Heat balance/balancing defined

Often in plant operations condensate at high pressures are let down to lower pressures. In such situations some low-pressure flash steam is produced, and the low-pressure condensate is either sent to a power plant or is cascaded to a lower pressure level. The following analysis solves the mass and heat balances that describe such a system, and can be used as an approximate calculation procedure. Refer to Figure 2 for a simplified view of the system and the basis for developing the mass and energy balances. We consider the condensate to be at pressure Pj and temperature tj, from whence it is let down to pressure 2. The saturation temperature at pressure Pj is tj. The vapor flow is defined as V Ibs/hr, and the condensate quality is defined as L Ibs/hr. The mass balance derived from Figure 2 is ... 

Chapter 1 provides a summary of important equations for estimating the terminal temperatures in a heat exchanger. Here we formalize a short estimating procedure for a countercurrent flow situation. Assume that a specifier of a heat exchanger has defined a preliminary sizing of the unit. The system requires heat and material balances. 

In contrast, most equipment can safely tolerate higher degrees of heat density than those defined for personnel. However, if anything vulnerable to overheating problems is involved, such as low melting point construction materials (e.g., aluminum or plastic), heat-sensitive streams, flammable vapor spaces, or electrical equipment, then the effect of radiant heat on them may need to be evaluated. When this evaluation is required, the necessary heat balance is performed to determine the resulting surface temperature, for comparison with acceptable temperatures for the equipment. 

In chemical processing the most fundamental constraint is that of the thermodynamics of the system. This constraint defines both the heat balance of the process and whether or not the processes in the reactor will be equilibrium limited. These constraints will limit the range of chemical engineering solutions to the problems of designing an economically viable process that can be found. 

Correlate temperature-versus-time (distance) data with an appropriate function T = 71(f), replace T with 7(f) in heat balance equation (5.4-130) and minimize SSres defined as... 

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,... 

The fundamental law of the conservation of energy leads to the following heat balance for well-defined systems ... 

When the fluidized bed consists of non-porous particles, solvent in the feed liquid is evaporated in a well-defined zone close to the spray nozzle and from fhe surface of the bed particles with which it inevitably comes into contact. No permanent gas jet or void exists in this region particle motion is not well ordered and no regular coating of parficles wifh feed solution takes place. The random and intense contact between particles and liquid results in agglomeration. Even if the mass and heat balances for the bed as a whole have been satisfied, both... 

Heat can be defined as a portion of the total energy flow across a system boundary and is caused by a temperature difference between the system and the surroundings. Heat can be exchanged by conduction, convection and/or radiation. We can evaluate heat transfer by use of the energy balance, which will be discussed later. 

Write the steady-state mass and heat balance equations for this system, assuming constant physical properties and constant heat of reaction. (Note Concentrate your modeling effort on the adiabatic nonisothermal reactor, and for the rest of the units, carry through a simple mass and heat balance in order to define the feed conditions for the reactor.)... 

To turn these heat-balance equations into nonisothermal heat balance design equations, we define the rate of reaction per unit volume (or per unit mass of catalyst, depending on the system) and the heat transfer per unit volume of the process unit (or per unit length), whichever is more convenient. 

The reactor and regenerator mass and heat-balance equations for the dense phase and the bubble phase are given by equations (7.29) to (7.45). The catalyst activities in the reactor and regenerator are defined by the following two relations... 

Since the sensitivity of the reaction rate towards temperature, and therefore of the heat release rate of a reaction, dominates the heat balance, it is important to define... 

When the slope of the heat balance line is close to the slope of the inflexion point of the mass balance curve, there is no longer a well-defined working point (solid fine in Figure 8.4) and the reactor may enter cyclic oscillations of temperature and conversion, even for constant working parameters. To avoid these oscillations, the condition must be fulfilled [2] ... 

A practical approach of heat balance, often used in assessment of heat accumulation situations, is the time-scale approach. The principle is as in any race the fastest wins the race. For heat production, the time frame is obviously given by the time to maximum rate under adiabatic conditions. Then the removal is also characterized by a time that is dependent of the situation and this is defined in the next sections. If the TMRld is longer than the cooling time, the situation is stable, that is, the heat removal is faster. At the opposite, when the TMRld is shorter than the characteristic cooling time, the heat release rate is stronger than cooling and so runaway results. 

Figure 10 presents the interface shape of the rivulet for wall superheat as 0.5 K and Re = 2.5. Here also presented the data on pressure in liquid and heat flux density in rivulet cross-section. The intensive liquid evaporation in near contact line region causes the interface deformation. As a result the transversal pressure gradient creates the capillarity induced liquid cross flow in direction to contact line. Finally the balance of evaporated liquid and been bring by capillarity is established. This balance defines the interface shape and apparent contact angle value.For the inertia flow model, the solution is obtained from a non-stationary system of equations, i.e., it is time-dependable. In this case the disturbances in flow interface can create the wave flow patterns. The solutions of unsteady state liquid spreading on heat transfer surface without and with evaporation are presented on Fig. 11. When the evaporation is not included (for zero wall superheat) the wave pattern appears on the interface. When the evaporation includes, the apparent contact angle increase immediately and deform the interface. It causes the wave suppression due to increasing of the film curvature.

Otlier heats of adsorption, defined differently, are also in use. However, tlie isosteric heat is the most common, and is tlie one needed for energy balances on adsorption columns. 

The most common procedure is pumping a substrate solution of a defined composition (concentration of substrate and other compounds having influence on the enzyme activity) through the microcalorimetric column. The basic information provided by the microcalorimetric measurement is the relation between reaction conditions and the steady-state heat response, ATr, measured as the temperature difference between the column input and output. Figure 2 is an illustration of such measurement. In the next part of this review, the mathematical assessment of the experimental data, based on mass and heat balances, is provided. 

When no heat losses cross the reactor wall are present, the local temperature change depends directly on the reaction rate. Then, material and heat balances can be defined as... 

The corresponding temperature equation for the interstitial gas is given by (11.6). To define the alternative model versions the effective heat of reaction term St = Pcat — in the basic model heat balance is... 

The procedure used for batch heating with external 1-2 multipass heat exchangers with non-isothermal heating media involves using the same heat balance as defined by the following equation ... 

The separation of a multi-component mixture into products with different compositions in a multistage process is governed by phase equilibrium relations and energy and material balances. It is not uncommon in simulation studies to require certain column product rates, compositions, or component recoveries to satisfy given specifications with no concern for conditions within the column. Such would be the case when downstream processing of the products is of primary interest. In these instances, one would be concerned only with overall component balances around the column but not necessarily with heat balances or equilibrium relations. Separation would thus be arbitrarily defined, and the problem would be to calculate product rates and compositions. The actual performance of the separation process is analyzed independently in all the following chapters. 

As in the case of batch reactors, dimensionless energy balance Eq. 5.2.53 is not conveniently used because the heat capacity of the reacting fluid, (FjCpj), is a function of the temperature and reaction extents and, consequently, varies along the reactor. To simplify the equation and obtain dimensionless quantities for heat transfer, we define the heat capacity of the reference stream and relate the heat capacity at any point in the reactor to it by... 

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