Design of Micro- and Milli-Channel Heat Exchanger Reactors for

Article pubs.acs.org/IECR

Design of Micro- and Milli-Channel Heat Exchanger Reactors for Homogeneous Exothermic Reactions in the Laminar Regime Yatziri Rodríguez-Guerra,*,† Luciano A. Gerling,† Enrique A. López-Guajardo,† Francisco J. Lozano-García,† Krishna D. P. Nigam,†,‡ and Alejandro Montesinos-Castellanos† †

Tecnologico de Monterrey, Escuela de Ingenieria y Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, Nuevo León 64849, Mexico Department of Chemical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110 016, India

‡

S Supporting Information *

ABSTRACT: Considerable efforts have been made to study heat exchanger microreactors. However, the starting point in design for the selection of an adequate length scale that takes into account both the maximum temperature rise and pressure drop, important criteria for the holistic design of such equipment, is still missing. An attempt has been made in the present communication to provide such relationship over a wide range of operating variables. Fast and simple guidelines are discussed for beginning to design a heat exchanger microreactor for exothermic reactions where the maximum temperature deviation inside the reactor, called the hotspot temperature, can be predicted by calculating the overall heat and the maximum heat release rate. The applicability of the proposed guidelines was tested using experimental and simulation data from other authors.

■

INTRODUCTION Robust design of micro- and milli-structured heat exchanger reactors must consider an adequate length scale that improves heat transfer in order to operate within the required process conditions as well as tolerable pressure drop. Guidelines and rules of thumb are a good starting point for basic design of traditional macroscale equipment.1 However, there are few design guidelines for microstructured devices. A robust reactor design should take into account the desired performance and operating conditions of the reaction. Figure 1 shows some of

their many advantages for process intensification, including improved heat and mass transfer,8−13 temperature control,12−14 selectivity, yield,4,13,14 and smaller ground footprint.5,15 However, microreactors also present disadvantages, including specialized fabrication,12,16 channel blockage,12,17,18 high pressure drop,18,19 and uneven flow distribution19−26 when multiple units work in parallel. Due to these disadvantages, the length scales, geometries, and channel arrangement of microreactors become important. A compromise between the advantages and disadvantages should be considered at the design stage. Researchers have addressed different aspects related to design. In the present study, we have focused on those relevant to our work. Bahrami et al.27,28 investigated the pressure drop for fully developed laminar incompressible flow in microchannels of different cross sections by solving the momentum balance equation. They proposed an analytical solution validated by experimental and simulation data and concluded that the Poiseuille number is only a function of the cross-section geometrical parameters and the polar moment of inertia. Saji et al.29 tested a compact tubular microheat-exchanger with an internal diameter of 0.5 mm that could achieve a temperature variation of less than 4 K. Bau30 studied the channel geometry, and Muzychka31 developed an arrangement of tubes of different diameters to increase heat transfer. Other important studies

Figure 1. Reactor performance factors considered in reactor design.

the many criteria that must be considered when designing a reactor from a holistic approach. All aspects are interconnected and affect the overall reactor performance. The term microstructured is generally used for equipment with a characteristic dimension up to 1 mm.2−6 Millimeter- and micrometer-sized structured reactors (further referred to here as “microreactors”) are a topic of research interest7 because of © XXXX American Chemical Society

Received: January 27, 2016 Revised: April 22, 2016 Accepted: May 10, 2016

A

DOI: 10.1021/acs.iecr.6b00323 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research deal with flow distribution and scaling,18−20 characteristic times,8,9 channel flow fields,32 heat-transfer augmentation,33,34 aspect ratio selection,35 scaling,36 and parameter optimization.37 Heat exchanger microreactors (HEMR) help to remove the heat generated by exothermic reactions8,32,38 more efficiently, thereby achieving isothermal operation. In those devices, the amount of heat transferred depends on the geometry configuration, the temperature difference, the properties of the cooling medium selected, the heat released by the reaction, and the heat exchange surface area. HEMR become particularly useful for reactions in which a temperature rise produces undesirable results, such as the promotion of a secondary reaction, product degradation, quality issues, etc. Holistic approaches for various reactor designs have recently been reported.35−37,39,40 For example, Fukuda et al.40 proposed a computer fluid dynamics (CFD) isothermal design basis for laminar flow between two parallel plates. Their reactor design conditions allowed a maximum deviation of 2 K from their target temperature. The authors found a numerical solution that correlated the maximum heat transferred at the wall with the separation distance between plates and the fluid velocity by keeping the maximum deviation temperature equal to 2 K. It would be advantageous to have a broader generalization for exothermic reactions with different temperature restrictions depending on several factors for each specific reaction, such as required purity, costs of downstream product separation, or temperature sensitivity of product materials. In this paper, guidelines for the adequate selection of microreactor tube diameters are presented for homogeneous exothermic reactions with a prediction for the deviation from isothermal conditions (hotspot temperature) and linear pressure drop. The microreactors studied were externally cooled circular tubes of different diameters in the milli- and micrometer range using CFD. The scope of this work is to provide easy guidelines to preselect a tube diameter by computing the values of two key variables, using the reaction rate model, the fluid properties, and the operation temperature restrictions. This guideline represents a step that can be done in the first stage of the reactor design.

circular with a diameter d, with a highly conductive metal wall. The reacting fluid is assumed incompressible and with constant fluid properties (ρ, μ, λ, Cp, Dj). The differential equations governing the laminar flow in the reactor could be written as follows: Continuity: (1)

∇·u = 0

Momentum: ∇·( −p + ρ∇u) = 0

(2)

Energy: ρCpu·∇T − ∇·(λ∇T ) =

∑ ΔHrxn,jrj

(3)

Mass (by component): rj = ∇·( −Dj∇cj) + u·∇cj

(4)

Boundary Conditions. The boundary conditions at the inlet (r, 0) consider that the reactive fluid enters at a temperature T0, a fully developed laminar velocity u0, and with reactant concentrations cj0 for each j species. The boundary conditions at the outlet (r, L) consider a fixed pressure pL, and ∂ the diffusion flux for all variables in the exit direction ∂n (u , p , T ) is set to zero. At the wall (d/2, z), a no-slip boundary condition (u = 0) is considered, and heat is transferred to the cooling medium formulas described by eq 5: q ̇ = hcool(Twall − T0)

(5)

The heat transfer coefficient of the cooling medium hcool can be calculated from correlations, depending on the nature of the cooling medium. A constant temperature of the cooling medium can be achieved during its phase change (liquefaction or boiling). The boiling heat transfer coefficient also depends on its convection regime, e.g., natural convection also called pool boiling,41 or forced convective boiling.42−46 Forced convective boiling provides a high heat transfer and can be implemented in a shell-and-tubes style apparatus. For example, an order of magnitude increase in the heat transfer coefficient of water can be obtained with a fluid velocity of ∼0.9 m/s in comparison with pool boiling,46 and higher Reynolds numbers can further increase it up to 2 orders of magnitude.42 Since the objective of the reactor is to achieve isothermal operation, the cooling medium in this study is considered to be saturated water at the target operating temperature T0 in a forced convective

■

METHODS Governing Equations. In the present study, the cylindrical coordinates (r, z, θ) are used to represent the reactor in the numerical simulation. The symmetrical axis at the center of the tube is used to simplify the simulation from a three-dimensional (3D) to a two-dimensional (2D) geometry with coordinates (r, z) since the variations in the θ coordinate are zero (see Figure 2). Reactive fluid enters at the reactor inlet, and heat is transferred at the pipe wall to the cooling medium. The process is considered to be at steady state. The reactor cross-section is

Figure 2. Representation of the tubular reactor geometry used (dotted area) for the axis-symmetrical 2D simulations. B


Article

Industrial & Engineering Chemistry Research boiling regime, flowing at an average velocity of 0.9 m/s, for which hcool can be calculated as hcool = 11 462(Twall − T0)1/3

average conversion at the exit is known or assumed, Q ov can also be calculated as π⎞ 2 T0 T0 ⎛ ⎜ ⎟d u c X Q ov = ΔHrxn FA 0XA = ΔHrxn ⎝ 4 ⎠ 0̅ A 0 A

(6)

Other studies23,36,37 have used a constant wall temperature boundary condition, in order to study the heat transfer inside the heat exchanger by considering a cooling medium with no heat transfer resistance. Forced convective boiling provides a higher heat transfer that can be achieved in practice, thus the subject of the present study. Variables of Interest. The heat generated by the exothermal reaction must be removed by the cooling medium. Because the flow is in the laminar regime, there will be a temperature gradient inside the reactor. The temperature profile at the center of the tube ΔTinc(0, z) is of interest because that is the furthest position away from the cooling medium and is expected to show the most pronounced deviation from isothermal conditions. This temperature profile along the z-axis is calculated as ΔTinc (0, z) = T (0, z) − T0. The maximum temperature deviation reached in the reactor is called the hotspot temperature, here calculated as ΔThotspot = max(ΔTinc)

because the average molar flow of species A can be calculated π with the formula FA 0 = 4 d 2u0̅ c A 0 .

()

Numerical Computation. The governing equations of the model are solved using CFD.47 The CFD model considers a free triangular fixed mesh distributed randomly with an average element quality higher than 0.83, calibrated for fluid dynamics, with up to 1.11 × 106 elements. The mesh size was refined near the walls and corners of the geometry for resolution improvement. Simulations were carried out in order to make the element size independent from the solution. The nonlinear steady-state simulations were performed with a PARDISO solver using a nested dissection multithreaded preordering algorithm and a pivoting perturbation of 10−8. Simulation Parameters. Internal diameter values of 0.5, 1, 5, and 10 mm were selected for the simulations. The reaction was of the form A → B with a simple first order reaction rate −rA = kcA, and the input values for the simulation parameters were calculated considering 100% conversion. A summary of the parameters and variables used in the simulations is presented in Table 1.

(7)

For design purposes, this temperature is the maximum deviation desired/allowed in the microreactor. ΔThotspot is needed as a restriction for the microreactor design, and its behavior depends on the reactor conditions and the given reaction. An Eulerian one-dimensional (1D) theoretical analysis clarifies the relationships between the variables that influence the behavior of the ΔThotspot (see the Supporting Information). In this analysis, it was found that, for a given reactor diameter, cooling medium, fluid properties, and regimen, the chemical reaction variables that influence the ΔThotspot are the heat of reaction, the rate of reaction, and the total moles reacted. A combination of those factors determine the ΔThotspot reached. The first factor is related to the heat rate produced by the reaction. A fast exothermic reaction will release heat more abruptly, and the maximum heat rate endured by the cooling medium can be calculated as T0 S = ΔHrxn, j max(|rj|)

(9)

Table 1. Parameters and Variables Used in the Simulations parameter or variable

value(s) or range of values

density, ρ (kg m−3) diffusion coefficient, D (m2 s−1) heat capacity, Cp (J kg−1K−1) initial concentration, cA0 (mol m−3) kinematic viscosity, μ (Pa s) overall heat generated, Q ov (W) Prandtl number, Pr (1) rate of heat generated, S (W m−3) reactor internal diameter, d (mm) Reynolds number, Re (1) thermal conductivity, λ (W m−1K−1) thermal diffusivity, α (m2 s−1)

1000 1.00 × 10−9 4182 100 1.00 × 10−3 0.5 to 200 6.97 105 to 5 × 109 0.5, 1, 5, 10 50 0.6 1.44 × 10−7

The dimensionless numbers Reynolds and Prandtl were kept constant (see Table 1) in order to isolate the effect of the diameter in the results between cases with dynamic and thermal similarity. The linear pressure drop was calculated from the results of the momentum equation, eq 2, from the CFD simulation. However, for practicality, the linear pressure drop can also be calculated from the Darcy−Weisbach equation, which is valid in the scales and conditions studied.6,27,28

(8)

where S is the maximum rate of heat generated, and its value is negative for exothermic reactions. The reaction rate varies in the reactor (radially and axially), and it has its largest absolute value at the reactor inlet40 or a position close to it. Thus, the term max(|rj|) in eq 8 can be considered to be the reaction rate at the inlet conditions. Because the reactor is intended for conditions near isothermal operation, the influence of the concentration decrease on the rate of reaction is expected to be more pronounced than the effect of the temperature increase. Special cases where this assumption is no longer valid should be taken into account, and a value as close as possible to the maximum heat of reaction should be used. The second factor is the overall heat released in the reactor, which is related to the total moles reacted inside the reactor volume. It is calculated by Q ov = ∫ ΔHTrxnrj dV. The heat of reaction can be considered constant and equal to its value at the inlet conditions for simplification in this reactor configuration. For tubular microreactor design, or other cases where only the

Δp 32μu ̅ = L d2

(10)

The linear pressure drop is inversely proportional to the diameter squared; thus, a reactor should be selected that achieves the target operating conditions with the largest diameter possible in order to reduce the pressure drop.

■

RESULTS ΔThotspot Prediction. Hotspot temperatures ΔThotspot were obtained for the selected heat exchanger microreactor diameters over the ranges of both the heat rate S and overall C


Article

Industrial & Engineering Chemistry Research

Figure 3. Contour lines present ΔThotspot in K for various reactor diameters; the axes of −S and −Q ov are shown in logarithmic scale, and the transition region is marked with a dotted line.

heat Q ov. The results of 433 simulations are presented graphically in Figure 3a−d, where ΔThotspot can be read for the diameters studied and the S and Q ov ranges are presented in the Simulation Parameters subsection. Higher values of heat rate and overall heat result in higher ΔThotspot, as expected. To compare the predicted ΔThotspot from a given reaction for different reactor diameters, the Q ov must be computed for each reactor diameter. To simplify calculations, a linear relationship between the Q ov and the reactor diameter can be used. This relationship results from using eq 9 and dividing a scenario number 2 by a scenario number 1

Q ov,2 Q ov,1

starting point for design, a balance between isothermal conditions and pressure drop must be made. From the results, three distinct regions can be observed in the contour graphs shown in Figure 3a−d: • A region where the influence of S on ΔThotspot is more evident (left-hand side of dotted line). The contour lines show that ΔThotspot is practically constant in this region for any Q ov value, and the ΔThotspot depends practically only on the S value. This means that, for slower heat production rates, the cooling medium will have enough capacity to cool the system down, and therefore, the overall quantity of moles reacted will only have a marginal influence on the ΔThotspot reached. • A transition region around the dotted line, where both S and Q ov influence the ΔThotspot; this is where the contour lines show inflection points. • The region where the effect of Q ov on ΔThotspot is more pronounced (right-hand side of the dotted line). This means that, for high heat rates, the heat generated is released quickly and the resulting ΔThotspot will be determined principally by the amount of moles that reacted. In this case, the reaction takes place so quickly that the

T

=

( π4 )d22u0,2̅ c A0,2XA ,2 . T0,2 π ΔHrxn,1 ( 4 )d12u0,1̅ c A0,1XA ,1

0,2 ΔHrxn,2

Also in order to account for the Reynolds number, we substitute the average fluid velocities from the Reynolds Re μ number definition u0,̅ n = d ρ , where n is the number of the n scenario. Then, for the same reactants, at the same concentration and exit conversion, and operating at the same conditions with the same Reynolds numbers, most of the variables Q d are canceled out and the relationship Q ov,2 = d2 is found. With ov,1

1

smaller tube diameters, keeping inlet concentration and Re constant, better temperature profiles can be obtained, with the trade-off of higher pressure drops. In order to select the best D


Article


An inverse method can also be employed for diameter selection by using the ΔThotspot contour lines as a restriction for calculating Q ov and using eq 9 to calculate the operating fluid velocity. Model Comparison. A test of the guidelines method was carried out by comparing the ΔThotspot predictions with the results presented by other authors (Fukuda et al.,40 Prat et al.,48 ̈ et al.;49 see Table 2). and Benaissa The predictions of the ΔThotspot for the production of α-triphenylsilyloxiranyllithium (α-TPSL) were compared with the results presented by Fukuda et al.40 for plate distance separations of 0.5 and 2 mm. For the calculation of the prediction at the 2 mm, the ΔThotspot from Figure 3b,c was linearly interpolated (1 and 5 mm, respectively). In the paper by Fukuda et al.,40 the authors analyze the operating conditions required to limit operating temperature deviation to 2 K, modeled with data from the experiment presented in ref 50. As can be seen from their simulation results, both plate reactors can achieve the target operating temperature range. However, from the prediction of this guideline, a tube diameter of 2 mm is estimated to have a ΔThotspot of 2.44 K. The quick calculation in this guideline had a prediction error of less than 30%, although the reaction studied by Fukuda et al.40 was made up of a set of two reactions in which the primary product reacts with reactant to produce a secondary product. A higher ΔThotspot is expected from the prediction because the second-order reaction concentration drop is more pronounced and the reaction rate will decrease more rapidly in comparison to a first-order reaction with the same S. Therefore, the cooling system would be able to cool down the reactor more easily for a second-order reaction than for a first-order reaction. On the other hand, a zero-order reaction is expected to release its heat uniformly and qualitatively will reach a higher ΔThotspot in comparison to a first-order reaction. Fukuda et al.’s40 analysis also considered a constant temperature boundary condition at the wall, corresponding to a system with no heat transfer resistance on the cooling side (hcool → ∞). It is expected that the constant temperature condition at the wall would result in a lower ΔThotspot in comparison to the prediction of this guideline. For this reason, in practice, a tube diameter smaller than 2 mm is recommended in order to maintain adequate ΔThotspot for the operating temperature range. However, the selected tube diameter must also take into account the linear pressure drop, since the 0.5 mm diameter reactor would present a linear pressure drop 64 times higher than the 2 mm diameter tube (calculated from eq 10 and substituting the physical and operating values, the 0.5 mm diameter has a linear pressure drop of 12 800 Pa/m whereas the 2 mm diameter has only 200 Pa/m), operating at the same Reynolds number. For the other comparisons, an equivalent hydraulic diameter of 7.07 mm was calculated for the reactors presented

cooling system will endure an abrupt surge of heat determined by the amount of moles that reacted. The theoretical analysis of the relationship between Q ov and the ΔThotspot of the 1D model (see Supporting Information) clarifies the behavior that can be expected from small diameters in general. The 1D analysis revealed that ΔThotspot is directly proportional to Q ov and inversely proportional to the Reynolds number. A 1D model is equivalent to a reactor with high axial mixing (plug flow reactor). However, for laminar flow, 2D simulations are necessary to take into account the effect of the flow dynamics over Q ov and the radial temperature variation. Therefore, for variations in Re numbers in the laminar regimen, a corrected Q*ov becomes necessary to be able to use Figure 3a−d. The constant Re condition translates into a different linear pressure drop for each diameter presented, which should be taken into account for adequate reactor diameter selection. The linear pressure drop is inversely proportional to the diameter squared. Thus, the recommendation for this condition is selecting the reactor design that achieves the maximum allowed ΔThotspot with the largest possible diameter. It can be seen from Figure 3a−d that, in order to obtain a lower ΔThotspot for any given reactor diameter, either the S or Q ov should be kept as low as possible. As stated before, S depends on the reaction rate and heat of reaction. Furthermore, the reaction rate depends on the reaction kinetics (intrinsic to the reaction) and the inlet conditions. Therefore, in order to decrease ΔThotspot in practice, the inlet conditions can be manipulated, which would in turn affect the value of Q ov such as by changing the molar flow of reactants. Diameter Selection Method. In order to have a rough starting point for reactor design, using Figure 3a−d, the following method is suggested: • Calculate S of the reaction. This value is different for each reaction; use the inlet conditions for simplicity when no data regarding the maximum heat generation is available; use eq 8. • Calculate the fluid velocity from the Reynolds number definition with the physical properties of the fluid at inlet conditions for each of the four diameters shown, because Figure 3a−d displays the data for a Reynolds number of 50. Calculate the linear pressure drop with eq 10. • Calculate Q ov for each diameter; use eq 9. For Reynolds numbers other than 50 in the laminar regimen (the generalization was tested with values of 10 ≤ Re ≤ 200), Q ov can be corrected in order to estimate an approximation. The corrected number to read from the figure should be calculated as Qov * = Q ov (Re*/50). This relationship is explained since there is a linear relationship between the ΔThotspot and Q ov. See the Supporting Information. • Read the predicted ΔThotspot from Figure 3a−d.

Table 2. Comparison of the Model Prediction and the Values Reported by Other Authors d [mm]

model

0.50 2.00 7.07a 7.07a

α-TPSL production α-TPSL production oxidation of sodium thiosulfate by hydrogen peroxide48 transposition of propionic anhydride esterification by 2-butanol49

−Q ov [W] −S [MW/m3] 0.3 4.3 4785b 3779e

30.6 30.6 3.89 0.0354

reported ΔThotspot [K]

predicted ΔThotspot [K]

error [%]

0.65 1.90 ∼35c ∼5f

0.83 2.44 ∼40d 7.36

28 28 ∼14 47

a Equivalent hydraulic diameter. bThe experiment had 87% conversion. cIn the results presented in ref. 48, the cooling medium was 1.76 m3/h of liquid water at 286 K. dExtrapolated result. eCalculated at 100% conversion. fIn the results presented in ref. 49, the cooling medium was 3 m3/h of glycol water at 343 K.

E


Article


reaction characteristics, fluid properties, and heat transfer was developed to predict the hotspot temperature (ΔThotspot). Results were presented for tube diameters of 0.5, 1, 5, and 10 mm. We found that the simulation of a simple first-order reaction is able to predict the ΔThotspot behavior of higher order reactions through simple calculations of the overall heat generated in the microreactor Q ov and the maximum rate of heat generated by the reaction S, and then, one can read ΔThotspot from the graph. Q ov can be manipulated through the reactor configuration and operating conditions so that larger diameters may be selected while still achieving low ΔThotspot in order to reduce the pressure drop in the reactor. A balance between isothermal operation and pressure drop should be sought for a sound reactor design.

in refs 48 and 49, since the patent51 reports that the reactor has a mainly squared cross-section of 0.5 cm2. Therefore, interpolation of the results between the graphs shown in Figure 3c,d was necessary for the ΔThotspot prediction for those cases. The reaction described in the experiment carried out by Prat et al.48 can be represented using second-order kinetics. The predicted ΔThotspot temperature for their operating conditions is ∼40 K, which would fall outside the accuracy range of the proposed guideline prediction because of the departure from desirable isothermal operating conditions (ΔThotspot < 10 K), which would affect several assumptions of this guideline: (a) the maximum reaction rate may no longer occur at the inlet, (b) the heat transfer coefficient correlation used may no longer apply, and (c) the physical properties and heat of reaction can no longer be considered constant. However, Figure 3 shows ΔThotspot > 10 K as a reference for quick estimation. Moreover, the order of magnitude of the prediction is close to the results presented by Prat et al.,48 and it again supports the behavior expected of the ΔThotspot for a second-order reaction to be lower than the prediction. In practice, by modifying operating conditions at the inlet, a lower ΔThotspot could be achieved, such as further diluting the reactants or staging a reactant input. ̈ et al.49 was modeled using The reaction described in Benaissa first-order reaction kinetics. In their study, the objective was to keep the reaction from boiling and under 373 K, while the cooling fluid had a temperature of 343 K. The maximum temperature increase reported in their experiment is approximately 5 K. The overestimation of this prediction (Table 2) may be due to the fact that the experiment they carried out shows that the reactants were introduced at near ambient temperature (∼300 K) because in their process diagram the reactants are fed to the reactor directly from their storage tanks, and there is no indication of heating along the feed line. The inlet temperature of the reactants in this case was lower than the cooling medium temperature, which would have helped reduce the hotspot temperature reached by the system. Their approach of having the reactants enter the system at a lower temperature is an option to reduce the ΔThotspot reached in the reactor. In summary, although the conditions established by other authors are different than our simulation conditions, the predictions of the present guidelines give a clear idea of the order of magnitude as shown with the comparison of the results of the other authors and can be used as a starting point for microreactor design. This information can be used as a previous step in microreactor design, with only simple calculations without the need of complete calculations or simulations. The idea of using the largest tube diameter that can accomplish the temperature conditions required for the reaction is also reinforced. Moreover, the linear pressure drop of the larger tube diameters is lower than that of the smaller tube diameters. The pressure drop shown in Figure 3a−d is a reference of the magnitude when selecting different tube diameters. Thus, it is necessary to have the pressure drop in mind at the design stage, particularly for microreactors, and work with the largest possible diameter that meets the process requirements in order to minimize pressure drops, channel blockage, and costs.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b00323. Equation derivations and relationships between variables of interest. (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +52 81 83582000 ext. 5435. E-mail: [email protected]. Author Contributions

The manuscript was written with contributions from all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was possible thanks to the funding of the Department of Chemical Engineering of ITESM for the materials and equipment. ITESM and CONACYT provided scholarship funds. Also, thanks to Dr. Alejandro Alvarez, Dr. Porfirio Caballero, Dr. Salvador Garcia, Dr. Sergio Morales, Maria del Rosario Covarrubias, and Ricardo Alanis for their help.

■

NOMENCLATURE Molar concentration of species j; additional subscript 0 indicates concentration at the inlet (mol m−3) Cp Heat capacity at constant pressure (J kg−1K−1) Dj Diffusion coefficient of the j component (m2s−1) d Inner diameter of circular tube (mm) Fj Molar flow rate of species j; additional subscript 0, at the inlet (mol s−1) hcool Heat transfer coefficient at the cooling side (W m−2K−1) ΔHrxn Enthalpy of reaction; superscript indicates a specific temperature at which it was evaluated (J mol−1) k Reaction rate constant (unit varies depending on reaction order), i.e., for a first order reaction (s−1) L Total length in z direction (mm) pL Reference pressure (Pa) Δp Pressure drop; difference between the inlet and the outlet pressure (Pa) cj

■

CONCLUSION Guidelines for the adequate selection of heat exchanger microreactor (HEMR) tube diameters were presented for homogeneous exothermic reactions with a prediction for the deviation from isothermal conditions. A relationship between the chemical F


Article


(9) Lomel, S.; Falk, L.; Commenge, J. M.; Houzelot, J. L.; Ramdani, K. The Microreactor: A Systematic and Efficient Tool for the Transition from Batch to Continuous Process? Chem. Eng. Res. Des. 2006, 84, 363−369. (10) Lerou, J. J.; Tonkovich, A. L.; Silva, L.; Perry, S.; McDaniel, J. Microchannel reactor architecture enables greener processes. Chem. Eng. Sci. 2010, 65, 380−385. (11) Schuster, A.; Sefiane, K.; Ponton, J. Multiphase mass transport in mini/micro-channels microreactor. Chem. Eng. Res. Des. 2008, 86, 527−534. (12) Agar, D. W. Multifunctional Reactors. In Re-Engineering the Chemical Processing Plant; CRC Press: Boca Raton, 2003. (13) Anxionnaz, Z.; Cabassud, M.; Gourdon, C.; Tochon, P. Heat exchanger/reactors (HEX reactors): Concepts, technologies: State-ofthe-art. Chem. Eng. Process. 2008, 47, 2029−2050. (14) Chambrey, S.; Fongarland, P.; Karaca, H.; Piché, S.; GribovalConstant, A.; Schweich, D.; Luck, F.; Savin, S.; Khodakov, A. Y. Fischer−Tropsch synthesis in milli-fixed bed reactor: Comparison with centimetric fixed bed and slurry stirred tank reactors. Catal. Today 2011, 171, 201−206. (15) Reay, D.; Ramshaw, C.; Harvey, A. Process Intensification Engineering for Efficiency, Sustainability and Flexibility; Elsevier: Oxford, UK, 2008. (16) Cruz, S.; Sanz, O.; Poyato, R.; Laguna, O. H.; Echave, F. J.; Almeida, L. C.; Centeno, M. A.; Arzamendi, G.; Gandia, L. M.; SouzaAguiar, E. F.; Montes, M.; Odriozola, J. A. Design and testing of a microchannel reactor for the PROX reaction. Chem. Eng. J. 2011, 167, 634−642. (17) Kandlikar, S. G.; Colin, S.; Peles, Y.; Garimella, S.; Pease, R. F.; Brandner, J. J.; Tuckerman, D. B. Heat Transfer in Microchannels 2012 Status and Research Needs. J. Heat Transfer 2013, 135, 091001− 091001. (18) Haber, J.; Jiang, B.; Maeder, T.; Borhani, N.; Thome, J.; Renken, A.; Kiwi-Minsker, L. Intensification of highly exothermic fast reaction by multi-injection microstructured reactor. Chem. Eng. Process. 2014, 84, 14−23. (19) Commenge, J. M.; Saber, M.; Falk, L. Methodology for multiscale design of isothermal laminar flow networks. Chem. Eng. J. 2011, 173, 541−551. (20) Al-Rawashdeh, M.; Yu, F.; Nijhuis, T. A.; Rebrov, E. V.; Hessel, V.; Schouten, J. C. Numbered-up gas−liquid micro/milli channels reactor with modular flow distributor. Chem. Eng. J. 2012, 207−208, 645−655. (21) Hao, Y.; Du, X.; Yang, L.; Shen, Y.; Yang, Y. Numerical simulation of configuration and catalyst-layer effects on micro-channel steam reforming of methanol. Int. J. Hydrogen Energy 2011, 36, 15611−15621. (22) Saber, M.; Commenge, J.-M.; Falk, L. Rapid design of channel multi-scale networks with minimum flow maldistribution. Chem. Eng. Process. 2009, 48, 723−733. (23) Saber, M.; Commenge, J. M.; Falk, L. Heat-transfer characteristics in multi-scale flow networks with parallel channels. Chem. Eng. Process. 2010, 49, 732−739. (24) Saber, M.; Commenge, J. M.; Falk, L. Microreactor numberingup in multi-scale networks for industrial-scale applications: Impact of flow maldistribution on the reactor performances. Chem. Eng. Sci. 2010, 65, 372−379. (25) Tondeur, D.; Fan, Y.; Commenge, J.-M.; Luo, L. Uniform flows in rectangular lattice networks. Chem. Eng. Sci. 2011, 66, 5301−5312. (26) Uriz, I.; Arzamendi, G.; Diéguez, P. M.; Echave, F. J.; Sanz, O.; Montes, M.; Gandía, L. M. CFD analysis of the effects of the flow distribution and heat losses on the steam reforming of methanol in catalytic (Pd/ZnO) microreactors. Chem. Eng. J. 2014, 238, 37−44. (27) Bahrami, M.; Yovanovich, M. M.; Culham, J. R. Pressure drop of fully-developed, laminar flow in microchannel of arbitrary crosssection. J. Fluids Eng. 2006, 128, 1036−1044. (28) Bahrami, M.; Michael Yovanovich, M.; Richard Culham, J. A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section. Int. J. Heat Mass Transfer 2007, 50, 2492−2502.

Q ov q̇ r rj

Overall heat generated in the microreactor (W) Heat flux (W m−2) Cylindrical radial coordinate (m) Rate of reaction for species j; subscript 0, at the inlet (mol m−3s−1) S Heat generation rate per unit volume (W m−3) T Temperature; subscripts: 0, of reacting flow at the inlet and of the cooling medium; “wall”, at the wall (K) ΔTinc (0, z) Temperature increase, defined as the difference between the temperature at the centerline and the inlet temperature ΔTinc (0, z) = T(0, z) − T0, 0 ≤ z ≤ L (K) ΔThotspot Hotspot temperature, defined as the maximum value of ΔTinc (0, z) (K) u Velocity (u̅ represents the radially averaged velocity); subscripts: 0, at the inlet; “max”, maximum (m s−1) V Volume (m3) Xj Conversion of species j z Coordinate, z-axis (m) Greek Symbols

α ρ μ λ τ Θ

Thermal diffusivity, α = λρ−1Cp−1 (m2 s−1) Density (kg m−3) Viscosity (Pa s) Thermal conductivity (W m−1K−1) Residence time (s) Angular coordinate (rad)

Dimensionless Numbers

Da =

−rA 0V

Damköhler

FA

Pe = RePr = Pr = Re =

Cpμ λ ρud μ

= =

ud α

ν α ud ν

Péclet (heat transfer) Prandtl Reynolds

Acronyms

CFD Computer fluid dynamics HEMR Heat exchanger microreactor α-TPSL α-Triphenylsilyloxiranyllithium

■

REFERENCES

(1) Woods, D. R. Rules of Thumb in Engineering Practice; Wiley-VCH: New York, 2007; p 479. (2) Dittmeyer, R.; Keim, W.; Kreysa, G.; Oberholz, A. Winnacker/ Küchler Chemische Technik: Prozesse und Produkte, Wiley-VCH: Weinheim, 2003, pp 759−815. (3) Wiles, C.; Watts, P. Recent advances in micro reaction technology. Chem. Commun. 2011, 47, 6512−6535. (4) Guettel, R.; Turek, T. Assessment of micro-structured fixed-bed reactors for highly exothermic gas-phase reactions. Chem. Eng. Sci. 2010, 65, 1644−1654. (5) Hari, B.; Goujon, F.; Theodoropoulos, C. Integrated Multi-Scale Models for Microreactor Simulation and Design, AIDIC Conference Series, 2009, 167−176. (6) Hetsroni, G.; Mosyak, A.; Pogrebnyak, E.; Yarin, L. P. MicroChannels: Reality and Myth. J. Fluids Eng. 2011, 133, 121202−121202. (7) Kolb, G. Review: Microstructured reactors for distributed and renewable production of fuels and electrical energy. Chem. Eng. Process. 2013, 65, 1−44. (8) Commenge, J. M.; Falk, L.; Corriou, J. P.; Matlosz, M. Analysis of Microstructured Reactor Characteristics for Process Miniaturization and Intensification. Chem. Eng. Technol. 2005, 28, 446−458. G


Article


(51) Chopard, F. Flow directing insert for a reactor chamber and a reactor. U.S. Patent 7,419,644, November 18, 2002.

(29) Saji, N.; Nagai, S.; Tsuchiya, K.; Asakura, H.; Obata, M. Development of a compact laminar flow heat exchanger with stainless steel micro-tubes. Phys. C 2001, 354, 148−151. (30) Bau, H. H. Optimization of conduits’ shape in micro heat exchangers. Int. J. Heat Mass Transfer 1998, 41, 2717−2723. (31) Muzychka, Y. S. Constructal multi-scale design of compact micro-tube heat sinks and heat exchangers. Int. J. Therm. Sci. 2007, 46, 245−252. (32) Hsueh, C.-Y.; Chu, H.-S.; Yan, W.-M.; Leu, G.-C.; Tsai, J.-I. Three-dimensional analysis of a plate methanol steam micro-reformer and a methanol catalytic combustor with different flow channel designs. Int. J. Hydrogen Energy 2011, 36, 13575−13586. (33) Bejan, A. Designed porous media: maximal heat transfer density at decreasing length scales. Int. J. Heat Mass Transfer 2004, 47, 3073− 3083. (34) Schwolow, S.; Ko, J. Y.; Kockmann, N.; Röder, T. Enhanced heat transfer by exothermic reactions in laminar flow capillary reactors. Chem. Eng. Sci. 2016, 141, 356−362. (35) Mathieu-Potvin, F.; Gosselin, L.; da Silva, A. K. Optimal geometry of catalytic microreactors: Maximal reaction rate density with fixed amount of catalyst and pressure drop. Chem. Eng. Sci. 2012, 73, 249−260. (36) Sreenath, K.; Pushpavanam, S. Issues in the scaling of exothermic reactions: From micro-scale to macro-scale. Chem. Eng. J. 2009, 155, 312−319. (37) Kim, G.-Y.; Mayor, J. R.; Ni, J. Parametric study of microreactor design for water gas shift reactor using an integrated reaction and heat exchange model. Chem. Eng. J. 2005, 110, 1−10. (38) Janicke, M. T.; Kestenbaum, H.; Hagendorf, U.; Schüth, F.; Fichtner, M.; Schubert, K. The Controlled Oxidation of Hydrogen from an Explosive Mixture of Gases Using a Microstructured Reactor/ Heat Exchanger and Pt/Al2O3 Catalyst. J. Catal. 2000, 191, 282−293. (39) Fukuda, T.; Maki, T.; Mae, K. Design of a Plate-Type Catalytic Microreactor with CO2 Permeation Membrane for Water-Gas Shift Reaction. Chem. Eng. Technol. 2012, 35, 1205−1213. (40) Fukuda, T.; Sawada, M.; Maki, T.; Mae, K. Basic Design Concept of a Microreactor for Isothermal Operation Including Heat Conductivity. Chem. Eng. Technol. 2013, 36, 968−974. (41) Holman, J. P. Heat Transfer, 10th ed.; McGraw Hill Higher Education: Boston, 2010; p xxii, 725 p. (42) Chen, J. C. Correlation for boiling heat transfer to saturated fluids in convective flow. Ind. Eng. Chem. Process Des. Dev. 1966, 5, 322−329. (43) Collier, J. G. Convective Boiling and Condensation, 2nd ed.; McGraw-Hill International Book Co.: New York; London, 1981; p xxxii, 435 p. (44) Gungor, K. E.; Winterton, R. H. S. A general correlation for flow boiling in tubes and annuli. Int. J. Heat Mass Transfer 1986, 29, 351− 358. (45) Kandlikar, S. G. General correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. J. Heat Transfer 1990, 112, 219−228. (46) McAdams, W. H. National Research Council (U.S.). Committee on Heat Transmission. Heat Transmission, 3rd ed.; R.E. Krieger Pub. Co.: Malabar, FL, 1985; p xiv, 532 p. (47) Kumar, V.; Nigam, K. D. P. Numerical simulation of steady flow fields in coiled flow inverter. Int. J. Heat Mass Transfer 2005, 48, 4811−4828. (48) Prat, L.; Devatine, A.; Cognet, P.; Cabassud, M.; Gourdon, C.; Elgue, S.; Chopard, F. Performance evaluation of a novel concept ″open plate reactor″ applied to highly exothermic reactions. Chem. Eng. Technol. 2005, 28, 1028−1034. (49) Benaïssa, W.; Gabas, N.; Cabassud, M.; Carson, D.; Elgue, S.; Demissy, M. Evaluation of an intensified continuous heat-exchanger reactor for inherently safer characteristics. J. Loss Prev. Process Ind. 2008, 21, 528−536. (50) Nagaki, A.; Takizawa, E.; Yoshida, J.-i. Generation and Reactions of α-Silyloxiranyllithium in a Microreactor. Chem. Lett. 2009, 38, 486− 487. H


Design of Micro- and Milli-Channel Heat Exchanger Reactors for

Recommend Documents