 14
    Hsieh, M.K., Li, H., Chien, S.H., Monnell, J.D., Chowdhury, I., Dzombak, D.A., & Vidic, R.D. (2010). Corrosion control when using secondary treated municipal wastewater as alternative makeup water for cooling tower systems, Water Environment Research, 82, 23452355.
  • 15
    Vidic, R.V., & Dzombak, D.A. (2009). Reuse of treated internal or external wastewaters in the cooling systems of coal-based thermoelectric power plants (DE-FC26-06NT42722). Submitted to U.S. Department of Energy, National Energy Technology Laboratory, Pittsburgh, PA.
  • 16
    Contreras, E.M. (2007). Carbon dioxide stripping in bubbled columns, Industrial & Engineering Chemistry Research, 46, 63326337.
  • 17
    Drane, H.S. (1924). The design and operation of gas scrubbing tower, Journal of the Society of Chemical Industry, 43, 329340.
  • 18
    Sherwood, T.K., Draemel, F.C., & Ruckman, N.F. (1937). Desorption of carbon dioxide from water in a packed tower, Industrial & Engineering Chemistry, 29, 282285.
  • 19
    Cabassud, C., Burgaud, C., & Espenan, J.M. (2001). Spring water treatment with ultrafiltration and stripping, Desalination, 137, 123131.
  • 20
    Hill, G.A. (2006). Measurement of overall volumetric mass transfer coefficient of carbon dioxide in a well-mixed reactor using a pH probe, Industrial & Engineering Chemistry Research, 45, 57965800.
  • 21
    Arrua, L.A., McCoy, B.J., & Smith, J.M. (1990). Gas-liquid mass transfer in stirred tanks, AIChE Journal, 36, 17681772.
  • 22
    Sperandio, M., & Paul, E. (1997). Determination of carbon dioxide evolution rate using on-line gas analysis during dynamic biodegradation experiments, Biotechnology and Bioengineering, 53, 243252.