Semenov diagram

Reaction sequences and Semenov representation 2.4.1. Semenov diagram 

Note 2.3.- The previous steps are likely to involve some principal components in one of each member. These components are represented by dots in chemical equations. 

A set of steps that are linked by a mechanism constitutes a sequence characterized by its entry point(s), its exit point(s) and its traversal direction(s). Depending on the reaction intermediates, two types of sequence are distinguished linear sequences and multipoint sequences. From the perspective of the Semenov diagram s shape, two types of sequence are distinguished open sequences and closed sequences. 

A sequence is linear if each intermediate is produced by a single step and is also consumed by a single step. Depending on the Semenov representation (see Fignre 2.2), there are  

A chain reaction is a reaction in which a small number of elementary steps are repeated a large nrrmber of times following each other through a small number of intermediate species that are constantly formed and destroyed. Such an example is given by the mechanism of the synthesis of hydrogen bromide, expressed in section 2.2. A repetitive secprence is called a repeat unit in the chain (like the two steps [2.R2a] and [2.R2b] in hydrogen bromide synthesis). 

Let us consider a simplified heat balance involving an exothermal reaction with zero-order kinetics. The heat release rate of the reaction q = f(T) varies as an exponential function of temperature. The second term of the heat balance, the heat removal by a cooling system qKX =f(T), with Newtonian cooling (Equation 2.18), varies linearly with temperature. The slope of this straight line is U-A and the intersection with the abscissa is the temperature of the cooling system Tc. This 

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To illustrate these Semenov diagrams in reasonable quantitative terms, n-heptane was selected with the following properties ... 

Figure 2.4 Semenov diagram the intersections S and I between the heat release rate of a reaction and the heat removal by a cooling system represent an equilibrated heat balance. Intersection S is a stable operating point, whereas I represent an instable operating point. Point C corresponds to the critical heat balance.

Figure 2.5 Semenov diagram effect of a change in the heat transfer characteristics of the reactor UA.

Figu re 2.6 Semenov-diagram calculation of the critical temperature. 

In Section 2.5.2, the Semenov diagram was used to show the critical cooling medium temperature. In the same way it allows discrimination of a stable operation conditions from a runaway situation. A stable operation is achieved for a limit value of the Semenov criterion / (also called Semenov number) ... 

Compared with the heat release rate by a reaction, which follows Arrhenius law, one obtains the Semenov diagram (Figure 2.6). From this diagram, we can calculate the critical temperature difference (Equations 2.32-2.34). But this also calculates the critical heat release rate as a function of q0 ... 

Fig. 4.4 Semenov diagram showing reaction heat sigmoid (curve 4) and subcritical (1), critical (2), and supercritical (5) lines of heat exchange for 7J = 1 and critical line (5) for Ij = T ...

Under the assumption C = 1 at each time r, the system evolves toward steady-state conditions that can be located graphically on the Semenov diagram of Fig. 4.4 as the intersections of the curves < r and q, this condition implies, indeed, that d%/dx = 0 in (4.16). For the sake of simplicity, let us first assume that %o = 7j = 1. When qE is given by line 1 with slope i, the steady-state condition is given by point A, characterized by a low operating temperature. Point A is an attractor since its temperature is spontaneously restored after any small perturbation of the system and, consequently, in these conditions thermal explosion does not occur. 

The SEMENOV diagram (Figure 6) consists of a representation of the variations in Qy and Qg as functions of T. The variations of Qy seem to be approximately exponential, whereas those of Qg are approximately linear. The three curves, represented by the letters a, b and c, represent the variations in Qy at three increasingly high concentrations c( ), c( ) and c( ). 

Summarizing, the critical point CR of the SEMENOV diagram separates the regions of slow reaction and of autoignition where the reaction is explosive. 

Example 3.5 Partial failure of reactor cooling and the Semenov diagram... 

Fig. 3.5 Representation of the process in the Semenov diagram (thermal power q as a function of temperature T)...

Solutions of Eq. (7.73) can be studied using a Semenov diagram, which reflects the dependences of the rate of heat generation and the rate of heat removal on the temperature. This diagram is similar to the dependence shown in Fig. 7.4, but with dimensionless coordinates. The points of intersection of Q Jj) and 2hg(jy) in Eq- (7.73) determine the temperature of the steady state knowing this temperature, the corresponding steady-state conversion can be calculated using Eq. (7.72). 

The Semenov diagram shows a cycle that has either parallel branches (see Figure 2.4) or is traversed in a single direction. 

Figure 8.2 represents a step that enables us to go from intermediate to JG +1 in the loop of a Semenov diagram. If this step determines the speed, whieh means that all the others are practieally at eqnilibriutn, then species X, and X) +1 are in equilibrium with the other side of the loop, regardless of its direction of traversal. Therefore, the speed of the determining step will be zero because it is the product of a finite rate with null distance between the actual conditions and the equilibrium conditions. 

In such a reaction, the intermediate is called the active center and reacts with a reactant to give another active center having the same properties and final products as the previous one. The initial active center is formed by initiation and disappears with the breaking reaction. From the perspective of an active center, the Semenov diagram is linear (see Figure 12.2). 

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