Capacity modeling

When considering pressure drop models based only on water, hydrocarbons system capacity can be significantly overstated. For Nutter random ring packings the pressure drop/capacity models fit the data within +10% over the range of commercial interest, i.e., 0.1 to 1.0 in. water/ft of packing. Pressure drop alues for design operation should... 

Example 15.7 Determine the washout function for the side capacity model... 

FIGURE 15.6 Side capacity model of stagnancy in a CSTR. 

FIGURE 15.7 Effect of a stagnant zone in a stirred tank reactor according to the side capacity model. 

FIGURE 15.8 Semilog plot of washout function showing two slopes that correspond to the two time constants in the side capacity model. 

C(t, z) capacity model Concentration of inert tracer in an unsteady tubular Exam. 15.4... 

Concentration of inert tracer in the side tank of the Exam. 15.7 capacity model... 

Tr capacity model Dimensionless velocity component in the axial 13.49... 

Vs Volume of side tank in side capacity model Exam. 15.7... 

The heat capacity models described so far were all based on a harmonic oscillator approximation. This implies that the volume of the simple crystals considered does not vary with temperature and Cy m is derived as a function of temperature for a crystal having a fixed volume. Anharmonic lattice vibrations give rise to a finite isobaric thermal expansivity. These vibrations contribute both directly and indirectly to the total heat capacity directly since the anharmonic vibrations themselves contribute, and indirectly since the volume of a real crystal increases with increasing temperature, changing all frequencies. The constant volume heat capacity derived from experimental heat capacity data is different from that for a fixed volume. The difference in heat capacity at constant volume for a crystal that is allowed to relax at each temperature and the heat capacity at constant volume for a crystal where the volume is fixed to correspond to that at the Debye temperature represents a considerable part of Cp m - Cv m. This is shown for Mo and W [6] in Figure 8.15. 

The process step causes significant additional costs for capacity installation, personnel and/or maintenance (material and utility costs are part of the recipe and are included irrespective of the capacity modeling approach selected) of the equipment and hence an explicit modeling of resource requirements is required in addition to capacity constraints. 

With FITEQL numeric procedure Hayes et al. fitted edl parameters to the three models of electric double layer DLM (diffuse layer model), CCM (constant capacity model) and TLM (three layer model) for the following oxides a-FeOOH, AI2O3 and TiC>2 in NaNC>3 solutions [51]. The fitting was performed for surface reaction constants, edl capacity and the densities of the hydroxyl groups on the surface of the oxides. The quality of the fitting was evaluated by the minimization of the function of the sum of the square deviations of the calculated value from the standard error of measured charge. The lower value of the function the better was the fit... 

At high ionic strength, the electric double layer is considered to be plane the so-called constant capacity model (Helmholtz model) is applied. 

We now specify the equation of state used to model detonation products. For the ideal gas portion of the Helmholtz free energy, we use a polyatomic model including electronic, vibrational, and rotational states. Such a model can be conveniently expressed in terms of the heat of formation, standard entropy, and constant pressure heat capacity of each species. The heat capacities of many product species have been calculated by a direct sum over experimental electronic, vibrational, and rotational states. These calculations were performed to extend the heat capacity model beyond the 6000K upper limit used in the JANAF thermochemical tables (J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985). Chebyshev polynomials, which accurately reproduce heat capacities, were generated. 

The heat capacities of many product species have been calculated by a direct smn over experimental electronic, vibrational, and rotational states. These calculations were performed to extend the heat capacity model beyond the 6000K upper limit used in the JANAF thermochemical tables. Chebyshev polynomials, which accurately reproduce the heat capacities, were generated. 

This is probably the most comprehensive set of heat capacity results available for any nickel salt in aqueous solution. Apparent molar heat capacities of aqueous Ni(C104)2 were measured calorimetrically from 25 to 85°C over a molality range of 0.02 to 0.80 moFkg. Standard molar heat capacities of Ni for the same temperature range were obtained by using the additivity rule and data for HC104(aq), given in literature. The results for C° (Ni " ) can be fitted with a conventional heat capacity model valid from... 

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