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International Journal of Heat and Mass Transfer 53 (2010) 2361–2368

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International Journal of Heat and Mass Transfer

journa

l homepage: www.elsevier.com/locate/ijhmt

Analytical modeling of water condensation in condensing heat exchanger

Kwangkook Jeong a,*, Michael J. Kessen b, Harun Bilirgen b, Edward K. Levy b

a b

Korea Electric Power Corporation, 65 Munji-Ro, Yuseong-Gu, Daejeon 305-380, Republic of Korea Energy Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA 18015, USA

a r t i c l e

i n f o

a b s t r a c t

An analytical model of heat and mass transfer processes in a ?ue gas condensing heat exchanger system was developed to predict the heat transferred from ?ue gas to cooling water and the condensation rate of water vapor in the ?ue gas. Flue gas exit temperature, cooling water outlet temperature, water vapor mole fraction, and condensation rate of water vapor were computed using the analytic model. A pilotscale heat exchanger was used to validate the analytical model. The experimental results show a very good agreement with analytical model results. The performance of the heat exchanger system was evaluated as functions of the ratio of the mass ?ow rate of cooling water to the mass ?ow rate of inlet ?ue gas, the inlet cooling water temperature and the ratio of ?ue gas ?ow rate to total heat transfer surface area. ? 2010 Elsevier Ltd. All rights reserved.

Article history: Received 24 August 2009 Received in revised form 1 February 2010 Available online 22 February 2010 Keywords: Analytical condensation modeling Boundary value problem Condensing heat exchanger design Heat and mass transfer coef?cient Power plant boiler ?ue gas Non-condensable gas Water recovery

1. Introduction Thermoelectric power plants utilize signi?cant quantities of water. For example, a 500 MW power plant that employs oncethrough cooling uses 4.5?104 m3/h (approximately 45?106 kg/h) of water for cooling and other process requirements. Water supply issues are increasing in importance for new and existing power plants because the freshwater supply is limited. For companies considering the development of new thermoelectric power plants, water is a ?rst-order concern. The impacts of water supply depend on the regional environment in which the power plant is to be built. Power plants located in some parts of the United States will ?nd it increasingly dif?cult to obtain the large quantities of water needed to maintain operations. In response to these concerns, DOE is funding research and development to reduce the amount of freshwater used by power plants [1]. The focus of this study is water recovery from exhaust gases of fossil-?red power plants. Power plant exhaust gases release large amounts of water vapor into the atmosphere. The ?ue gas is a potential source for obtaining much needed cooling water for a power plant. There is almost 40% (wet coal mass basis) moisture in lignite coal, which is translated to 16% moisture by volume (wet basis) in the ?ue gas. For example, a 600 MW power plant ?ring lignite exhausts a ?ue gas ?ow rate of 2.7?106 kg/h, which includes a moisture ?ow rate of 0.43?106 kg/h, or about 16 wt% of

* Corresponding author. E-mail addresses: kkj206@lehigh.edu, kjeong@kepco.co.kr (K. Jeong). 0017-9310/$ - see front matter ? 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.02.004

the ?ue gas. In contrast, typical cooling tower evaporation rates for a 600 MW unit are 0.7?106 kg/h [2]. If a power plant could recover and reuse a portion of this moisture, it could reduce its total cooling water intake requirement. The most practical way to recover water from ?ue gas is to use a condensing heat exchanger. The power plant could also recover latent heat due to condensation as well as sensible heat due to lowering the ?ue gas exit temperature. In addition, harmful acid gases such as H2SO4, HCl, and HNO3 can be condensed by the heat exchanger preventing them from entering the atmosphere. Condensation in ?ue gas is a complicated phenomenon since heat and mass transfer of water vapor and various acid vapors simultaneously occur in the presence of non-condensable gases. To design a full scale heat exchanger for a power plant, the condensation process must be modeled correctly. Several investigators have proposed analytical solutions. In 1980, Webb and Wanniarachchi [3] developed a one dimensional numerical model to predict the effect of non-condensable gases in a 10-row by 10-column ?nned tube heat exchanger by solving the Colburn–Hougen equation for refrigerant R-11 and air mixture. An iterative solution procedure was applied to solve the equation. The modeling results were not veri?ed with measured data. From 1999 to 2003, Osakabe et al. [4–7] carried out one-dimensional heat and mass balance calculations for the condensation of ?ue gas in bare and ?nned tube heat exchangers. Experimental studies using actual ?ue gas from propane, natural gas and oil combustion were conducted to investigate the effect of parameters such as ?ue gas ?ow rate, cooling water temperature and cooling water ?ow rate. The results of both modeling and experiments

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Nomenclature A a, b, c cp D d F f h kD jH jm km L Le l M NuD _ m P Pr R ReD Sc St T U V Y area constants speci?c heat binary mass diffusivity tube diameter fouling factor friction factor convective heat transfer coef?cient convective mass transfer coef?cient Colburn j factor for heat transfer Colburn j factor for mass transfer mass transfer coef?cient tube length Lewis number latent heat molecular weight Nusselt number mass ?ow rate pressure Prandtl number thermal resistance Reynolds number Schmidt number Stanton number temperature overall heat transfer coef?cient velocity mole fraction Greek symbols a thermal diffusivity g ef?ciency k thermal conductivity q density Subscripts c cooling water cd water condensate dew dew point eff effective f liquid ?lm g wet ?ue gas i interfacial in inlet is inner surface lm log mean difference m mass transfer nb non-condensable at bulk ni non-condensable at interface o outer surface out outlet s tube surface tot total w tube wall

were compared for variables such as ?ue gas temperature, cooling water temperature and condensation rate. For tests using ?ue gas obtained from oil combustion, cooling water ?ow rate was varied from 1000 to 3700 kg/h while ?ue gas ?ow rate was varied from 60 to 176 kg/h. The results showed that the general temperature pro?les and total amount of condensate could be predicted well with one-dimensional mass and heat balance calculations. The prediction for total amount of condensate was more accurate than that for amount of condensate from each heat exchanger. The condensation started from the ?ue gas inlet and the main condensation region was generated at the heat exchanger inlet due to a high ?ow rate of cooling water. It was found that cooling water ?ow rate was an important factor affecting condensation rate. In 2004, Valencia [8] performed a CFD simulation for the condensation of water vapor and acids on the plate using a commercial code, FLUENT and a user de?ned subroutine. A numerical simulation using the commercial code and a simulation based on empirical correlations using the Engineering Equation Solver (EES) were carried out for a two dimensional (2D) vertical water-cooled plate. Experiments were conducted for the condensation of nitric acid, sulfuric acid and water vapor in the presence of air on a vertical water-cooled plate. The discrepancies between experiments and simulation are in a range of 7–25% depending on the combustion conditions and the average surface temperature of the plate. The numerical model was applied to real 3D geometries including an annular ?n heat exchanger and a pin ?n heat exchanger. In 2008, Levy et al. [9,10] investigated use of condensing heat exchangers to recover water vapor from ?ue gas at coal-?red power plants. Pilot scale heat transfer tests were performed to determine the relationship between ?ue gas moisture concentration, heat exchanger design and operating conditions, and water vapor condensation rate. A theoretical heat and mass transfer model was developed for predicting rates of heat transfer and water vapor condensation and comparisons were made with pilot scale

measurements. Analyses were also carried out to estimate how much ?ue gas moisture it would be practical to recover from boiler ?ue gas and the magnitude of the heat rate improvements which could be made by recovering sensible and latent heat from ?ue gas. This paper describes an analytical model of the heat and mass transfer process in a countercurrent cross ?ow tubular heat exchanger with cooling water inside and ?ue gas outside the tubes. The analytical results are compared to experiments made using a pilot-scale heat exchanger and the performance of the heat exchanger system is shown as a function of various parameters. 2. Analytical modeling 2.1. Control volume and main variables The control volume used for deriving the governing equations is de?ned as a ?xed region in space that encompasses the ?ue gas and the cooling water tubes. A countercurrent cross ?ow heat exchanger with smooth-wall tubes is presumed. Fig. 1 shows the variables in the control volume which affect water vapor conden-

Fig. 1. Control volume and variables for analytical modeling.

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sation. Heat and mass transfer for water condensation are considered with this control volume. The ?ue gas temperatures at the inlet and outlet of this control volume are expressed as Tg,in and Tg,out, respectively. The parameters Tc,in and Tc,out express cooling water temperatures at the inlet and outlet, respectively. Tube wall temperature is expressed by Tw. The parameters Tg and Tc are average values of ?ue gas and cooling water temperatures between the inlet and outlet, respectively. Heat transfer in this control volume is controlled by heat transfer coef?cients on the ?ue gas side (hg) and cooling water side (hc). Mass transfer of water vapor towards the wall occurs at locations where the tube wall temperature is below the local water dew point temperature. In this paper, the mole fraction of water vapor at the inlet and outlet are expressed as yH2O,in and yH2O,out, respectively. The parameter yH2O is an average mole fraction of yH2O,in and yH2O,out. The dew point temperature of water vapor Tdew is the saturation temperature corresponding to the partial pressure of water vapor in the ?ue gas. The parameter Ti is temperature of water vapor at the interface between the gas and liquid ?lm. Mass transfer coef?cient is expressed as km. In the analytical model, both mass transfer of water vapor and heat transfer from ?ue gas to cooling water are considered. Entering the heat exchanger, the ?ue gas is ?rst cooled by sensible heat transfer to cooling water. Then, water vapor in the ?ue gas condenses on the cooling water tube surface if the wall temperature is lowered below the dew point of the water vapor, simultaneously releasing latent heat that transfers to the cooling water. Two-phase ?ow, which consists of the gas phase (uncondensed ?ue gas) and liquid phase (water condensate), is assumed on the ?ue gas side (Jeong [11]). 2.2. Governing equations and assumptions Colburn and Hougen developed a fundamental transport equation for condensation in the presence of a non-condensable gas [12]. When the wall temperature is lower than the dew point temperature, water condensation occurs on the tube surface as a result of diffusion of water vapor through the ?ue gas to the liquid–vapor interface. Therefore, water vapor exists in the ?ue gas as a superheated vapor at Tg. Sensible heat transfers from the ?ue gases to the liquid–vapor interface in addition to the latent heat transferred from the condensing vapors. The heat transfer to the cooling water is the sum of sensible and latent heat. The Colburn–Hougen equation is de?ned as follows:

1 1 1 1 ? ? F is ? Rw ? U o Aeff hc Ais hf Aeff

?2?

where Aeff and Ais are the heat transfer areas based on the tube outer diameter including ?lm thickness and the inner diameter of tube, respectively. hc and hf are the heat transfer coef?cients on the cooling water side and liquid ?lm side, respectively. Fis is the fouling factor on the inside of the tubes. Rw is the conductive resistance of the tube wall and is expressed as ln(do/dis)/(2pkwL). The fouling factor and the tube wall resistance are assumed to be negligible in this analysis. The thermal resistance due to the condensate ?lm is negligible since it contributes only about 1–3% of the total thermal resistance [13]. Thicknesses of water ?lm and tube are neglected in this research, and subsequently, Aeff and Ais are replaced by Ao (the heat transfer area based on the tube outer diameter). Then Eq. (2) is simpli?ed to Eq. (3) with the assumptions.

1 1 % U o Ao hc Ao

?3?

Applying these approximations, the ?rst governing equation is established as shown in Eq. (4). The heat transfer coef?cients on the ?ue gas side (hg) and cooling water side (hc) are calculated using empirical correlations of forced convective heat transfer for tube banks and inside a tube, respectively.

hg ?T g ? T i ? ? km ? l ? ?yH2 O ? yi ? ? hc ?T i ? T c ?

?4?

The second governing equation, Eq. (5) is the energy balance between the enthalpy change of the ?ue gas and the heat transfer rate from the ?ue gas to the liquid ?lm. This ordinary differential equation is integrated over the control volume, which is presumably small enough to assume that all other variables are constant.

_ g ? cp?g ? dT ? hg ? ?T g ? T i ? ? dA m

?5?

For the case of no water vapor condensation, heat transfer from the ?ue gas is directly transferred to the tube wall, which has a temperature, Tw, instead of the liquid–?lm interface. The third governing equation is for the case when no condensation is occurring and is shown in Eq. (6). Eq. (6) re?ects energy conservation between the enthalpy change of the ?ue gas and the heat transfer rate from the ?ue gas to the tube wall surface.

_ g ? cp?g ? dT ? hg ? ?T g ? T w ? ? dA m

?6?

hg ?T g ? T i ? ? km ? l ? ?yH2 O ? yi ? ? U o ?T i ? T c ?

? 1?

Eq. (1) includes the interfacial temperature, Ti, for the cases when water is condensing. The parameter l is the latent heat of water vapor. As shown Fig. 2, Uo is the overall heat transfer coef?cient, taking into account resistances from the condensate liquid ?lm to the cooling water. These resistances expressed in terms of the associated heat transfer coef?cients as shown below:

The fourth governing equation, the overall energy balance equation is derived by modifying the Colburn–Hougen equation (4). Since the total heat transferred to the cooling water, represented by the right hand side of Eq. (4), is equal to the enthalpy change of the cooling water, Eq. (4) can be rewritten as Eq. (7).

_ c ? C p?c ? dT c ?hg ? ?T g ? T i ? ? km l?yH2 O ? yi ?? ? dA ? m

?7?

For the case of no condensation of water vapor, the interfacial temperature, Ti in Eq. (7), is replaced by tube wall temperature Tw, and the mass transfer term is eliminated on the left hand side of Eq. (7). The ?fth governing equation is derived from Eq. (7) as shown hereunder.

_ c ? cp?c ? dT c hg ? ?T g ? T w ? ? dA ? m

?8?

The sixth governing equation balances the enthalpy change of cooling water with the convective heat transferred from tube wall to the cooling water. This is written in Eq. (9).

_ c ? cp?c ? dT c hc ? ?T w ? T c ? ? dA ? m

?9?

Fig. 2. Thermal resistances from condensate to cooling water side.

The ordinary differential equations, from Eqs. (5)–(9), are integrated over a discretized cell, which is presumably small enough to assume that the all other variables are constant.

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The condensation rate of water vapor is proportional to both the mass transfer coef?cient, km [kg/s m2 mol] and the concentration differences in the vapor phase between the interface and bulk ?ow. This can be calculated by integration of the following ordinary differential equation.

Subsequently, the mass diffusivity of water vapor in ?ue gas is estimated from the known properties of water vapor in air and the calculated thermal diffusivity of ?ue gas,

DH2 O—gas ?

ag ? DH2 O—air aair

?18?

_ cd ? km ? ?yH2 O ? yi ? ? dA dm

?10?

To calculate km, the relationship between mass diffusion and heat transfer obtained from the Lewis relation is used. The Colburn j factors for heat and mass transfer with their applicable ranges are de?ned as, [14,15]:

jH ? St ? Pr2=3 ?

h

q ? cp ? V

? Pr 2=3

0:6 < Pr < 60

?11? ?12?

jm ? St m ? Sc2=3 ?

kD ?Sc?2=3 V

0:6 < Sc < 3000

where ag and aair are the thermal diffusivities of ?ue gas and air, respectively. Calculated values of thermal diffusivity and mass diffusivity for water vapor in ?ue gas are listed in Table 1. The measured mass diffusivity of water vapor in air at 15 oC and one atmosphere is 2.61?10?5 m2/s [18]. Al-mutawa [19] used 0.845 as a Lewis number for water vapor. The interfacial mole fraction of water vapor used in Eq. (10) can be calculated by Eq. (19), the Antoine equation [20], which is a vapor pressure equation and describes the relation of saturated vapor pressure and temperature for pure components:

where h is convective heat transfer coef?cient [W/m2 K] and kD is convective mass transfer coef?cient [m/s]. The Lewis analogy requires equating Eq. (11) and (12), that is, jH = jm. Then an expression is derived for the mass transfer coef?cient as:

yi ?

exp?a ? T ib ? ?c ?19?

Ptot a ? 16:262 b ? 3799:89 c ? 226:35

km ?

hg ? M H2 O

=3 cp;g ? M g ? ylm ? Le2 H2 O—gas

?13?

The mass transfer coef?cient is shown to be a function of the gas side heat transfer coef?cient, the logarithmic mole fraction difference of the non-condensable gas and the properties of ?ue gas side including Lewis number of water vapor in ?ue gas. To predict the convective heat transfer coef?cient on the gas side of a bare tube bank, an empirical correlation, Eq. (14), proposed by Zhukauskas [16] was used.

where Ti is interfacial temperature in oC and Ptot is in kPa. The heat transfer coef?cient on the cooling water side was calculated by using Eq. (20) provided by Gnielinski [21].

NuD ?

?f =8??ReD ? 1000?Pr 1 ? 12:7?f =8?1=2 ?Pr2=3 ? 1? ?20?

0:5 6 Pr 6 2000 3000 6 ReD 6 5 ? 106

1=4 Pr :63 0:36 NuD ? 0:27 ? Re0 ? Pr ? D;max Prs 0:7 6 Pr 6 500 1000 6 ReD;max 6 2 ? 105

?14?

The Reynolds number appearing in Eq. (14) is based on the maximum velocity Vg,max which is in the minimum ?ow area between the tubes. The maximum velocity Vg,max ranged from 0.8 to 4.0 m/s, while the upstream ?ue gas velocity at the duct inlet ranged from 0.3 to 1.5 m/s in this study. All properties are calculated based as mixtures, and ylm, the logarithmic mole fraction difference of the non-condensable gas between the free stream and the wall, is calculated as [5,17]:

Eq. (20) can be applied for both uniform surface heat ?ux and constant tube wall temperature. The friction factor f can be obtained from the Moody diagram. The Reynolds number in Eq. (20) is based on the average velocity Vc of the cooling water in the tubes which ranged from 0.1 to 0.2 m/s in this study. Analytical modeling in this study was developed with the following assumptions and simpli?cations. Steady state one dimensional ?ow. Countercurrent cross ?ow condensing heat exchanger. Two phase ?ow (gas and liquid) for the ?ue gas side and one phase ?ow for the cooling water side. Film condensation only occurs on the tube wall surface. The thermal resistance due to the ?lm is negligible since it contributes about 1–3% of the total thermal resistance. Negligible thermal resistance from the tube wall. No evaporation of water vapor and no chemical reactions. No heat loss to the environment. Flue gas contains CO2(g), O2(g), and N2(g) and H2O(g).

ylm ?

yni ? ynb ln?yni =ynb ?

?15?

where yni and ynb are the mole fractions of non-condensable gases at the gas/?lm interface and in the bulk ?ow, respectively. The parameter LeH2 O—gas , the Lewis number of water vapor in ?ue gas, is de?ned as Eq. (16), in which DH2 O—gas is the binary mass diffusion coef?cient of water vapor in ?ue gas.

LeH2 O?gas ?

Sc ag ? Pr DH2 O-gas

?16?

Table 1 Calculated and reference properties. Properties Calculated thermal diffusivity of ?ue gas at 15 °C in this study Reference of thermal diffusivity of air at 15 °C [18] Calculated mass diffusivity of water vapor in ?ue gas at 15 °C in this study Reference of mass diffusivity of water vapor in air at 15 °C [18] Calculated Le at 15 °C in this study Reference of Le [19] Values 1.96?10?5 [m2/s] 2.22?10?5 [m2/s] 2.56?10?5 [m2/s] 2.61?10?5 [m2/s] 0.77 0.845

The Lewis number is typically of order unity for gases. This implies that changes in the thermal and species distributions progress at approximately the same rates in gases that undergo simultaneous heat transfer and mass diffusion processes [18,19]. Therefore, unknown mass diffusivity (D? AB;unknown ) can be estimated with known other properties from Eq. (17).

Legas % 1 ?

aknown

DAB;known

?

? known ? DAB;unknown

a

?17?

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The chemical composition of non-condensable dry ?ue gas is assumed as 15 vol% of CO2, 3.78 vol% of O2 and 81.3 vol% N2 at dry basis. The U-bends in the tube bank are simpli?ed and modeled as a straight tube having the same length as the multiple bend tube.

2.3. Numerical scheme The governing equations for the boundary value problem were solved using an iterative numerical scheme and a one dimensional ?nite difference method with forward differencing. The known variables were: inlet ?ue gas temperature, inlet ?ue gas ?ow rate, inlet cooling water temperature, cooling water ?ow rate, and inlet mole fraction of water vapor. The inlet cooling water temperature was used as a target value and served as the criterion for convergence. In order to calculate inlet cooling water temperature, a value for the exit cooling water temperature was initially assumed, and the calculations were carried out. The scheme iterated until the correct inlet cooling water temperature was calculated. The entire system was discretized with control volumes in each cell. For this study, the total heat transfer area, 6.74 m2, was discretized into 1000 cells. 3. Experimental An experimental study was carried out to validate the analytical model. Fig. 3 shows the overall experimental set up. The experimental setup consisted of six stages of heat exchangers, an inlet and outlet duct, an induced draft fan, cooling water lines, and an electric hot water heater. Flue gas was channeled from the exit duct of the boiler to the inlet of the heat exchanger system. All heat exchangers were countercurrent cross ?ow, with ?ue gas ?owing around the cooling water tube bundles. Cooling water was distributed to an inline tube bundle arrangement with eight parallel rows of multiple U-bend tubes (0.0127 m O.D.). Manifolds were at the inlet and exit of each counter-cross-?ow heat exchanger to distribute the water. Heat exchangers one through six had 3, 5, 9, 13, 13, and 13 U-bends. The tube banks had a transverse pitch ST of 0.7 and longitudinal pitch SL of 2.0. The cooling water was taken from the local municipal water line. The duct housing the heat exchangers was thermally insulated using ?exible ?ber glass and rigid foam insulation. The ?rst heat exchanger (HX1) was not needed in the experiments described in this paper because of a relatively low inlet ?ue gas temperature. For data acquisition during the test, thermocouples, rotameters, and a manometer with a pitot tube were used to measure the ?ue

gas and cooling water temperatures, cooling water ?ow rate, and ?ue gas ?ow rate, respectively. Flue gas temperature was measured using sheath-type K thermocouples which were inserted into the center of the rectangular duct at the inlet of each heat exchanger. There was a rotameter on each heat exchanger measuring cooling water ?ow rate. Downstream of the heat exchangers, an eight foot straight section of PVC pipe was used to create a fully developed ?ow region for an accurate ?ow rate measurement. In this section, a pitot tube and manometer were used to measure ?ue gas ?ow velocity. Rigid plastic containers were used to collect condensate from the bottom of each heat exchanger. The mass of condensate and elapsed time for the test were measured to determine condensation rates. Moisture content of the ?ue gas at the inlet of the heat exchanger was calculated by adding the measured condensation rate in each heat exchanger to the vapor ?ow rate in the ?ue gas, on a molar basis. Wet bulb and dry bulb temperature measurements made in the ?rst few tests showed the ?ue gas at the exit of the apparatus was saturated. As a result, the exit vapor ?ow rate in the ?ue gas was calculated by assuming the ?ue gas to be fully saturated at the cooling water tube-wall temperature at the exit of the heat exchanger system. Tests were carried out with ?ue gas from three different fuels: #6 oil, natural gas and coal. Tests with the ?ue gas from #6 oil and natural gas were performed in the Boiler House at Lehigh University [9,10]. Tests using coal combustion gas were conducted at a coal-?red power plant. In this paper, test results related only to ?ue gas derived from coal ?ring are presented. All of the data were obtained by using bare tube bank heat exchangers. The parameters which could have an impact on the performance of condensing heat exchangers were selected for experimental study: (1) inlet cooling temperature, (2) cooling water ?ow rate, and (3) ?ue gas ?ow rate. A term used in this study, condensation ef?ciency, is the weight% ratio of total condensation rate to inlet water vapor ?ow rate. This is used to evaluate the performance of the condensing heat exchangers. Condensation ef?ciency is expressed as follows:

gcd ?wt%? ? _i?1 cd;i ? 100 mH2 O;in

P5

_ m

?21?

Flue Gas Inlet

Flue Gas Outlet Exhaust Duct

Cooling Water Outlet

Cooling Water Inlet

Fan

The numerator represents total condensation rate, which is calculated by summing individual condensation rates from the various heat exchanger stages. The denominator represents the mass ?ow rate of water vapor at the system inlet. It was found that the mass ?ow rate of cooling water is an important factor affecting condensation ef?ciency since it is related to the heat absorption capacity of the cooling water. How_ c ) is more ever, the mass ?ow rate of cooling water (m meaningful when known relative to the mass ?ow rate of wet ?ue _ g;in ). Moreover, better condensation ef?ciencies gas at the inlet (m were expected with higher ratios of cooling water to ?ue gas ?ow rates. The ratio of the mass ?ow rate of wet ?ue gas to the total heat _ g;in =Ao ?kg=h m2 ?? is another important transfer surface area ?m parameter. It is expected that higher ratios of ?ue gas ?ow rate to heat transfer surface area result in poor performance since it could mean relatively insuf?cient heat transfer surface area. 4. Results and discussion Analytical modeling for water vapor condensation in pilot scale condensing heat exchangers was performed using the experimental test conditions. Five input variables are needed to simulate the pilot scale test: inlet ?ue gas ?ow rate and temperature; inlet cooling water ?ow rate and temperature; and inlet moisture fraction.

HX 1

HX 2

HX 3

HX 4

HX 5

HX 6

Support Frame

Fig. 3. Schematic of experimental setup for bare tube heat exchanger test.

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Experimental data selected to verify the analytical model were conducted with inlet cooling water temperatures ranging from 23.9 oC to 32.3 oC. Fig. 4 shows axial variations of predicted and measured ?ue gas and cooling water temperatures. The x-axis represents the normalized cumulative surface area of the heat exchangers starting from the HX2 in the ?ue gas ?ow direction. The operating conditions for the test are listed under the graph. For this particular test con_ g;in was 2.92. Given this high ratio, _ c =m dition in Fig. 4, the ratio of m it was expected to have high condensation ef?ciency even though the inlet cooling water temperature was relatively high. The ratio _ g;in =Ao was 27.6 [kg/h?m2] for this test point. of m Predicted and measured data are expressed with lines and symbols, respectively. It is shown with the measured data that the ?ue gas was cooled from 149.5 °C to 32 °C while the cooling water temperature was increased from 31 °C to 51.8 °C. As can be seen from this ?gure, there is good agreement between the measured and the predicted values of both ?ue gas and cooling water temperatures. These results show that the theoretical model used in this study can predict the heat transfer phenomenon in the condensing heat exchangers with good accuracy. Fig. 5 shows a comparison between calculated and measured condensation rates for the same test point (0816 T90c), in terms of individual and total condensation rates. Predicted individual condensation rates agree with measured rates to within 16% and total condensation rates agree with measured values to within 0.1% according to the errors obtained by the least squares method. Individual condensation rates have relatively greater differences than the total condensation rate does. The average uncertainties of the measured individual and total condensation rates for all tests were 3.4% and 1.7%, respectively. The analytical model correctly predicted the distribution of condensate among the ?ve heat exchangers; the maximum condensation occurring in HX4, and the minimum occurring in HX2. The condensation ef?ciency predicted by the analytical model was the same as what was measured in experiment, being 67.6%. The results showed that the analytical model can accurately predict the mass transfer phenomenon for water condensation among the heat exchangers. Fig. 6 shows the effect of inlet cooling water temperature on the condensation ef?ciency. The results show strong dependence of condensation ef?ciency on inlet cooling water temperature since condensation ef?ciency linearly decreased from 74 to 46 wt% as inlet cooling water temperature increased from 24.4 °C to 38.1 °C.

Fig. 5. Individual and total condensation rates from each heat exchanger for Test 0806 T90c (Inlet wet ?ue gas ?owrate: 185.7 kg/h, inlet ?ue gas temperature: 149.5 °C, inlet moisture fraction: 14.4 vol%, cooling water ?owrate: 542.9 kg/h and inlet cooling water temperature: 31.0 °C).

Fig. 6. Effect of inlet cooling water temperature on condensation ef?ciency for coal ?ue gas condensation modeling (inlet wet ?ue gas ?owrate: 152–192 kg/h, inlet ?ue gas temperature: 140.9–150.9 °C, inlet moisture fraction: 11.9–14.5 vol%, cooling water ?owrate: 281–404 kg/h and inlet cooling water temperature: 24.4– 38.1 °C).

Fig. 4. Predicted and measured temperatures of ?ue gas and cooling water for Test 0806 T90c (inlet wet ?ue gas ?owrate: 185.7 kg/h, inlet ?ue gas temperature: 149.5 °C, inlet moisture fraction: 14.4 vol%, cooling water ?owrate: 542.9 kg/h and inlet cooling water temperature: 31.0 °C).

When inlet cooling water temperature was increased, both tube wall temperature and interfacial temperature increased. Then, interfacial water vapor mole fraction increased due to its dependence on interfacial temperature. So the smaller difference in moisture fraction (see Eq. (10)) reduced the condensation rate and ef?ciency. Fig. 7 shows the effect of the ratio of the mass ?ow rate of cool_ g;in ? on con_ c =m ing water to the mass ?ow rate of inlet ?ue gas ?m densation ef?ciency. It is also shown that predicted condensation ef?ciencies are in good agreement with the corresponding measured ef?ciencies. As shown with the measured data, condensation _ g;in increased from _ c =m ef?ciencies improved from 56 to 67 wt% as m 1.5 to 3.5. Condensation ef?ciency is strongly affected by changing _ g;in . The higher values of m _ c =m _ g;in result in higher condensa_ c =m m _ c ? cp;c ? of cooling tion ef?ciencies owing to higher thermal mass ?m water side. Fig. 8 shows the condensation ef?ciency as a function of the ratio of inlet wet ?ue gas ?ow rate to total heat transfer surface area, _ g;in =Ao . It is seen that condensation ef?ciency linearly decreased m _ g;in =Ao decreased from 22.4 to 28.3 kg/ from 77 to 70 wt% as m _ g;in =Ao . h m2, which implies a weak dependence on m

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_ c =m _ g;in on condensation ef?ciency for coal ?ue gas condensation Fig. 7. Effect of m modeling (inlet wet ?ue gas ?owrate: 177–190 kg/h, inlet ?ue gas temperature: 122.9–152.9 °C, inlet moisture fraction: 12.4–14.5 vol%, cooling water ?owrate: 281–662 kg/h and inlet cooling water temperature: 30.9–32.9 °C).

Fig. 9. Predicted vs. measured condensation ef?ciencies for coal ?ue gas condensation (inlet wet ?ue gas ?owrate: 152–192 kg/h, inlet ?ue gas temperature: 140.9– 150.9 °C, inlet moisture fraction: 11.9–14.5 vol%, cooling water ?owrate: 281– 404 kg/h and inlet cooling water temperature: 23.9–37.9 °C).

_ g;in =Ao on condensation ef?ciency for coal ?ue gas condensation Fig. 8. Effect of m modeling (inlet wet ?ue gas ?owrate: 150–192 kg/h, inlet ?ue gas temperature: 145.9 –150.9 °C, inlet moisture fraction: 11.9–13.5 vol%, cooling water ?owrate: 363–401 kg/h and inlet cooling water temperature: 23.9–25.9 °C).

_ c =m _ g;in on condensation ef?ciency for 0:5 6 m _ c =m _ g;in 6 3:5 Fig. 10. Effect of m (measured: inlet wet ?ue gas ?owrate: 181–189 kg/h, inlet ?ue gas temperature: 136.9–152.9 °C, inlet moisture fraction: 12.3–14.5 vol%, cooling water ?owrate: 519–662 kg/h and inlet cooling water temperature: 30.9–32.9 °C, predicted: inlet wet ?ue gas ?owrate: 129–907 kg/h, inlet ?ue gas temperature: 148.9 °C, inlet moisture fraction: 14.5 vol%, cooling water ?owrate: 453 kg/h and inlet cooling water temperature: 31.9 °C).

Fig. 9 illustrates predicted condensation ef?ciency versus corresponding measured condensation ef?ciency for all the coal?red tests. The dotted line in Fig. shows the ±10% standard deviation band. All predicted data are within ±10% with an average discrepancy of 2.5% between experimental data and predicted results. Therefore, the analytical model was able to predict heat and mass transfer in the condensing heat exchangers with good accuracy. A case study was performed to predict condensation ef?_ g;in 6 3:5 after the accuracy of the analyti_ c =m ciency for 0:5 6 m cal model was veri?ed. This broad range of ?ow conditions was not tested in experiments due to limitations in the experimental setup. In these cases, cooling water ?ow rate was ?xed at 453.6 kg/h and 31.9 °C to assure fully turbulent ?ow and the inlet wet ?ue gas ?ow rate was varied from 907 to 129 kg/h. Fig. 10 illustrates the modeling results and several measured points for which experiments were performed. The results show that condensation ef?ciency decreases steadily with a decrease _ g;in , and condensation ef?ciencies from 10 to 30 wt% will _ c =m in m _ g;in 6 1:0 . _ c =m occur for values 0:5 6 m

5. Conclusions An analytical model of heat and mass transfer processes in a ?ue gas condensing heat exchanger system was developed using fundamental heat and mass transfer relations. The modeling approach is based on conservation of energy and mass for the ?ue gas and cooling water. All governing equations were solved using an iterative solution technique with appropriate assumptions and simpli?cations. Experiments were carried out to validate the analytical model. Flue gas exhausted from a boiler was channeled to the pilot scale heat exchanger. Measurements were made and experimental results were compared to the results from the theoretical model. The term ‘condensation ef?ciency’ was de?ned to make a quantitative performance evaluation of the condensing heat exchangers. The ratio of the mass ?ow rate of cooling water to the mass _ g;in , which was the _ c =m ?ow rate of inlet ?ue gas was de?ned as m most important operating parameter used to evaluate the condensation ef?ciency.

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K. Jeong et al. / International Journal of Heat and Mass Transfer 53 (2010) 2361–2368 [4] M. Osakabe, T. Itoh, K. Yagi, Condensation heat transfer of actual ?ue gas on horizontal tubes, in: Proceedings of the 5th ASME/JSME Joint Thermal Engineering Conference, 1999. [5] M. Osakabe, Thermal-hydraulic behavior and prediction of heat exchanger for latent heat recovery of exhaust ?ue gas, in: Proceedings of the ASME Heat Transfer Division, vol. 2, 1999. [6] M. Osakabe, Latent Heat Recovery from Oxygen-Combustion Flue Gas, Energy Conversion Engineering Conference and Exhibit, vol. 2, 2000, pp. 804–812. [7] M. Osakabe, K. Yagi, T. Itoh, K. Ohmasa, Condensation heat transfer on tubes in actual ?ue gas (parametric study for condensation behavior), Heat Transfer – Asian Res. 32 (2003). [8] M.P.P. Valencia, Condensation of Water Vapor and Acid Mixtures from Exhaust Gases, Dr. Ing Dissertation, Technical University of Berlin, 2004. [9] E. Levy, H. Bilirgen, C. Samuelson, K. Jeong, M. Kessen, C. Whitcomb, Separation of water and acid vapors from boiler ?ue gas in a condensing heat exchanger, in: Proceedings of the 33rd International Technical Conference on Coal Utilization and Fuel Systems, 2008. . [10] E. Levy, H. Bilirgen, K. Jeong, M. Kessen, C. Samuelson, C. Whitcombe, Recovery of Water from Boiler Flue Gas, DOE Final Technical Report (952467), 2008. [11] K. Jeong, Condensation of Water and Sulfuric Acid Vapor in Boiler Flue Gas, Ph.D. Dissertation, Lehigh University, AAT 3354749, 2009. [12] A.P. Colburn, O.A. Hougen, Design of cooler condensers for mixtures of vapors with non-condensing gases, Ind. Eng. Chem. 26 (1934) 1178–1182. [13] M. Goldbrunner, Lokale Ph?nomene bei der Kondensation von Dampf in Anwesenheit eines nightkondensierbaren Gases, VDI Verlag. Dissertation Universit?t Munchen, 2003. [14] A.P. Colburn, Trans. Am. Inst. Chem. Eng. 29 (1933) 174. [15] T.H. Chilton, A.P. Colburn, Ind. Eng. Chem. 26 (1934) 1183. [16] A. Zhukauskas, Heat transfer from tubes in cross ?ow, Advances Heat Transfer, vol. 8, Academic Press, New York, 1972. [17] K. Stephan, Heat Transfer in Condensation and Boiling, Springer-Verlag, New York, 1992. [18] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, sixth ed., Wiley, 2007. [19] N. Al-mutawa, Experimental Investigations of Frosting and Defrosting of Evaporator Coils at Freezer Temperature, Ph.D. dissertation, The University of Florida, 1997. [20] C. Antoine, Tensions des vapeurs; nouvelle relation entre les tensions et les températures, Comptes Rendus des Séances de l’Académie des Science 107 (1888) 681–837. [21] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel ?ow, Int. Chem. Eng. 16 (1976) 359–368.

The results from analytical modeling, using the same operational conditions as the experiments, agreed well with experimental results. The condensation rates in each heat exchanger and temperature distributions for the ?ue gas and cooling water were used to compare the tests. The average discrepancy between the results of the analytical model and experiments were within a few percent. In order to determine how condensation ef?ciency with rela_ g;in , the analytical model developed in this _ c =m tively low ratios of m study was used to determine the condensation ef?ciency. It was predicted that the condensation ef?ciency would range from 10 _ g;in was varied from 0.5 to 1.0. _ c =m to 30 wt% as the ratio of m

Acknowledgements This research and paper were prepared with the support of the U.S. Department of Energy, under Award No. DE-FC26-06NT42727. However, any opinions, ?ndings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily re?ect the views of the DOE. The authors are also grateful to the Pennsylvania Infrastructure Technology Alliance for providing partial funding.

References

[1] T.J. Feeley, S. Pletcher, B. Carney, A.T. McNemar, Department of Energy/ National Energy Technology Laboratory’s Power Plant – Water R&D Program, Power-Gen International 2006, 2006. [2] D.G. Kroger, Air-Cooled Heat Exchangers and Cooling Towers, PennWell Corporation, USA, 2004. [3] R.L. Webb, A.S. Wanniarachchi, The effect of non-condensible gases in water chiller condensers – literature survey and theoretical predictions, ASHRAE Trans. 80 (1980) 142–159.

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