Adiabatic Reactor Temperature

Flow-reactor problems are just as simple as batch-reactor problems. In fact, they are the same mathematical problem even though the reactor configuration and operation are totally different. 

A chemical reaction cannot be made to produce a conversion beyond that of chemical equihbriurti, AG — 0, where r = 0, as we discussed previously. This is an apphcation of the Second-Law of Thermodynamics. 

Chemical reactors can liberate or absorb very large amounts of ener, and the handling of this energy is a major concern in reaction engineering. This topic is an application of the First Law of Thermodynamics, which says that mechanical and thermal ener is conserved in ary process. When we describe a chemical reaction, we designate its rate, but we should also be very concerned about the heat of the reaction so we need to specify A and AG for every reaction. 

These are aU industrially important reactions that we will discuss throughout this book in the text and in homework problems. The student might want to try to identify the type of reaction represented by each equation and why it is important. 

These values of A Hr are standard state enthalpies of reaction (aU gases in ideal-gas states) evaluated at 1 atm and 298 K. 7VU values of A are in kilojoules per mole of the first species in the equation. When A Hr is negative, the reaction hberates heat, and we say it is exothermic, while, when A Hr is positive, the reaction absorbs heat, and we say it is endothermic. Tks Table 2-2 indicates, some reactions such as isomerizations do not absorb or liberate much heat, while dehydrogenation reactions are fairly endothermic and oxidation reactions are fairly exothermic. Note, for example, that combustion or total oxidation of ethane is highly exothermic, while partial oxidation of methane to synthesis gas (CO + H2) or ethylene (C2H4) are only slightly exothermic. 

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Results for the two reactors are given in Figure 5.27. In the adiabatic reactor, temperature increases down the reactor as chlorine is consumed and products are formed. In the constant-coolant temperature reactor, temperature reaches a maximum of 411 K at about 0.6 m from the inlet. Note that very little allyl chloride is formed in the cooled reactor because the temperatures are low. In the adiabatic reactor, the high temperatures increase the allyl chloride reaction rates because of the higher activation energy. 

Be able to use the energy balance for a general black-box chemical reactor and compute the adiabatic reactor temperature (Sec. 14.3)... 

The most common approach to maintaining the desired reaction temperature is to operate with a significant excess of phenol in the reactor. An adiabatic reactor fed with 2 moles of phenol and 1 mole of isobutylene at 40°C would reach about 180°C if all the isobutylene formed PTBP. The selectivity towards the desired mono alkylphenol product almost always improves as the phenol to alkene mole ratio increases. These gains must be weighed... 

The hydrocarbon gas feedstock and Hquid sulfur are separately preheated in an externally fired tubular heater. When the gas reaches 480—650°C, it joins the vaporized sulfur. A special venturi nozzle can be used for mixing the two streams (81). The mixed stream flows through a radiantly-heated pipe cod, where some reaction takes place, before entering an adiabatic catalytic reactor. In the adiabatic reactor, the reaction goes to over 90% completion at a temperature of 580—635°C and a pressure of approximately 250—500 kPa (2.5—5.0 atm). Heater tubes are constmcted from high alloy stainless steel and reportedly must be replaced every 2—3 years (79,82—84). Furnaces are generally fired with natural gas or refinery gas, and heat transfer to the tube coil occurs primarily by radiation with no direct contact of the flames on the tubes. Design of the furnace is critical to achieve uniform heat around the tubes to avoid rapid corrosion at "hot spots."... 

Chlorine free radicals used for the substitutioa reactioa are obtaiaed by either thermal, photochemical, or chemical means. The thermal method requites temperatures of at least 250°C to iaitiate decomposition of the diatomic chlorine molecules iato chlorine radicals. The large reaction exotherm demands close temperature control by cooling or dilution, although adiabatic reactors with an appropriate diluent are commonly used ia iadustrial processes. Thermal chlorination is iaexpeasive and less sensitive to inhibition than the photochemical process. Mercury arc lamps are the usual source of ultraviolet light for photochemical processes furnishing wavelengths from 300—500 nm. 

The preceding equation assumes the reaction is completely quenched immediately after the relief point is reached. This behavior is closely approximated if the reaction stops in the quench pool and the reactor empties quickly and thoroughly. If the reaction continues in the quench pool, the temperature Tr should be increased to the maximum adiabatic exotherm temperature. An equation is presented by CCPS (AIChE-CCPS, 1997) that includes the heat of reaction. In some cases, an experiment is necessary to confirm that the reaction indeed stops in the quench pool. 

Figure 1.3.2 gives another perspective for scale-down to recycle reactor studies. In this actual case, after preliminary studies in a recycle reactor, a 5-stage adiabatic reactor was envisioned (Betty 1979.) Scaling down the proposed commercial reactor, a 3 diameter tube was designed with elaborate temperature compensation (heating and insulation) for pilot-plant studies (Betty 1968, 1969.) Small squares in the proposed reactor represent side views of cylindrical catalyst cutouts for the recycle reactor... 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

The unit was built in a loop because the needed 85 standard m /hour gas exceeded the laboratory capabilities. In addition, by controlling the recycle loop-to-makeup ratio, various quantities of product could be fed for the experiments. The adiabatic reactor was a 1.8 m long, 7.5 cm diameter stainless steel pipe (3 sch. 40 pipe) with thermocouples at every 5 centimeter distance. After a SS was reached at the desired condition, the bypass valve around the preheater was suddenly closed, forcing all the gas through the preheater. This generated a step change increase in the feed temperature that started the runaway. The 20 thermocouples were displayed on an oscilloscope to see the transient changes. This was also recorded on a videotape to play back later for detailed observation. 

The original van Heerden diagram, as presented in his paper of 1953, was constructed for an adiabatic reactor case. In that case, at fixed feed temperature, there was a different slope (representing heat removal rate) for each feed rate. There was also a different heat generation versus temperature... 

The need to keep a concave temperature profile for a tubular reactor can be derived from the former multi-stage adiabatic reactor example. For this, the total catalyst volume is divided into more and more stages, keeping the flow cross-section and mass flow rate unchanged. It is not too difficult to realize that at multiple small stages and with similar small intercoolers this should become something like a cooled tubular reactor. Mathematically the requirement for a multi-stage reactor can be manipulated to a different form ... 

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. 

The chapter by Haynes et al. describes the pilot work using Raney nickel catalysts with gas recycle for reactor temperature control. Gas recycle provides dilution of the carbon oxides in the feed gas to the methanator, hence simulating methanation of dilute CO-containing gases which under adiabatic conditions gives a permissible temperature rise. This and the next two papers basically treat this approach, the hallmark of first-generation methanation processes. 

The scheme of commercial methane synthesis includes a multistage reaction system and recycle of product gas. Adiabatic reactors connected with waste heat boilers are used to remove the heat in the form of high pressure steam. In designing the pilot plants, major emphasis was placed on the design of the catalytic reactor system. Thermodynamic parameters (composition of feed gas, temperature, temperature rise, pressure, etc.) as well as hydrodynamic parameters (bed depth, linear velocity, catalyst pellet size, etc.) are identical to those in a commercial methana-tion plant. This permits direct upscaling of test results to commercial size reactors because radial gradients are not present in an adiabatic shift reactor. 

Dr. Moeller I think to answer this question now is a bit difficult. It s just a mechanical problem of the maximum temperature the recycle compressor can handle. So, in the end, we will go to the inlet temperature to the compressor in the range of the inlet temperature to the reactor. So what we are endeavoring to attain is a simple reaction system consisting of an adiabatic reactor in series with waste heat boilers and nothing more than one recycle compressor. These compressors are used in the chemical industry with no problem in operation. So, in the end, you can go to hot recycle with an inlet compressor temperature the same as the inlet reactor temperature. All the heat from... 

Example 5.6 Hydrocarbon cracking reactions are endothermic, and many different techniques are used to supply heat to the system. The maximum inlet temperature is limited by problems of materials of construction or by undesirable side reactions such as coking. Consider an adiabatic reactor with inlet temperature Tm. Then T z) < T, and the temperature will gradually decline as the reaction proceeds. This decrease, with the consequent reduction in reaction rate, can be minimized by using a high proportion of inerts in the feed stream. 

Why are the CSTRs worth considering at all They are more expensive per unit volume and less efficient as chemical reactors (except for autocatalysis). In fact, CSTRs are useful for some multiphase reactions, but that is not the situation here. Their potential justification in this example is temperature control. BoiUng (autorefrigerated) reactors can be kept precisely at the desired temperature. The shell-and-tube reactors cost less but offer less effective temperature control. Adiabatic reactors have no control at all, except that can be set. 

Solution A program for evaluating the adiabatic reactor is given below. Subroutine Reactor solves the simultaneous ODEs for the concentrations and temperature. The equation for temperature includes contributions from both reactions according to the methods of Section 5.2. 

Adiabatic Reactors. Like isothermal reactors, adiabatic reactors with a flat velocity profile will have no radial gradients in temperature or composition. There are axial gradients, and the axial dispersion model, including its extension to temperature in Section 9.4, can account for axial mixing. As a practical matter, it is difficult to build a small adiabatic reactor. Wall temperatures must be controlled to simulate the adiabatic temperature profile in the reactor, and guard heaters may be needed at the inlet and outlet to avoid losses by radiation. Even so, it is hkely that uncertainties in the temperature profile will mask the relatively small effects of axial dispersion. 

A reactor is run adiabatically when no heat is exchanged between the reaction zone and the surroundings. The reaction temperature can then only be controlled by quenching with a cold stream of the reaction mixture or by inter-stage heat exchangers. For highly thermally sensitive large molecules treated in the fine chemicals sector this is a very impractical mode of operation. Therefore, adiabatic reactors will not be discussed here. 

In practice, nearly all reactors used for the manufacture of fine chemicals are neither isothermal nor adiabatic. The temperature-versus-time (location) profile is determined by the kinetic and physical characteristics of the reaction mixture as well as by the reactor geometry and hydrodynamics. The relationships governing this profile will be discussed in Section 5.4.2. 

In many respects, the solutions to equations 12.7.38 and 12.7.47 do not provide sufficient additional information to warrant their use in design calculations. It has been clearly demonstrated that for the fluid velocities used in industrial practice, the influence of axial dispersion of both heat and mass on the conversion achieved is negligible provided that the packing depth is in excess of 100 pellet diameters (109). Such shallow beds are only employed as the first stage of multibed adiabatic reactors. There is some question as to whether or not such short beds can be adequately described by an effective transport model. Thus for most preliminary design calculations, the simplified one-dimensional model discussed earlier is preferred. The discrepancies between model simulations and actual reactor behavior are not resolved by the inclusion of longitudinal dispersion terms. Their effects are small compared to the influence of radial gradients in temperature and composition. Consequently, for more accurate simulations, we employ a two-dimensional model (Section 12.7.2.2). 

Hence the relation between the temperature and the fraction conversion at any point in the adiabatic reactor is given by... 

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