A generalized approach to heat transfer in pipe flow with internal heat generation

In the last few years, there has been a renewed interest in the molten salt reactor (MSR), one of the “Generation IV International Forum” concepts, which adopts a circulating molten salt mixture as both heat generator (fuel) and coolant. The heat transfer of a fluid with internal heat generation depends on the strength of the source whose influence on the heat exchange process is significant enough to demand consideration. At present, few studies have been performed on the subject from either an experimental or a numerical point of view.This study considers fluids with a wide range of Reynolds numbers, flowing through smooth and straight circular tubes within which the flow is hydrodynamically developed but thermally developing (conditions of interest for MSR core channels). The study aims at an assessment of the heat transfer modelling for a large variety of fluids (with Prandtl numbers in the range 0≤Pr≤10⁴), in particular taking into account the influence of the internal heat generation on the temperature distribution, which plays an important role in the case of molten salts for nuclear reactors. To this purpose, the general and unified solution of the heat transfer equation is applied to the turbulent Graetz problem with boundary conditions of the third kind and arbitrary heat source distribution, incorporating recent formulations for turbulent flow and convection.Computed results are shown to be in a good agreement with experimental data concerning heat transfer evaluations for both fully developed and thermally developing flow conditions, over a large range of Prandtl numbers (10^?2<Pr<10⁴). Finally, a preliminary correlation, which includes the Prandtl number range of interest for molten salts, is proposed for the Nusselt number predictions in the case of simultaneous uniform wall heat flux and internal heat generation.     

Multiphysics phase-field modeling of quasi-static cracking in urania ceramic nuclear fuel

This work presents phase-field modeling of quasi-static cracking in urania (UO₂) ceramic nuclear fuel under neutron radiation at high temperatures. Considering the tightly coupled multi-physics processes within the fuel during reactor power operation, a diffusion model including Fickian and Soret effects is used to describe the oxygen hyper-stoichiometry (x in UO_2+x), and the temperature field is given by a thermal model involving non-uniform fission-generated heat source and heat flow across fuel pellet, pellet-cladding gap and cladding to the outside heat sink. Both temperature and irradiation effects are taken into account for the basic thermo-mechanical properties and irradiation behaviors of the nuclear fuel. Especially, the acceleration of fuel thermal creep by oxygen hyper-stoichiometry is included. The fracture due to the above physical processes is approximated by a scalar phase-field variable based upon a cohesive phase-field fracture method. A granite fracture experiment is simulated to validate the thermo-fracture coupling approach. For the first time, the diffusion-thermo-mechanical-fracture coupling model is applied to UO₂ fuel pellet cracking during reactor startup, power ramp and reactor shutdown. UO₂ creep is found to play an important role on the fuel pellet fragmentation. The developed capability supports interpretation of experimental data and can guide material design of ceramic nuclear fuels.     

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics®

The present paper reports the results obtained applying the general purpose software COMSOL Multiphysics^® to the finite elements simulation of Cyclic Voltammetries (CV’s) at microelectrodes arrays (MEA). CV’s at inlaid micro disk electrode arrays have been simulated benchmarking our results with those obtained by Compton with the finite difference method. Then the influence of meshing on the quality of the simulated data have been investigated showing that bad meshing may provide shapes with no physical meaning. Simulations have also been performed on recessed micro disk arrays in order to show the effect of the depth of the recess on the voltammetric wave shape. We found that COMSOL Multiphysics^® provides a flexible and straightforward route to the simulation of electrochemical systems with complex geometry.     

Computational fluid dynamics study of the synthesis process for a PET radiotracer compound, [11C]raclopride on a microfluidic chip

Recent synthetic applications conducted on microfluidic chips have shown improved yields and shorter reaction times as compared to conventional methods. These have generated great interest in the microfluidic synthesis of radiotracer compounds with short lived radioisotopes, such as carbon-11 (t_1/2 – 20.4 min). For the purpose of microreactor design optimization and to predict synthetic behavior, we launched a study of the radiosynthesis of [¹¹C]raclopride on three different microchip designs by computational fluid dynamics, using COMSOL Multiphysics^®. COMSOL's Reaction Engineering Lab^® tool and convection and diffusion models were used first to investigate the “ideal” reactor and then to study reaction progress in the microchip geometry. Examining the concentration distribution within the microchannel geometry, it was clear that the microchannel length can predict passive mixing and higher product generation than microchannel length. Reducing the flow rate of reagents, premixing the reagents, and increasing reagent concentrations also increased product generation due to increased space times and molecular interactions. For the purpose of simulation, the yield is undesirably reduced by decreasing the diffusion coefficient and the reaction rate constant. This study provides the optimized parameters to redesign the microchip in order to increase the efficiency of micromixing within the microchannels and, therefore, increase the reaction yield.     

Comparison of the performance of a direct-contact bubble reactor and an indirectly heated tubular reactor for solar-aided methane dry reforming employing molten salt

A theoretical approach is presented for the comparison of two different atmospheric pressure reactors—a direct-contact bubble reactor (DCBR) and an indirectly heated tubular reactor (IHTR)—to evaluate the reactor performance in terms of heat transfer and available catalytic active surface area. The model considers the catalytic endothermic reactions of methane dry reforming that proceeds in both reactors by employing molten salts at elevated temperatures (700–900 °C) in the absence of catalyst deactivation effects. The methane conversion process is simulated for a single reactor using both a reaction kinetics model and a heat transfer model. A well-tested reaction kinetics model, which showed an acceptable agreement with the empirical observations, was implemented to describe the methane dry reforming. In DCBR, the heat is internally transferred by direct contact with the three phases of the system: the reactant gas bubbles, the heat carrier molten salts and the solid catalyst (Ni-Al₂O₃). In contrast, the supplied heat in the conventional shell-and-tube heat exchanger of the IHTR is transferred across an intervening wall. The results suggest a combination system of DCBR and IHTR would be a suitable configuration for process intensification associated with higher thermal efficiency and cost reduction.     

Experimental and numerical thermal analysis for direct microwave heating of silicon carbide

A comparison between experiment and numerical simulation of microwave heating of a parallelepipedic silicon carbide (SiC) sample is presented. Using a-2.45 GHz single-mode cavity, the evolution of the surface temperature is first experimentally studied for different orientations of the sample. A finite element analysis of this electromagnetic-thermal coupled problem is then conducted with the COMSOL Multiphysics^® software. Despite the different approximations of our model, a good agreement between experimental and numerical results is found, confirming that the heating of SiC depends only on the electric field. The effect of sample orientations and the cavity length on heating is also highlighted and analyzed.     

A multi-function compact fuel reforming reactor for fuel cell applications

A multi-function compact chemical reactor designed for hydrocarbon steam reforming was evaluated. The reactor design is based on diffusion bonded laminate micro-channel heat exchanger technology. The reactor consists of a combustor layer, which is sandwiched between two steam reforming layers. Between the two function layers, a temperature monitor and control layer is placed, which is designed to locate the temperature sensors. The combustor layer has four individually controlled combustion zones each connected to a separate fuel supply. The reactor design offers the potential to accurately control the temperature distribution along the length of the reactor using closed loop temperature control. The experimental results show that the variance of temperature along the reactor is negligible. The conversion efficiency of the combustor layer is approximately 90%. The heat transfer efficiency from combustion layer to reforming layers is 65-85% at 873 K and 673 K, respectively. The heat transfer rate to the reforming layers is sufficient to support a steam reformation of propane at a rate of 0.7 dm³/min (STP) with a steam to carbon ratio of 2 at 873 K.     

Thermal conductivities from temperature profiles in the polymer electrolyte fuel cell

We report measured temperatures inside the single polymer fuel cell, and thermal conductivities and heat transfer coefficients calculated from these. Temperatures were measured next to the membrane on its two sides, and in the gas channels. Higher temperatures (5 °C or more at 1 A/cm²) were found at the membrane electrode surface than in the gas channels. The thermal conductivity of the membrane (λ^m) was small, as expected from the properties of water and polymer, while the heat transfer coefficient of the electrode surfaces (λ^s) was smaller, 1000±300 W/m² K for a layer thickness of 10 μm. The real coefficient is smaller, since the measured temperatures are systematically smaller than the real ones. The electrode surface heat transfer coefficient is not previously reported. The average value for the catalyst surface plus gas diffusion layer was 0.2 W/m K.     

Bed-to-wall heat transfer in a downer reactor

The effects of superficial gas velocity (0.5 to 4.5 m/s), solid circulating rate (0 to 40 kg/m²·s), suspension density (0 to 19 kg/m³) and particle sizes (83, 103, 163, 236 μm) on the bed-to-wall heat transfer coefficient have been determined in a downer reactor (0.1 m I. D. × 3.5 m high). Bed-to-wall heat transfer coefficient increases with increasing suspension density. The heat transfer coefficient by gas convection played a significant role, especially at lower solid circulation rates or suspension densities and larger particle sizes. At a given particle suspension density in the downer reactor, the heat transfer coefficient increases with decreasing particle size. A model is proposed to predict the bed-to-wall heat transfer coefficient in a downer reactor.     

CFD modelling of liquid–liquid multiphase microstructured reactor: Slug flow generation

Microreactor technology, an important method of process intensification, offers numerous potential benefits for the process industries. Fluid–fluid reactions with mass transfer limitations have already been advantageously carried out in small-scale geometries. In liquid–liquid microstructured reactors (MSR), alternating uniform slugs of the two-phase reaction mixture exhibit well-defined interfacial mass transfer areas and flow patterns. The improved control of highly exothermic and hazardous reactions is also of technical relevance for large-scale production reactors. Two basic mass transfer mechanisms arise: convection within the individual liquid slugs and diffusion between adjacent slugs. The slug size in liquid–liquid MSR defines the interfacial area available for mass transfer and thus the performance of the reactor. There are two possibilities in a slug flow MSR depending on the interaction of the liquids with the solid wall material: a dispersed phase flow in the form of an enclosed slug in the continuous phase (with film—complete wetting of the continuous phase) and an alternate flow of two liquids (without film—partial wetting of the continuous phase). In the present work, a computational fluid dynamics (CFD) methodology is developed to simulate the slug flow in the MSR for both types of flow systems. The results were validated with the experimental results of Tice et al. (J.D. Tice, A.D. Lyon and R.F. Ismagilov, Effects of viscosity on droplet formation and mixing in microfluidic channels, Analytica Chimica Acta507 (1) (2004), pp. 73–77.).     

Corrosion product transport in water-cooled nuclear reactors. Part III: Boiling water with indirect cycle operation

Corrosion products from out-core surfaces are made radioactive when deposited in the core of a water-cooled nuclear power reactor. Their release and deposition on out-core surfaces causes gamma radiation fields to grow with time around these surfaces. Deposition and release of corrosion products in the reactor core is strongly influenced by the mode of heat transfer and by the water chemistry. Here, the deposition of corrosion products from boiling water onto nuclear fuel sheaths was studied in a water loop and in the CANDU Nuclear Power Demonstration (NPD) reactor as a function of possible water chemistries for indirect cycle operation. Deposits on sheaths in the boiling water region of test sections were very heavy (35 g Fe/m²) when ammonium hydroxide at 10 to 20 mg NH₃/kg controlled the pH, or when the pH was controlled with 0.02 mg Li/kg added as LiOD. Deposits were light (∽ 50 mg Fe/m²) if the pH was controlled with at least 1 mg Li/kg. A mathematical model for deposition and release of corrosion products at fuel sheaths in non-boiling water was modified and found to apply also in boiling water for the high pH test.     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

Hydrogen generation in a Pd membrane fuel processor: assessment of methanol-based reaction systems

The feasibility of a Pd membrane fuel processor that integrates several methanol-based chemistries and hydrogen purification steps is assessed. The assessment involves membrane reactor simulations to determine the effects of operating and design parameters on performance metrics including hydrogen utilization, hydrogen productivity, device volume, and Pd requirements. Methanol decomposition (direct and oxidative) on Pd/SiO₂, methanol steam reforming (MSR) on Cu/ZnO/Al₂O₃, and methanol partial oxidation (MPOX) on Cu/Al₂O₃ are evaluated. The membrane reactor model includes detailed treatments of the catalytic kinetics from the literature, accounts for reaction on the Pd membrane and hydrogen permeation inhibition by site blockage, among other features. The simulations reveal that a maximum in the hydrogen productivity occurs at an intermediate value of the space velocity, implying a trade-off between reactor size, methanol conversion and hydrogen utilization. The assessment involves a determination of the Pd membrane surface to reactor volume ratio that maximizes productivity and the requisite Pd to realize that productivity. We show that MSR on Cu/ZnO and MPOX on Cu are promising reaction systems to practice the membrane concept for fuel processing, whereas direct methanol decomposition is reaction limited, making it infeasible. Several approaches for improving membrane fuel processor performance are evaluated and discussed. We show that oxygen addition can increase the hydrogen productivity in the Pd system, while water addition is beneficial for the MPOX system. The extent of enhancement in both cases depends on supply rate and kinetic factors.     

催化剂颗粒形状对甲烷水蒸气重整反应的影响及工业反应器模拟

甲烷水蒸气重整工艺是现阶段最主要的工业制氢技术,催化剂颗粒形状和反应器操作条件是影响重整反应器性能和产物组成的重要因素。首先从颗粒尺度研究催化剂形状对甲烷水蒸气重整反应的影响,在不同的反应温度和压力下,计算并比较了球形、柱形和环形催化剂的效率因子,其大小顺序为:柱形 < 球形 < 环形。其次,将反应器床层的质量、热量和动量传递与环形催化剂颗粒的扩散-反应方程相结合,建立了用于描述甲烷水蒸气重整工业反应器的一维轴向数学模型。计算并分析了反应器进口温度和压力对反应器床层的温度和压力分布、催化剂效率因子以及甲烷转化率和各组分浓度分布的影响,确定了适宜的工业反应器进口温度和压力,分别为773 K和3 MPa。     

Characterization of the performances of an innovative heat-exchanger/reactor

The use of heat exchanger/reactors (HEX/reactors) is a promising way to overcome the barrier of poor heat transfer in batch reactors. However to reach residence time long enough to complete the chemistry, low Reynolds number has to be combined with both a plug flow behaviour and the intensification of heat and mass transfers. This work concerns the experimental approach used to characterize an innovative HEX/reactor. The pilot is made of three process plates sandwiched between five utility plates. The process stream flows in a 2 mm corrugated channel. Pressure drop and residence time distribution characterizations aim at studying the flow hydrodynamics. Identified Darcy correlations point out the transition between laminar and turbulent flow around a Reynolds number equal to 200. Moreover the flow behaves like a quasi-plug flow (Pe > 185). The heat transfer and mixing time have also been investigated. The ratio between the reaction kinetics and the mixing time is over 100 and the intensification factor ranges from 5000 to 8000 kW m⁻³ K⁻¹. As a consequence, no limitations were identified which allows the implementation of an exothermic reaction. It has been successfully performed under severe temperature and concentration conditions, batchwise unreachable. Thus, it highlights the interest of using this continuous HEX/reactor.     

Electricity Generation and Wastewater Treatment of Oil Refinery in Microbial Fuel Cells Using Pseudomonas putida

Microbial fuel cells (MFCs) represent a novel platform for treating wastewater and at the same time generating electricity. Using Pseudomonas putida (BCRC 1059), a wild-type bacterium, we demonstrated that the refinery wastewater could be treated and also generate electric current in an air-cathode chamber over four-batch cycles for 63 cumulative days. Our study indicated that the oil refinery wastewater containing 2213 mg/L (ppm) chemical oxygen demand (COD) could be used as a substrate for electricity generation in the reactor of the MFC. A maximum voltage of 355 mV was obtained with the highest power density of 0.005 mW/cm² in the third cycle with a maximum current density of 0.015 mA/cm² in regard to the external resistor of 1000 Ω. A maximum coulombic efficiency of 6 × 10⁻²% was obtained in the fourth cycle. The removal efficiency of the COD reached 30% as a function of time. Electron transfer mechanism was studied using cyclic voltammetry, which indicated the presence of a soluble electron shuttle in the reactor. Our study demonstrated that oil refinery wastewater could be used as a substrate for electricity generation.     

Chemical Recycling of Polyolefins with the Molten Metal Reactor at 460 °C

This paper describes the pyrolysis of high-density polyethylene (HDPE) in a molten metal reactor, where the HDPE is initially in direct contact with molten metal at 460 °C. Due to the equal temperature across the molten metal, secondary reactions are minimised, and long-chain waxes with boiling points over 600 °C accumulate on the molten metal. Once enough wax has accumulated, further HDPE pyrolysis occurs within the wax in a direct heat transfer reaction.     

Intensification principle of a new three-phase catalytic slurry reactor. Part I: Performance characterisation

This paper presents the concept and the performances of a mini horizontal stirred tank reactor, used for hydrogenation reaction. A simple analytical model based on characteristic times of heat and mass transfer illustrates the intensification principle and shows that the relevant intensification parameter is the mass to heat transfer characteristics times ratio. The proof of concept is made through a small scale reactor named RAPTOR^® (French acronym for Reactor with Polyvalent Rectilinear Stirred Reactor with Optimised Transfer). The mass transfer performances are measured and compared to conventional stirred tank reactor and other multiple impeller continuous reactors. In a following second paper, a comparative study is proposed to evaluate the eco-efficiency and the techno-economic advantages of a continuous process involving a RAPTOR^® versus a classical batch process based on a stirred reactor.     

What is the leanest stream to sustain a nonadiabatic loop reactor: Analysis and methane combustion experiments

While previous studies experimentally demonstrated that loop reactor (LR) can be sustained with a lean feed (using ethylene combustion) and have analyzed the single‐reaction adiabatic case, this work analyzes the effects of heat loss and of reactor size to determine the leanest stream (expressed in terms of adiabatic temperature rise ΔT_lim) that will sustain the operation. For an adiabatic infinitely long reactor ΔT_lim→0 while for a finite reactor ΔT_lim scales as (1 + Pe/4)^?1 where Pe = Luρc_pf/k, and heat loss increases this limit by (β/Pe)^1/2. Thus, a good design of a LR will aim to decrease conductivity (k) and radial heat‐transfer coefficient (β) while increasing throughput (u) and reactor length. This article is also the first experimental demonstration of auto‐thermal operation in a LR for catalytic abatement of low‐concentration of methane, showing the leanest stream to be of 8000 ppm vs. 33,000 ppm in a once‐through reactor. Experimental combustion results of methane and of ethylene are compared with model predictions. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2030–2042, 2017