Heat balancing

Fig. 6.7a. Above the pinch (in temperature terms), the process is in heat balance with the minimum hot utility Qnmin- Heat is received from hot utility, and no heat is rejected. The process acts as a heat sink. Below the pinch (in temperature terms), the process is in heat balance with the minimum cold utility Qcmin- No heat is received, but heat is rejected to cold utility. The process acts as a heat source.

Next, we carry out a heat balance within each shifted temperature interval according to Eq. (6.1). The result is given in Fig. 6.17. Some of the shifted intervals in Fig. 6.17 are seen to have a surplus of heat... 

Now, carry out a heat balance within each shifted temperature interval, as shown in Fig. 6.20. 

Figure 6.20 Temperature-interval heat balances for Example 6.1.

Solution The fraction of liquid vaporized on release is calculated from a heat balance. The sensible heat above saturated conditions at atmospheric pressure provides the heat of vaporization. The sensible heat of the superheat is given by... 

Since enthalpy interval k is in heat balance, then summing over all cold stream matches with hot stream i gives the stream duty on hot stream i ... 

For example a process flow scheme for crude oil stabilisation might contain details of equipment, lines, valves, controls and mass and heat balance information where appropriate. This would be the typical level of detail used in the project definition and preliminary design phase described in Section 12.0. 

Each of abovementioned processes of heat transfer is described by a set of equations of a heat balance, written for each Dirichlet cell. 

Were we can give these equations for the heat transfer process along radius R. The other processes of heat transfer can be simulated analogously by changing formula for heat transfer area and distances between centers of cells. For Dirichlet cells, bordering a gas medium, an equation of heat balance can be written in the form ... 

For a cell, located close to an outer surface of a kiln the equation of heat balance can be written in the form ... 

Derivation of the working equations of upwinded schemes for heat transport in a polymeric flow is similar to the previously described weighted residual Petrov-Galerkm finite element method. In this section a basic outline of this derivation is given using a steady-state heat balance equation as an example. 

When the heat duty requirement, is specified and the fluid temperature change, AT, is fixed, as a result of operating or equipment limitations, the required volumetric pumping rate from the heat balance is... 

Fig. 6. Temperature—relative enthalpy plots showing network parameters of minimum utiUty for (a) the case requiring infinite area (b) where heat balance...

Mass and energy balances are used to evaluate blast furnace performance. Many companies now use sophisticated computeri2ed data acquisition and analysis systems to automatically gather the required data for daily calculation of the mass and heat balances. Typical mass and heat balances are shown in Figure 4 and Table 5, respectively. 

When the dryer is seen as a heat exchanger, the obvious perspective is to cut down on the enthalpy of the air purged with the evaporated water. Minimum enthalpy is achieved by using the minimum amount of air and cooling as low as possible. A simple heat balance shows that for a given heat input, minimum air means a high inlet temperature. However, this often presents problems with heat-sensitive material and sometimes with materials of constmction, heat source, or other process needs. AH can be countered somewhat by exhaust-air recirculation. 

Assuming a linear relation between surface temperature and corresponding vapor pressure of the condensable component allows a heat balance to be written from gas phase to the surface ... 

No external heat source is required. In all types of steelmaking that employ pig iron, which melts at temperatures well below low carbon steel, the heat balance between exothermic oxidation of elements, such as C, Si, and Mn, and the cooling provided by scrap or sometimes other endothermic coolants, such as iron ore, are critical issues. The numerical factors are well understood and are routinely contained in computer programs used by operators. If the balance is such that the temperature after blowing is too high, refractory consumption is increased significantly. 

Overall comparison between amine and carbonate at elevated pressures shows that the amine usually removes carbon dioxide to a lower concentration at a lower capital cost but requires more maintenance and heat. The impact of the higher heat requirement depends on the individual situation. In many appHcations, heat used for regeneration is from low temperature process gas, suitable only for boiler feed water heating or low pressure steam generation, and it may not be usefiil in the overall plant heat balance. 

Thus the ECCU always operates in complete heat balance at any desired hydrocarbon feed rate and reactor temperature this heat balance is achieved in units such as the one shown in Eigure 1 by varying the catalyst circulation rate. Catalyst flow is controlled by a sHde valve located in the catalyst transfer line from the regenerator to the reactor and in the catalyst return line from the reactor to the regenerator. In some older style units of the Exxon Model IV-type, where catalyst flow is controlled by pressure balance between the reactor and regenerator, the heat-balance control is more often achieved by changing the temperature of the hydrocarbon feed entering the riser. 

Fig. 2. Heat balance of the FCCU. Heat balance around the reactor A, heat balance around the regenerator B, and the overall heat balance around the entire...

Thus the amount of heat that must be produced by burning coke ia the regenerator is set by the heat balance requirements and not directly set by the coke-making tendencies of the catalyst used ia the catalytic cracker or by the coking tendencies of the feed. Indirectly, these tendencies may cause the cracker operator to change some of the heat-balance elements, such as the amount of heat removed by a catalyst cooler or the amount put iato the system with the feed, which would then change the amount of heat needed from coke burning. 

If FCCU operations are not changed to accommodate changes ia feed or catalyst quaUty, then the amount of heat required to satisfy the heat balance essentially does not change. Thus the amount of coke burned ia the regenerator expressed as a percent of feed does not change. The consistency of the coke yield, arising from its dependence on the FCCU heat balance, has been classified as the second law of catalytic cracking (7). 

The burning of coke in the regenerator provides the heat to satisfy the FCCU heat balance requirements as shown in equation 1. The heat released from the burning of coke comes from the reaction of carbon and hydrogen to form carbon monoxide, carbon dioxide, and water. The heat generated from burning coke thus depends on the hydrogen content of the coke and the relative amounts of carbon that bum to CO and CO2, respectively. 

The impact that variations in coke content and burning conditions can have on the overall heat of coke combustion is shown in Table 2. Because the heat balance dictates the amount of heat that is required from burning coke, the heat of combustion then determines the amount of coke that must be burned. 

J. L. Mauleon and J. C. CourceUe, "FCC Heat Balance Considerations with Heavy Feeds," presented at Katalistiks 6th MnnualFCC Symposium, Munich, Germany, May 1985. 

J. R. Murphy and Y. L. Cheng, "The Interaction of Heat Balance and Operating Variables in ZeoUtic Catalyst Operations," presented at Katalistiks 5th Annual FCC Symposium, Vieima, Austria, May 1984. 

J. L. Mauleon, J. B. Sigaud, and G. Heinrich, "FCC Heat Balance Management with Heavy Feeds, MTC Approach," presented at JPIPetroleum Eefmery Conference, Tokyo, Japan, Oct. 1986. 

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