Effective heat transfer in a metal-hydride-based hydrogen separation process

Effective heat transfer in a metal-hydride-based hydrogen separation process

International Journal of Hydrogen Energy 26 (2001) 711–724 www.elsevier.com/locate/ijhydene E$ective heat transfer in a metal-hydride-based hydrogen...

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International Journal of Hydrogen Energy 26 (2001) 711–724

www.elsevier.com/locate/ijhydene

E$ective heat transfer in a metal-hydride-based hydrogen separation process William H. Fleminga , Jamil A. Khanb; ∗ , Curtis A. Rhodesb b University

a Bechtel Savannah River, Inc., Aiken, SC 29808, USA of South Carolina, Department of Mechanical Engineering, Columbia, SC 29208, USA

Received 23 June 2000; received in revised form 29 November 2000; accepted 4 December 2000

Abstract This paper presents the results of experimental and analytical study of the thermal cycling absorption process (TCAP); which is a metal-hydride-based hydrogen separation system con7gured as a helical shell-and-tube heat exchanger. The column (tube side) is packed with Palladium deposited on kieselguhr (Pd=k). This packed column is thermally cycled by a hot and cold nitrogen gas on its exterior surface (shell side), while a stream of hydrogen mixed with other inert gases are passed through the packed column. Hydrogen gas is absorbed and desorbed from the Palladium, causing a separation from the gas stream. The rate at which the hydrogen is separated depends only on how quickly the Pd=k can be thermally cycled. In this paper we present a transient heat transfer analysis to model the heat transfer in the Pd=k packed column. To improve the e:ciency of the TPAC, metallic foam was added in the Pd=k packed column. It was observed that adding metallic foam signi7cantly improved the separation rate of hydrogen. Thermal cycling times for varying packed column diameters, materials, and compositions are also determined. Comparison of performance is made between an existing 1.25 in (31.75 mm) column versus a 2 in (50.8 mm) column tube. A parametric argument is presented to optimize the material selection and geometric design of a TCAP heat exchanger. ? 2001 Published by Elsevier Science Ltd. on behalf of the International Association for Hydrogen Energy.

1. Introduction 1.1. General Based on EPA report in 1993, about 66% of CO emissions, 50% of smog-forming emissions, and about 33% of the air pollutants that a$ect the ozone layer come from gasoline-powered vehicles. Due to environmental concerns a greater e$ort is necessary to provide automobiles with cleaner burning fuels. Hydrogen as an alternate energy source can be obtained by three methods: electrolysis of water, steam reforming of natural gas, and gas separation techniques. The focus of this paper is separation of hydrogen by thermal cycling of materials, which are capable of absorbing and desorbing hydrogen. Metal hydrides reversibly absorb relatively large amounts of ∗ Corresponding author. Tel.: +1-803-777-1578; +1-803-777-0106. E-mail address: [email protected] (J.A. Khan).

fax:

hydrogen at ambient temperatures and pressures. This technology allows hydrogen to be stored in a solid form. In general, metal hydrides have relatively fast reaction rates, large heats of reactions, and low thermal conductivities. Consequently, the limiting factor in the rates of absorption and desorption in metal hydrides is the rate at which the heat of reaction can be supplied to, or removed from, the metal hydride. Therefore, accurate modeling of the heat transfer is of prime importance in optimizing the performance of a metal-hydride-based system. The thermal cycling absorption process (TCAP) is a metal-hydride-based, thermally cycled hydrogen gas separation process invented by Myung W. Lee of the Savannah River Site. The main component of this separation process is a shell-and-tube-type heat exchanger utilizing a Palladium deposited on kieselguhr (Pd=k) packed column. Palladium is a metal hydride, which absorbs hydrogen reversibly due to the relatively small size of the hydrogen molecule.

0360-3199/01/$ 20.00 ? 2001 Published by Elsevier Science Ltd. on behalf of the International Association for Hydrogen Energy. PII: S 0 3 6 0 - 3 1 9 9 ( 0 0 ) 0 0 1 2 9 - 4

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Nomenclature area, cross-sectional or surface, ft 2 free cross-sectional area in the annulus, ft 2 aluminum foam atmospheres British thermal units constant for Zukauskas tube bank correlations correction factor for Zukauskas tube bank correlations ◦ Cp speci7c heat, Btu=lb F Cu copper Cufoam copper foam D diameter, inside or outside, ft Dp particle diameter, ft dp pressure drop, psi Eg energy generation, Btu Ein energy transfer into a control volume, Btu Eout energy transfer out of a control volume, Btu Est energy stored within a control volume, Btu f friction factor Fo fourier number G mass velocity, ft=s ft2 gc gravitational constant, 32:17 ft lb=lbf s2 ◦ h heat transfer coe:cient, Btu=h ft2 F hc convective heat transfer coe:cient, Btu=h ◦ ft2 F ◦ hcontact thermal contact conductance, Btu=h ft 2 F hN nitrogen side heat transfer coe:cients, Btu=h ◦ ft2 F hpdk Pd=k packed column side heat transfer coe:◦ cient, Btu=h ft 2 F hpdkfoam Pd=k with foam packed column side heat trans◦ fer coe:cient, Btu=h ft 2 F hw apparent heat transfer coe:cient at packed col◦ umn wall, Btu=h ft2 F ◦ k thermal conductivity, Btu=h ft F ke e$ective thermal conductivity in packed col◦ umn, Btu=h ft F ke$wfoam e$ective thermal conductivity in packed col◦ umn with foam, Btu=h ft F kf thermal conductivity of Juid in packed column, ◦ Btu=h ft F kfoam thermal conductivity of foam in packed column, ◦ Btu=h ft F kow apparent thermal conductivity of Juid in packed ◦ column at wall, Btu=h ft F ks thermal conductivity of solid in packed column, ◦ Btu=h ft F L length, ft NL number of tubes in longitudinal direction nofoam no foam NuD Nusselt number based upon diameter A Aannulus Alfoam atm Btu C C2

OD p Pr psi psia R Re ReD Rem

outside diameter, ft porosity Prandtl number pounds-force per square inch pounds-force per square inch absolute outer radius, ft Reynolds number Reynolds number based upon diameter Modi7ed reynolds number for use in packed column rpm Rotations per minute slpm Standard liters per minute SS stainless steel (Type 316) ◦ STP standard temperature and pressure, 32 F at 1 atm ◦ Ts surface temperature, F ◦ T∞ free stream temperature, F ◦ Uo overall heat transfer coe:cient, Btu=h ft2 F V velocity, ft=sec Vs super7cial velocity in packed column, ft=sec vol volume, ft 3 w mass Jow rate, lbs=h Greek letters  thermal di$usivity, ft 2 =s  correction factor for in-line tube arrangement from Zukauskas correlation K characteristic length Kp pressure drop, psi Kt time interval, s  average void fraction in packed column w average void fraction in packed column in vicinity of wall  e$ective thickness of Juid 7lm w e$ective thickness of Juid 7lm in packed column in vicinity of wall  constant for e$ective thermal conductivity in geometric arrays absolute viscosity, lb=ft s ! mass density, lb=ft3 Subscripts f 7nal conditions i initial conditions, inner max maximum Juid velocity o outer s swirl-Jow x cross-Jow Superscripts m constant for Zukauskas tube bank correlations

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Kieselguhr, a highly porous diatomite, has a low-pressure drop during the gas Jow in the packed column and provides a large surface area for deposition of the palladium metal. In this paper, a model is presented which describes heat transfer in a low-pressure, stagnant packed metal-hydridebased system with and without a heat transfer-enhancing medium. The time-dependent temperature pro7les calculated by the model are compared with the experimental measurements in di$erent arrangements of hydride material packed beds to determine the ability of the model to accurately reJect the process. 1.2. Literature review Flow in the inlet and outlet sections and internal shell of the TCAP heat exchanger is turbulent Jow in circular tubes, Dittus and Boelter [1] correlation is valid for this. For the shell side annulus of the heat exchanger containing the helical packed column, Zukauskas [2] correlation for tube banks is applicable. The heat transfer within the packed column may be found by determining the e$ective thermal conductivity within the packed bed. The axial e$ective thermal conductivity is negligible due to the low Reynolds number Jow and negligible axial temperature gradient in the packed column. For radial conductivity, the Legawiec and Ziolkowski [3] correlation provides an axial e$ective thermal conductivity only 1% of that of the hydrogen thermal conductivity in the column. Ofuchi and Kunii [4] studied packed beds with larger void fractions (0.34 – 0.6) and stagnant Juids, (Reynolds number ≈ 0). Their studies with Juid Jows approaching Reynolds numbers of zero compared closely with the theoretical equation of stagnant conductivities found by Kunii and Smith [5]. Due to the higher void fractions and their dependence on Reynolds numbers approaching zero- Kunii and Smith’s correlation for e$ective thermal conductivity presented by Ofuchi and Kunii [4] are more appropriate. Yagi and Kunii [6,7] provide a correlation for 7nding the heat transfer coe:cient at the wall for Reynolds number approaching zero. Ofuchi and Kunii [4] provide this calculated heat transfer coe:cient as a correction term when the e$ective thermal conductivity is assumed to be constant throughout the bed. Heat transfer in packed beds result from contributions of conduction, convection, and radiation. Yovonovich [8] states the contribution to the total heat transfer from conduction, which is most signi7cant, depends on the thermal conductivity of the packing material and the surrounding gas, and also on the interJuid contact areas through which heat Jows along with the thermal contact resistance at these temperatures. Chen and Churchill [9] concluded in their study of packed beds that radiation e$ects are important only for tem◦ peratures above 1600 F (1145 K). Wakao and Vortmeyer [10] have shown that the convective contribution depends on the Juid pressure and the void fraction of the packed bed. Between pressures of about 1 torr to 10 atm the e$ect of

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pressure is negligible on thermal conductivity of gases [11]. Therefore, the average operating pressure of 1 atm for this process is assumed to have no e$ect on the e$ective thermal conductivity. In the absence of available information for 7nding the e$ective thermal conductivity of the metallic foam embedded in the Pd=k packed column, the literature review focused on geometrical correlations. Roshenow et al. [12] provide a method for approximating the e$ective thermal conductivity for composites arranged into geometric arrays. The imbedded metal foam is modeled as spherical inclusions (the Pd=k) in a cubic array (the foam continuous lattice). 1.3. Problem statement The absorption and desorption of hydrogen by the Pd=k is almost instantaneous and is heat transfer limited rather than chemical kinetic limited. Consequently, throughput depends almost entirely on heat transfer between the Pd=k and nitrogen. Due to the need for increased capacity for a new TCAP heat exchanger, a 2 in (50.8 mm) diameter Pd=k column was studied and compared with the existing 1.25 in (31.75 mm) column, while maintaining the uncoiled length of 39 feet (11.89 m). This increase in diameter yielded a 180% increase in cross-sectional area=volume, potentially increasing the volume of hydrogen to be separated. The challenge was to increase the throughput by a factor of 2.8, but maintain the same cooling and heating time as that of the existing TCAP heat exchanger. Also, the increase in cross-sectional area increased the required heat Jux through the packed column wall. The purpose of testing and analysis was to determine to what extent the presence of a heat transfer-enhancement medium, such as metallic foam, would compensate for the e$ect of the larger diameter. In order to establish the maximum throughput of the heat exchanger, the design was optimized by performing parametric studies. These parametric studies include: (1) comparison of di$erent materials to minimize heat capacitance and increase thermal di$usion; (2) assessment of heat transfer enhancement within the packed column by addition of metallic foam; (3) comparison of di$erent geometries in order to maximize both the packed bed-tube side heat transfer and the nitrogen gas-tube side heat transfer coe:cients; (4) optimization of the hot and cold nitrogen gas temperatures and Jow rates; (5) application of a time-dependent analysis with su:ciently small time increments; and (6) knowledge and consideration of practical limitations of fabrication and commercially available equipment. 2. Theoretical analysis 2.1. Introduction The model for studying the heat transfer in the TCAP heat exchanger considers the nitrogen Jow in the shell side of

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(10) Heat transfer between pipe and heat exchanger with environment is neglected due to polished Inconel 625 outer shell that is perfectly insulated. (11) The void fraction is 0.34 in the Pd=k packed column, with or without foam (due to high porosity), and 0.4 at the column wall. 2.2. Critical parameters

Fig. 1. Axial cross section of TCAP heat exchange showing Jow paths.

the heat exchanger, and its a$ect on the coiled Pd=k packed column (tube side) in the annulus of the inner and outer shells. See Fig. 1 for an axial cross section showing the heat exchanger Jow paths. The complexity of this heat transfer problem is simpli7ed without signi7cant compromise by making the following assumptions. (1) The hydride phase and the gas in the void space are in thermal equilibrium. (2) There is no pressure gradient within the packed column. (3) The hydrogen in gas phase behaves as an ideal gas. (4) The temperature in the packed column is only a function of time and is uniform throughout the system at any instant. (5) The hydrogen pressure inside the packed column is one atmosphere. (6) The hydrogen’s heat of absorption=desorption during cooling=heating is uniform and proportional to the ◦ 342 F (445 K) temperature change of Pd=k-hydrogen hydride through heating and cooling cycles. Of the 400 STP l of gas mixture in the 2 in (50:8 mm) packed column, 50% is hydrogen and 50% inert gases with hydrogen completely absorbed=desorbed into=from the Pd=k. Whereas, the existing 1.25 (31:75 mm) inch column contains 145 STP l of gas mixture. (7) The thermophysical properties of nitrogen, with the exception of density, do not vary signi7cantly with pressure and temperature in the operating range. (8) The operating pressure of the nitrogen in hot and cold loops is 150 psia (1:034 Mpa). (9) Heat transfer between the valves and piping and the nitrogen is considered negligible due to vacuum jacketing.

The critical parameters a$ecting the heat transfer in the TCAP column can be better understood by reviewing the geometry of the TCAP heat exchanger in Fig. 1. The 2 in (50:8 mm) OD, 0:065 in (1:65 mm) thick wall, 39 foot (11:89 m) long column is formed into two identical coils. The coil diameter is 20 in (508 mm) center to center. The new 2 in (50:8 mm) packed column is 7lled with metal (aluminum or copper) foam to enhance heat transfer. The Pd=k particles occupy the pores of the metallic foam. An inner shell and an outer shell form an annular space to house the column coil. The inner shell is closed at one end, so that the hot=cold nitrogen Jows into one end of the inner shell, through a number of holes into the annular space housing the packed column. The critical parameters for heat transfer of the heat exchanger are (1) heating and cooling loads; (2) the hot and cold nitrogen temperatures and the nitrogen circulation rate; and (3) the heat transfer coe:cients controlling the heat transfer between the nitrogen and the Pd=k in the packed column. 2.3. Input and related data The dimensions for the TCAP heat exchanger are obtained from fabrication drawings. Thermophysical properties of Pd=k and heats of absorption and desorption for a Pd=k–hydrogen metal hydride system are obtained from Heung [13]. The thermophysical properties of the nitrogen and hydrogen are taken at the time cycle average temperatures at pressures of 10 and 1 atm, respectively. Thermophysical properties for the metallic foam, such as density and speci7c heat, are equivalent to the pure copper or aluminum material of which the foam is formed. However, the information provided by ERG of Oakland, California, the manufacturer of the foam, states that the thermal conductivity of the aluminum foam for a 93.2% porosity is 4.7 Btu=h ◦ ft F (26:69 W=m − K), and for copper foam of the same ◦ porosity is 8.0 Btu=h ft F (45:42 W=m − K). The material for the existing 1.25 in (31:75 mm) TCAP packed column wall is 316 stainless steel. The new 2 in column studied will be either copper or 316 stainless steel. From Knight [14], the target temperature of the Pd=k ◦ ◦ during the cooling cycle is −13 F (−25 C); and target ◦ ◦ temperature during heating cycle is 329 F (165 C). To avoid excessive refrigeration cost [15], the minimum cold ◦ nitrogen supply temperature was set at −40 F (−40C), while the maximum hot nitrogen supply temperature was ◦ set at 349 F (449 K), and was not varied. The second

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consideration for the hot and cold nitrogen was its Jow rate, which was varied between 500 lbs=h (0:063 kg=s), and 20; 000 lbs=h (2:52 kg=s). An optimum Jow rate was determined and chosen for calculation of the nitrogen heat transfer coe:cients and subsequent heating and cooling times of the Pd=k in the new column. The selection of the optimum Jow considers pressure drop, as well as gain in cooling time versus increase in Jow rate. The existing 1:25 in (31:75 mm) heat exchanger has a design nitrogen Jow rate of 3800 lbs=h (0:479 kg=s), which was not varied. 2.4. Shell side — nitrogen heat transfer coe:cients

(1)

where NuD = hD=k; and ReD = (!DV )= , hydraulic diameter was used in Eq. (1) [16]. Irrespective of the pressure drop, the gap between the Pd=k packed column and the inner and outer shells forming the annulus is limited by manufacturing tolerances. Therefore, the gap between the outer shell and column is 7xed at 0.4375 in (11.11 mm), the gap between the inner shell and column is 7xed at 0.3625 in (9.21 mm) (average of 0.4 in, 10.2 mm). The Zukauskas [2] equation was used to determine the heat transfer coe:cient for the nitrogen Jow over the coiled packed column in the annulus of the heat exchanger, which is NuD =

m CReDmax

Pr

0:36

C2 :

Kunii [4] correlations. The Reynolds number in the column is given by Ofuchi and Kunii: Rem =

!Vs Dp

:

(4)

Neglecting radiation e$ects per Chen and Churchill [9], Ofuchi and Kunii [4] provide the following reduced equations for the e$ective thermal conductivity:    (1 − ) ke = kf  + ; (5) ( + 23 kf =ks ) where

The Dittus–Boelter equation for fully developed turbulent Jow in smooth tubes is the following: NuD = 0:023 ReD0:8 Pr 0:4 ;

715

(2)

It should be noted that Eq. (2) was developed for cross Jow through perpendicular rows of tubes. In this case the coiled packed column in the annular space is not exactly perpendicular to the Jow and forms a potential swirl path along the length of the heat exchanger. This was accounted by Eqs. (5) – (6) of Perry [11] and its modi7cation from Heung [17]. For compressible Jow through a conduit, the Jow rate is directly proportional to the Jow area and inversely proportional to the square root of the Jow path: Gx (A=L0:5 )x = : (3) Gs (A=L0:5 )s For approximation, the cross Jow area is the gap between the packed column and the inner=outer shells, and the length is the coiled length of the column. The pitch distance between the sequential coil turns de7nes the swirl Jow area, and the length is the uncoiled length of the column. 2.5. Tube side — Pd=k packed column heat transfer coe:cients The Pd=k packed column is a packed bed with spherical particles of Pd=k with a particle diameter of 0.001 ft and packing void fraction of 0.34 in the bed and 0.4 at the column wall. The Reynolds number based on Pd=k particle diameter approaches zero, allowing the use of the Ofuchi and

 = 1 + (1 − 2 )

 − 0:260 0:216

(6)

and 1 and 2 are a function of ks =kf , found graphically from Fig. 3 of Ofuchi and Kunii [4]. The heat transfer coe:cient at the wall is a function of thermal conductivity at the wall. Ofuchi and Kunii provide the following reduced equation for Reynolds number approaching zero:  −1  1 Dp 0:5 hw = 0 + ; (7) − kf (kow =kf ) ke =kf where kow = kf





(1 − w ) (w )(2) + (w + 13 (kf =ks ))

 (8)

Eqs. (7) and (8) are correction factors and are a consequence of assuming the thermal conductivity as constant throughout the packed column. Again, with w as a function of ks =kf was found graphically from Fig. 3 of Ofuchi and Kunii [4]. With the e$ective thermal conductivity known within the packed column and the heat transfer coe:cient found for the wall, the overall e$ective heat transfer coe:cient can be found for the packed column by considering thermal resistances in series. −1  D=2 1 hpdk = + : (9) ke hw In order to model the inclusion of metal foam in the column, the goal is to 7nd an e$ective thermal conductivity of the packed bed with the Pd=k material, the hydrogen gas, and the metal (aluminum or copper) foam. The Pd=k and hydrogen thermal conductivity was combined and given the value calculated by Eq. (5). This value was used in the correlation for e$ective thermal conductivity of a cubic array with spherical inclusions provided by Roshenow [18]: ke$wfoam     −1  1 =kfoam 1 − K 1 + √ ; cot √ − − 1 − − 1 (10)

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where  (1=3) p K= (=6)

(11)

and =

(4=K2 )kfoam =ke : (1 − (kfoam =ke ))

(12)

Eq. (11) provides a characteristic length as a function of the porosity of the foam. Eq. (12) is an assigned variable for the calculation of the e$ective thermal conductivity in the cubic array. The contact resistance, or contact conductance, varies by material types and has been provided by Cengel [19]. The overall e$ective heat transfer coe:cient in the packed bed with metal foam can be found by −1  D 1 1 hpdkfoam = + + : (13) 2=ke$wfoam hw hcontact 2.6. Heats of reaction Absorption and desorption of hydrogen into or from the Pd=k is a surface phenomenon and the mass transfer is uniform as long as the sites for absorption and desorption are available. As the hydrogen gas in the Pd=k column is cooled and absorbed by the palladium to form a metal-hydride, the exothermic chemical heat of absorption is linearly proportional to the temperature change of the Pd=k and hydrogen compound. Due to its linear dependence upon temperature, the total amount of energy can be determined based upon the number of moles of hydrogen in the column and divided by the total temperature swing of the Pd/k–hydrogen compound. This ratio of energy to temperature change provides a quantity commonly called heat capacitance — the product of the mass and speci7c heat of the material. Similarly, as the hydrogen gas in the Pd/k column is heated and desorbed by the palladium, a heat of reaction is released, decreasing the temperature of the Pd/k. These equivalent heat capacitances for absorption and desorption of hydrogen will be used in a manner similar to the heat capacitances. 2.7. Transient temperature calculation In order to develop a method for calculating the transient temperature change within the heat exchanger over an increment of time, conservation of energy must be applied. Here, the conservation of energy equation can be introduced as d d d d (14) Ein + Eg − Eout = Est : dt dt dt dt The second term, the thermal energy generation rate, is associated with the rate of conversion of chemical energy to thermal energy — as in the case of heat of absorption and desorption. This heat generation will be combined with the heat capacitance stored in the Pd=k column. Therefore, energy equation in terms of convection and capacitance is wcp (Tin − Tout ) = hc A(Ts − T ) = mcp (Ti − Tf )=(Kt):

(15)

Fig. 2. Axial cross section of TCAP heat exchanger showing sections as used in transient temperature calculations.

Eq. (15) can be used on a time interval basis to 7nd an energy balance between the energy change in the Jowing heat transfer medium, the convective heat transfer within the shell side or column side of the heat exchanger, and change in energy storage due to temperature change in the mass being cooled or heated. It allows the calculation of heat transfer between the nitrogen and an exposed section within the heat exchanger, with the section’s temperature change equivalent to the energy transferred during the speci7ed time interval divided by its capacitance. The transient analysis was performed by dividing the heat exchanger into several sections (control volumes). The heat exchanger is 7rst divided into two halves of equivalent geometry and capacity. The inlet to center point contains one coiled column, and the center point to outlet contains the second coiled column. This not only provides for a more concise model, but also allows the study of the two packed columns as separate entities. Within each of the two halves, 7ve sections were designated, for a total of 10 sections in the analysis. The 10 sections of the heat exchanger are shown in Fig. 2. Applying Eq. (15) to the 10 sections, the heat transfer is calculated during a speci7ed time increment. This heat transfer is balanced with the heat capacitance of the section to estimate its new temperature for the same time interval. The amount of energy is also balanced with the nitrogen mass Jow rate in the same time increment to estimate the exit temperature of the nitrogen which becomes the inlet nitrogen temperature to the succeeding section. The detailed transient equations can be found in Fleming [20].

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2.8. Pressure drop in the nitrogen side For determining the pressure drop for internal pipe Jow the following is used: Kp = f

!V 2 L; 2Dgc

f = 0:184 ReD−0:2 :

(16) (17)

For the Jow inside of the inner shell, the hydraulic diameter is used in the above equations. The pressure drop in the annulus over the packed column can be found by the following correlation:  2  !Vmax Kp = NL  f; (18) 2 where f and  are graphically determined from Fig. 63 of Zukauskas [2] for an in-line arrangement with speci7ed geometry. 3. Experimental analysis The e$ective thermal conductivities for stainless-steel coils containing Pd=k for the purpose of the TCAP heat exchanger were measured at the Thermal Fluids Laboratory at the Savannah River Site Technology Center, Steimke and Fowley [21]. The following is a brief description of the experimental investigation, the details are contained in [20,21]. To determine the e$ective thermal conductivities for packed columns transient experiments were performed on packed coils and packed spheres. Three coils were with a wall thickness of 0.065 in (1.65 mm) were used. Coil #1 containing kieselguhr, was made from 2 in (50.8 mm) OD tubing bent into a coil having 2.4 turns and an outer diameter of 16 in (406.4 mm). Coil #2 was similar to Coil #1 except that it also contained copper foam (93.2% void), it had 1.1 turns and the outer diameter was 21.5 in (546.1 mm). Coil #3 contained only kieselguhr, had an OD of 1.25 in (31.75 mm), 1.75 turns and an outer diameter of 11 in (297.4 mm). Thus the e$ects of diameter, and packing material could be studied. The actual TCAP process will use Pd=k. The tests reported here were conducted with kieselguhr only because su:cient Pd=k was not available to 7ll a coil. A smaller scale test, with a sphere with an outer diameter of 2.25 in (57.15 mm) and a wall thickness of 0.016 in (0.406 mm), was performed for this purpose. The sphere was 7lled with Pd=k and weighed before and after 7lling so that the mass of Pd=k could be calculated. A vacuum was pulled on the sphere overnight, then the sphere was back7lled with helium at 1 atm. Two thermal transient tests were conducted with this con7guration. Later the Pd=k was replaced with kieselguhr and the process was repeated. The tests were conducted with helium gas instead of hydrogen for safety reasons.

Fig. 3. Lab equipment schematic.

The test facility is shown in Fig. 3 and consisted of an insulated stainless-steel tank, an agitator, an electric hoist, two 1000 W electric heaters, instrumentation and a data acquisition system. The coil was connected to one of the two pressures. A pressure transducer was used to measure pressures. Assuming ideal gas behavior of the gas in the coil the pressure was correlated with temperature. Four temperatures inside the tank were measured with Type J thermocouples. Ambient temperature was measured. The data acquisition software was Labview V5.0. Tank temperature was controlled using an E-type thermocouple connected to an Omega CN9000A controller. The convective heat transfer coe:cient in the tank was determined from lumped capacitance experiments performed on two 12 in (304.8 mm) long aluminum bars with diameters of 2.00 in (50.8 mm) and 1.50 in (38.1 mm). The thermal di$usivities of the three coils were calculated using transient conduction analysis of the experimental results. E$ective thermal conductivities were calculated by multiplying the thermal di$usivities in Table 1 by density and speci7c heat. For Coil #2 a weighted average was used for the product of density and the speci7c heat for copper and kieselguhr. It should be noted that the thermal conductivities in Table 2 are more uncertain than the thermal di$usivities in Table 1 because they are products of three measured quantities, each having an uncertainty. The purpose of the experiments with the sphere was to allow a comparison of thermal response for Pd=k and

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Table 1 Coil thermal di$usivity in ft 2 =h for transient tests Coil #1 1 atm

Coil #2 1 atm

Coil #3 1 atm

0.022 5:677 × 10−7 m2 =s

0.048 1:239 × 10−6 m2 =s

0.020 5:161 × 10−7 m2 =s

the external Biot number and therefore to external heat transfer coe:cient. 4. Based on the transient tests that compared the response of kieselguhr and Pd=k it is estimated that the coils would have responded approximately 40% faster if they had been 7lled with Pd=k rather than kieselguhr. 4. Results and discussion

Table 2 Coil e$ective thermal conductivity in Btu=h ft



F for transient tests

Coil #1 1 atm

Coil #2 1 atm

Coil #3 1 atm

0.13 0.225(W=m K)

0.43 0.727(W=m K)

0.12 0.208(W=m K)

kieselguhr. Normalized temperature at the center of the sphere was plotted as a function of time (not shown here) for the four transients. Normalized temperature is de7ned as the following: Tnorm = (T − T0 )=(Tbath − T0 ); where T0 is the initial temperature of the sphere. It was observed that the temperature response is slower with kieselguhr than with Pd=k. From calculation it was found that, the thermal di$usivity for Pd=k is a factor of 1.4 larger than the thermal di$usivity listed for kieselguhr in Table 1. For example, the thermal di$usivity of Pd=k in Coil #1 with helium at 1 atm is estimated to be 0:031 ft 2 =h (8 × 10−7 m2 =s). By extension, if the transient coil tests had been run with Pd=k instead of kieselguhr, the transients would be expected to be 40% faster. The thermal conductivity of Pd=k in helium at 1 atm can be estimated using the estimated thermal di$usivity, the density, speci7c heat and the de7nition of thermal di$usiv◦ ity. The estimated thermal conductivity is 0:17 Btu=h ft F (0.294 W=m K). Experimental conclusions 1. The three coils used in the transient tests were 7lled with kieselguhr instead of Pd=k. Coils #2 and #3 responded almost equally fast and more than twice as fast as Coil #1. Therefore, the use of copper foam is an e$ective method to compensate for e$ect of increasing the diameter of the tubing used in the coils. 2. Thermal di$usivity was nearly the same for Coils #1 and #3, the two coils that contained only kieselguhr and helium. 3. Coil #3 responded only 10% more slowly when the bath was not agitated. This e$ect was expected to be small because the coils were intentionally operated in a condition where internal heat conduction was nearly insensitive to

4.1. Review of analytical model ◦

With the nitrogen supply temperatures 7xed at −40 F ◦ (233 K) and 349 F (449 K), nitrogen Jow is the only available variable. Therefore, the parametric studies are focused on the optimization of the packed column. In order to meet the cooling times of the existing 1.25 in (31.75 mm) packed column with the 2 in (50.8 mm) column (providing 180% additional throughput), accurate modeling of the packed column with various wall materials and heat transfer enhancement medium (metal foam) is imperative. 4.2. De=nition of cases A total of seven di$erent cases for the Pd=k packed column are modeled. One with the existing (1.25 in, 31.75 mm) reactor and additional six new cases. These seven cases are de7ned below in Table 3. 4.3. E>ect of varying nitrogen ?ow rate Using Case 6, the heat transfer coe:cients for the nitrogen side of the heat exchanger are calculated for nitrogen Jow rates of between 500 lbs=h (0:063 kg=s) and 20; 000 lbs=h (2:52 kg=s). The e$ective heat transfer coe:cient in the Pd=k column with copper foam is calculated as well. The transient heat transfer calculations are performed using the time-dependent equations using a time interval of 0.1 min (6 s). The results of the transient heat transfer calculations for Case 6 shown in Fig. 4 for cooling and Fig. 5 for heating. To assist in the selection of the optimum nitrogen Jow, pressure drop is also considered through the shell side of the heat exchanger. Based on the pro7les shown in Figs. 4 and 5, the optimum Jow rate for the nitrogen system is chosen as 7000 lbs=h (0:882 kg=s). Very little gain in cycle time is realized beyond this established design point; the life cycle cost for heat transfer equipment and compressors beyond this optimum would be impractical. For the cooling cycle, ◦ ◦ the time to reach −13 F (−25 C) is about 7.9 min and for ◦ heating to reach 329 F (438 K) is about 8.3 min. The Reynolds number in the three main sections (shown in Fig. 6) may be examined to gain a better understanding of the controlling factors for heat transfer. From the Fig. 6, at cooling and heating times (heating time is not shown) of approximately 8 min, it can be noted that the Reynolds

W.H. Fleming et al. / International Journal of Hydrogen Energy 26 (2001) 711–724

719

Table 3 De7nition of cases of models Case No.

1 2 3 4 5 6 7

Column outside diameter (in)

Column wall thickness (in)

Column wall material

1.25 2 2 2 2 2 2

0.065 0.065 0.065 0.065 0.065 0.065 0.065

316 SS Copper 316 SS Copper 316 SS Copper 316 SS

Foam material

Nitrogen Jow rate∗ (lbs=h)

None None None Aluminum Aluminum Copper Copper

3800 7000 7000 7000 7000 7000 7000

Fig. 4. Cooling time vs. cold nitrogen Jow rate.

number in the annulus over the coiled packed column is considerably smaller than that in the other sections of the heat exchanger, thus limiting heat transfer. 4.4. E>ect of increasing column diameter Using Eqs. (5) – (8), the e$ective thermal conductivity in the packed column are calculated for Cases 1–3 and found to ◦ be 0:25 Btu=h ft F (0:433 W=m K) for the cold cycle and ◦ 0:30 Btu=h ft F (0:519 W=m K) for the hot. The e$ective thermal conductivity in the packed column is a function of both the thermal conductivity of the Pd=k and of the hydrogen and is independent of the path length for heat transfer. The e$ective heat transfer coe:cients within the Pd=k packed columns without foam are summarized in Table 4.

For Cases 2 and 3, the e$ective heat transfer coe:cient is independent of the column wall material. The decrease in e$ective heat transfer coe:cient by a factor of 1.6 with increase in diameter is consistent with the earlier argument. Note that the factor of 1.6 is simply the increase in diameter, i.e. heat Jow path. The increase in e$ective heat transfer coe:cient from cold to hot conditions is expected due to the increased thermal conductivity of hydrogen in the packed column at the higher temperatures. 4.5. E>ect of di>erent column wall materials The column wall tubing is modeled as either copper or 316 stainless steel. The column wall material impacts the cooling or heating time by a$ecting the heat capacitance and the thermal resistance through the column wall. Since copper or stainless-steel (SS) tubing would have

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W.H. Fleming et al. / International Journal of Hydrogen Energy 26 (2001) 711–724

Fig. 5. Heating time vs. hot nitrogen Jow rate.

Fig. 6. Reynolds number in sections vs. cooling time.

Table 4 E$ective heat transfer coe:cients for di$erent diameters Case No.

Column outside diameter (in)

Column wall material

Cold cycle ◦ (Btu=h ft 2 F)

Hot cycle ◦ (Btu=h ft 2 F)

1 2 3

1.25 2 2

316 SS Copper 316 SS

4.7 3.0 3.0

5.7 3.6 3.6

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Table 5 E$ective heat transfer coe:cients for di$erent foams & wall materials Case No.

Column outside diameter (in)

Column wall material

Foam material

Cold cycle ◦ (Btu=h ft 2 F)

Hot cycle ◦ (Btu=h ft 2 F)

4 5 6 7

2 2 2 2

Copper 316 SS Copper 316 SS

Aluminum Aluminum Copper Copper

15.6 15.6 30.3 30.3

14.4 14.4 29.2 29.2

the same dimensions, mass would depend on density, with copper being slightly higher. However, the copper has a lower speci7c heat, o$setting the increased mass and resulting in a lower heat capacitance than SS. For the 2 in (50.8 mm) column, the capacitance for the copper wall ◦ is found to be 5:4 Btu= F (10:254 kJ=K), while the SS is ◦ 6:2 Btu= F (11:774 kJ=K). 4.6. E>ect of adding di>erent metal foams With the goal of increasing the heat transfer coe:cient within the packed column, metal foam is inserted into the Pd=k packed columns. The aluminum 6101 foam is manufactured by ERG of Oakland California, however, commercially pure copper foam is currently being developed. The e$ective thermal conductivity within the packed bed is 7rst calculated by Eqs. (5) and (6) and the metal foam is inserted into the Pd=k packed column and modeled by equations provided by Roshenow [18] for e$ective thermal conductivity of a cubical array with spherical inclusions. See Eqs. (9) and (10). For the cold nitrogen cycle, the e$ective thermal conduc◦ tivity is increased from 0:25 Btu=h ft F (0:433 W=m K) ◦ without foam to 1:31 Btu=h ft F (2:267 W=m K) for ◦ aluminum foam and 2:55 Btu=h ft F (4:413 W=m K) for copper. For the hot nitrogen cycle, the e$ective ◦ thermal conductivity is increased from 0:30 Btu=h ft F ◦ (0:520 W=m K) without foam to 1:21 Btu=h ft F (2:094 ◦ W=m K) for aluminum foam and 2:46 Btu=h ft F (4:257 W=m K) for copper. With the addition of the metal foam into the packed bed, a contact resistance must be considered between the foam and the column wall, see Eq. (13). The e$ective heat transfer coe:cients within the Pd=k packed columns with foam calculated from Eqs. (5) – (13) and are summarized in Table 5. As mentioned earlier, no di$erence in heat transfer coe:cient within the packed bed is expected for di$erent column wall materials, only for foam material, and its associated contact resistance with the wall. 4.7. Cycle times with varied parameters The calculated parameters are combined and the heating and cooling cycle times calculated by the transient equations.

With the new nitrogen supply set at 7000 lbs=h (0.882 kg=s) for Cases 2–7, and 3800 lbs=h (0.479 kg=s) for Case 1, each of the seven cases are shown in Figs. 7 and 8 and are summarized in Table 6. From examination of the cooling cycle in Fig. 7 and Table 6, three major groupings of the seven di$erent cases occur. Cases 1, 6, and 7 reach the cooling cycle goal temperature of ◦ ◦ −13 F(−25 C) within the same approximate cycle time of 8 min. The second major grouping consists of Cases 4 and 5, which reaches the target temperature in approximately 9:5 min. And the third grouping, Cases 2 and 3, reaches the desired temperature in approximately 24 min. The addition of copper foam to the 2 in (50:8 mm) column provides for cooling as quickly as the existing 1.25 in (31:75 mm) column. Although the copper foam increases the heat transfer coe:cient in the packed column by a factor of 10, and the aluminum increases it by a factor of 5, the same magnitude of increase is not realized in the cooling of the entire heat exchanger. The aluminum foam cases are found to lag by only 1:5 min. However, the cooling times for the 2 in columns without any foam are signi7cantly greater, on the order of 2– 3 times as long as the existing 1.25 in (31:75 mm) column. For each of the three major groupings of cases, no signi7cant di$erence is noticed in the cooling pro7les due to the variation of the column wall materials. Similar observations can be made regarding the heating cycle. 4.8. Comparison of results From Steimke’s and Fowley’s experimental results, a comparison can be made for the applicability of the model developed in this work. The experiments involved the use of three coils: #1 with 2 in (50.8 mm) diameter SS with kieselguhr in helium; #2 with 2 in (50.8 mm) diameter SS with kieselguhr with copper foam in helium; and #3 with 1.25 in (31.75 mm) diameter SS with kieselguhr in helium, each at one atmosphere. Additional tests were run to allow correlation between Pd=k and kieselguhr. The relative di$erences between cycle times for the analytical model and experimental tests compare well. But if the e$ective thermal conductivities of the columns with and without foam are compared, some di$erences are noted. Although the coil tests experiments were run with kieselguhr, further tests were run to make a correlation from the kieselguhr to the Pd=k — which is the actual case. The

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W.H. Fleming et al. / International Journal of Hydrogen Energy 26 (2001) 711–724

Fig. 7. Cooling time at 7000 lb=h nitrogen for all cases.

Fig. 8. Heating time at 7000 lb=h nitrogen for all cases.

temperature response was 1.4 times greater with Pd=k, implying that a factor of 1.4 could be applied to the e$ective thermal conductivity calculated for kieselguhr in helium. The e$ective thermal conductivity of the kieselguhr in ◦ helium was found to be 0.13 Btu=h ft F (0:225 W=m K) ◦ without foam and 0:43 Btu=h ft F (0:744 W=m K) with copper foam. After applying the factor for Pd=k in helium, the tests indicated an e$ective thermal conductivity of the



Pd=k in helium to be 0:17 Btu=h ft F (0:294 W=m K) ◦ without foam and 0:60 Btu=h ft F (1:038 W=m K) with copper foam. The thermal conductivity of hydrogen is approximately 20% greater than helium at a given temperature. If this factor is applied to the above thermal conductivity for Pd=k in helium, the tests could be extrapolated to show the e$ective thermal coductivity of the Pd=k ◦ in hydrogen is 0:2 Btu=h ft F (0:346 W=m K) without

W.H. Fleming et al. / International Journal of Hydrogen Energy 26 (2001) 711–724

723

Table 6 Cycle times with varied parameters Case No.

Column outside diameter (in)

Column wall material

Foam material

Nitrogen Jow rate (lbs=h)

Cooling cycle, time to reach ◦ −13 F (Min)

Heating cycle, time to reach ◦ 329 F (Min)

1 2 3 4 5 6 7

1.25 2 2 2 2 2 2

316 SS Copper 316 SS Copper 316 SS Copper 316 SS

None None None Aluminum Aluminum Copper Copper

3800 7000 7000 7000 7000 7000 7000

8.1 23.5 23.6 9.4 9.7 7.9 8.2

8.8 23.4 23.5 10.4 10.6 8.3 8.5



foam and 0:72 Btu=h ft F (1:246 W=m K) with copper foam. When the analytical result for e$ective thermal conductivity in the Pd=k packed column is compared with that of the experimental result, the analytical model provides a value 25% greater (0.25 vs. 0.2). Although the di$erence is not large, another literature search was performed to 7nd a more accurate correlation for e$ective thermal conductivities of stagnant packed beds. Schumann and Voss [22] provided a correlation by plotting the ratio of conductivity of the bed to the gas (hydrogen) versus the ratio of conductivity of the solid (Pd=k) to the gas (hydrogen) for various void fractions. With a void fraction of 0.34 and solid to gas conductivity ratio of approximately 7, the graph indicates a bed to gas conductivity ratio of 2.9 — resulting in an e$ective thermal ◦ conductivity of 0:26 Btu=h ft F (0:45 W=m K). Roshenow [12] provides a graphical comparison of six di$erent correlations for e$ective thermal conductivity from di$erent investigators at a void fraction of 0.38. With adjustment for the di$erence in void fraction (0.34 vs. 0.38), this graph also indicates a bed to gas conductivity ratio of 2.9. These seven di$erent correlations agree well with the analytical model. If the analytical result for the improvement of the e$ective thermal conductivity by adding copper foam is compared to the experimental value, the analytical model provides a factor of 10 improvements (2.55 vs. 0.25), while the experimental tests provided a factor of 3.6 enhancement. However, from the Hydrogen Bus Project at the Savannah River Site, Heung [23,24] reported that the e$ective heat transfer coef7cient in a metal hydride hydrogen storage bed increased by a factor of 5 when aluminum foam was added to the packed bed. This information directly correlates with the analytical model. Copper has a thermal conductivity which is two times that of aluminum. Therefore, a greater bene7t from copper foam would be expected over that of aluminum. According to Heung [17], the copper foam used in the experimentally tested coil is from a manufacturer other than ERG. The ERG foam has higher thermal conductivity as a result of the ligaments formed during manufacturing. The ligaments in the tested copper foam are coarse and poorly

connected. In addition, Heung [17] also states that the copper foam in the tests were not tightly in contact with the inner wall of the column. Given these issues, the copper foam was unable to serve as a matrix of extended surfaces from the Pd=k to the column wall, thus impeding the heat transfer and lowering the e$ective heat transfer coe:cient within the packed bed.

5. Conclusions Considering pressure drop and thermal cycle duration, an optimum nitrogen Jow rate is selected. Although the helical column has a slight pitch out of the normal Jow direction, the swirl Jow following the length of the column is negligible. Increasing the column diameter has no impact on the e$ective thermal conductivity within the bed, but does decrease the e$ective heat transfer coe:cient in the packed bed. Using a column wall material of either 316 stainless steel or copper, has essentially no e$ect on the cooling or heating times of the Pd=k material. The model predicts accurate results for the cases without foam. Adding aluminum and copper foams to the packed column, increases the e$ective heat transfer coe:cient by factors of 5 and 10, respectively. The cycle times for the 2 in (50.8 mm) columns with copper foam are equivalent to the 1.25 in (31.75 mm) column without foam, and about 2.5 times shorter than the 2 in (50.8 mm) column without copper foam. The cycle times for the 2 in (50.8 mm) columns with aluminum foam are approximately 25% longer than those with copper foam. The analysis in this paper provides an accurate model of the metal-hydride-based hydrogen separation process. TCAP heat exchanger. The general trends provided in the laboratory tests and technology application are reinforced by published results. The new larger TCAP heat exchanger with copper foam will be able to separate an additional 180% of hydrogen in the available gas stream within the same cycle time as the existing column.

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References [1] Dittus FW, Boelter LMK. University of California, Berkeley, publications on Engineering, vol. 2, 1930. p. 443. [2] Zukauskas A. Heat transfer from tubes in cross Jow. In: Hartnett JP, Irvine Jr TF, editors. Advances in heat transfer, vol. 8. New York: Academic Press, 1972. [3] Legawiec B, Ziolkowski D. Axial thermal e$ective conductivity in packed-bed catalytic tubular reactors. Chem Engng Sci 1997;52(12):1875–82. [4] Ofuchi K, Kunii D. Heat transfer characteristics of packed beds with stagnant Juids. Int J Heat Mass Transfer 1964;8:749–57. [5] Kunii D, Smith JM. Heat transfer characteristics of porous rocks. AIChE J 1960;6(1):71–8. [6] Yagi S, Kunii D. Studies on heat transfer near wall in packed beds. AIChE J 1960;6:97. [7] Yagi S, Kunii D. Studies on heat transfer in packed beds. Int Dev Heat Transfer, Part IV 1962;750. [8] Yovanovich MM. Thermal contact resistance across elastically deformed spheres. J Spacecraft Rockets 1967;4:119–22. [9] Chen JC, Churchill SW. Radiant heat transfer in packed beds. AIChE J 1963;9(1):35– 41. [10] Wakao N, Vortmeyer D. Pressure dependency of e$ective thermal conductivity of packed beds. Chem Engng Sci 1971;26:1753– 65. [11] Perry JH. Chemical engineer’s handbook. 4th ed. New York: McGraw-Hill, 1963. p. 5 –24. [12] Roshenow WM, Hartnett JP, Cho YI. Handbook of heat transfer fundamentals, 3rd ed., Figs. 9–4. New York: McGraw-Hill, 1998. p. 9 –7. [13] Heung LK. WSRC-TR-97-00412, Rev. 0: conceptual design of the Jow through bed. Westinghouse Savannah River Company Technical Report, Unclassi7ed, 1997.

[14] Knight JR. SRT-CHT-98-2015TL: TCAP design basis and fabrication concerns. Westinghouse Savannah River Company Intero:ce Memorandum, Unclassi7ed, 1999. [15] Klein JE et al., editors. WSRC-TR-97-00340TL: conceptual design for consolidation TCAP. Westinghouse Savannah River Company Technical Report, Unclassi7ed and Released, 1997. [16] Incropera FP, DeWitt DP. Fundamentals of heat and mass transfer, 3rd ed., Appendix A. New York: Wiley, 1990. p. 504. [17] Heung LK. WSRC-TR-99-00071, Rev. 1: TFM&C heat transfer (U). Westinghouse Savannah River Company Technical Report, Unclassi7ed, 1999. [18] Roshenow WM, Hartnett JP, Ganic EN. Handbook of heat transfer fundamentals, 2nd ed. New York: McGraw-Hill, 1985. p. 4 –163–7, p. 4 –57. [19] Cengel YA. Heat transfer: a practical approach. New York: McGraw-Hill, 1998. p. 142–3. [20] Fleming WH. Analysis of heat transfer in a metal hydride based hydrogen separation process. MS thesis, University of South Carolina, 1999. [21] Steimke JL, Fowley MD. WSRC-TR-98-00431: transient heat transfer in TCAP coils (U). Westinghouse Savannah River Company Technical Report, Unclassi7ed and Released, 1999. [22] Schumann TEW, Voss V. Fuel 1934;13:239. [23] Heung LK. Hydrogen power: theoretical and engineering solutions. Proceedings of the Hypothesis II Symposium held in Grimstad, Norway, August 18–22, 1997. [24] Shanmuganathan N, Fleming Jr WH. M-CLC-H-01697, Rev. B: calculate the times required for heating and cooling the Pd=K in the HT-TCAP coil (U). Westinghouse Savannah River Company Calculation, Unclassi7ed, 1999.