Isothermic reaction

In the Godrej-Lurgi process, olefins are produced by dehydration of fatty alcohols on alumina in a continuous vapor-phase process. The reaction is carried out in a specially designed isothermal multitube reactor at a temperature of approximately 300°C and a pressure of 5—10 kPa (0.05—0.10 atm). As the reaction is endothermic, temperature is maintained by circulating externally heated molten salt solution around the reactor tubes. The reaction is sensitive to temperature fluctuations and gradients, hence the need to maintain an isothermal reaction regime. 

When the flow pattern is known, conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first-order irreversible isothermal reactions, the conversion equation can be obtained from the R sfer function by replacing. s with the specific rate k. Thus, if G(.s) = C/Cq = 1/(1 -i- t.s), then C/Cq = 1/(1 -i-kt). Complete knowledge of a network enables incorporation of energy balances into the solution, whereas the RTD approach cannot do that. 

Figure 1.6.1 Comparison of asymptotic and exact solutions for a first order, non-isothermal reaction in a spherical catalyst pellet. ...

Simulation of a non-isothermal reaction in a batch reactor involving the hydrolysis of acetylated castor oil... 

An isothermal reaction can proceed spontaneously only if the total Gibbs free energy of the system decreases, i.e. the free energy of the reactants must be greater than the free energy of the products. For a reaction... 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

Tenets (i) and (ii). These are applicable only where the reactant undergoes no melting and no systematic change of composition (e.g. by the diffusive removal of a constituent) and any residual solid product phase offers no significant barrier to contact between reactants or the escape of volatile products [33,34]. When all these conditions are obeyed, the shape of the fraction decomposed (a) against time (f) curve for an isothermal reaction can, in principle, be related to the geometry of formation and advance of the reaction interface. The general solution of this problem involves intractable mathematical difficulties but simplifications have been made for many specific applications [1,28—31,35]. 

RATE EQUATIONS COMMONLY USED IN KINETIC ANALYSES OF ISOTHERMAL REACTIONS OF SOLIDS... 

Any experimentally measured set of (at, ti) values for an isothermal reaction contains errors including (inter alia) inaccuracies in yield and time determinations and departure of temperature from the constant value temporarily and locally. In any quantitative kinetic analysis, several interdependent factors must be considered. 

The kinetics of the contributory rate processes could be described [995] by the contracting volume equation [eqn. (7), n = 3], sometimes preceded by an approximately linear region and values of E for isothermal reactions in air were 175, 133 and 143 kJ mole-1. It was concluded [995] that the rate-limiting step for decomposition in inert atmospheres is NH3 evolution while in oxidizing atmospheres it is the release of H20. A detailed discussion of the reaction mechanisms has been given [995]. Thermal analyses for the decomposition in air [991,996] revealed only the hexavanadate intermediate and values of E for the two steps detected were 180 and 163 kJ mole-1. 

A mathematical model for this polymerization reaction based on homogeneous, isothermal reaction is inadequate to predict all of these effects, particularly the breadth of the MWD. For this reason a model taking explicit account of the phase separation has been formulated and is currently under investigation. 

One must now realize that extreme caution should be exercized in drawing conclusions about RIM polymerization from batch isothermal reactions at high temperature. 

In the general case of a piston flow reactor, one must solve a fairly small set of simultaneous, ordinary differential equations. The minimum set (of one) arises for a single, isothermal reaction. In principle, one extra equation must be added for each additional reaction. In practice, numerical solutions are somewhat easier to implement if a separate equation is written for each reactive component. This ensures that the stoichiometry is correct and keeps the physics and chemistry of the problem rather more transparent than when the reaction coordinate method is used to obtain the smallest possible set of differential... 

Most kinetic experiments are run in batch reactors for the simple reason that they are the easiest reactor to operate on a small, laboratory scale. Piston flow reactors are essentially equivalent and are implicitly included in the present treatment. This treatment is confined to constant-density, isothermal reactions, with nonisothermal and other more complicated cases being treated in Section 7.1.4. The batch equation for component A is... 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

The fed-batch scheme of Example 14.3 is one of many possible ways to start a CSTR. It is generally desired to begin continuous operation only when the vessel is full and when the concentration within the vessel has reached its steady-state value. This gives a bumpkss startup. The results of Example 14.3 show that a bumpless startup is possible for an isothermal, first-order reaction. Some reasoning will convince you that it is possible for any single, isothermal reaction. It is not generally possible for multiple reactions. 

Figure 5.4-36. Fit of first-order kinetics for three Figure 5.4-37. Arrhenius plot for rate constants isothermal reaction periods (reprinted with obtained from the isothermal reaction periods permission from Landau et al. (1994). Copyright (reprinted with permission from Landau et al. (1994) American Chemical Society). (1994). Copyright (1994) American Chemical...

A system of three continuous stirred-tank reactors is used to carry out the first-order isothermal reaction... 

The dispersion model of example DISRE is extended for non-isothermal reactions to include the dispersion of heat from a first-order reaction. 

The Effectiveness Factor for a Straight Cylindrical Pore Second- and Zero-Order Reactions. This section indicates the predictions of the straight cylindrical pore model for isothermal reactions that are zero- and second-... 

Using the SFM and the data from Example 19-8(b), calculate fA for the first-order, liquid-phase, isothermal reaction A - products, if kA = 0.05 s. For comparison, calculate /A for the reactor as a PFR and as a CSTR. 

In those cases where concentrations are not measured directly, the problem of calibration of the in-situ technique becomes apparent. An assurance must be made that no additional effects are registered as systematic errors. Thus, for an isothermal reaction, calorimetry as a tool for kinetic analysis, heat of mixing and/or heat of phase transfer can systematically falsify the measurement. A detailed discussion of the method and possible error sources can be found in [34]. 

Conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first order irreversible isothermal reactions, the conversion equation can be obtained from the transfer function if that is known by replacing the parameter s by the... 

For simple power law rate equations the effectiveness can be expressed in terms of the Thiele modulus, Eq 7.28. In those cases restriction is to irreversible, isothermal reactions without volume change. Other cases can be solved, but then the Thiele modulus alone is not sufficient for a correlation. 

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. 

The chemical-source-term closure problem occurs even for relatively simple isothermal reactions. For example, consider again the simple two-step reaction (5.21) where26... 

Recall that the one-step isothermal reaction has a non-zero chemical source term for Y = 0. Thus, premixing for the fast-reaction limit yields immediate conversion to the equilibrium limit, regardless of the local scalar dissipation rate. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

S. Sunner, I. Wadso. On the Design and Efficiency of Isothermal Reaction Calorimeters. Acta Chem. Scand. 1959,13, 97-108. 

FIGURE 8.1 The effect of superequilibrium radical concentrations on NO formation rates in the isothermal reaction of 13% methane in air ( = 1.37). The upper curve is the ratio of the maximum NO formation rate calculated using the detailed reaction mechanism of Ref. [6] to the initial NO formation rate calculated using the Zeldovich model. The lower curve is the ratio of the NO concentration at the time of the maximum NO formation rate calculated using the detailed reaction mechanism to the equilibrium NO concentration (from Miller and Bowman [6]). 

Frumkin isotherms, reaction order, 38 53 Fuel, 24 222, 223 potential poisons in, 27 315, 316 unleaded, 27 312 Fuel cells... 

Write the component continuity equations for a perfectly mixed batch reactor (no inflow or outflow) with first-order isothermal reactions ... 

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