Thermal reaction power

In positive terms, this restriction means that recommendations shall be provided for the assessment of deviations which influence either the chemically generated thermal reaction power or the plant specific cooling capacity installed. A simplification of this problem results from the fact that the effects of such deviations on factors determining both powers mentioned act in the same direction. The following Table 4-9 shall give proof to this statement by providing some selected examples. 

Selected deviations influencing the thermal reaction power... 

The specific thermal reaction power is calculated by arithmetically averaging the specific powers corresponding to the maximum and set temperature, respectively. 

To record the rate q of heat release by a chemical reaction (thermal reaction power) under strictly isothermal condition in the measuring-kettle of a calorimeter, the apparatus must be able... 

The robustness of Type 2 apparatus speaks well for its use. However, against its general use for accurately measuring the thermal reaction power itself—a prerequisite for performing a thorough thermokinetic analysis of a complex chemical conversion—are the following factors ... 

Fig. 2.1 Principle of accurate determination of thermal reaction power during an isothermal, discontinuous reaction [based on the same measuring principle of the calorimeter, this system of intermediate thermostat—controlled heater, base thermostat (controlled heat sink)—was replaced recently [54] by a new type of intermediate thermostat metal, bordering controlled Peltier elements, thermostat (controlled heat sink)]...

The reason and the necessity for using an intermediate thermostat in addition to the measuring kettle to estimate the exact thermal reaction power q t) appears to the naked eye as follows. 

Fig. 2.3 Connection between thermal reaction power q, electric heating power p2 and baseline ps Conclusion...

Equation (2.5) shows the only thing that the solely course of the electric heat power Px t) in the measuring kettle versus time does not allow for the estimation of the thermal reaction power q t) It can be determined only when the course of a reference power, the baseline Pb(0> is known. The intermediate thermostat contributes essentially to its registration. 

Fig. 2.4 Estimating the thermal reaction power q from the heating powerusing the baseline p composition of p ...

Even classic electronics allows one to record the thermal reaction power in a... 

In addition to the electromotor without armature retroaction, the use of the intermediate thermostat is necessary to determine the baseline by analogous measurement and ultimately to determine the thermal reaction power by physical means in the classic working manner, i.e. by simple potentiometric addition and multiplication of measured quantities. The modem method of recording measured quantities and proceeding on the basis of digital electronics makes it possible—with limitations—to neglect the intermediate thermostat and to determine an adequately precise course of the baseline proceeding from one point in time to another as follows. 

A precise determination of the thermal reaction power q is only possible when the precise baseline p is known. This is valid for any type of calorimeter. 

In particular, the prerequisite for a thorough thermokinetic investigation is the precise determination of the thermal reaction power q. This applies for the... 

It is widely known that a logarithmic plot gives a straight line only for a reaction velocity (thermal reaction power) of order 1. The plots show that there is only a small curvature in the profile of order two and three up to a high degree of conversion. 

This principle stands to reason, especially with respect to the thermokinetic analysis of the thermal reaction power of a complex chemical conversion (i.e. analysis of the superposition of thermal reaction powers of individual reactions, see Chap. 4) demands the precise registration of the baseline during the complete reaction run. 

The first parenthetic expression is constant because (k F)i and psn are independent of the chemical conversion in the measuring kettle. The difference Ti — Ts) is maintained as constant by the control system Rl. Therefore, the equation for the thermal reaction power is obtained as... 

Fig. 2.29 shows the characteristic change in temperature T2 during an exothermic reaction. From previous equation follows the equation determining the thermal reaction power q[Ti(t)]. 

As a rule, only an approximate determination of the thermal reaction power q is possible because there is insufficient knowledge of the dependence of C2,... 

The temporal course of the thermal reaction power q (due to the temperature dependence of the reaction rate)... 

In case that C2, k-F)i and Psn change during the reaction approximately > 20 % the use of the intermediate thermostat is unconditionally necessary to determine the accurate thermal reaction power q. The heat balances of the measuring kettle and the intermediate thermostat are... 

Fig. 2.34 Determination of thermal reaction power q and thermal mixing power Mi of an isothermal, continuous chemical conversion...

However, under certain conditions, this measurement can be carried out indirectly by measuring the rate of heat release from the condensation of vapour in the condenser, which is recorded by the condenser/ intermediate thermostat (Fig. 2.36). The conditions for equality of the thermal reaction power and the rate of heat release by condensation are as follows ... 

To find the thermal reaction power in an ideally mixed tank reactor, it is recommended to use an appropriately designed flow calorimeter placed as a sensor in a short, thermally insulated by-pass. To equalize the specific rates of heat production in the tank reactor and sensor, the latter must be designed in such a way that both the composition and the temperature of the reaction mixture in the sensor correspond to those in the tank reactor. 

The following measurement setup is proposed for the online determination of the thermal reaction power (Figs. 2.37 and 2.38). 

Consequently, in Eq. (2.34) determining the rate of heat release in the measuring kettle, const(Ti, Ts, IV2) and the effective heat capacity C2 are known. p f) and T2(t) are measured online. d7 2(0/dt can be determined using a numeric online differentiation of 7 2(0- Experience has shown that the result of such a numeric operation is usually unsatisfactory because of unavoidable flucmations in the measured course of T2(t). A determination of the thermal reaction power q by means of numeric differentiation of T2 can be avoided using the stochastic estimate algorithm of the Kalman-Bucy filter [6]. 

The quotient of the determined thermal reaction power q and the reaction mass G in the measuring kettle yields the desired specific rate q. ... 

The prerequisite for the usability of the determining equations for the thermal reaction power q or the temperature, derived earlier, is that the temperature Ts of the base thermostat remains at a constant level during measurement or changes at least quasi-statically, i.e. in a quasi-continual equilibrium state of the total system. The following possibilities are appropriate for this purpose ... 

P2 at a value higher than the assumed peak in the thermal reaction power during the run of reaction. 

According to (4.1) the rate of heat release or thermal reaction power q, i.e. the heat released in volume V per unit of time, is given by... 

In the case of a not-too-complex system of reaction, the mechanism of reaction, together with the relevant rates of reaction and the heats of reaction can be worked out from the courses of the recorded thermal reaction powers over time, measured under varied conditions. The elaboration can be made easier with the aid of additional life signs of the conversion during a run, for example... 

The thermokinetic analysis of the measuring results starts with a hypothesis. A mechanism, the stoichiometry and the relevant function equations of the reaction rates are assumed [4,10, 14,16, 36,44]. From that, the run of both concentrations and thermal reaction power versus time are calculated on the basis of (4.2)-<4.9) [ 1, 9, 18]. Then we examine whether the measuring results are in accordance with the calculated ones. If there is insufficient congruence between the two, the hypothesis must be revised. Hence, the thermokinetic elaboration of the kinetics of a chemical... 

From (4.3) and (4.25) follows the determining equation for the thermal reaction power... 

A comparison of the thermal reaction power q for conversions with rate orders n greater and smaller than 1 shows that q decreases down to zero for order 0 < n < 1 within a finite time interval and for orders n > 1 after infinite time. 

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