Heat-Balance Calculations

Using the operating data from the case study. Example 5-5 shows heat balance calculations around the stripper-regenerator. The results are used to determine the catalyst circulation rate and the delta coke. Delta coke is the difference between coke on the spent catalyst and coke on the regenerated catalyst. 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

It must be emphasised that it is unnecessary to correct a heat of reaction to the reaction temperature for use in a reactor heat-balance calculation. To do so is to carry out two heat balances, whereas with a suitable choice of datum only one need be made. For a practical reactor, the heat added (or removed) Qp to maintain the design reactor temperature will be given by (from equation 3.10) ... 

An interesting application of this approach in another field has been described by Keller (K2). In the design of steam turbines rather complicated heat-balance calculations are required. While each particular installation is different, and therefore requires a different mathematical model, the components of each turbine are always similar. A large-scale computer program was developed, therefore, which would through suitable instructions combine the calculations required for each component into an over-all heat balance for the turbine. 

However, to assign a specific meaning to the numerical value for this heat release, it is customary to specify a reference temperature and pressure for the reaction, these being 25°C and 1 atmosphere in the example cited. In making heat balance calculations, it is then convenient to choose these conditions as tine datum level and then calculate the heat input and heat output quantities above or below the reference state. 

The design exit temperature for the reaction gases leaving the cooler/condenser is 60°C. The average heat capacity of the reaction gases in the temperature range 185°C to 60°C is 1. 13 kJ/(kg K). The heat of reaction/condensation/solution at this stage is approximately 0.442 times the sensible heat. For the heat balance calculations, the acid formed is assumed to be vapour until the exit from the cooler/ condenser. 

The mathematical model developed to describe the nitric acid absorption process isdiscussed in detail in Section G.2. It uses a tray-by-tray approach that incorporates reaction-mass balance corrections and heat balance calculations. Tray efficiency calculations are also included in the model, the efficiency being a function of the tray geometry and gas velocity. Rate equations and other data specific to the nitric acid/nitrous gas system are applied. 

Results of the enthalpy balance for this test show that the method of calculation cannot account for 1.5% of the total enthalpy input. This difference is small and may arise from the accuracy of the individual measurements and by the approximation used to calculate some of the quantities, as described above. A preliminary error analysis indicates an uncertainty of +3.356 for the heat balance calculation. The two methods for calculating the efficiency will agree only if the heat balance closes exactly. In general, when the... 

These data are almost identical to those calculated above for normal corpses131 and confirm the accuracy of our heat balance calculations for both the triple- and the eight-muffle ovens. 

Because the data in Table III originate from mass and heat balance calculations, the balance closure is 100% for the mass and heat balance. 

Clearly, the user of any thermodynamic tables must become familiar with the tables and the interrelationships of the data if he plans to make extensive use of the values. Moreover, he must not use them blindly. The actual numbers tabulated for the different thermodynamic functions are not so significant as the final equilibrium constants that are to be calculated from them. These tables are designed to yield equilibrium constants of as high an accuracy as can be obtained from the available data. Thus, the uncertainty of a given heat of sublimation may be considerably smaller in regard to its use for calculation of vapor pressures than in regard to its use for heat balance calculations. 

Nitrogen in the converter gas carries away about 45% of the heat provided. Based on converter heat balance calculations,25 with 30% 02 in the converter air (9% 02 enrichment) about 1.8 x 106 Btu/ton (0.48 MW/t) oxygen can be saved at... 

Example of heat balance calculation for a ceramic honeycomb regenerator. 

The reaction-vessel temperature as a function of time is presented in Figure 5. Only in the first two runs were results obtained which would be considered satisfactory for cleaning components — i.e., the temperature rises were very moderate. In the other runs, the temperature excursions were excessive. Based on these temperatures and heat-balance calculations, the instantaneous heat of reaction for each run was determined. These calculations, presented in Figure 6, readily explain the temperature excursions experienced. 

To supply the heat necessary sensible, latent, heat of solution, and heat of crystallization. (The last two are sometimes improperly omitted in heat-balance calculations.)... 

Once the dryer size and the configuration are determined, the size of all the components can be calculated. This is done by calculating a heat and mass balance on the drying process. This involves doing a heat balance, a mass balance on the water, a mass balance on the dry ingredients, and a mass balance on any other volatile components. Table 18.2 shows a typical result from a heat balance calculation on a four heat... 

The heat released in every zone, depending on the polymerisation rate and amount of a monomer reacting in the reaction zone is small, and heat exchange coefficients are such as to meet the requirement of temperature uniformity in every reaction zone. In accordance with this condition in the reaction zone, the polymer should be formed with a MWD and MW corresponding to the temperature determined by the heat balance. Calculations show that such conditions are performed for the following equation [3] ... 

Simple heat balance calculations reveal that the AH associated with the first two reactions alone can result in excessive temperatures that can lead to combustion. 

First, heat exchanger heat balance calculations are conducted in a flowsheet simulation software, which has adequate thermal data and can describe process streams according to their physical properties and operating conditions. By providing measured temperatures, the simulation can determine the heat transfer duty from Q = m Cp AT. At the same time, the simulation calculates transfer capability by lumping overall heat transfer coefficient and surface area together as U - A = 2/ATlm> where ATlm is defined in equation (6.7) in Chapter 6. 

From heat balance calculations it is possible to determine the heat load (i.e. heat transferred in the heat exchangers of the sulphonation, dilution and neutralisation loops) at each stage of the total process, and hence the amount of cooling water needed. The results of these calculations are summarised in table 42. The recirculation ratio (volume of recirculating material divided by the volume of throughput) is 15 1 to give small temperature differences in the sulphonation, dilution and neutralisation loop process-side streams. 

Heat balance calculations are usually carried out when developing new rotary kiln chemical processes or when improving old ones. No thermal process would work if too much heat is released or if there is a lack of sufficient thermal energy to drive the process, in other words, to maintain the reaction temperature. Heat balance can only be calculated with given mass balances as the boundary conditions, hence a quantitative description of the chemical processes on the basis of physical or chemical thermodynamics is required. While chemical thermodynamics establishes the feasibility of a particular reaction under certain reactor conditions, chemical kinetics determines the rate at which the reaction will proceed. Before we establish the global rotary kiln mass and energy balance, it is important to examine some fundamental concepts of thermodynamics that provide the pertinent definitions essential for the design of new rotary kiln bed processes. 

Reflux pumparound rates can usually be calculated from a heat balance around individual towers. This is the best way to account for unrecorded flows. It is not uncommon for a reflux or pumparound duty, calculated from the tower heat balance, to be 10% to 20% higher than the measured flow would indicate. This is probably due to ambient heat losses. For the sake of consistency of the total test report, it is best to stick with the duties from the heat balance calculations. If the difference between a duty calculated in the two ways described above is much more than 20%, there is a significant error in the test data. 

The driving force for mass transfer is the difference between the partial pressure of COg in the gas phase and the vapor pressure of CO2 above the liquid phase. A mass and heat balance across the absorber will fix the outlet rich solvent temperature and composition, enabling the vapor pressure of CO2 above the effluent liquid to be determined. For purposes of initial heat balance calculations, the exit gas stream temperature can be assumed to be the same as the inlet lean solvent temperature. 

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