Evaluation of heat transfer in a catalytic fixed bed reactor at high temperatures

Evaluation of heat transfer in a catalytic fixed bed reactor at high temperatures

L. M. M. JORGE ¹, R. M. M. JORGE ², F. FUJII ³ and R. GIUDICI 3^*

¹Departamento de Engenharia Química, Universidade Estadual de Maringá,

Av. Colombo 5790, Bloco D-90, Maringá - PR, Brazil, CEP 87020-900, E-mail: [e-mail]

²Departamento de Tecnologia Química, Universidade Federal do Paraná, Centro Politécnico,

C.P. 19011, CEP 81531-900, Curitiba - PR, Brazil, E-mail: [e-mail]

³Departamento de Engenharia Química, Escola Politécnica, Universidade de São Paulo,

C. P. 61548, CEP 05424-970, São Paulo - SP, Brazil, E-mail: [e-mail]

(Received: August 3, 1999; Accepted: September 10, 1999)

Abstract - Experimental results of fixed-bed heat-transfer experiments with no chemical reaction are presented and discussed. The runs were carried out in a tubular integral reactor heated by an electrical furnace at temperatures in the range of 100 to 500°C. Experimental temperature profiles were determined for the electrical furnace, for the reactor wall, and for the fixed bed center. Industrial catalyst for the prereforming of hydrocarbons was employed as the packing material. The effects of process conditions (furnace temperature, gas flow rate) on the heat-transfer coefficients were evaluated. The experimental results were analyzed in terms of the external, wall, and internal thermal resistances, associated in series, and compared with model predictions. Under the conditions studied, the overall coefficient was mostly a function of the external effective heat-transfer coefficient. An alternative data treatment was proposed to determine the internal heat-transfer coefficient in fixed beds when wall temperature is not constant.

Keywords: fixed bed, catalytic reactor, overall heat-transfer coefficient

INTRODUCTION

Heat transfer plays an important role in several catalytic processes, e.g., the steam reforming of hydrocarbons. A typical reformer may contain 40 to 400 tubes, with internal diameters in the range of 70 to 160 mm with tube thicknesses of 10 to 20 mm. These tubes are placed inside a furnace chamber and have a heated section measuring from 6 to 12 m in length depending on the type of furnace. They are heated by burners that may be distributed laterally at the top or at the bottom of the furnace chamber (Rostroup-Nielsen, 1984).

In these reactors, there are three distinct thermal transfer terms: heat transfer from the furnace chamber to the reactor wall (mainly dominated by radiation), in the wall itself (conduction), and from the wall to the catalytic fixed bed. As shown in Figure 1, the total heat-transfer resistance (R_eq) incorporates three thermal resistances associated in series: the effective resistance in the furnace chamber (R_ext), the reactor wall resistance (R_k), and the effective catalytic fixed bed resistance (R_int):

(1)

The association of these resistances results in

(2)

where r and A are the internal (subscript i) and external (subscript e) radius and area of the reactor tube and A_lm is the logarithmic mean area.

Figure 1:
Radial heat flow through the reactor.

The overall heat-transfer coefficient inside the catalytic bed (U_int.) has been extensively studied in the last three decades. However, there are only a few studies on the behavior of this coefficient at high temperatures, for example the work presented by Wellauer et al. (1982).

The use of U_int for the simulation of a catalytic fixed bed requires knowing the reactor wall temperature (T_W). However, this temperature is difficult to evaluate in reactors heated by furnaces and may show variations along the reactor length. An alternative is to use furnace wall temperature (T_furnace) as the reference. By adopting this change, modeling is simplified, but another problem appears due to the incorporation of wall and furnace resistances in the equivalent overall coefficient (U_eq.), which has also been little studied at high temperature conditions.

With the purpose of exploring how these thermal resistances or the respective heat-transfer coefficients interact in reactors heated by a furnace, a bench-scale fixed-bed reactor heated by an electrical furnace was employed. This equipment was also used for studying the steam reforming of methane in an integral reactor (Jorge, 1998). In this article, however, only heat-transfer experiments with no reaction are presented and discussed.

EXPERIMENTAL SETUP AND PROCEDURE

A schematic diagram of the equipment, with the positions of the thermocouples in the system, is shown in Figure 2. The air flowing through the bed comes from a compressor, passes through a demister and a filter, and then flows to a rotameter and a valve where the air flow rate is adjusted. The reactor is a 645 mm long, vertically mounted, stainless steel tube with an internal diameter of 21.8 mm and an external diameter of 27.0 mm, which has been placed inside an electrical furnace.

Figure 2:
Schematic diagram of the equipment.

The reactor tube was packed with an industrial catalyst of nickel supported on alumina (ICI 65-2, with 79%w/w of NiO ), employed in the steam prereforming of hydrocarbons. Particles are cylindrical, with an average diameter and length of 3.54 mm and 2.75 mm, respectively, and a particle density of 2.61g/cm³.

Temperature measurements on the axis of the reactor tube (Tc) were made by twelve thermocouples, 0.5 mm OD, placed inside a 3 mm OD stainless steel well at fixed positions. The top and the bottom of the reactor were closed by flanges to which the thermocouple well was attached. Along the reactor wall, seven 3 mm OD thermocouples were inserted radially across the furnace insulation, which is made of alumina.

The furnace is composed of three independent sections. Each section, with a 65 mm ID, and a length of 200 mm, has one PID controller connected to the electrical resistance distributed along the inner heating section surface. A thermocouple was installed at the inner wall of each furnace section.

After setting the air flow rate, the reactor was submitted to a sequence of changes in furnace temperature (100, 200, 300, 400, 500^oC) at a heating rate of 20^oC/min, and each setpoint temperature is maintained for about one hour. This time is sufficient for the system to reach steady state conditions. Steady-state and unsteady-state temperature readings were recorded by a Data Acquisition System (DAS) at intervals of 30 seconds. This system is composed of a personal computer, an acquisition card (Model PCL-812PG), and three multiplexer and amplifier eight-channel boards (Advantech Co., Model PCLD-779). All thermocouples were of the K type (chromel-alumel).

Figure 3 shows the behavior of temperatures measured at the reactor axis at selected axial positions.

Figure 3:
Temperatures measured at different axial positions at the fixed bed center.

At each axial position, the mean cross-section temperature () was evaluated, assuming a parabolic radial temperature profile (not a bad hypothesis, specially for nonreacting conditions as studied here), thus averaging the temperatures measured at the wall (T_W) and at the center (T_C). Figure 4 shows the behavior of wall, center and mean temperatures, indicating the presence of radial and axial temperature gradients in the system.

Figure 4:
Temperatures measured at the wall (T_W) and at the bed center (T_C) and estimated mean cross-section temperature (

EVALUATION OF THE EQUIVALENT OVERALL HEAT TRANSFER COEFFICIENT

The overall heat-transfer coefficient (U_eq) was determined in experiments with no reaction in steady state. The fluid (air) entered the reactor at a lower temperature than that in the furnace and then it was heated as it flowed through the bed ("cold-flow experiments"). The value of U_eq was estimated by fitting the one-dimensional pseudohomogeneous plug-flow model given by

(3)

with initial condition at where is the mean cross-section temperature (^oC), is the mean cross-section temperature at the reactor inlet (^oC), Z is the axial position in the reactor (m), G is the superficial mass flow velocity (kg/m²/s), C_p is the specific heat capacity of the fluid (J/kg/^oC), and d_t is the internal tube diameter (m). Since the furnace temperature (T_furnace) is constant, the analytical solution of Equation (3) is

(4)

Figure 5 shows a comparison between the fitted model, Equation (4), and a typical experimentally measured axial temperature profile.

Figure 5:
Comparison between experimental data in the axial temperature profiles and model predictions by Equation (4).

EVALUATION OF THE INTERNAL HEAT-TRANSFER COEFFICIENT

The internal heat-transfer coefficient (U_int) corresponds to the thermal resistance between the inner wall of the reactor and the catalytic fixed bed. Martinez et al. (1986) summarized the experimental techniques currently used to evaluate the overall heat-transfer coefficient and classified them as radial or axial methods. However, all methods reported were restricted to experiments with a constant wall temperature.

For reactors where the wall temperature (T_W) is maintained constant, the aforementioned model (Equation 3) can also be readily applied by replacing the reference temperature, T_furnace, by T_W and U_eq by U_int. This situation is commonly achieved in laboratory reactors where heating is by a molten salt bath (Wellauer et al., 1982) or by a saturated steam jacket (Verschoor and Schuit, 1950). However, as the results shown in Figure 6 indicate, for our reactor heated by an electrical furnace, the assumption of a constant T_w is not valid for higher furnace temperatures.

Figure 6:
Temperature profiles measured at the reactor wall.

To overcome this problem, the observation in Figure 6 suggests that the axial profile of wall temperature may be approximated by a linear function of the axial position in the following form:

T_w = aZ + b (5)

Therefore, by replacing T_furnace by T_w(Z) and U_eq by U_int in Equation (3), the alternative model shown bellow is obtained:

T(Z=0)=To (6)

Where

(7)

The analytical solution of this first-order linear differential equation is given by

(8)

Parameter U_int was estimated using the least squares criterion, F :

(9)

where and are experimental and predicted temperatures (by Equation 8) at the i^th position, and np is the number of experimental temperatures. To minimize the objective function in Equation (9), one must solve the following equation:

(10)

Equation (10) was easily solved for parameter P using the MATLAB "fzero" routine. Coefficient U_int was then obtained from Equation (7).

Figure 7 shows a comparison of temperatures, obtained experimentally and predicted by the alternative model Equation (8), with U_int. estimated as described above. Clearly this model adequately represents the experimental behavior.

Figure 7:
Comparison between experimental data in the axial temperature profile and model predictions by the alternative model, Equation (8).

EVALUATION OF THE EXTERNAL HEAT-TRANSFER COEFFICIENT

As shown in Equation (1), the external heat-transfer resistance (R_ext) may be expressed as a combination of the equivalent resistance (R_eq), the fixed bed resistance (R_int), and the wall resistance (R_k). Since the wall resistance is negligible when compared with other resistances (R_eq and R_int), Equation (1) may be simplified and solved for h_ext to give

(11)

In the furnace chamber the radiation heat transfer from the surface is accompanied by natural convection as follows:

h_ext = h_rad + h_conv (12)

where h_rad is the radiation heat-transfer coefficient (W/m²/K) and h_conv is the natural convection heat-transfer coefficient (W/m²/K).

In order to model the radiant heat transfer, the furnace and the reactor tube were assumed to behave as two long concentric gray cylinders, filled with a gas transparent to radiation. Therefore h_rad may be expressed as

(13)

where s is the Stefan-Boltzman constant (= 5.676 x 10^-8 W/m²/K⁴), is the mean reactor wall temperature (K), e _W and e _furnace are the emissivity of the reactor wall and furnace wall, respectively, and A_e and A_furnace are the external reactor wall area and inner furnace area, respectively (m²).

The natural convection heat-transfer coefficient between the reactor tube and the furnace was evaluated using a simple correlation for natural convection in vertical cylinders presented in Perry and Chilton (1984):

(14)

where L is the length of the furnace (m).

RESULTS AND DISCUSSION

Internal (Wall-to-Bed) Heat-Transfer Coefficient

As pointed out by Wellauer et al. (1982), the internal heat-transfer coefficient increases with the flow rate and with the reactor wall temperature. This behavior is observed in Figure 8. In the present case, since wall temperature is not constant, the mean wall temperature () was used to analyze the results. Experimental results shown in Figure 8 can be represented by a simple empirical expression in the following form:

(15)

where a=0.0255+0.055G and b=38 W/m²/K. While the slope (a) was adequately fitted by a linear function of the superficial mass flow velocity, the intercept (b) did not present significant temperature and flow dependence, so a mean value was used.

Figure 8:
Effect of temperature and flow rate on the internal coefficient. Lines are model predictions by Equation (14).

Table 1 presents some simple correlations for internal coefficient U_int selected from the literature. These correlations were tested by comparison with our experimental values obtained under selected conditions of flow rate and temperature, as shown in Figure 9. Although there is qualitative agreement between the trends in the correlations and the experimental data, different quantitative values are observed, even for the lower temperatures (=120^oC) at which the correlations from the literature were obtained.

calculated by Kunii and Smith (1960) ceramic cylindersReferenceCorrelationDeWasch and Froment (1972) calculated by Kunii and Smith (1960) ceramic cylinders30 £ Re £ 100010.4 £ dt/dp£ 27.6TW =100 oCVerschoor and Schuit (1950)spherical and cylindrical ceramic packing170 £ Re £ 34504.3 £ dt/dp£ 14.3 100 oC £ TW£ 150 oCLeva (1931)nearly spherical ceramic packing46 £ Re £ 34103.9 £ dt/dp£ 11.6TW = 100 oC

Reference	Correlation
DeWasch and Froment (1972)	calculated by Kunii and Smith (1960) ceramic cylinders 30 £ Re £ 1000 10.4 £ dt/dp£ 27.6 TW =100 oC
Verschoor and Schuit (1950)	spherical and cylindrical ceramic packing 170 £ Re £ 3450 4.3 £ dt/dp£ 14.3 100 oC £ TW£ 150 oC
Leva (1931)	nearly spherical ceramic packing 46 £ Re £ 3410 3.9 £ dt/dp£ 11.6 TW = 100 oC

Table 1: Some correlations for U_int .

Figure 9:
Comparison of different correlations from the literature and the experimental data for the internal coefficient.

External (Furnace-to-Wall) Heat-Transfer Coefficient

Figure 10 shows that the external heat-transfer coefficient is influenced by furnace temperature, as expected. A little dependence on the air flow rate can be seen at higher temperatures, and this dependence must be ascribed to the variation in average wall temperature as the flow rate changes, as shown in Figure 11, which is important at higher furnace temperatures. At the lowest furnace temperature (100ºC), the flow rate inside the reactor does not significantly affect wall temperature, an indication that the heat transfer is dominated by external resistance.

Figure 10:
Effect of furnace temperature on the external heat-transfer coefficient.

Figure 11:
Influence of gas flow rate on the experimentally measured wall temperature.

The model represented by Equations (12), (13), and (14) was successfully used to predict the external heat-transfer coefficient, as shown in Figure 10. The model calculations used typical values for the emissivity of the internal wall of the furnace (e _furnace=0.17) and of the external wall of the reactor (e _W=0.9), taken from Hottel and Sarofin (1967).

Overall (Furnace-to-Bed) Heat-Transfer Coefficient

As previously mentioned, the equivalent overall heat-transfer coefficient represents the overall heat-transfer resistance between the furnace wall and the catalytic fixed bed. As the catalytic fixed bed temperature is directly influenced by the air flow rate, it would be expected that U_eq is also affected by the air flow rate. However, this influence was found to be negligible within the range of variation, as shown in Figure 12. This is an indication that the internal coefficient (the only parameter that may truly depend on the flow rate) is not the limiting step. Apart from the marginal effect of mass velocity on U_eq, the equivalent overall coefficient increases as the furnace temperature rises. Figure 12 shows a comparison between experimental values of U_eq and model predictions by equations (2), (12), and (15), assuming negligible wall resistance. Satisfactory agreement is observed.

Figure 12:
Effect of furnace temperature and gas flow rate on the equivalent overall heat-transfer coefficient. Lines are model predictions.

Thermal Resistances

Each of the heat-transfer coefficients represents specific thermal resistance that depends on the operational conditions. The behavior of these resistances as the furnace temperature changes, shown in Figure 13, reveals interesting information about how these resistances interact and distribute according to the operational conditions studied:

(a) Wall resistance (R_k) is negligible, as compared to other resistances (this was evaluated using the conductivity of stainless steel); (b) While catalytic fixed bed resistance (R_int) decreases only slightly as the furnace temperature increases, furnace resistance (R_ext) decreases quickly, defining the trend in equivalent resistance; (c) For lower temperatures (e.g., below 300⁰C) furnace chamber resistance (R_ext) is the limiting heat-transfer step (dominating resistance), but at higher temperatures (>500ºC) both internal and external resistances tend to become equally important.

Figure 13:
Effect of furnace temperature on the thermal resistances.

CONCLUDING REMARKS

An experimental study of heat transfer in a bench-scale packed bed reactor heated by an electrical furnace was performed. Besides air flow rate, reactor wall temperature also plays a role in the catalytic fixed bed (internal) heat-transfer coefficient.

For the conditions studied, the external coefficient could be reasonably predicted a priori using Equation 12.

The reactor wall heat-transfer resistance is negligible in comparison with other thermal resistances. The furnace chamber (external) heat transfer resistance continuously decreases as the temperature rises, eventually equaling the catalytic fixed bed resistance at about 500^oC. Above 500^oC the fixed bed (internal) resistance tends to be the limiting heat-transfer step. The furnace temperature has little influence on the catalytic fixed bed (internal) resistance as compared with its effect on the external resistances.

The behavior of the equivalent heat-transfer resistance is a function of furnace chamber (external) heat-transfer resistance within the range of experimental conditions explored.

ACKNOWLEDGEMENTS

The authors are grateful to CAPES, FAPESP, and CNPq for providing financial support for this research work.

NOMENCLATURE

A heat-transfer area (m²)

a,b parameters in Equation (4)

C_p heat capacity (J/kg/°C)

d_t tube diameter (m)

G superficial mass flow velocity (kg/m²/s)

h heat-transfer coefficient (W/m²/°C)

k conductivity (W/m/°C)

L furnace length (m)

np number of points

P parameter defined in equation (7)

R thermal resistance (°C/W)

r tube radius (m)

T temperature (°C)

U heat-transfer coefficient (W/m²/°C)

z axial position (m)

f residue

e emissivity

s Boltzman constant

Subscripts

eq equivalent, overall

int internal

ext external

furnace furnace

g gas

rad radiation

conv natural convection

k relative to wall conduction

w wall

0 at z=0

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^*

To whom correspondence should be addresed

Publication Dates

• Publication in this collection
  01 Mar 2000
• Date of issue
  Dec 1999

History

• Accepted
  10 Sept 1999
• Received
  03 Aug 1999