Endothermic and exothermic chemically reacting plumes

2008 ◽  
Vol 612 ◽  
pp. 291-310 ◽  
Author(s):  
DEVIN T. CONROY ◽  
STEFAN G. LLEWELLYN SMITH
Keyword(s):  
Reaction Rate ◽  
Exothermic Reaction ◽  
Entrainment Rate ◽  
Heat Of Reaction ◽  
Exothermic Reactions ◽  
Plume Dynamics ◽  
Turbulent Plume ◽  
Chemically Reacting ◽  
Rise Height ◽  
Maximum Rise

We develop a model for a turbulent plume in an unbounded ambient that takes into account a general exothermic or endothermic chemical reaction. These reactions can have an important effect on the plume dynamics since the entrainment rate, which scales with the vertical velocity, will be a function of the heat release or absorption. Specifically, we examine a second-order non-reversible reaction, where one species is present in the plume from a pure source and the other is in the environment. For uniform ambient density and species fields the reaction has an important effect on the deviation from pure plume behaviour as defined by the source parameter Γ. In the case of an exothermic reaction the density difference between the plume and the reference density increases and the plume is ‘lazy’, whereas for an endothermic reaction this difference decreases and the plume is more jet-like. Furthermore, for chemical and density-stratified environments, the reaction will have an important effect on the buoyancy flux because the entrainment rate will not necessarily decrease with distance from the source, as in traditional models. As a result, the maximum rise height of the plume for exothermic reactions may actually decrease with reaction rate if this occurs in a region of high ambient density. In addition, we investigate non-Boussinesq effects, which are important when the heat of reaction is large enough.

Reactive Multilayer Foils for Silicon Wafer Bonding

2006 ◽  
Vol 968 ◽  
Author(s):  
Xiaotun Qiu ◽  
Jiaping Wang
Keyword(s):  
Wafer Bonding ◽  
Heat Exposure ◽  
Exothermic Reaction ◽  
Local Heat ◽  
Heat Of Reaction ◽  
Heat Sources ◽  
Exothermic Reactions ◽  
Multilayer Foils ◽  
Leakage Test ◽  
Localized Heating

ABSTRACTIn this study silicon wafers were bonded using Al/Ni reactive multilayer foils as local heat sources for melting solder layers. Exothermic reactions in Al/Ni reactive multilayer foils were investigated by XRD and DSC. XRD measurements showed that dominant product after exothermic reaction was ordered B2 AlNi compound. The heat of reaction was calculated to be -57.9 KJ/mol by DSC. With Al/Ni reactive multilayer foil, localized heating can be achieved during bonding process. Both experimental measurements and numerical simulation showed that the heat exposure to the wafers was highly limited and localized. Moreover, leakage test showed that this bonding approach possessed a good hermeticity.

Temperature profiles in endothermic and exothermic reactions and the interpretation of experimental rate data

1970 ◽  
Vol 320 (1540) ◽  
pp. 71-100 ◽  
Keyword(s):  
Steady State ◽  
Correction Factor ◽  
Exothermic Reaction ◽  
Kinetic Studies ◽  
Activation Energies ◽  
Uniform Temperature ◽  
Exothermic Reactions ◽  
Arrhenius Function ◽  
Point To Point ◽  
Reacting Systems

Any endothermic or exothermic reaction is accompanied by self-cooling or self-heating. In reacting systems in which heat transfer is controlled by conduction, non-uniform temperature-position profiles are established. Examples of this situation are the exothermic decomposition of gaseous diethyl peroxide and the endothermic decomposition of nitrosyl chloride at low pressures (when convection is unimportant). In kinetic studies, allowance must be made for the non-uniform temperature to derive accurate isothermal velocity constants and Arrhenius parameters. In the present paper, the necessary corrections have been derived for a reactant in the steady state whose reaction rate varies exponentially with temperature and in which the temperature excess varies from point to point, being zero at the boundary (Frank-Kamenetskii’s conditions). The geometries considered are the slab, cylinder and sphere. The temperature gradient at the surface in the steady state ( Г ) occupies a key position, and this is exploited to find the correction factor required to convert 'observed’ rate constants to isothermal conditions, and thence to correct ‘observed’ activation energies and pre-exponential factors. The correction factor is found to be simply related to Frank- Kamenetskii’s δ (a dimensionless measure of heat-release rate). A similar analysis is given for systems hotter or cooler than their surroundings but uniform in temperature—such as well stirred fluid systems or small solid crystals (Semenov’s conditions). In these circumstances, systems of arbitrary geometry may be studied, and no approximation need be made to the Arrhenius function. For either type of boundary condition, uncorrected activation energies are overestimates in exothermic reactions and underestimates in endothermic reactions. Explicit relations are derived for making corrections. Boundary conditions intermediate between the two extremes investigated can also be treated though the resulting expressions are more cumbersome. In an appendix, an alternative ‘experimental’ approach is made to the elimination of errors from measured reaction velocities. This approach identifies the measured velocities with a temperature intermediate between those at centre and surface. The optimum choice, which weights the central and surface temperatures in the ratios 2:1 (slab), 1:1 (cylinder) and 2:3 (sphere), gives exactly correct results for the cylinder and acceptable precision for the slab and sphere even to within 5 K of the explosion limit. Other correction methods are also discussed.

Performance Prediction of High-Temperature CO2 Capture System Utilizing Lithium Silicate for Pulverized Coal-Fired Power Plant

2005 ◽  
Author(s):  
Takao Nakgaki ◽  
Katsuya Yamashita ◽  
Masahiro Kato ◽  
Kenji Essaki ◽  
Takayuki Iwahashi ◽  
...  
Keyword(s):  
Power Plant ◽  
Co2 Capture ◽  
Flue Gas ◽  
Reaction Rate ◽  
Exothermic Reaction ◽  
Significant Loss ◽  
Pulverized Coal ◽  
Lithium Silicate ◽  
Reactor Performance ◽  
Co2 Sorbent

Lithium silicate is a solid CO2-sorbent that can be used repeatedly, and uniquely features absorption of CO2 at temperatures between 500°C and 600°C with an exothermic reaction and regeneration at temperatures above 700°C with an endothermic reaction. This paper introduces the conceptual model and feasibility study of the CO2 capture system utilizing the lithium silicate applicable to a pulverized coal-fired power plant. In this system, assuming a moving bed, the sorbent reactor is installed in a 500MW boiler and absorbs CO2 in the flue gas, and after the absorption process, recirculation of CO2 transports the heat for regeneration. To design the system, unsteady state numerical analysis was used to predict the reactor performance in a 60-minute cycle for absorption and regeneration, which includes the reaction rate based on experimental data. The analysis result indicates that about 20% of CO2 can be captured from flue gas without significant loss in the power generation efficiency.

Effect of Heat of Reaction on Temperature Distribution and Acid Penetration in a Fracture

1980 ◽  
Vol 20 (06) ◽  
pp. 501-507 ◽  
Author(s):  
M.H. Lee ◽  
L.D. Roberts
Keyword(s):  
Temperature Distribution ◽  
Thermal Energy ◽  
Balance Equation ◽  
Reaction Rate ◽  
Energy Equation ◽  
Fluid Temperature ◽  
Heat Of Reaction ◽  
Mass Balance Equation ◽  
Acid Rock ◽  
First Time

Abstract In a fracture acidizing treatment the acid reacts with the fracture faces. This acid/rock reaction generates heat that causes the acid temperature itself to increase. To predict accurately the temperature profile and acid spending rate of acid traveling down a hydraulically created fracture, this heat must be considered.Since the heat generated by reaction depends on the reaction rate, the thermal energy equation must be coupled with the acid spending equation. A model has been developed that, for the first time, examines the effect of the heat of reaction on fluid temperature and acid penetration in a fracture. Some sample calculations have also been made to illustrate the effects of the most important parameters on acid penetration in a fracture. Introduction Acid hydraulic fracturing is a common method of stimulating a reservoir. Acid selectively reacts with, and dissolves, portions of the fracture wall so that a finite fluid conductivity remains when the well is returned to production. An important aim in designing such fracturing treatments is determining the distance that live acid will penetrate down the hydraulically induced fracture. This distance is usually called the acid penetration distance and is essential to estimate the production improvement from a given treatment.Because of its importance in predicting stimulation ratio, acid penetration in fractures has been studied by numerous investigators. They assumed the temperature in the fracture was uniform. In real fractures, however, the temperature will vary from the wellbore to the tip of the fracture. Therefore, the assumption of constant temperature seems to be an oversimplification.Whitsitt and Dysart were among the first to study the temperature distribution in a fracture. They constructed a model but it could be applied only to a nonreacting fluid flowing in a fracture because the heat generated by an acid/rock reaction was not considered. In a fracture acidizing treatment, the acid is reacting with the rock walls. This acid/rock reaction generates heat, which causes the acid temperature itself to increase. To predict accurately the temperature profile along the fracture, this heat also must be considered. A model has been developed that, for the first time, examines the effect of the heat of reaction on fluid temperature and acid penetration distance. Mathematical Development The mathematical model is a modification of that introduced by Whitsitt and Dysart to allow for the heat of reaction in the energy-balance equation. Since the heat generated by the acid reaction also depends on the reaction rate, the thermal-energy equation is coupled with the mass-balance equation. These two equations must be solved simultaneously .The model for acid spending in a fractures is illustrated in Fig. 1. The fluid leakoff velocity Vw is assumed constant over the fracture length. Assuming steady-state flow in a vertical fracture and constant fluid properties, the mass-balance equation for acid flowing in a fracture is ................(1) SPEJ P. 501＾

The contribution of turbulent plume dynamics to long-range spotting

2017 ◽  
Vol 26 (4) ◽  
pp. 317 ◽  
Author(s):  
William Thurston ◽  
Jeffrey D. Kepert ◽  
Kevin J. Tory ◽  
Robert J. B. Fawcett
Keyword(s):  
Transport Model ◽  
Fire Spread ◽  
Substantial Impact ◽  
Landing Position ◽  
Plume Dynamics ◽  
Large Eddy ◽  
Rapid Spread ◽  
Fire Front ◽  
Turbulent Plume ◽  
Physical Realism

Spotting can start fires up to tens of kilometres ahead of the primary fire front, causing rapid spread and placing immense pressure on suppression resources. Here, we investigate the dynamics of the buoyant plume generated by the fire and its ability to transport firebrands. We couple large-eddy simulations of bushfire plumes with a firebrand transport model to assess the effects of turbulent plume dynamics on firebrand trajectories. We show that plume dynamics have a marked effect on the maximum spotting distance and determine the amount of lateral and longitudinal spread in firebrand landing position. In-plume turbulence causes much of this spread and can increase the maximum spotting distance by a factor of more than 2 over that in a plume without turbulence in our experiments. The substantial impact of plume dynamics on the spotting process implies that fire spread models should include parametrisations of turbulent plume dynamics to improve their accuracy and physical realism.

Studies of the Hard Rubber Reaction. I. Heat of Reaction

1963 ◽  
Vol 36 (4) ◽  
pp. 1059-1070 ◽  
Author(s):  
M. L. Bhaumik ◽  
D. Banerjee ◽  
Anil K. Sircar
Keyword(s):  
Thermal Analysis ◽  
Hydrogen Sulfide ◽  
Differential Thermal Analysis ◽  
Exothermic Reaction ◽  
Heat Evolution ◽  
Linear Increase ◽  
Heat Of Reaction ◽  
Dehydrogenation Reaction ◽  
Rate Of Reaction

Abstract A method for the determination of the heat of the hard-rubber reaction by the application of differential thermal analysis is reported. The heat of reaction was determined with stocks containing different rubber/sulfur ratios and also with a 68/32 stock, preheated to contain different amounts of combined sulfur. Heat evolution is observed first with samples containing about 7 per cent sulfur and therefrom the amount of heat evolved shows a nearly linear increase up to 30 per cent sulfur. With increasing combined sulfur in the 68/32 stock, the quantity of exothermic heat gradually diminishes; so also does the temperature of initiation, i.e., the temperature at which heat evolution appears to begin. Initiation of the exothermic reaction appears to be a function of composition and temperature of the mass. An increase in the rate of reaction was observed when the composition reached 0.5 g-atom of sulfur per isoprene unit. An endothermic dehydrogenation reaction is observed at the end of the hard-rubber reaction. This, however, does not affect the determination of exothermic heat, because there is similar dehydrogenation taking place in the reference material (ebonite) which almost balances this heat loss. The final product has a lower sulfur content due to loss of sulfur as hydrogen sulfide.

Self-Blowing Process of Al Foam Assisted by Exothermic Reaction

2006 ◽  
Vol 519-521 ◽  
pp. 1335-1340 ◽  
Author(s):  
Makoto Kobashi ◽  
Naoyuki Kanetake
Keyword(s):  
Aluminum Foam ◽  
Liquid Aluminum ◽  
Exothermic Reaction ◽  
External Source ◽  
Processing Parameters ◽  
Hydrogen Gas ◽  
Heat Of Reaction ◽  
Aluminum Foams ◽  
Gas Generation ◽  
Reactive Powder

Aluminum foam is a class of porous materials; in which closed pores are produced by a gas generation in liquid (or semi-liquid) aluminum. Aluminum foams are, generally, fabricated by heating a foamable precursor (a powder compact consisting of aluminum and TiH2 powders). Decomposition of TiH2, which is followed by a hydrogen gas release, produces bubbles in molten aluminum. In this research, aluminum foam was fabricated with the help of a chemical exothermic reaction. Titanium and boron carbide (B4C) powders were blended in the Al-TiH2 precursor as reactive powder elements. When one end of the precursor was heated, a strong exothermic reaction between titanium and B4C took place (3Ti + B4C 􀃆 2TiB2 +TiC + 761KJ), and the neighboring part of the precursor was heated by the heat of reaction. Hence, once the reaction happens at the end of the precursor, it propagates spontaneously throughout the precursor. The blowing process takes place at the same time as the reaction because aluminum melts and TiH2 decomposes by the heat of reaction. The advantage of this process is that the energy to make aluminum foam is not necessarily supplied form the external source, but generated form inside of the precursor. Therefore the blowing process is self sustainable (Self-Blowing Process). In this work, the effect of processing parameters on the Self-Blowing Process was observed. The processing parameters we focused on were blending ratio of the starting powders (aluminum, TiH2, titanium, B4C) and heating methods.

Homotopy Continuation Method to Evaluate Catalytic Rates for Highly Exothermic Reaction Systems

2018 ◽  
Vol 16 (4) ◽  
Author(s):  
Fernando Tiscareño-Lechuga
Keyword(s):  
Nonlinear Differential Equations ◽  
Continuation Method ◽  
Exothermic Reaction ◽  
Equation System ◽  
Reaction Rates ◽  
Homotopy Continuation ◽  
Algebraic Equations ◽  
Shooting Methods ◽  
Exothermic Reactions ◽  
Homotopy Continuation Method

AbstractCalculation of simultaneous catalytic reaction rates represents a system of nonlinear differential equations with two boundaries; additionally, nonlinear algebraic equations are added if external mass and energy resistances are significant. For highly exothermic reactions and some reaction networks, numerical solution with typical shooting methods encounters difficulties to find good initial guesses since the equation system becomes very rigid. A Numerical Homotopy Continuation approach is proposed in which the particle size is progressively increased until the specified dimensions; shooting variables corresponding at the center of the particle are used as nearby solutions which allows to trace and update the initial guesses.

scholarly journals Optimal Homotopy Asymptotic Solution for Exothermic Reactions Model with Constant Heat Source in a Porous Medium

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Exothermic Reaction ◽  
Energy Balance Equation ◽  
Force Model ◽  
Constant Heat ◽  
Exothermic Reactions ◽  
Conduction State ◽  
Heat Transfer Simulation ◽  
Optimal Homotopy Asymptotic Method

The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM) is used to compute the solutions of the exothermic reactions equation.

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