Enthalpy balance streams

The principles outlined so far may be used to calculate the tower height as long as it is possible to estimate the temperature as a function of Hquid concentration. The classical basis for such an estimate is the assumption that the heat of solution manifests itself entirely in the Hquid stream. It is possible to relate the temperature increase experienced by the Hquid flowing down through the tower to the concentration increase through a simple enthalpy balance, equation 68, and thus correct the equiHbrium line in ajy—a diagram for the heat of solution as shown in Figure 9. 

In a process such as liquid-liquid extraction the enthalpy balance is usually unimportant, and the temperature can be assumed constant through the column of stages. Here the question is simply how do the components of the input feed streams distribute. Any other process, such as washing, isotope separation, etc. for which the enthalpy balance is unimportant, requires only the answer to the same simple question. 

Classical Adiabatic Design Method The classical adiabatic design method assumes that the heat of solution serves only to heat up the liquid stream and there is no vaporization of the solvent. This assumption makes it feasible to relate increases in the liquid-phase temperature to the solute concentration x by a simple enthalpy balance. The equilibrium curve can then be adjusted to account for the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will be concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-10 in Example 6. 

The calculation procedure consists of a determination of the air/fuel molar ratio that will result in a combustor outlet temperature of 2000F, followed by the calculation of enthalpy and entropy of flow streams at the various state points in the cycle. The net work output from the turbine is calculated by subtracting the compressor work requirements from the total turbine expansion work determined from the enthalpy balance. Irreversible entropy productions are calculated by a routine entropy balance around each process step. 

The enthalpy balance around softener V considers the sensible heats and the endothermic reaction enthalpy of 4.51 kg/s(db) 0.4 MJ/kg(db) = 1.80 MW. The flow rate of the recycle water stream is found to be 1,20 the feed stream (on the basis of water). The enthalpy to be supplied in heater E3 is 10,4 MW. 

As with mass balances (see Chapter 2), an enthalpy balance may be performed within any properly defined boundary, whether real or imaginary. For example, an enthalpy balance can be applied across the entire unit or process. The enthalpy of the feed stream(s) is equated with the enthalpy of the product stream(s) plus the heat loss from the process. All the enthalpy terms must be based on the same reference temperature. 

The enthalpy balance sums up the CPs of the cold streams within an enthalpy interval, sums up the CPs of the hot streams within the same interval, subtracts the latter from the former, and then multiplies the result by the temperature difference across the interval. The resulting heat balance might be a positive or a negative value. A positive value indicates that there is a net deficit of heat within a temperature interval. A negative value indicates that there is a net surplus of heat in an interval. The interval heat balances for all of the intervals are shown in Fig. 10. Such interval heat balances allow for heat recovery within each temperature interval. However, to complete the picture, the algorithm must consider heat recovery between intervals. Where an interval has a surplus of heat in Fig. 10, this should be used, where possible, to supply... 

The calculation of multi-stage separation processes involves the solution of phase equilibrium relationships, mass balances, and energy balances. Energy balances require the computation of enthalpies of streams entering and leaving an equilibrium stage. The enthalpy is a function of state, defined in Section 1.1.2 as H = U -i- PV. It is a function of the stream composition, its temperature, and its pressure. 

Multi-stage separation calculations require heat balances involving transition between the phases. The enthalpy balance equations must, therefore, include heats of vaporization and condensation. Usually these heats are not calculated separately but are implied by using appropriate methods for calculating liquid enthalpies and vapor enthalpies. Consider, for instance, a system where a vapor stream and a liquid stream enter with enthalpies and // respectively, and leave as a mixed phase stream with vapor enthalpy and liquid enthalpy h2. These are total stream enthalpy rates with units such as kJ/h. If no heat is added to or removed from the system, an energy balance is written as... 

The enthalpy balance (Equation 12.35) is satisfied, giving a residual of 8 kJ/h. Compared with the rigorous perturbed model results, the reduced model predicts the products enthalpies and temperatures fairly well. The products compositions can use some improvement. It is noted that Equation 12.38, used for calculating the stream enthalpies in the reduced model, does not take into account the effect of composition. This could be improved by using the ideal solution method as applied in Example 12.5. This method is still computationally simple enough to satisfy the reduced model conditions of reduced computing time. 

The above equations relate the heat-transfer rate to the local temperatnre difference (J - t) and the heat-transfer area A throngh the overall heat-transfer coefficient U. In almost all practical sitnations, one or both temperatnres will vary along the length of the heat exchanger. The change in temperatnre of each stream is calcnlated from the enthalpy balance on that stream. To apply Equation (6.98) to the design of a heat exchanger in which the temperature difference is not constant, the equation needs to be written in differential form ... 

ENTHALPY BALANCES IN HEAT EXCHANGERS. In heat exchangers there is no shaft work, and mechanical, potential, and kinetic energies are small in comparison with the other terms in the energy-balance equation. Thus, for one stream through the exchanger... 

The actual variations in the V and L streams in a distillation column depend on the enthalpies of the vapor and liquid mixtures. The limitations imposed by assuming constant molal overflow can be removed by enthalpy balances used in conjunction with material balances and phase equilibria. The enthalpy data may be available from an enthalpy-concentration diagram, such as the one in Fig. 18.24. Since benzene-toluene solutions are ideal, this diagram was constructed using molar average heat capacities and heats of vaporization. Some... 

As shown in the previous section, the diameter of a packed absorption tower depends on the quantities of gas and liquid handled, their properties, and the ratio of one stream to the other. The height of the tower, and hence the total volume of packing, depends on the magnitude of the desired concentration changes and on the rate of mass transfer per unit of packed volume. Calculations of the tower height, therefore, rest on material balances, enthalpy balances, and estimates of driving force and mass-transfer coefficients. 

Construct an exchanger operating diagram. The plot provides the local shellside fluid equilibrium temperature Ts as a function of the corresponding fluid specific enthalpy (see Fig. 17.59). A correlation between the shellside and tubeside fluid enthalpies is provided by the enthalpy balance, therefore the tubeside temperature dependence T, can be presented as well. The local equilibrium temperature is assumed to be the temperature of the stream well mixed at the point in question. Note that this step does not involve an estimation of the overall heat transfer coefficient. 

An enthalpy balance can be made in which the total enthalpy of all leaving streams minus the total enthalpy of all entering streams is equal to the heat absorbed from external sources by the process. 

Balanced composite curves are similar with those discussed above, with the difference that now the utilities are considered as streams. Since the utilities covers any imbalance between the streams selected for integration, the enthalpy balance is closed. Moreover, the design of the heat exchangers is done in the balanced grid diagram. 

Solution. The original network is presented in Fig. 10.35. The smallest unit E6 has a duty of 2000. Visual inspection can identify a loop passing through the units El and E6. The next step is to suppress the unit E6 by shifting its load to El. The unit El becomes Ela, its duty going from 3000 to 5000. This operation keeps constant the enthalpy balance of the streams hotl and coldl, but modifies the temperatures. 

In the splitter, composition of Lqut is not equal to Lout or Also, stream compositions are not related by equilibrium constraints, nor need the outlet streams be at the same temperature or pressure. Thus, the only relationships are (C- 1) component balances, one total material balance, an enthalpy balance, and three mole fraction constraints, so that... 

When the pressure of a liquid stream of known composition, flow rate, and temperature (or enthalpy) is reduced adiabatically across a valve as in Fig. l. a, an adiabatic flash calculation can be made to determine the resulting temperature, compositions, and flow rates of the equilibrium liquid and vapor streams for a specified flash drum pressure. In this case, the procedure of Fig. 7.4o is applied in an iterative manner, as in Fig. 7.8, by choosing the flash temperature Tv as the iteration or tear variable whose value is guessed. Then X, y, and L are determined as for an isothermal flash. The guessed value of Tv (equal to TJ is checked by an enthalpy balance obtained by combining (7-15) for Q = 0 with (7-14) to give... 

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