Heat-balance measurement

All planned heat balance measurements have been established and heat loss from both reactor and from vapour stack determined, the former more and the latter rather less satisfactorily. 

State-point data, including secondary system heat balance measurements, are obtained at various power levels up to full licensed power. This information is used to project plant performance during power escalation, provide calibration data for the various plant control and protection systems and provide the bases for plant trip set-points. 

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

One of the critical measurements is torque or shaft power. A variety of methods is recognized direct methods such as torque meters or reaction mounted drivers (dynamometers) and indirect methods such as electrical power input to drive motors, heat balance, or heat input to a loop cooler. See Part 7, Measurement of Shaft Power, PTC 19.7 1961 [3] for additional information. 

If the instruments are in, the meter run was available, and gas composi-tion can be accurately determined as needed, one last minor hurdle should be addressed. This is power measurement. The indirect method, such as heat balance can be used. In fact, it should be used as a redundant method. 

Coefficient fCg can be evaluated through measurements in field or on a scaled model. Also, it is possible to predict the value using the method of zone-by-zone heat balances.According to this method,... 

The noncontact measurement principle, usually called optical or radiation temperature measurement, is based on detecting electromagnetic radiation emitted from an object. In ventilation applications this method of measurement is used to determine surface temperatures in the infrared region. The advantage is that the measurement can be carried out from a distance, without contact with the surface, which possibly influences the heat balance and the temperatures. The disadvantages are that neither air (or other fluid) temperature nor internal temperature of a material can be measured. Also the temper-... 

Instrument measurement response can often be important in the overall system response. The thermal response of a simple thermometer bulb, immersed in fluid, as shown in Fig. 2.6, is the result of a simple heat balance in which... 

Axial heat flux parameter Y The parameter Y, which replaces the heat flux shape factor in the CHF correlation, is not only a measure of the nonuniformity of the axial heat flux profile but also a means of converting from the inlet subcooling (AHin) to the local quality, X, form of the correlation via the heat balance equation. It is defined as... 

Subchannel imbalance factor Y The parameter Y was used in the heat balance equation to account for enthalpy transfer between subchannels. It is defined as the fraction of the heat retained in the subchannel and is a measure of this subchannel imbalance relative to that of its neighbors. Thus,... 

Figure 8. Measurements in a heat treatment chamber for hardboard. In a few channels of the carload of 100 single-laid boards, the air velocity and the temperature increase from ingoing air to outgoing air were measured as indicated. Also, measuring points used to determine the total heat balance in the chamber are indicated. (Reproduced with permission from ref. 10. Copyright 1989 De Gruyter.)...

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

The Contalab, initially supplied by Contraves, was purchased by Mettler-Toledo, which is now placing less emphasis on this design than on the RC1. Some comments here are appropriate, however, since it is another type of bench-scale calorimeter, and units continue to be used. Its measuring system is based on the heat balance principle, in which a heat balance is applied over the cooling/heating medium. For this purpose, both the flow rate of the coolant and its inlet and outlet temperatures must be known accurately. Figure 3.12 is a schematic plan of the Contalab. 

The polymerization reactor is of the heat-balance type because of the change in the heat transfer characteristics of the reaction mass during the polymerization. As the viscosity increases, the rate of heat dissipation by mixing will generally decline, which must be taken into consideration in setting up the equipment and in taking the appropriate measurements. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Flow Measurements Measurement of flow rates of clean gases presents no problem. Flow measurement of gas streams containing solids is almost always avoided. The flow of solids is usually controlled but not measured except solids flows added to or taken from the system. Solids flows in the system are usually adjusted on an inferential basis (temperature, pressure level, catalyst activity, gas analysis, heat balance, etc.). In many roasting operations, the color of the calcine discharge material indicates whether the solids feed rate is too high or too low. 

The EPA Method 2 probe uses a standard S-type Pitot tube to determine the velocity pressure by measuring gas flow as a unidirectional vector. This method is typically 10-20% higher than the calculated flue gas rate from the FCC heat balance. The newly develop EPA Method 2F probe is a five-holed prism tip with a thermocouple. A centrally located tap measures the stagnation pressure, while two lateral taps measure the static pressure. The yaw angle is determined by rotating the probe until the difference between the two lateral holes is zero. This method closely matches the... 

The temperature dependence of the rate constant for the step A -> B leads to the term /(0) in the dimensionless mass- and heat-balance eqns (4.24) and (4.25). The exact representation of an Arrhenius rate law is f(9) — exp[0/(l + y0)], where y is a dimensionless measure of the activation energy RTa/E. As mentioned before, y will typically be a small quantity, perhaps about 0.02. Provided the dimensionless temperature rise 9 remains of order unity (9 < 10, say) then the term y9 may be neglected in the denominator of the exponent as a first simplification. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Here, the enthalpy of the products of mass flowrate G and specific heat c is measured relative to T0, the inlet temperature of the reactants. The term for rate of heat generation on the left-hand side of this equation varies with the temperature of operation T, as shown in diagram (a) of Fig. 1.20 as T increases, lA increases rapidly at first but then tends to an upper limit as the reactant concentration in the tank approaches zero, corresponding to almost complete conversion. On the other hand, the rate of heat removal by both product outflow and heat transfer is virtually linear, as shown in diagram (b). To satisfy the heat balance equation above, the point representing the actual operating temperature must lie on both the rate of heat production curve and the rate of heat removal line, i.e. at the point of intersection as shown in (c). 

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