Adiabatic-reaction

A reaction that occurs on a single potential energy surface within the Born-Oppenheimer approximation. 

An adiabatic constraint An AR will be constructed when an adiabatic energy balance is introduced. The implications of how this constraint impacts AR construction will provide for an interesting discussion. Temperature will be an important consideration in this instance, and hence it is important to understand how temperature may be accommodated in AR constructions. 

A reactor type constraint In this scenario, the construction of the AR is carried out by using PFRs alone. This approach is similar to that discussed in Chapters 2 and 3. This is done because situations might arise when only access or knowledge to a specific reactor type is available. We will be interested in how this constraint impacts construction of the AR, and ultimately how this influences what states are achieved. 

Constraints such as these are significant because many practical problems in reality might arise that manifest themselves as a combination of these two types. For example, in ammonia synthesis, a series of adiabatic reactors with intermediate cooling between stages is employed to increase the overall conversion of reactants past what would be achieved in a single adiabatic reactor (Denbigh and Turner, 1984 Howard, 1977). Thus, despite what is known about the true AR and its optimal structures, practical considerations may restrict us from implementing these recommendations, and alternate ways of advancement must be found. 

2 Problem Statement In Chapter 5, a system involving multiple CSTR steady states is shown (the isola example). Multiple steady states often arise in isothermal constructions when the kinetics is nonlinear. Nonlinearity is also often introduced in nonisothermal systems (i.e., in adiabatic systems, for example), and thus multiple steady states appear in these systems as well this is true even with simple kinetics. Consider an adiabatic reaction of the following form (Hildebrandt et al. 1990)  

Two independent reactions are present, and thus the AR must reside in IR. We aim to compute the AR for this system in concentration space. This will allow for the determination of all feasible concentrations for components A and B (component C can then be found by mass balance). Before we proceed, we can simplify the notation of the system slightly by combining certain terms in the rate expression. The ratio of r and rg is given by 

The thermal potential is at its maximum at the beginning of the reaction, when conversion has not yet occurred and it decreases as the reactants convert. Thus, the MTSR is given by 

Hence the knowledge of the adiabatic temperature rise is sufficient to calculate the MTSR. The data required for the safety assessment are the maximum heat release rate of the reaction at the desired temperature (q ) and the reaction energy (Qpt). The first datum is needed to calculate the required cooling capacity of the industrial reactor. The second calculates the adiabatic temperature rise necessary to assess the behavior of the reactor in case of cooling failure. The calorimetric techniques used for batch reactors are presented in Section 6.9.1. 

A reaction is performed under adiabatic conditions, if there is no heat exchange with the surroundings, that is, no cooling. This means that the heat of reaction is converted into a temperature variation for exothermal reactions into a temperature increase  

The final temperature can be calculated from the initial temperature T0, from the specific enthalpy of reaction, and from the specific heat capacity or from the adiabatic temperature rise  

Besides these purely static aspects, the dynamic behavior of an adiabatic batch reactor must also be considered. The adiabatic temperature course is a function of the thermal properties of the reaction mixture. The adiabatic temperature increase influences the final temperature as well as the rate of the temperature increase. For highly exothermal reactions, even for small increase in conversion, the increase in temperature is important (see Section 2.4.3). 

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Fehrensen B, Luckhaus D and Quack M 1999 Inversion tunneling in aniline from high resolution infrared spectroscopy and an adiabatic reaction path Hamiltonian approach Z. Phys. Chem., NF 209 1-19... 

Because this reaction is highly exothermic, the equiUbrium flame temperature for the adiabatic reaction with stoichiometric proportions of hydrogen and chlorine can reach temperatures up to 2490°C where the equiUbrium mixture contains 4.2% free chlorine by volume. This free hydrogen and chlorine is completely converted by rapidly cooling the reaction mixture to 200°C. Thus, by properly controlling the feed gas mixture, a burner gas containing over 99% HCl can be produced. The gas formed in the combustion chamber then flows through an absorber/cooler to produce 30—32% acid. The HCl produced by this process is known as burner acid. 

Adiabatic Reactions Aside from the Thiele modulus, two other parameters are necessary in this case ... 

Polymerization processes are characterized by extremes. Industrial products are mixtures with molecular weights of lO" to 10. In a particular polymerization of styrene the viscosity increased by a fac tor of lO " as conversion went from 0 to 60 percent. The adiabatic reaction temperature for complete polymerization of ethylene is 1,800 K (3,240 R). Heat transfer coefficients in stirred tanks with high viscosities can be as low as 25 W/(m °C) (16.2 Btu/[h fH °F]). Reaction times for butadiene-styrene rubbers are 8 to 12 h polyethylene molecules continue to grow lor 30 min whereas ethyl acrylate in 20% emulsion reacts in less than 1 min, so monomer must be added gradually to keep the temperature within hmits. Initiators of the chain reactions have concentration of 10" g mol/L so they are highly sensitive to poisons and impurities. 

Computed Adiabatic Reaction Temperature (CART) at constant pressure and/or volume... 

Comparison of (1.14), (2.47a) and (2.60a) reveals the universality of the golden rule in the description of both the nonadiabatic and adiabatic chemical reactions. However, the matrix elements entering into the golden-rule formula have quite a different nature. In the case of an adiabatic reaction it comes from tunneling along the reaction coordinate, while for a nonadiabatic... 

Adiabatic reactions, occurring on a single-sheet PES correspond to B = 1, and the adiabatic barrier height occurs instead of E. The low-temperature limit of a nonadiabatic-reaction rate constant equals... 

Consider a first order adiabatic reaction in a CFSTR with the following characteristics ... 

If no heat is nltimately lost to the snrronndings, all of the energy released by a flame raises the temperatnre of the reaction prodncts, and the final temperatnre is called the adiabatic flame temperatnre. The adiabatic flame temperatnre can be calcnlated with the assnmption that the reaction prodncts achieve chemical eqnilibrinm at the calcnlated temperatnre, which is sometimes denoted as CART (calcnlated adiabatic reaction temperatnre). There are two general cases. 

Adiabatic reaction rate constant [(L/mol)" s] Isothemal reaction rate constant [(L/ mol)"" s]... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

Figure 2-82. Schematic representation to calculate the adiabatic reaction temperature (T ).

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

FIGURE 3.2 Annular packed-bed reactor used for adiabatic reactions favored by low pressure. 

Correlations for E are not widely available. The more accurate model given in Section 9.1 is preferred for nonisothermal reactions in packed-beds. However, as discussed previously, this model degenerates to piston flow for an adiabatic reaction. The nonisothermal axial dispersion model is a conservative design methodology available for adiabatic reactions in packed beds and for nonisothermal reactions in turbulent pipeline flows. The fact that E >D provides some basis for estimating E. Recognize that the axial dispersion model is a correction to what would otherwise be treated as piston flow. Thus, even setting E=D should improve the accuracy of the predictions. 

The other entries in Table 13.2 show that heat removal is not a problem for most ring-opening and condensation polymerizations. Polycaprolactam (also called Nylon 6) is an addition polymer, but with rather similar bond energies for the monomer and the polymer. The reaction exotherm is small enough that large parts are made by essentially adiabatic reaction in a mold. An equilibrium between monomer and polymer does exist for polycaprolactam, but it occurs at commercially acceptable molecular weights. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

Simulations also provided values of the maxiinum catalyst temperature in case of very rich H2-content in the fuel, they locally exceed the adiabatic reaction... 

An important physical quantity determining the transition probability for the adiabatic reactions is the preexponential frequency [see eq. (34.21) with replaced by 1]. This quantity can be calculated using the relationship... 

We have established an important principle in electron transfer theory that is not present in conventional one-dimensional models. The reaction coordinate is always localizing and corresponds to coordinate Aj. The coordinate X2 corresponds to the direction in which the matrix element between ground and excited states is switched on. If this coordinate has zero length then the branching space becomes one dimensional and an adiabatic reaction path does not exist. We now consider two examples. 

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