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Heat transfer in conductive monolith structures
Chemical Engineering Science 60 (2005) 1823 – 1835 www.elsevier.com/locate/ces
Heat transfer in conductive monolith structures Thorsten Bogera,∗ , Achim K. Heibelb a Corning GmbH, Abraham-Lincoln-Str. 30, D-65189 Wiesbaden, Germany b Corning Incorporated, Process Technologies, Corning, NY 14831, USA
Received 27 April 2004; received in revised form 4 November 2004; accepted 29 November 2004 Available online 21 January 2005
Abstract Honeycomb structures made of highly thermal conductive materials (e.g. certain metals) have been proposed as attractive catalyst supports with enhanced heat transfer properties. Recently prototypes of such materials have become available, enabling experimental investigations on their heat transfer properties, including packaging into tubes. This work is focused on the heat transfer performance of conductive monolith structures packaged into heat exchanger tubes. Several parameters such as monolith material structure and properties and packaging tolerances are investigated. Heat transfer coefficients on the order of 1000 W/m2 K and higher were measured. The results are analyzed applying a detailed model based on a fundamental understanding of the relevant phenomena. It is demonstrated that it is necessary to consider the variations of the thermal expansion of the monolith and the tube over the length of the monoliths. By including thermal expansion, the model is in excellent agreement with the experimental results without the need of any fitting parameter. The results are used to develop some design guidelines. In addition some implications of the heat transfer performance for the relevant applications in multitubular reactors as well as some new potential application areas are discussed. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Monolith; Honeycomb; Heat conduction; Heat transfer; Modeling; Catalyst support
1. Introduction Recently, monolithic structures made out of materials with a high thermal conductivity have been proposed as an attractive alternative to conventional catalyst supports for the use in highly exothermic reactions (e.g. partial oxidations) employing multitubular reactors (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005; Carmello et al., 2000; Tronconi et al., 2004). Significantly higher heat transfer rates compared to random catalyst packings (e.g. spheres or rings) were predicted, by changing the dominant heat transfer process from convection to conduction. Simulations (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005) as well as experiments (Carmello et al., 2000; Tronconi et al., 2004) for highly exothermic reaction revealed significantly lower hot spot temperatures. This resulted in improved
∗ Corresponding author. Tel.: +49 611 7366 168; fax: +49 611 7366 112.
E-mail address: [email protected] (T. Boger). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.11.031
operating characteristics and the potential for significant economic benefits. A method and process to prepare suitable extruded metal monoliths with a high thermal conductivity was recently developed by Corning Incorporated (Cutler et al., 2001). A picture of a monolith made for example from copper is shown in Fig. 1. These copper monolithic catalyst supports were evaluated for a heterogeneously catalyzed CO oxidation reaction and showed no radial temperature gradients even at very high reactive heat loads (Tronconi et al., 2004), demonstrating the excellent radial heat removal due to the thermal conduction of the structure. The heat transfer from the monolith to the reactor resulting from the packaging was identified as bottleneck. So far most of the investigations of the heat transfer in these conductive monolith structures was of theoretical nature and limited to the heat transport within the structures itself. To our knowledge, no detailed experimental and theoretical evaluation of the heat transfer of such monolith structures packaged into reactor or heat exchanger tubes is available. As the resistance due to the packaging was identified
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monolith structures based on geometric data (the void fraction ) and the thermal conductivity kS of the monolith walls. −1 √ √ . (1) kS,R = kS (1 − ) + √ √ (1 − + kkGS )
Fig. 1. Photo of copper based monolithic catalyst support with high thermal conductivity.
Fig. 2 also shows in a qualitative manner some typical temperature profiles inside the monolith (see item 1). Additionally the temperature profiles of the gas inside the channels in case of an operation in which a hot gas is cooled (dashed lines, item 5) are illustrated. For most applications the flow inside the channels is laminar since the hydraulic diameter is small (in the order of a 1–3 mm). Because of the small dimensions compared to the monolith diameter the thermal exchange between gas and channel wall is usually described by a film model and using a heat transfer coefficient hGS and the according Nusselt number N uc . Suitable engineering correlations for the Nusselt number inside monolith channels can be readily obtained from the literature (Vortruba et al., 1975) based on experimental investigations, including inlet and outlet effects as well as the thermally and hydraulically developing profiles. N u c kG , dh,c dh,c 2/3 N uc = 0.571 Rec . L hGS =
as the main bottleneck (Tronconi et al., 2004) the objective of the present paper is to further elucidate the effect and improve the overall performance. The results are based on an extensive experimental study combined with a detailed theoretical analysis. The extremely high heat transfer coefficients as well as the favorable ratio between heat transfer and pressure drop leads to additional areas for the use of such monolithic structures beyond the applications discussed so far (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005; Carmello et al., 2000; Tronconi et al., 2004). Some of them will be addressed in the discussion section.
2. Theoretical background In Fig. 2 a schematic of the cross-section of a monolith inserted into a tube is shown. The monolith is represented by a number of channels that are separated from each other by the channel walls of the monolith. No radial exchange of gas between the channels is feasible and therefore, no convective heat transfer in this direction occurs. On the other hand the walls in these extruded structures are connected throughout the entire diameter. Therefore high heat transfer rates can be achieved. Monolith structures as shown in Figs. 1 and 2 with square channels experience some anisotropy with respect to the radial heat flow. However, this is a second order effect and therefore is usually negligible. The rate of the conductive heat transfer is a function of the thermal conductivity of the wall material and of the solid fraction. Groppi and Tronconi (1996) developed a correlation to calculate the effective radial conductivity kS,R in such
(2)
(3)
In case of inserting the monoliths into a heat exchanger (or reactor) tube the heat needs to be transferred across the gap between the skin of the monolith and the inner surface of the tube (item 2 in Fig. 2). This heat transfer resistance is characterized by the size of the gap gap and by the thermal conduction through the usually stagnant fluid film that fills this gap. Expressing the inverse resistance in form of a heat transfer coefficient we obtain hgap = gap /kG . In reality the geometric imperfections of monolith and tube as well as the not perfect centering of the monolith in the tube will result in gap size variations along the circumference of the tube. Therefore the gap size defined above should be considered as a kind of mean effective gap size. In the tube itself the radial heat conduction occurs (step 3 in Fig. 2), which is dependent on the thickness of the tube and its thermal conductivity. The heat transfer between the outside surface of the tube and the external heat exchange medium (step 4 in Fig. 2) depends on the underlying hydrodynamics and the physical properties of the heat exchange medium. This heat transfer is usually described by means of a heat transfer coefficient hext and the according Nusselt number. Reasonable engineering correlations can be found in the literature (Jones, 2002). N uext =
hext dh,ext = c Rebext P r 0.33 ext . kH E
(4)
With c=0.613 and b=0.47 for Reext < 1000 and c=0.384 and b = 0.54 for Reext > 1000. All the dimensionless groups
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Fig. 2. Schematic of the cross-section of a monolith inserted into a tube, which is surrounded by a heat transfer medium. On the right a typical radial temperature profile is shown. In the lower half the gas temperature inside the monolith is also shown (dashed lines, 5) in addition to the solid temperature.
in Eq. (4) are defined with the physical properties of the heat exchange medium and the hydraulic diameter of the external space. Monoliths with a dense skin can be immersed directly into a heat exchange medium, avoiding the use of the tube. In this case only steps 1, 4 and 5 are relevant. Under the conditions of typical heat transfer operation the following steady state enthalpy balances can be used to describe the two dimensional temperature field inside the monolith, assuming constant temperature of the tube and the heat exchange medium, TH E , over the length of the reactor. For the gas plug flow is assumed.
are lumped into a single effective heat transfer coefficient, heff , used for the radial boundary condition at r = R of the solid phase (Eq. (7)). The heat transfer resistance of the tube itself as well as on the shell side of the tube can be calculated, leaving only the resistance of the gap as an unknown lumped parameter. The description can be condensed to a one-dimensional model, where the heat transfer resistance of the monolith itself is expressed by means of an effective heat transfer coefficient, hmono , in series with the resistance at the monolith skin, e.g. heff . The enthalpy balance of the solid phase can then be rewritten.
• Enthalpy balance—Gas phase,
−(1 − )kS
j2 TG (r, z) jTG (r, z) − kG jz jz 2 = hGS GSA(TS (r, z) − TG (r, z)).
cpG Gz,G
(5)
• Enthalpy balance—Solid phase (monolith), j2 TS (r, z) 1 j jTS (r, z) − (1 − )kS rk S,R − jz 2 r jr jr = −hGS GSA(TS (r, z) − TG (r, z)). (6) • Boundary conditions at the monolith skin, r = R: j jTS (R, z) kS,R jr jr 4heff =− (TS (R, z) − TH E ). DM ≈
(7)
4heff DT
In addition, a zero gradient boundary condition at the centerline, r = R, and the typical Danckwerts boundary conditions at the inlet and outlet, e.g. z = 0 and z = L are applied. All the heat transfer resistances between the monolith skin and the heat exchange medium (steps 2–4 in Fig. 2)
j2 TS (z) = − hGS GSA(TS (z) − TG (z)) jz2
−1 1 1 + + heff hmono 4 × (TH E − TS (z)). DM
(8)
To maintain the resistance of the gap as the only unknown parameter a correlation to calculate hmono from the dimensions and properties of the monolith is required. Analytical approaches to obtain such a correlation commonly assume a fully developed, parabolic radial temperature profile. This assumption combined with the boundary conditions yields the following correlation for hmono , based on the effective radial conductivity and the diameter of the monolith (Appendix A): hmono =
KM kS,R , DM
(9)
with KM = 8. However, under practical conditions the requirement of a developed, parabolic temperature profile is often not met. Therefore, a number of numerical simulations with a two-dimensional model were performed, covering a large range of critical parameters, e.g. monolith diameter, length, radial conductivity and gas flow. The analysis
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14 12
KM
10 8 6 4 0.001
0.01
0.1
1
St*. L/DM Fig. 3. Factor KM as function of the system and operating characteristics. Symbols are values for KM derived from detailed two-dimensional simulations for monoliths of different diameter, radial conductivity and length and different gas flow rates.
of the results of the two-dimensional simulations with the one-dimensional model, Eq. (8), resulted in more realistic values for KM . Fig. 3 summarizes the results of this analysis, demonstrating the successful correlation of KM to a characteristic dimensionless group, representing the product of a modified Stanton number St ∗ = (kS,R /DM )/(Gz,G cpG ) and a characteristic length scale L/DM . For small values of St ∗ (L/DM ), high values of KM are observed, representing some sort of inlet effects as under these conditions the temperature profile is not developed. For St ∗ (L/DM ) > 0.05 a plateau is obtained at KM =5.8, representing fully developed conditions. In most cases this value for KM can be applied, as the criterion is met under most practical conditions.
3. Experimental For the experimental investigation of the heat exchange performance of the monoliths a simple heat exchange setup as shown schematically in Fig. 4 was used. The setup consists of a gas supply section, comprising a mass flow controller (A) and an electrical heater (B), followed by a static mixer (C) ensuring thermal plug flow (also enabling a simple one point temperature measurement) to the heat exchanger section (D). The gas flow was varied in the range of 0–60 m3 /h (STP) and heated to temperatures up to 400 ◦ C at the inlet into the heat exchanger section. The heat exchanger section consisted of a horizontally installed, stainless steel tube of 300 mm length and 25–30 mm inner diameter into which the monoliths were packaged. Some initial experiments were performed with a longer heat exchanger section of 560 mm. The tube itself was located within a shell and surrounded by flowing cooling water. Custom baffles were installed in the shell to ensure high external heat transfer. The cooling water temperature was in all cases kept constant at TH E = 20 ◦ C. The water flow rate was adjusted to a high enough value to ensure nearly isothermal operation
between the inlet (T5 ) and the outlet (T4 ) of the water (less than 0.5 ◦ C, accuracy of the thermocouple). Initial trials were performed to ensure, that the external heat transfer from the tube to the water, e.g. hext , was not limiting. For some experiments a 300 mm long monolith was installed directly into the heat exchanger without the addition of an external tube to minimize/eliminate the gap resistance. During the experiments the inlet and the outlet temperature of the gas were measured with thermocouples. At the outlet the gas temperature was measured directly after the monolith (T2 ), in the middle of the tube as well as after a short static mixer (E, T3 ) that was well insulated to ensure that the true average temperature was measured. Usually both temperatures were in agreement and did only in a few cases differ by 1–2 ◦ C. Additionally the pressure drop p across the heat exchanger tube was measured. Air as well as nitrogen were used as the gas phase. The experiments were performed with monoliths made of different materials (cordierite, copper and aluminum) and different cell geometry as described in Table 1. It is worth mentioning that for the achievement of the desired geometric properties, it was necessary to prepare the copper samples by core drilling them out of larger parts and then pressing them into a standard copper tube obtaining an artificial skin with well defined dimensions. Good contact between the monolith and the copper tube was established by first core drilling the monoliths to a diameter slightly larger than the copper tube and then pressing them into the tubes. In Fig. 5 examples of core drilled samples and the copper tube are shown prior and after assembly. Additionally the clearance between the outer diameter of the monolith and the inner diameter of the tube as well as the general packaging method was varied. Comparative and base line experiments with an empty pipe, ceramic rings (5 mm × 3 mm × 5 mm) as well as an metallic monoliths made out of corrugated, wrapped and brazed FeCrAlloy foil were performed. For the analysis of the experiments the measured temperatures were used to determine an integral heat transfer coefficient hint , representing a lump of all the resistances discussed above and represented by the steps 1–5 in Fig. 2.
TG,in − TH E hint A = m . (10) ˙ G cpG ln TG,out − TH E This integral heat exchange coefficient can be directly used for the design of a heat exchanger. For fundamental understanding and interpretation of the results, especially with respect to the heat transfer resistance between the monolith and the tube the raw data was also analyzed with the detailed models described above (Eqs. (1)–(9)).
4. Results In Fig. 6 examples of the measured outlet temperatures are shown for the heat exchanger tube packed with 10 pieces
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Fig. 4. Experimental setup for the heat exchange experiments.
Table 1 Monolith samples used in the experiments Sample
Material
Cell density
Hydraulic channel diameter(mm)
Wall thickness (mm)
Channel geometry
Open
A B C D
Cordierite Porous copper Porous copper Aluminum
400 cpsi 560 cpsi 260 cpsi 200 cpsi
1 0.92 1.26 1.52
0.18 0.15 0.26 ∼0.2–0.5
Square Square Square Round
74 60 57 63
Fig. 5. Photo of the core drilled copper monoliths and the copper tubing prior (left) and after pressing the monoliths into the tube (right). Note, that in most cases longer copper monoliths were used.
100
Outlet Temperature in °C
80
60
40
20
0 0
10
20
30
Gas Velocity uG,0 in mN/s Fig. 6. Outlet temperatures measured for sample D (aluminum) at different gas flow rates. Inlet temperatures: ( ) Tin = 250 ◦ C, () Tin = 400 ◦ C. Length of the monolith section: L = 250 mm.
of 25 mm long aluminum monoliths (sample D). The inner diameter of the tube was 28.4 mm. The data are shown as a function of the gas (nitrogen) flow rate for an inlet temperature of 250 ◦ C and 400 ◦ C. As expected with increasing gas flow rate the outlet temperature increases. Noteworthy 3 /h, equivto mention that even at high flow rates, e.g. 40 mN alent to a superficial velocity of 17.5 mN /s or a mass flux of about 21 kg/(m2 s), the gas is cooled down to 70–80 ◦ C across this very short length of the heat exchanger, equivalent to 190 kW/m2 for the 400 ◦ C inlet temperature. For comparison, we have measured a heat transfer rate of 38 kW/m2 for a longer empty tube (560 mm length) at comparable con3 /h and 350 ◦ C inlet temditions of a gas flow rate of 30 mN perature. In Fig. 7 the integral heat transfer coefficients determined by Eq. (10) with the raw experimental data from Fig. 6 are shown. The data for hint as well as the superficial gas velocity are based on the inner diameter of the tube. For comparison the results for an empty tube with a comparable inner diameter of 25.4 mm are given. Very high heat transfer coefficients, in excess of 1000 W/m2 K are achieved. The values for a gas inlet temperature of 400 ◦ C are 10–15% higher compared to those at Tin = 250 ◦ C. This effect of the temperature level on hint is also shown in Fig. 8 for two gas flow rates. The reason for this temperature dependence will be discussed later in detail. In Fig. 9 results for monolith structures made from different materials and with different cell structure are presented (sample A–D in Table 1). All monoliths were packaged in the tube with the same clearance tolerances. The best results are obtained for the dense aluminum monoliths (sample D). The heat transfer coefficients determined for the copper
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1500
1500
1000
1000
hint in W/m2K
hintin W/m2K
1828
500
500
0
0 0
10
20
30
0
5
10
15
20
Gas Velocity uG,0 in mN/s
Gas Velocity uG,0 in mN/s Fig. 7. Integral heat transfer coefficients hint as function of the superficial gas velocity u0 determined for sample D (aluminum). Monolith experiments: ( ) Tin = 250 ◦ C, () Tin = 400 ◦ C. For comparison: empty tube at Tin = 400 ◦ C ( ), length of the monolith section: L = 250 mm.
Fig. 9. Effect of the material properties on the integral heat exchange coefficient hint . Symbols: experimental data for cordierite (sample A), 䊉 porous copper 560 cpsi (sample B), porous copper 260 cpsi (sample C) and aluminum 200 cpsi (sample D). Lines: predictions from detailed simulations with hgap according to (Eq. (11)). Conditions: inlet gas temperature 400 ◦ C, length of the monolith section: L = 250 mm.
hint in W/m2K
1500
1000
500
0 0
100
200
300
400
500
Gas Inlet Temperature in °C Fig. 8. Effect of the gas inlet temperature on the integral heat exchange coefficient hint . Symbols: experimental data at superficial gas velocity of 䊉 uG,0 = 17 mN /s and uG,0 = 26 mN /s. Lines: predictions from detailed simulations (lines) with hgap according to (Eq. (11)). Conditions: sample D, length of the monolith section: L = 250 mm.
monoliths, samples C and D, are lower especially at higher gas flow, although the thermal conductivity of the porous copper is slightly higher compared to the one for the aluminum samples. This might be explained by an additional contact resistance created between the copper monolith material and the copper tube used as skin. Although the applied force ensured good contact between both parts it cannot be excluded that there might remain an additional heat transfer
resistance. The difference between the two copper samples demonstrates that in the heat exchange experiments the channel size and geometric surface area has an effect on the integral heat exchange coefficient. Slightly better results are obtained for the structure with a higher cell density, sample B. This is explained by the better gas–solid heat transfer (higher GSA) in the channels as the void fraction and therefore the bulk thermal conductivity are rather similar. The importance of a structure with intrinsically high thermal conductivity can be investigated by comparing the result for a cordierite monolith, sample A, with low thermal conductivity. For the latter very poor heat transfer results were found. The measured heat transfer coefficients are even lower compared to the one for an empty tube, shown in Fig. 7. This is explained by the low thermal conductivity of the cordierite material, which allows only very limited radial conductive heat transfer, even lower than the convective heat transfer of the turbulent flow for the empty pipe. Experiments with the corrugated and wrapped metal foil monolith delivered results that were in the same order as those for the cordierite monoliths. Only slightly higher integral heat exchange coefficients were measured, e.g. in the order of 130–140 W/m2 K at a gas velocity of 5 mN /s. The moderate intrinsic thermal conductivity of the material (10–20 W/mK) in combination with the high void fraction (> 90%) and the bad radial connectivity of the structure, results in limited radial heat conduction performance. In the case of the cordierite and the metal foil monoliths the limiting heat transfer is dominated by the resistance in the structure itself and not so much the gap resistance.
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1500
1829
2000
hint in W/m2K
hint in W/m2K
1500 1000
500
1000
500
0 0
5
10
15
20
Gas Velocity uG,0 in mN/s Fig. 10. Effect of the gap size during the monolith loading on the integral heat exchange coefficient hint . Symbols: experimental data for () base case, gap,0 = gap,ref , (䊉) gap,0 = 2gap,ref and () gap,0 = 4gap,ref . Lines: predictions from detailed simulations with hgap according to (Eq. (11)). Conditions: sample D, inlet gas temperature 400 ◦ C, length of the monolith section: L = 250 mm.
Fig. 11. Effect of the skin structure of the monolith on the integral heat exchange coefficient hint . Symbols: experimental data at inlet gas temperatures of 䊉 100 ◦ C, 200 ◦ C, 300 ◦ C and 400 ◦ C. Conditions: sample D, superficial gas velocity 17 mN /s and length of monolith section 250 mm.
The effect of the clearance between the monolith and the inner tube diameter is shown in Fig. 10. The clearance of the base case has been increased by a factor of 2 and 4 in subsequent experiments. The gap size has a significant impact on the obtained heat transfer performance. Further insights are gained by the information provided in Fig. 11. These experiments were performed to identify the relationship between
0 0
5
10
15
20
Gas Velocity uG,0 in mN/s Fig. 12. Performance of core drilled copper monoliths (sample B) pressed into a copper tube and installed directly into the heat exchanger without stainless steel tube. 3 monolith pieces installed with no gap, 䊉 10 monolith pieces (25 mm length) installed without gap, 10 monolith pieces (24 mm) installed with spacers (1.6 mm length). For reference: 2 core drilled copper monolith pieces pressed into a copper tube as skin and installed into a stainless steel tube at base clearance. Conditions: copper tube length 300 mm, total installed monolith length 240–250 mm, gas inlet temperature 400 ◦ C.
the heat transfer performance and the contact area properties between the monolith skin and the tube. To perform a defined experiment subsequently parts of the skin area were removed by machining grooves into the monolith, which had a defined depth 2 and area A2 (see also the schematic on top of Fig. 11). In Fig. 11, A2 therefore represent the relative portion of the skin, which was machined down to the larger clearance. The results demonstrate that the heat transfer coefficient decreases proportional to the machined area and approaches the limiting value for the new clearance. This trend was the same for all temperatures considered in this experiment. The results allow the conclusion that the tolerances between the monoliths and the tubes are of significant importance for the heat transfer performance. Alternatively, in the case of monoliths with dense and impermeable skin it is also possible to directly use the monolith without a packaging tube. In this case the monoliths will be directly mounted to the tube sheets and will be immersed into the heat exchange medium. Results for such a configuration with the copper sample B are shown in Fig. 12. Three different configurations were investigated to understand the effect of the length of the monolith segments as well as the stacking of them. Stacking impacts the gas to solid heat transfer, as a result of inlet effects and the redevelopment of the hydraulic and thermal profile in the channel, as well as the axial thermal conductivity, which is interrupted to some extent at the interface between two pieces. The comparison of the results
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for the three configurations shows that at low gas velocities, e.g. up to 5 mN /s, all configurations deliver comparable performance. As the gas velocity is further increased the results diverge and are affected by the gas velocity. The best results are obtained with the short monolith sections combined with spacers. The assembly with only 3 monoliths shows the worst results. Further investigations on the contribution of the different phenomena (axial conductivity, gas–solid heat transfer) will be elucidated more in the discussion section. For reference Fig. 12 also includes results for the copper monolith loaded into a stainless steel tube with a base case clearance (see also Fig. 9). Comparing these results to the configuration with 3 pieces (square symbols) shows the significant impact of the gap resistances between monolith and tube, even for an already very tight clearance tolerance.
5. Discussion The results showed that with the conductive metal monoliths high integral heat transfer coefficients hint are achieved. The observed qualitative trends for the impact of the clearance between the monolith and the tube, the surface structure of the contact area and the stacking of monoliths are well explained by technical intuition. Somewhat unexpected at first sight is the general observation of the strong dependence of the integral heat transfer coefficient on the gas velocity, for a transfer process dominated by conduction and not convection. The resistance of the monolith body and the heat transfer resistance on the shell side can be excluded, as they do not depend on the gas flow rate. Furthermore, the difference between the aluminum and the copper samples cannot be totally explained, as the porous copper sample had actually a somewhat higher conductivity. The contact resistance due to the pressing into the copper tube is also assumed to be relatively low, at least relative to the heat transfer resistance of the gap between the monolith skin and the tube. This section focuses on developing basic understanding of these observations applying the physical model described above and considering three potential sources: • gas–solid heat transfer in the monolith channels, • axial conductivity in the monolith, • impact and variation of the gap resistance. Based on our findings discussed earlier, it is sufficient to use the one-dimensional model with the only unknown parameter being the resistance of the gap. All other parameters and physical properties can be calculated and predicted a priori. Fig. 13 shows the experimental results obtained with sample D at an inlet gas temperature of 250 ◦ C together with different modeling results. The solid lines marked with (1) and (2) are predictions for constant gap heat transfer values of 1500 and 3000 W/m2 K, respectively. Similar to the experimental data both data sets also show a dependence on
Fig. 13. Comparison of the integral heat exchange coefficient hint determined in the experiments with an aluminum sample ( ) and from detailed simulations (lines). Lines: (1) constant hgap = 1500 W/m2 K, (2) constant hgap = 3000 W/m2 K, (3) temperature dependent gap heat transfer coefficient hgap = gap (T )/kG (T ). Solid lines: axial conductivity 200 W/mK; dashed lines: axial conductivity 2 W/mK. Conditions: sample D, inlet gas temperature 250 ◦ C, length of the monolith section: L = 250 mm.
the gas velocity but level off to a plateau value at higher gas velocities. The dependence on the gas velocity in these cases results mostly from the dependence of the gas–solid heat transfer (Eq. (3)) on the Reynolds number and therefore the gas velocity. The predictions with the lower value for hgap reasonably describe the experimental data at low velocities but are unable to predict the high heat transfer coefficients obtained in the experiments at higher gas flow rates. The doubling in hgap allows reaching higher heat transfer coefficients but does not describe the dependence on the gas velocity at all. One shortcoming in the analysis of experimental data with Eq. (10) is certainly that the implicit assumption of a thermal plug flow in the monolith is probably not met considering the high thermal conductivity of aluminum (∼ 200 W/mK). This simplification can in fact lead to a gas velocity dependence of the integral heat transfer coefficient based on the flattening of the temperature profile which, however, will vanish at higher axial Peclet numbers, e.g. higher gas flow rates. Simulations with a reduced axial conductivity of the solid phase to 1%, e.g. 2 W/mK, are included in Fig. 13 (dashed lines) and show that this effect is marginal and as expected limited to low gas velocities. A better explanation of the experimental observations is found if the variation of the thermal expansion of the steel tube and the monolith based on the axial temperature gradient is included. This is shown as line 3 in Fig. 13 as well as the lines in Figs. 8–10. The simulations represent predictions based on applying the physical properties for the monoliths
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Table 2 Material properties Material steel
Stainless
Aluminum
Porous copper
Cordierite
Thermal conductivity kS Coefficient of thermal expansion (CTE)
15 W/mK 16 × 10−6 /K
200 W/mK 24 × 10−6 /K
260 W/mK 18 × 10−6 /K
1.4 W/mK 1 × 10−6 /K
Fig. 14. Axial temperature profiles of the gas (solid lines) and solid phase (dashed lines) for a temperature dependent hgap according to Eq. (11). Also shown is the axial distribution of the gap size relative to the one during loading at 20 ◦ C.
(i.e. thermal conductivity and coefficient of thermal expansion (Table 2)) and the gas (i.e. thermal conductivity of air) combined with the initial gap clearance between monoliths and tube during loading at room temperature (gap,0 ). No fitting parameter was required in the model analysis. Therefore the heat transfer coefficient of the gap is a function of the axial location and calculated according to Eq. (11). hgap (z) =
kG (T (z)) . gap (gap,0 , TS (z), TT (z), CTES , CTET )
(11)
Evident from the data in Table 2 aluminum has a significantly higher coefficient of thermal expansion than steel. From Eq. (11) it can be derived, that the size of the gap between the steel tube and an aluminum monolith under operating or test conditions is a function of the temperature level as well as the temperature difference between the monolith and the tube. As an example in Fig. 14 the axial temperature gradients of the gas and solid phase within the monolith, together with the size of the gap relative to the initial clearance during loading are summarized. In the experiments the temperature of the steel tube is maintained to the initial loading temperature by applying intensive cooling. Near the inlet zone (z = 0–30 mm), where the solid temperature is highest, the expansion of the monolith leads to interference between the monolith and the tube, essentially reducing the gap clearance to zero. Further downstream, as the solid temperature
drops, the size of the gap increases resulting in an gradual increase in the heat transfer resistance. The gas velocity dependence observed for the integral heat exchange coefficient can now be explained by the fact that as the gas flow rate is increased the average monolith temperature increases (see also Fig. 6) and, as a result, the average gap size is reduced and therefore the heat transfer in the gap improved. An analogous explanation holds for the relationship of hint and the inlet gas temperature (Fig. 8). Furthermore the differences in the experimental results between the copper and the aluminum samples (Fig. 9) can also be explained. Although, copper has a higher coefficient of thermal expansion than steel the difference is much less pronounced than for aluminum (Table 2). Therefore under experimental conditions the gap size reduction is lower resulting in an overall lower integral heat transfer coefficient. As the gap size resistance is dominating, this effect is sufficient to overcome the potential benefits the copper monoliths might have from a thermal conductivity perspective. It is also important to notice, that the model well predicts the impact of the cell structure of the two copper samples evaluated. Based on the gained fundamental understanding of the relevant mechanisms it is now possible to make more general predictions about the heat transfer performance of the conductive monoliths as a function of (a) the temperature level during operation, (b) the clearance between the monolith, (c) the physical properties, (d) the inner tube diameter and (e) the temperature differences between the monoliths and the tube (∼ the heat exchange medium). Aluminum and porous copper are used as monolith materials in the predictions. For the gas phase air as well as hydrogen, as representative of a gas with higher thermal conductivity, are considered. Examples of such design plots are given in Figs. 15 and 16. The results show the lumped effective heat transfer coefficient of monolith and gap. It should be noted that both are independent of the gas flow rate. The resistances of the steel tube wall and on the shell side are not included as they depend on the application and can be added accordingly. The heat transfer between the gas and the solid phase is also not included as it can be determined separately, e.g. through Eqs. (2) and (3), and because it has a minor effect in case of the important application in heterogeneously catalyzed processes, where the heat is released on the solid surface (e.g. the catalyst). Furthermore, the results shown in Fig. 12 demonstrate that in case that the gas to solid heat transfer becomes limiting one option is to use more, but shorter monolith pieces and possibly include spacers. This will yield
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Fig. 15. Effective heat transfer coefficient between the monolith body and the inner tube wall (resistance of monolith and gap) as function of the temperature difference between the monolith and the coolant. Data are for aluminum and porous copper monoliths loaded into stainless steel tubes with air (solid lines) and hydrogen (dashed lines) as gas phase. Temperature of the heat exchange medium TH E of (1) 50 ◦ C, (2) 200 ◦ C and (3) 400 ◦ C. Inner tube diameter is 25 mm, void fraction of monoliths is 65%, clearance between tube and monolith during loading at 20 ◦ C is 150 m.
Fig. 16. Effective heat transfer coefficient between the monolith body and the inner tube wall (resistance of monolith and gap) as function of the temperature difference between the monolith and the coolant. Data are for aluminum and porous copper monoliths loaded into stainless steel tubes with air (solid lines) and hydrogen (dashed lines) as gas phase. Clearance between the monolith and the tube during loading at 20 ◦ C of (1) 100 m, (2) 200 m and (3) 400 m. Inner tube diameter is 25 mm, void fraction of monoliths is 65%, temperature of the coolant is 200 ◦ C.
additional entrance effects with high local gas to solid heat transfer coefficients. The use of spacers will also reduce the effective axial conductivity. However, as shown in Fig. 13, will this only improve the results at low gas flow rates. From Figs. 15 and 16 the following conclusions can be derived: up to a certain value the difference between the monolith and the heat exchange (tube) temperature, TM −TH E , has only a minor effect and the heat exchange performance depends primarily on the temperature level. This effect is more pronounced for aluminum compared to copper, due to the higher coefficient of thermal expansion. For the same reason the onset of when the temperature difference TM − TH E becomes dominant for aluminum is shifted to lower values compared to porous copper. As expected the heat transfer coefficients obtained with a high thermal conductivity gas (e.g. hydrogen) are significantly higher than for a gas with a lower thermal conductivity (e.g. air). With respect to practical applications this also means, that for applications with
a higher thermal conductivity gas phase larger clearances and gaps can be tolerated to obtain sufficient heat transfer performance (see Fig. 16).
6. Conclusions The experimental investigations showed the successful application of conductive monoliths to achieve very high heat transfer coefficients up to values of 1000 W/m2 K and higher. The effective packaging of the monoliths in the tube is of key importance to achieve high overall heat transfer performance and leverage the conductivity of the monolith material. The heat transfer coefficients found in this study are beyond the typical values obtained for other types of packings or inserts. For comparison we measured heat transfer coefficients for rings (]5 mm × 7 mm length), being roughly 50% of those of the packaged monoliths at 5–10
T. Boger, A.K. Heibel / Chemical Engineering Science 60 (2005) 1823 – 1835
times higher pressure drops. The physical model allowed to develop a clear understanding of the relevant phenomena and can be used for reliable prediction of the heat transfer performance, if the thermal expansion under operating conditions is considered. Smaller gap clearances between the monoliths and the tube result in better heat transfer performance. Monoliths with dense skin can be directly immersed into the heat exchange medium without tubes and therefore eliminate the gap resistance. Practical limitations require to trade-off between the improved heat transfer performance, due to the smaller gap size and the ease of loading the monoliths in the reactor tube. Experimental studies with a 2.4 m long standard of the shelf stainless steel tube showed that the clearances used in this work are all feasible from a loading perspective. In some cases with clearances of 50–100 m some force was required to push the monoliths into the tubes to overcome local restrictions. As the aluminum and copper monoliths are softer than stainless steel no damage occurs to the tube itself. In any case there is a trade-off between the effort for loading and the achievable performance but even with loose tolerances we obtained very good heat transfer performance. The use of these conductive monoliths as catalyst support for highly exothermic reactions was already suggested in Boger and Menegola (2005); Carmello et al. (2000); Cutler et al. (2001); Groppi and Tronconi (1996), and Groppi and Tronconi (2000). The heat transfer performance is about two to three times better than with conventional randomly packed catalyst supports (e.g. rings). An attractive feature derived from the current results is the self regulating effect of the concept. As shown in Figs. 15 and 16, the heat transfer performance improves as the temperature difference between the monolith (e.g. the catalyst) and the heat exchange medium (e.g. the coolant) increases. Therefore under reaction conditions the heat transfer performance is best in the zones with the highest reaction and heat release rates, where usually a hot spot occurs. This feature of the conductive metal monoliths therefore improves the heat management and temperature control of the reactor and adds additional margins to the overall process safety. Another characteristic derived from the present work is the improved heat transfer at higher process temperatures, with the upper limits being given by the softening temperature of the monolith materials. Also, for a gas phase with higher thermal conductivity better heat transfer performance will be realized. For exothermic hydrogenations, for example, the requirements on the clearance between monolith and tube will be less stringent than for oxidation processes. Beyond the use in heterogeneously catalyzed applications as catalyst support with enhanced heat transfer characteristics the conductive monoliths can be also applied in pure heat exchange applications. Debottlenecking of units with heat transfer limitations on the tube side can be envisioned by retrofitting with conductive monoliths, also leveraging the favorable pressure drop characteristics. Another potential area of applications is the use as a very fast quench or
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heating device for fluids. For example reactions operated at high temperatures can have some of the products react back to the reactants during cooling, e.g. because they are thermodynamically favored at low temperatures. The amount of loss in yield due to this backward reaction is usually a function of the time the fluids are exposed to temperatures at which the kinetics of the backward reactions are fast enough. We have shown that with the metal monoliths a gas can be cooled from 400 ◦ C to 80 ◦ C (or lower) over a length of 250 mm within 0.015 s (see Fig. 6). The benefits for the higher cost of the heat exchanger quench zone are very likely to be more than balanced by the gain in yield. The use of conductive monoliths with a dense skin without additional tube was already mentioned earlier. In our experimental investigations we obtained heat transfer coefficients up to 1500 W/m2 K. The calculation of the effective heat transfer coefficient of the monolith itself with Eqs. (1) and (9) suggests that actually heat transfer coefficients beyond this value are expected. Recently the use of microreactors is discussed for several application areas, where heat control is essential and the production volumes are small to medium. Drawbacks of microreactors, however, are their cost, the high pressure drop and the added complexity, if many reactors are needed to handle the overall capacity. The use of the high conductive monoliths directly installed into a heat exchange medium might offer an attractive alternative solution for such applications with similar heat transfer performance but much simpler connection requirements. Additionally, are engineering tools and knowledge readily available for monoliths and in the case of heterogeneously catalyzed processes the catalyzing methods are well known and applied. To summarize, the performance characteristics experimentally determined in this work proved thermally conductive monoliths as an attractive solution for a number of application areas, some of them being outside of the scope considered so far. The fundamental understanding of the relevant phenomena developed in this paper enables the design and performance predictions, which might possibly facilitate the development of new applications areas.
Notation A cpG CTE dh,c dh,ext DM Gz,G GSA hGS
heat exchange area defined with the inner tube diameter, m2 specific heat capacity of the gas, J/kg K coefficient of thermal expansion, 1/K hydraulic diameter of the monolith channels, m hydraulic diameter of the heat exchanger shell section, m monolith diameter, m axial mass velocity, kg/m2 s geometric surface area of the monolith, m2 /m3 gas–solid heat transfer coefficient, W/m2 K
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hext heff hgap hint hmono k kS,R KM L m ˙ Nuc Pr r R Re St ∗ T uG,0 z gap
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tube-heat exchange medium heat transfer coefficient, W/m2 K effective transfer coefficient, W/m2 K heat transfer coefficient of the gap (basis is the monolith diameter), W/m2 K integral heat transfer coefficient defined by Eq. (10), W/m2 K heat transfer coefficient of the monolith, W/m2 K thermal conductivity, W/mK radial conductivity of the monolith, W/mK constant in Eq. (9) length of the monolith section, m gas mass flow, kg/s Nusselt number Prandtl number radialcoordinate, m radius of monolith, m Reynolds number modified Stanton number, St ∗ = (kS,R /DM )/(Gz,G cpG ) temperature, K superficial gas velocity (at STP), mN /s axial coordinate of the monolith section, m gap size between the monolith skin and the inner tube wall, m void fraction, m3 /m3
The mean temperature is obtained via integration: R 1 1 4 2 R 4 Ar + 2 Cr 0 0 T (r)r dr TM = R = 1 2 R 0 r dr 2r 0 1 = AR 2 + C. 2 For the wall temperature follows: Tw = Ar 2 + C = AR 2 + C. r=R
monolith channel shell side of the tube gas phase heat exchange medium at inlet of monolith section monolith at outlet of monolith section solid phase
(A.3)
(A.4)
Integration constant A results from (A.4)–(A.3): 1 2 AR 2 = TW − TM ⇒ A = 2 (TW − TM ) 2 R
(A.5)
and C by inserting in (A.4): C = 2TM − TW .
(A.6)
Finally the temperature profile is described by T (r) =
2 (TW − TM )r 2 + 2TG − TW . R2
(A.7)
On the other hand the heat flux is defined as q˙ = hmono (TM − TW ).
(A.9)
The heat transfer coefficient can be obtained from (A.8) and (A.9): hmono =
Acknowledgements
KM kS,R , DM
(A.10)
with KM = 8 for the parabolic temperature profile.
Lin He and Lorraine Owens of Corning, Inc. are acknowledged for providing the copper monoliths. Special thanks go to Jeff Amsden, Josh Jamison and Neil Partridge, for the experimental investigations from equipment design and construction over sample preparation to experimental execution and initial data analysis. Appendix A. Derivation of film heat transfer coefficient for the monolith Assumption of homogeneous model and parabolic temperature profile: T (r) = Ar 2 + Br + C.
(A.2)
The heat flux can be obtained from the gradient at the wall: dT 4kS,R = − (T − T )r q˙ = − kS,R W M 2 dr r=R R r=R 4kS,R (TW − TM ). = − (A.8) R
Subscripts c ext G HE in M out S
Boundary condition in the center of the monolith: dT = 0 ⇒ B = 0. dr r=0
(A.1)
References Boger, T., Menegola, M., 2005. Monolithic catalysts with high thermal conductivity for improved operation and economics in the production of phthalic anhydride. Industrial and Engineering Chemistry Research 44, 30–40. Carmello, D., Marsella, A., Forzatti, P., Tronconi, E., Groppi, G., 2000. Metallic monolith catalyst support for selective gas phase reactions in tubular fixed bed reactors. European Patent Application 1 110 605 A1. Cutler, W.A., et al., 2001. US Patent Application 20030100448. Groppi, G., Tronconi, E., 1996. Continuous vs. discrete models of nonadiabatic monolith catalysts. A.I.Ch.E. Journal 42, 2382. Groppi, G., Tronconi, E., 2000. Design of novel monolith catalyst supports for gas/solid reactions with heat exchange. Chemical Engineering Science 55, 2161–2171.
T. Boger, A.K. Heibel / Chemical Engineering Science 60 (2005) 1823 – 1835 Groppi, G., Tronconi, E., 2001. Simulation of structured catalytic reactors with enhanced thermal conductivity for selective oxidation reactions. Catalysis Today 69, 63. Jones, A.E., 2002. Thermal design of the shell-and-tube. Chemical Engineering 60. Tronconi, E., Groppi, G., Boger, T., Heibel, A.K., 2004. Monolithic catalysts with high conductivity honeycomb supports for gas/solid
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exothermic reactions: characterization of the heat-transfer properties. Accepted for publication at the Eighteenth International Symposium on Chemical Reaction Engineering, 2004. Chemical Engineering Science 59, 4941–4949. Vortruba, J., Mikus, O., Nguen, K., Hlavacek, V., Skrivanek, J., 1975. Heat and mass transfer in honeycomb catalysts—II. Chemical Engineering Science 30, 201–206.
Heat transfer in conductive monolith structures Thorsten Bogera,∗ , Achim K. Heibelb a Corning GmbH, Abraham-Lincoln-Str. 30, D-65189 Wiesbaden, Germany b Corning Incorporated, Process Technologies, Corning, NY 14831, USA
Received 27 April 2004; received in revised form 4 November 2004; accepted 29 November 2004 Available online 21 January 2005
Abstract Honeycomb structures made of highly thermal conductive materials (e.g. certain metals) have been proposed as attractive catalyst supports with enhanced heat transfer properties. Recently prototypes of such materials have become available, enabling experimental investigations on their heat transfer properties, including packaging into tubes. This work is focused on the heat transfer performance of conductive monolith structures packaged into heat exchanger tubes. Several parameters such as monolith material structure and properties and packaging tolerances are investigated. Heat transfer coefficients on the order of 1000 W/m2 K and higher were measured. The results are analyzed applying a detailed model based on a fundamental understanding of the relevant phenomena. It is demonstrated that it is necessary to consider the variations of the thermal expansion of the monolith and the tube over the length of the monoliths. By including thermal expansion, the model is in excellent agreement with the experimental results without the need of any fitting parameter. The results are used to develop some design guidelines. In addition some implications of the heat transfer performance for the relevant applications in multitubular reactors as well as some new potential application areas are discussed. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Monolith; Honeycomb; Heat conduction; Heat transfer; Modeling; Catalyst support
1. Introduction Recently, monolithic structures made out of materials with a high thermal conductivity have been proposed as an attractive alternative to conventional catalyst supports for the use in highly exothermic reactions (e.g. partial oxidations) employing multitubular reactors (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005; Carmello et al., 2000; Tronconi et al., 2004). Significantly higher heat transfer rates compared to random catalyst packings (e.g. spheres or rings) were predicted, by changing the dominant heat transfer process from convection to conduction. Simulations (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005) as well as experiments (Carmello et al., 2000; Tronconi et al., 2004) for highly exothermic reaction revealed significantly lower hot spot temperatures. This resulted in improved
∗ Corresponding author. Tel.: +49 611 7366 168; fax: +49 611 7366 112.
E-mail address: [email protected] (T. Boger). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.11.031
operating characteristics and the potential for significant economic benefits. A method and process to prepare suitable extruded metal monoliths with a high thermal conductivity was recently developed by Corning Incorporated (Cutler et al., 2001). A picture of a monolith made for example from copper is shown in Fig. 1. These copper monolithic catalyst supports were evaluated for a heterogeneously catalyzed CO oxidation reaction and showed no radial temperature gradients even at very high reactive heat loads (Tronconi et al., 2004), demonstrating the excellent radial heat removal due to the thermal conduction of the structure. The heat transfer from the monolith to the reactor resulting from the packaging was identified as bottleneck. So far most of the investigations of the heat transfer in these conductive monolith structures was of theoretical nature and limited to the heat transport within the structures itself. To our knowledge, no detailed experimental and theoretical evaluation of the heat transfer of such monolith structures packaged into reactor or heat exchanger tubes is available. As the resistance due to the packaging was identified
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monolith structures based on geometric data (the void fraction ) and the thermal conductivity kS of the monolith walls. −1 √ √ . (1) kS,R = kS (1 − ) + √ √ (1 − + kkGS )
Fig. 1. Photo of copper based monolithic catalyst support with high thermal conductivity.
Fig. 2 also shows in a qualitative manner some typical temperature profiles inside the monolith (see item 1). Additionally the temperature profiles of the gas inside the channels in case of an operation in which a hot gas is cooled (dashed lines, item 5) are illustrated. For most applications the flow inside the channels is laminar since the hydraulic diameter is small (in the order of a 1–3 mm). Because of the small dimensions compared to the monolith diameter the thermal exchange between gas and channel wall is usually described by a film model and using a heat transfer coefficient hGS and the according Nusselt number N uc . Suitable engineering correlations for the Nusselt number inside monolith channels can be readily obtained from the literature (Vortruba et al., 1975) based on experimental investigations, including inlet and outlet effects as well as the thermally and hydraulically developing profiles. N u c kG , dh,c dh,c 2/3 N uc = 0.571 Rec . L hGS =
as the main bottleneck (Tronconi et al., 2004) the objective of the present paper is to further elucidate the effect and improve the overall performance. The results are based on an extensive experimental study combined with a detailed theoretical analysis. The extremely high heat transfer coefficients as well as the favorable ratio between heat transfer and pressure drop leads to additional areas for the use of such monolithic structures beyond the applications discussed so far (Groppi and Tronconi, 2000, 2001; Boger and Menegola, 2005; Carmello et al., 2000; Tronconi et al., 2004). Some of them will be addressed in the discussion section.
2. Theoretical background In Fig. 2 a schematic of the cross-section of a monolith inserted into a tube is shown. The monolith is represented by a number of channels that are separated from each other by the channel walls of the monolith. No radial exchange of gas between the channels is feasible and therefore, no convective heat transfer in this direction occurs. On the other hand the walls in these extruded structures are connected throughout the entire diameter. Therefore high heat transfer rates can be achieved. Monolith structures as shown in Figs. 1 and 2 with square channels experience some anisotropy with respect to the radial heat flow. However, this is a second order effect and therefore is usually negligible. The rate of the conductive heat transfer is a function of the thermal conductivity of the wall material and of the solid fraction. Groppi and Tronconi (1996) developed a correlation to calculate the effective radial conductivity kS,R in such
(2)
(3)
In case of inserting the monoliths into a heat exchanger (or reactor) tube the heat needs to be transferred across the gap between the skin of the monolith and the inner surface of the tube (item 2 in Fig. 2). This heat transfer resistance is characterized by the size of the gap gap and by the thermal conduction through the usually stagnant fluid film that fills this gap. Expressing the inverse resistance in form of a heat transfer coefficient we obtain hgap = gap /kG . In reality the geometric imperfections of monolith and tube as well as the not perfect centering of the monolith in the tube will result in gap size variations along the circumference of the tube. Therefore the gap size defined above should be considered as a kind of mean effective gap size. In the tube itself the radial heat conduction occurs (step 3 in Fig. 2), which is dependent on the thickness of the tube and its thermal conductivity. The heat transfer between the outside surface of the tube and the external heat exchange medium (step 4 in Fig. 2) depends on the underlying hydrodynamics and the physical properties of the heat exchange medium. This heat transfer is usually described by means of a heat transfer coefficient hext and the according Nusselt number. Reasonable engineering correlations can be found in the literature (Jones, 2002). N uext =
hext dh,ext = c Rebext P r 0.33 ext . kH E
(4)
With c=0.613 and b=0.47 for Reext < 1000 and c=0.384 and b = 0.54 for Reext > 1000. All the dimensionless groups
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Fig. 2. Schematic of the cross-section of a monolith inserted into a tube, which is surrounded by a heat transfer medium. On the right a typical radial temperature profile is shown. In the lower half the gas temperature inside the monolith is also shown (dashed lines, 5) in addition to the solid temperature.
in Eq. (4) are defined with the physical properties of the heat exchange medium and the hydraulic diameter of the external space. Monoliths with a dense skin can be immersed directly into a heat exchange medium, avoiding the use of the tube. In this case only steps 1, 4 and 5 are relevant. Under the conditions of typical heat transfer operation the following steady state enthalpy balances can be used to describe the two dimensional temperature field inside the monolith, assuming constant temperature of the tube and the heat exchange medium, TH E , over the length of the reactor. For the gas plug flow is assumed.
are lumped into a single effective heat transfer coefficient, heff , used for the radial boundary condition at r = R of the solid phase (Eq. (7)). The heat transfer resistance of the tube itself as well as on the shell side of the tube can be calculated, leaving only the resistance of the gap as an unknown lumped parameter. The description can be condensed to a one-dimensional model, where the heat transfer resistance of the monolith itself is expressed by means of an effective heat transfer coefficient, hmono , in series with the resistance at the monolith skin, e.g. heff . The enthalpy balance of the solid phase can then be rewritten.
• Enthalpy balance—Gas phase,
−(1 − )kS
j2 TG (r, z) jTG (r, z) − kG jz jz 2 = hGS GSA(TS (r, z) − TG (r, z)).
cpG Gz,G
(5)
• Enthalpy balance—Solid phase (monolith), j2 TS (r, z) 1 j jTS (r, z) − (1 − )kS rk S,R − jz 2 r jr jr = −hGS GSA(TS (r, z) − TG (r, z)). (6) • Boundary conditions at the monolith skin, r = R: j jTS (R, z) kS,R jr jr 4heff =− (TS (R, z) − TH E ). DM ≈
(7)
4heff DT
In addition, a zero gradient boundary condition at the centerline, r = R, and the typical Danckwerts boundary conditions at the inlet and outlet, e.g. z = 0 and z = L are applied. All the heat transfer resistances between the monolith skin and the heat exchange medium (steps 2–4 in Fig. 2)
j2 TS (z) = − hGS GSA(TS (z) − TG (z)) jz2
−1 1 1 + + heff hmono 4 × (TH E − TS (z)). DM
(8)
To maintain the resistance of the gap as the only unknown parameter a correlation to calculate hmono from the dimensions and properties of the monolith is required. Analytical approaches to obtain such a correlation commonly assume a fully developed, parabolic radial temperature profile. This assumption combined with the boundary conditions yields the following correlation for hmono , based on the effective radial conductivity and the diameter of the monolith (Appendix A): hmono =
KM kS,R , DM
(9)
with KM = 8. However, under practical conditions the requirement of a developed, parabolic temperature profile is often not met. Therefore, a number of numerical simulations with a two-dimensional model were performed, covering a large range of critical parameters, e.g. monolith diameter, length, radial conductivity and gas flow. The analysis
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14 12
KM
10 8 6 4 0.001
0.01
0.1
1
St*. L/DM Fig. 3. Factor KM as function of the system and operating characteristics. Symbols are values for KM derived from detailed two-dimensional simulations for monoliths of different diameter, radial conductivity and length and different gas flow rates.
of the results of the two-dimensional simulations with the one-dimensional model, Eq. (8), resulted in more realistic values for KM . Fig. 3 summarizes the results of this analysis, demonstrating the successful correlation of KM to a characteristic dimensionless group, representing the product of a modified Stanton number St ∗ = (kS,R /DM )/(Gz,G cpG ) and a characteristic length scale L/DM . For small values of St ∗ (L/DM ), high values of KM are observed, representing some sort of inlet effects as under these conditions the temperature profile is not developed. For St ∗ (L/DM ) > 0.05 a plateau is obtained at KM =5.8, representing fully developed conditions. In most cases this value for KM can be applied, as the criterion is met under most practical conditions.
3. Experimental For the experimental investigation of the heat exchange performance of the monoliths a simple heat exchange setup as shown schematically in Fig. 4 was used. The setup consists of a gas supply section, comprising a mass flow controller (A) and an electrical heater (B), followed by a static mixer (C) ensuring thermal plug flow (also enabling a simple one point temperature measurement) to the heat exchanger section (D). The gas flow was varied in the range of 0–60 m3 /h (STP) and heated to temperatures up to 400 ◦ C at the inlet into the heat exchanger section. The heat exchanger section consisted of a horizontally installed, stainless steel tube of 300 mm length and 25–30 mm inner diameter into which the monoliths were packaged. Some initial experiments were performed with a longer heat exchanger section of 560 mm. The tube itself was located within a shell and surrounded by flowing cooling water. Custom baffles were installed in the shell to ensure high external heat transfer. The cooling water temperature was in all cases kept constant at TH E = 20 ◦ C. The water flow rate was adjusted to a high enough value to ensure nearly isothermal operation
between the inlet (T5 ) and the outlet (T4 ) of the water (less than 0.5 ◦ C, accuracy of the thermocouple). Initial trials were performed to ensure, that the external heat transfer from the tube to the water, e.g. hext , was not limiting. For some experiments a 300 mm long monolith was installed directly into the heat exchanger without the addition of an external tube to minimize/eliminate the gap resistance. During the experiments the inlet and the outlet temperature of the gas were measured with thermocouples. At the outlet the gas temperature was measured directly after the monolith (T2 ), in the middle of the tube as well as after a short static mixer (E, T3 ) that was well insulated to ensure that the true average temperature was measured. Usually both temperatures were in agreement and did only in a few cases differ by 1–2 ◦ C. Additionally the pressure drop p across the heat exchanger tube was measured. Air as well as nitrogen were used as the gas phase. The experiments were performed with monoliths made of different materials (cordierite, copper and aluminum) and different cell geometry as described in Table 1. It is worth mentioning that for the achievement of the desired geometric properties, it was necessary to prepare the copper samples by core drilling them out of larger parts and then pressing them into a standard copper tube obtaining an artificial skin with well defined dimensions. Good contact between the monolith and the copper tube was established by first core drilling the monoliths to a diameter slightly larger than the copper tube and then pressing them into the tubes. In Fig. 5 examples of core drilled samples and the copper tube are shown prior and after assembly. Additionally the clearance between the outer diameter of the monolith and the inner diameter of the tube as well as the general packaging method was varied. Comparative and base line experiments with an empty pipe, ceramic rings (5 mm × 3 mm × 5 mm) as well as an metallic monoliths made out of corrugated, wrapped and brazed FeCrAlloy foil were performed. For the analysis of the experiments the measured temperatures were used to determine an integral heat transfer coefficient hint , representing a lump of all the resistances discussed above and represented by the steps 1–5 in Fig. 2.
TG,in − TH E hint A = m . (10) ˙ G cpG ln TG,out − TH E This integral heat exchange coefficient can be directly used for the design of a heat exchanger. For fundamental understanding and interpretation of the results, especially with respect to the heat transfer resistance between the monolith and the tube the raw data was also analyzed with the detailed models described above (Eqs. (1)–(9)).
4. Results In Fig. 6 examples of the measured outlet temperatures are shown for the heat exchanger tube packed with 10 pieces
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Fig. 4. Experimental setup for the heat exchange experiments.
Table 1 Monolith samples used in the experiments Sample
Material
Cell density
Hydraulic channel diameter(mm)
Wall thickness (mm)
Channel geometry
Open
A B C D
Cordierite Porous copper Porous copper Aluminum
400 cpsi 560 cpsi 260 cpsi 200 cpsi
1 0.92 1.26 1.52
0.18 0.15 0.26 ∼0.2–0.5
Square Square Square Round
74 60 57 63
Fig. 5. Photo of the core drilled copper monoliths and the copper tubing prior (left) and after pressing the monoliths into the tube (right). Note, that in most cases longer copper monoliths were used.
100
Outlet Temperature in °C
80
60
40
20
0 0
10
20
30
Gas Velocity uG,0 in mN/s Fig. 6. Outlet temperatures measured for sample D (aluminum) at different gas flow rates. Inlet temperatures: ( ) Tin = 250 ◦ C, () Tin = 400 ◦ C. Length of the monolith section: L = 250 mm.
of 25 mm long aluminum monoliths (sample D). The inner diameter of the tube was 28.4 mm. The data are shown as a function of the gas (nitrogen) flow rate for an inlet temperature of 250 ◦ C and 400 ◦ C. As expected with increasing gas flow rate the outlet temperature increases. Noteworthy 3 /h, equivto mention that even at high flow rates, e.g. 40 mN alent to a superficial velocity of 17.5 mN /s or a mass flux of about 21 kg/(m2 s), the gas is cooled down to 70–80 ◦ C across this very short length of the heat exchanger, equivalent to 190 kW/m2 for the 400 ◦ C inlet temperature. For comparison, we have measured a heat transfer rate of 38 kW/m2 for a longer empty tube (560 mm length) at comparable con3 /h and 350 ◦ C inlet temditions of a gas flow rate of 30 mN perature. In Fig. 7 the integral heat transfer coefficients determined by Eq. (10) with the raw experimental data from Fig. 6 are shown. The data for hint as well as the superficial gas velocity are based on the inner diameter of the tube. For comparison the results for an empty tube with a comparable inner diameter of 25.4 mm are given. Very high heat transfer coefficients, in excess of 1000 W/m2 K are achieved. The values for a gas inlet temperature of 400 ◦ C are 10–15% higher compared to those at Tin = 250 ◦ C. This effect of the temperature level on hint is also shown in Fig. 8 for two gas flow rates. The reason for this temperature dependence will be discussed later in detail. In Fig. 9 results for monolith structures made from different materials and with different cell structure are presented (sample A–D in Table 1). All monoliths were packaged in the tube with the same clearance tolerances. The best results are obtained for the dense aluminum monoliths (sample D). The heat transfer coefficients determined for the copper
T. Boger, A.K. Heibel / Chemical Engineering Science 60 (2005) 1823 – 1835
1500
1500
1000
1000
hint in W/m2K
hintin W/m2K
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500
500
0
0 0
10
20
30
0
5
10
15
20
Gas Velocity uG,0 in mN/s
Gas Velocity uG,0 in mN/s Fig. 7. Integral heat transfer coefficients hint as function of the superficial gas velocity u0 determined for sample D (aluminum). Monolith experiments: ( ) Tin = 250 ◦ C, () Tin = 400 ◦ C. For comparison: empty tube at Tin = 400 ◦ C ( ), length of the monolith section: L = 250 mm.
Fig. 9. Effect of the material properties on the integral heat exchange coefficient hint . Symbols: experimental data for cordierite (sample A), 䊉 porous copper 560 cpsi (sample B), porous copper 260 cpsi (sample C) and aluminum 200 cpsi (sample D). Lines: predictions from detailed simulations with hgap according to (Eq. (11)). Conditions: inlet gas temperature 400 ◦ C, length of the monolith section: L = 250 mm.
hint in W/m2K
1500
1000
500
0 0
100
200
300
400
500
Gas Inlet Temperature in °C Fig. 8. Effect of the gas inlet temperature on the integral heat exchange coefficient hint . Symbols: experimental data at superficial gas velocity of 䊉 uG,0 = 17 mN /s and uG,0 = 26 mN /s. Lines: predictions from detailed simulations (lines) with hgap according to (Eq. (11)). Conditions: sample D, length of the monolith section: L = 250 mm.
monoliths, samples C and D, are lower especially at higher gas flow, although the thermal conductivity of the porous copper is slightly higher compared to the one for the aluminum samples. This might be explained by an additional contact resistance created between the copper monolith material and the copper tube used as skin. Although the applied force ensured good contact between both parts it cannot be excluded that there might remain an additional heat transfer
resistance. The difference between the two copper samples demonstrates that in the heat exchange experiments the channel size and geometric surface area has an effect on the integral heat exchange coefficient. Slightly better results are obtained for the structure with a higher cell density, sample B. This is explained by the better gas–solid heat transfer (higher GSA) in the channels as the void fraction and therefore the bulk thermal conductivity are rather similar. The importance of a structure with intrinsically high thermal conductivity can be investigated by comparing the result for a cordierite monolith, sample A, with low thermal conductivity. For the latter very poor heat transfer results were found. The measured heat transfer coefficients are even lower compared to the one for an empty tube, shown in Fig. 7. This is explained by the low thermal conductivity of the cordierite material, which allows only very limited radial conductive heat transfer, even lower than the convective heat transfer of the turbulent flow for the empty pipe. Experiments with the corrugated and wrapped metal foil monolith delivered results that were in the same order as those for the cordierite monoliths. Only slightly higher integral heat exchange coefficients were measured, e.g. in the order of 130–140 W/m2 K at a gas velocity of 5 mN /s. The moderate intrinsic thermal conductivity of the material (10–20 W/mK) in combination with the high void fraction (> 90%) and the bad radial connectivity of the structure, results in limited radial heat conduction performance. In the case of the cordierite and the metal foil monoliths the limiting heat transfer is dominated by the resistance in the structure itself and not so much the gap resistance.
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1500
1829
2000
hint in W/m2K
hint in W/m2K
1500 1000
500
1000
500
0 0
5
10
15
20
Gas Velocity uG,0 in mN/s Fig. 10. Effect of the gap size during the monolith loading on the integral heat exchange coefficient hint . Symbols: experimental data for () base case, gap,0 = gap,ref , (䊉) gap,0 = 2gap,ref and () gap,0 = 4gap,ref . Lines: predictions from detailed simulations with hgap according to (Eq. (11)). Conditions: sample D, inlet gas temperature 400 ◦ C, length of the monolith section: L = 250 mm.
Fig. 11. Effect of the skin structure of the monolith on the integral heat exchange coefficient hint . Symbols: experimental data at inlet gas temperatures of 䊉 100 ◦ C, 200 ◦ C, 300 ◦ C and 400 ◦ C. Conditions: sample D, superficial gas velocity 17 mN /s and length of monolith section 250 mm.
The effect of the clearance between the monolith and the inner tube diameter is shown in Fig. 10. The clearance of the base case has been increased by a factor of 2 and 4 in subsequent experiments. The gap size has a significant impact on the obtained heat transfer performance. Further insights are gained by the information provided in Fig. 11. These experiments were performed to identify the relationship between
0 0
5
10
15
20
Gas Velocity uG,0 in mN/s Fig. 12. Performance of core drilled copper monoliths (sample B) pressed into a copper tube and installed directly into the heat exchanger without stainless steel tube. 3 monolith pieces installed with no gap, 䊉 10 monolith pieces (25 mm length) installed without gap, 10 monolith pieces (24 mm) installed with spacers (1.6 mm length). For reference: 2 core drilled copper monolith pieces pressed into a copper tube as skin and installed into a stainless steel tube at base clearance. Conditions: copper tube length 300 mm, total installed monolith length 240–250 mm, gas inlet temperature 400 ◦ C.
the heat transfer performance and the contact area properties between the monolith skin and the tube. To perform a defined experiment subsequently parts of the skin area were removed by machining grooves into the monolith, which had a defined depth 2 and area A2 (see also the schematic on top of Fig. 11). In Fig. 11, A2 therefore represent the relative portion of the skin, which was machined down to the larger clearance. The results demonstrate that the heat transfer coefficient decreases proportional to the machined area and approaches the limiting value for the new clearance. This trend was the same for all temperatures considered in this experiment. The results allow the conclusion that the tolerances between the monoliths and the tubes are of significant importance for the heat transfer performance. Alternatively, in the case of monoliths with dense and impermeable skin it is also possible to directly use the monolith without a packaging tube. In this case the monoliths will be directly mounted to the tube sheets and will be immersed into the heat exchange medium. Results for such a configuration with the copper sample B are shown in Fig. 12. Three different configurations were investigated to understand the effect of the length of the monolith segments as well as the stacking of them. Stacking impacts the gas to solid heat transfer, as a result of inlet effects and the redevelopment of the hydraulic and thermal profile in the channel, as well as the axial thermal conductivity, which is interrupted to some extent at the interface between two pieces. The comparison of the results
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for the three configurations shows that at low gas velocities, e.g. up to 5 mN /s, all configurations deliver comparable performance. As the gas velocity is further increased the results diverge and are affected by the gas velocity. The best results are obtained with the short monolith sections combined with spacers. The assembly with only 3 monoliths shows the worst results. Further investigations on the contribution of the different phenomena (axial conductivity, gas–solid heat transfer) will be elucidated more in the discussion section. For reference Fig. 12 also includes results for the copper monolith loaded into a stainless steel tube with a base case clearance (see also Fig. 9). Comparing these results to the configuration with 3 pieces (square symbols) shows the significant impact of the gap resistances between monolith and tube, even for an already very tight clearance tolerance.
5. Discussion The results showed that with the conductive metal monoliths high integral heat transfer coefficients hint are achieved. The observed qualitative trends for the impact of the clearance between the monolith and the tube, the surface structure of the contact area and the stacking of monoliths are well explained by technical intuition. Somewhat unexpected at first sight is the general observation of the strong dependence of the integral heat transfer coefficient on the gas velocity, for a transfer process dominated by conduction and not convection. The resistance of the monolith body and the heat transfer resistance on the shell side can be excluded, as they do not depend on the gas flow rate. Furthermore, the difference between the aluminum and the copper samples cannot be totally explained, as the porous copper sample had actually a somewhat higher conductivity. The contact resistance due to the pressing into the copper tube is also assumed to be relatively low, at least relative to the heat transfer resistance of the gap between the monolith skin and the tube. This section focuses on developing basic understanding of these observations applying the physical model described above and considering three potential sources: • gas–solid heat transfer in the monolith channels, • axial conductivity in the monolith, • impact and variation of the gap resistance. Based on our findings discussed earlier, it is sufficient to use the one-dimensional model with the only unknown parameter being the resistance of the gap. All other parameters and physical properties can be calculated and predicted a priori. Fig. 13 shows the experimental results obtained with sample D at an inlet gas temperature of 250 ◦ C together with different modeling results. The solid lines marked with (1) and (2) are predictions for constant gap heat transfer values of 1500 and 3000 W/m2 K, respectively. Similar to the experimental data both data sets also show a dependence on
Fig. 13. Comparison of the integral heat exchange coefficient hint determined in the experiments with an aluminum sample ( ) and from detailed simulations (lines). Lines: (1) constant hgap = 1500 W/m2 K, (2) constant hgap = 3000 W/m2 K, (3) temperature dependent gap heat transfer coefficient hgap = gap (T )/kG (T ). Solid lines: axial conductivity 200 W/mK; dashed lines: axial conductivity 2 W/mK. Conditions: sample D, inlet gas temperature 250 ◦ C, length of the monolith section: L = 250 mm.
the gas velocity but level off to a plateau value at higher gas velocities. The dependence on the gas velocity in these cases results mostly from the dependence of the gas–solid heat transfer (Eq. (3)) on the Reynolds number and therefore the gas velocity. The predictions with the lower value for hgap reasonably describe the experimental data at low velocities but are unable to predict the high heat transfer coefficients obtained in the experiments at higher gas flow rates. The doubling in hgap allows reaching higher heat transfer coefficients but does not describe the dependence on the gas velocity at all. One shortcoming in the analysis of experimental data with Eq. (10) is certainly that the implicit assumption of a thermal plug flow in the monolith is probably not met considering the high thermal conductivity of aluminum (∼ 200 W/mK). This simplification can in fact lead to a gas velocity dependence of the integral heat transfer coefficient based on the flattening of the temperature profile which, however, will vanish at higher axial Peclet numbers, e.g. higher gas flow rates. Simulations with a reduced axial conductivity of the solid phase to 1%, e.g. 2 W/mK, are included in Fig. 13 (dashed lines) and show that this effect is marginal and as expected limited to low gas velocities. A better explanation of the experimental observations is found if the variation of the thermal expansion of the steel tube and the monolith based on the axial temperature gradient is included. This is shown as line 3 in Fig. 13 as well as the lines in Figs. 8–10. The simulations represent predictions based on applying the physical properties for the monoliths
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Table 2 Material properties Material steel
Stainless
Aluminum
Porous copper
Cordierite
Thermal conductivity kS Coefficient of thermal expansion (CTE)
15 W/mK 16 × 10−6 /K
200 W/mK 24 × 10−6 /K
260 W/mK 18 × 10−6 /K
1.4 W/mK 1 × 10−6 /K
Fig. 14. Axial temperature profiles of the gas (solid lines) and solid phase (dashed lines) for a temperature dependent hgap according to Eq. (11). Also shown is the axial distribution of the gap size relative to the one during loading at 20 ◦ C.
(i.e. thermal conductivity and coefficient of thermal expansion (Table 2)) and the gas (i.e. thermal conductivity of air) combined with the initial gap clearance between monoliths and tube during loading at room temperature (gap,0 ). No fitting parameter was required in the model analysis. Therefore the heat transfer coefficient of the gap is a function of the axial location and calculated according to Eq. (11). hgap (z) =
kG (T (z)) . gap (gap,0 , TS (z), TT (z), CTES , CTET )
(11)
Evident from the data in Table 2 aluminum has a significantly higher coefficient of thermal expansion than steel. From Eq. (11) it can be derived, that the size of the gap between the steel tube and an aluminum monolith under operating or test conditions is a function of the temperature level as well as the temperature difference between the monolith and the tube. As an example in Fig. 14 the axial temperature gradients of the gas and solid phase within the monolith, together with the size of the gap relative to the initial clearance during loading are summarized. In the experiments the temperature of the steel tube is maintained to the initial loading temperature by applying intensive cooling. Near the inlet zone (z = 0–30 mm), where the solid temperature is highest, the expansion of the monolith leads to interference between the monolith and the tube, essentially reducing the gap clearance to zero. Further downstream, as the solid temperature
drops, the size of the gap increases resulting in an gradual increase in the heat transfer resistance. The gas velocity dependence observed for the integral heat exchange coefficient can now be explained by the fact that as the gas flow rate is increased the average monolith temperature increases (see also Fig. 6) and, as a result, the average gap size is reduced and therefore the heat transfer in the gap improved. An analogous explanation holds for the relationship of hint and the inlet gas temperature (Fig. 8). Furthermore the differences in the experimental results between the copper and the aluminum samples (Fig. 9) can also be explained. Although, copper has a higher coefficient of thermal expansion than steel the difference is much less pronounced than for aluminum (Table 2). Therefore under experimental conditions the gap size reduction is lower resulting in an overall lower integral heat transfer coefficient. As the gap size resistance is dominating, this effect is sufficient to overcome the potential benefits the copper monoliths might have from a thermal conductivity perspective. It is also important to notice, that the model well predicts the impact of the cell structure of the two copper samples evaluated. Based on the gained fundamental understanding of the relevant mechanisms it is now possible to make more general predictions about the heat transfer performance of the conductive monoliths as a function of (a) the temperature level during operation, (b) the clearance between the monolith, (c) the physical properties, (d) the inner tube diameter and (e) the temperature differences between the monoliths and the tube (∼ the heat exchange medium). Aluminum and porous copper are used as monolith materials in the predictions. For the gas phase air as well as hydrogen, as representative of a gas with higher thermal conductivity, are considered. Examples of such design plots are given in Figs. 15 and 16. The results show the lumped effective heat transfer coefficient of monolith and gap. It should be noted that both are independent of the gas flow rate. The resistances of the steel tube wall and on the shell side are not included as they depend on the application and can be added accordingly. The heat transfer between the gas and the solid phase is also not included as it can be determined separately, e.g. through Eqs. (2) and (3), and because it has a minor effect in case of the important application in heterogeneously catalyzed processes, where the heat is released on the solid surface (e.g. the catalyst). Furthermore, the results shown in Fig. 12 demonstrate that in case that the gas to solid heat transfer becomes limiting one option is to use more, but shorter monolith pieces and possibly include spacers. This will yield
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Fig. 15. Effective heat transfer coefficient between the monolith body and the inner tube wall (resistance of monolith and gap) as function of the temperature difference between the monolith and the coolant. Data are for aluminum and porous copper monoliths loaded into stainless steel tubes with air (solid lines) and hydrogen (dashed lines) as gas phase. Temperature of the heat exchange medium TH E of (1) 50 ◦ C, (2) 200 ◦ C and (3) 400 ◦ C. Inner tube diameter is 25 mm, void fraction of monoliths is 65%, clearance between tube and monolith during loading at 20 ◦ C is 150 m.
Fig. 16. Effective heat transfer coefficient between the monolith body and the inner tube wall (resistance of monolith and gap) as function of the temperature difference between the monolith and the coolant. Data are for aluminum and porous copper monoliths loaded into stainless steel tubes with air (solid lines) and hydrogen (dashed lines) as gas phase. Clearance between the monolith and the tube during loading at 20 ◦ C of (1) 100 m, (2) 200 m and (3) 400 m. Inner tube diameter is 25 mm, void fraction of monoliths is 65%, temperature of the coolant is 200 ◦ C.
additional entrance effects with high local gas to solid heat transfer coefficients. The use of spacers will also reduce the effective axial conductivity. However, as shown in Fig. 13, will this only improve the results at low gas flow rates. From Figs. 15 and 16 the following conclusions can be derived: up to a certain value the difference between the monolith and the heat exchange (tube) temperature, TM −TH E , has only a minor effect and the heat exchange performance depends primarily on the temperature level. This effect is more pronounced for aluminum compared to copper, due to the higher coefficient of thermal expansion. For the same reason the onset of when the temperature difference TM − TH E becomes dominant for aluminum is shifted to lower values compared to porous copper. As expected the heat transfer coefficients obtained with a high thermal conductivity gas (e.g. hydrogen) are significantly higher than for a gas with a lower thermal conductivity (e.g. air). With respect to practical applications this also means, that for applications with
a higher thermal conductivity gas phase larger clearances and gaps can be tolerated to obtain sufficient heat transfer performance (see Fig. 16).
6. Conclusions The experimental investigations showed the successful application of conductive monoliths to achieve very high heat transfer coefficients up to values of 1000 W/m2 K and higher. The effective packaging of the monoliths in the tube is of key importance to achieve high overall heat transfer performance and leverage the conductivity of the monolith material. The heat transfer coefficients found in this study are beyond the typical values obtained for other types of packings or inserts. For comparison we measured heat transfer coefficients for rings (]5 mm × 7 mm length), being roughly 50% of those of the packaged monoliths at 5–10
T. Boger, A.K. Heibel / Chemical Engineering Science 60 (2005) 1823 – 1835
times higher pressure drops. The physical model allowed to develop a clear understanding of the relevant phenomena and can be used for reliable prediction of the heat transfer performance, if the thermal expansion under operating conditions is considered. Smaller gap clearances between the monoliths and the tube result in better heat transfer performance. Monoliths with dense skin can be directly immersed into the heat exchange medium without tubes and therefore eliminate the gap resistance. Practical limitations require to trade-off between the improved heat transfer performance, due to the smaller gap size and the ease of loading the monoliths in the reactor tube. Experimental studies with a 2.4 m long standard of the shelf stainless steel tube showed that the clearances used in this work are all feasible from a loading perspective. In some cases with clearances of 50–100 m some force was required to push the monoliths into the tubes to overcome local restrictions. As the aluminum and copper monoliths are softer than stainless steel no damage occurs to the tube itself. In any case there is a trade-off between the effort for loading and the achievable performance but even with loose tolerances we obtained very good heat transfer performance. The use of these conductive monoliths as catalyst support for highly exothermic reactions was already suggested in Boger and Menegola (2005); Carmello et al. (2000); Cutler et al. (2001); Groppi and Tronconi (1996), and Groppi and Tronconi (2000). The heat transfer performance is about two to three times better than with conventional randomly packed catalyst supports (e.g. rings). An attractive feature derived from the current results is the self regulating effect of the concept. As shown in Figs. 15 and 16, the heat transfer performance improves as the temperature difference between the monolith (e.g. the catalyst) and the heat exchange medium (e.g. the coolant) increases. Therefore under reaction conditions the heat transfer performance is best in the zones with the highest reaction and heat release rates, where usually a hot spot occurs. This feature of the conductive metal monoliths therefore improves the heat management and temperature control of the reactor and adds additional margins to the overall process safety. Another characteristic derived from the present work is the improved heat transfer at higher process temperatures, with the upper limits being given by the softening temperature of the monolith materials. Also, for a gas phase with higher thermal conductivity better heat transfer performance will be realized. For exothermic hydrogenations, for example, the requirements on the clearance between monolith and tube will be less stringent than for oxidation processes. Beyond the use in heterogeneously catalyzed applications as catalyst support with enhanced heat transfer characteristics the conductive monoliths can be also applied in pure heat exchange applications. Debottlenecking of units with heat transfer limitations on the tube side can be envisioned by retrofitting with conductive monoliths, also leveraging the favorable pressure drop characteristics. Another potential area of applications is the use as a very fast quench or
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heating device for fluids. For example reactions operated at high temperatures can have some of the products react back to the reactants during cooling, e.g. because they are thermodynamically favored at low temperatures. The amount of loss in yield due to this backward reaction is usually a function of the time the fluids are exposed to temperatures at which the kinetics of the backward reactions are fast enough. We have shown that with the metal monoliths a gas can be cooled from 400 ◦ C to 80 ◦ C (or lower) over a length of 250 mm within 0.015 s (see Fig. 6). The benefits for the higher cost of the heat exchanger quench zone are very likely to be more than balanced by the gain in yield. The use of conductive monoliths with a dense skin without additional tube was already mentioned earlier. In our experimental investigations we obtained heat transfer coefficients up to 1500 W/m2 K. The calculation of the effective heat transfer coefficient of the monolith itself with Eqs. (1) and (9) suggests that actually heat transfer coefficients beyond this value are expected. Recently the use of microreactors is discussed for several application areas, where heat control is essential and the production volumes are small to medium. Drawbacks of microreactors, however, are their cost, the high pressure drop and the added complexity, if many reactors are needed to handle the overall capacity. The use of the high conductive monoliths directly installed into a heat exchange medium might offer an attractive alternative solution for such applications with similar heat transfer performance but much simpler connection requirements. Additionally, are engineering tools and knowledge readily available for monoliths and in the case of heterogeneously catalyzed processes the catalyzing methods are well known and applied. To summarize, the performance characteristics experimentally determined in this work proved thermally conductive monoliths as an attractive solution for a number of application areas, some of them being outside of the scope considered so far. The fundamental understanding of the relevant phenomena developed in this paper enables the design and performance predictions, which might possibly facilitate the development of new applications areas.
Notation A cpG CTE dh,c dh,ext DM Gz,G GSA hGS
heat exchange area defined with the inner tube diameter, m2 specific heat capacity of the gas, J/kg K coefficient of thermal expansion, 1/K hydraulic diameter of the monolith channels, m hydraulic diameter of the heat exchanger shell section, m monolith diameter, m axial mass velocity, kg/m2 s geometric surface area of the monolith, m2 /m3 gas–solid heat transfer coefficient, W/m2 K
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hext heff hgap hint hmono k kS,R KM L m ˙ Nuc Pr r R Re St ∗ T uG,0 z gap
T. Boger, A.K. Heibel / Chemical Engineering Science 60 (2005) 1823 – 1835
tube-heat exchange medium heat transfer coefficient, W/m2 K effective transfer coefficient, W/m2 K heat transfer coefficient of the gap (basis is the monolith diameter), W/m2 K integral heat transfer coefficient defined by Eq. (10), W/m2 K heat transfer coefficient of the monolith, W/m2 K thermal conductivity, W/mK radial conductivity of the monolith, W/mK constant in Eq. (9) length of the monolith section, m gas mass flow, kg/s Nusselt number Prandtl number radialcoordinate, m radius of monolith, m Reynolds number modified Stanton number, St ∗ = (kS,R /DM )/(Gz,G cpG ) temperature, K superficial gas velocity (at STP), mN /s axial coordinate of the monolith section, m gap size between the monolith skin and the inner tube wall, m void fraction, m3 /m3
The mean temperature is obtained via integration: R 1 1 4 2 R 4 Ar + 2 Cr 0 0 T (r)r dr TM = R = 1 2 R 0 r dr 2r 0 1 = AR 2 + C. 2 For the wall temperature follows: Tw = Ar 2 + C = AR 2 + C. r=R
monolith channel shell side of the tube gas phase heat exchange medium at inlet of monolith section monolith at outlet of monolith section solid phase
(A.3)
(A.4)
Integration constant A results from (A.4)–(A.3): 1 2 AR 2 = TW − TM ⇒ A = 2 (TW − TM ) 2 R
(A.5)
and C by inserting in (A.4): C = 2TM − TW .
(A.6)
Finally the temperature profile is described by T (r) =
2 (TW − TM )r 2 + 2TG − TW . R2
(A.7)
On the other hand the heat flux is defined as q˙ = hmono (TM − TW ).
(A.9)
The heat transfer coefficient can be obtained from (A.8) and (A.9): hmono =
Acknowledgements
KM kS,R , DM
(A.10)
with KM = 8 for the parabolic temperature profile.
Lin He and Lorraine Owens of Corning, Inc. are acknowledged for providing the copper monoliths. Special thanks go to Jeff Amsden, Josh Jamison and Neil Partridge, for the experimental investigations from equipment design and construction over sample preparation to experimental execution and initial data analysis. Appendix A. Derivation of film heat transfer coefficient for the monolith Assumption of homogeneous model and parabolic temperature profile: T (r) = Ar 2 + Br + C.
(A.2)
The heat flux can be obtained from the gradient at the wall: dT 4kS,R = − (T − T )r q˙ = − kS,R W M 2 dr r=R R r=R 4kS,R (TW − TM ). = − (A.8) R
Subscripts c ext G HE in M out S
Boundary condition in the center of the monolith: dT = 0 ⇒ B = 0. dr r=0
(A.1)
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exothermic reactions: characterization of the heat-transfer properties. Accepted for publication at the Eighteenth International Symposium on Chemical Reaction Engineering, 2004. Chemical Engineering Science 59, 4941–4949. Vortruba, J., Mikus, O., Nguen, K., Hlavacek, V., Skrivanek, J., 1975. Heat and mass transfer in honeycomb catalysts—II. Chemical Engineering Science 30, 201–206.