Enthalpy departures

Example 4 Calculation of the BP Method Use the BP method with the SRK eqiiation-of-state for K values and enthalpy departures to compute stage temperatures, interstage vapor and hqiiid flow rates and compositions, and rehoiler and condenser duties for the light-hydrocarhon distdlation-coliimn specifications shown in Fig. 13-51 with feed at 260 psia. The specifications are selected to obtain three products, a vapor distillate rich in Cri and C3, a vapor side-stream rich in n-C4, and a bottoms rich in n-C and n-Cg. 

Example 5 Calculation of the SR Method Use the SR method with the PR equation of state for K values and enthalpy departures. The oil was taken as n-dodecane. To compute stage temperatures and interstage vapor and hquid flow rates and compositions for ahsorher-column specifications shown in Fig. 13-52. Note that a secondary ahsorher oil is used in addition to the main ahsorher oil and that heat is withdrawn from the seventh theoretical stage. 

Calculations were made with the Grayson-Streed modification of the Chao-Seader method for K values and the Lee-Kesler method for enthalpy departures. Initial estimates for stage temperatures and flow rates were as follows, where numbers in parentheses are consistent with specifications ... 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

Combining Equations 4.75 to 4.77 gives the difference between the enthalpy at pressure P and that at the standard pressure Po and is known as the enthalpy departure. 

Equation 4.78 defines the enthalpy departure from a reference state at temperature T and pressure Po ... 

The value of (8Z/dT)P can be obtained from an equation of state, such as the Peng-Robinson equation of state, and the integral in Equation 4.78 evaluated3. The enthalpy departure for the Peng-Robinson equation of state is given by3 ... 

To calculate the enthalpy of liquid or gas at temperature T and pressure P, the enthalpy departure function (Equation 4.78) is evaluated from an equation of state2. The ideal gas enthalpy is calculated at temperature T from Equation 4.81. The enthalpy departure is then added to the ideal gas enthalpy to obtain the required enthalpy. Note that the enthalpy departure function calculated from Equation 4.78 will have a negative value. This is illustrated in Figure 4.9. The calculations are complex and usually carried out using physical property or simulation software packages. However, it is important to understand the basis of the calculations and their limitations. 

Some data comparisons were made of several predictive methods with steam mixture enthalpy data obtained by Professor Wormald (3). To provide a basis of comparison, Figure 6 illustrates how three methods currently in vogue in the thermodynamics world perform in predicting the enthalpy departures from ideality of methane. The predictions of the Lee-Kesler equation-of-state seem to best replicate the data, with a maximum error of 1.2 kJ/kg. 

Figure 6. Comparisons of predicted and experimental enthalpy departures for pure...

Figure 9 provides a comparison of the predictions of empirical methods with Wormald s data for a 50/50 mole percent mixture of steam and methane. As can be seen, the frequently used artifices of calculating mixture enthalpies by blending the pure component enthalpies at either total or partial pressures are very inaccurate. Likewise, the assumption of ideal gas enthalpy for the real gas mixture, equivalent to a zero enthalpy departure on the diagram, is an equally poor method. 

Figure 9. Comparisons of predicted and experimental enthalpy departures for an equimolar steam-methane mixture at 598 K (equation-of-state methods)...

Experimental Determination of Enthalpy Departures of Well Defined Simulated Natural Gas/Water Mixtures." In addition, densities and dew points are being measured. 

Predictions of the vapor volume and enthalpy departure for a water containing natural gases were compared with data being generated by Hall and coworkers at Texas A M under GPA sponsorship (10). Both equations of state performed well the average error Tn the predicted volume was less than one percent (abs) and the absolute average error in the predicted enthalpy departure was about four KJ/kg. 

Simple vapor and liquid enthalpy models may be developed by recognizing that, on a mass basis, vaporization enthalpies and vapor and liquid heat capacities do not vary widely from component to component, and the latter are relatively independent of temperature. Enthalpy departure functions in mass units are first defined as follows ... 

The enthalpy models are actually for the enthalpy departure function. Normally, the molar enthalpy of a phase is found from the ideal gas enthalpy and the enthalpy departure... 

FIGURE 1.6 Enthalpy departure from ideal-gas state Zc = 0.23. (Yen and Alexander—A1CHE Journal 11 -334 1965.)... 

The Peng-Robinson equation of state was used to estimate K values and enthalpy departures [as opposed to the De Priester charts used in Example 1 and by Seader (ibid.) who solved this problem by using the Thiele-Geddes (op. 

This more complicated example features a partial condenser (with vapor product) and a vapor sidestream withdrawn from the 13th stage. The SRK equation of state may be used for estimating the K values and enthalpy departures for thennodynamic properties. 

In general, the estimation of enthalpy (departure) can be represented in the following manner ... 

The enthalpy departure (and other thermodynamic properties) is then calculated using equations obtained from the compressibility factor via the usual thermodynamic relationships. 

In the case of reacting systems in petroleum refining, the required estimates of heats of reaction are obtained, as usual, by the difference between the enthalpy departures of the products and reactants. As an example, the endothermic heat of... 

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