Bubble heat balance

Hatton and Hall (1966) further improve the model by taking into consideration the heat capacity of the heating element, since during the waiting period the heat surf ace has to be heated to a sufficiently high temperature to initiate the new bubble. The heat balance used by Hatton and Hall is... 

Either the temperatures or flows could be adjusted first. The common choice is to correct the temperature. Correction of temperatures is usually done through either bubble-point or dew-point determinations on the calculated stage compositions. After correcting the stage temperatures, the liquid and vapor enthalpies may be obtained from the calculated compositions, and the flows corrected by solution of the now linear heat balance equations of Table I. 

The heat balance on the bubble phase in Figure 4.24 that is assumed to be in plug flow mode and to have a negligible rate of reaction, as well as a negligible heat transfer with the heating/cooling coil, leads to... 

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... 

The plots in Figures 7.8 and 7.9 make both Qer and Qeg infinite and therefore the dense phase and bubble phase conditions are identical and are equal to the output conditions of the reactor and the regenerator in this example. In case of finite exchange rates between the bubble and dense phases in reactor and regenerator, the output conditions from the reactor and the regenerator can be obtained by mass and heat balances for the concentration and the temperature of both phases and these expressions use the same symbols as before, but without the subscript D (used to signify the dense phase before). 

The energy at the stripper overhead was 392 Btu/lb, and the enthalpy at the debutanizer bubble point was 202 Btu/lb, a difference of 190 Btu/lb. This figure was the previous duty multiplier for the cooler calculation. Therefore the free energy not used in this heat balance is the 158 Btu/lb calculated. It appears we need only take the enthalpy difference of 202 and 158, and that is the cooler duty answer. This answer is not feasible, however, as our debutanizer feed starts at 34.7 psia and ends at 99.7 psia. A compressor between these two points would be required. To avoid the expense of a compressor, cool the stripper overhead to a sub-bubble point temperature and then use a pump. 

The current efficiency increases with increasing anode-cathode distance, because for a longer anode-cathode distance there is less convection, less interaction between gas bubbles and the metal, and more stable conditions. It was found that the current efficiency is independent of the anode-cathode distance above a certain distance. However, the ohmic drop in the electrolyte increases with the interpolar distance, so the cell voltage increases. These two factors influence the energy efficiency in an opposite manner. Furthermore, the heat balance of the cell sets limits to the variation of the anode-cathode distance. 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

An illustrative way to visualize the flow/toughness/heat balance is to view the key resin properties in a bubble plot as shown in Figure 15.9. It can easily be... 

Due to their complexity, the model equations will not be derived or presented here. Details can be found elsewhere [Adris, 1994 Abdalla and Elnashaie, 1995]. Basically mass and heat balances arc performed for the dense and bubble phases. It is noted that associated reaction terms need to be included in those equations for the dense phase but not for the bubble phase. Hydrogen permeation, the rate of which follows Equation (10-51b) with n=0.5, is accounted for in the mass balance for the dense phase. Hydrodynamic parameters important to the fluidized bed reactor operation include minimum fluidization velocity, bed porosity at minimum fluidization, average bubble diameter, bubble rising velocity and volume fraction of bubbles in the fluidized bed. The equations used for estimating these and other hydrodynamic parameters are taken from various established sources in the fluidized bed literature and have been given by Abdalla and Elnashaie [1995]. 

The above discussions pertain to models assuming three regions the dense phase, bubble phase and separation side of the membrane. The membrane is assumed to be inert to the reactions. There are, however, cases where the membrane is also catalytic. In these situations, a fourth region, the membrane matrix, needs to be considered. The mass and heat balance equations for the catalytic membrane region will both contain reaction-related terms. 

Zuber (Z4) writes for the heat balance on the growing bubble... 

Electrolytic gas evolution is a significant and complicated phenomenon in most electrochemical processes and devices. In the Hall process for aluminum production, for example, bubbles evolved on the downward-facing carbon anodes stir the bath and resist the current, both of which directly affect the heat balance and the cell voltage. Bubbles appear as a result of primary electrode reactions in chlorine and water electrolysis, and as the result of side reactions in the charging of lead-acid batteries and some metal electrowinning. Stirring of the electrolyte by gas evolution is an important phenomenon in chlorate production. Electrolytically evolved bubbles have also been used in mineral flotation. Relatively few major electrochemical processes do not evolve gas. 

For the partial condenser, Figure 5.21, a reflux ratio specification is used instead of the energy balance, since the condenser duty is unknown and depends upon the state of the overhead product (vapor, liquid, or liquid below bubble point). The feed tray, Figure 5.23, naturally has the feed stream included as an input term. Otherwise it is similar to the other trays. The reboiler s heat balance, Figure 5.25, reflects the heat duty of the reboiler, Qh... 

When a liquid is heated under constant pressure, or when the pressure is reduced at constant temperature, vapor or gas and vapor-filled bubbles are generated and grow. The former process of cavity production is known as boiling, the latter as cavitation. The hypothesis of boiling was checked by Sharbaugh and Watson (1962) under pulses of a few ys in a uniform field. The current was assumed to be space-charge limited, and the following relationship derived from the heat balance ... 

This section outlines procedures for calculating product draw tray temperatures at all points in the tower and for making an overall heat balance around the system. The method is based on calculating the hydrocarbon product partial pressure in the vapor above each draw tray and converting the bubble point of the product liquid on the tray to this pressure. Prior to beginning these calculations, the overall system material balance and the properties of all product streams must have been defined. 

Heat transfer between the gas bubbles and the emulsion phase may be calculated in a somewhat similar manner. However, in the establishment of a heat balance about the bubble we shall assume that the rate of transfer between the cloud surrounding the bubble and the emulsion is fast enough so that this process does not contribute a resistance. However, in contrast to the formulation of the mass transfer problem, here too we have to take into consideration the heat capacity of the solids contained in the bubbles. 

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