A plot of

The low-pressure extrapolated data points were generated by linear extrapolation of the lowest 4-6 points on a plot of... 

Figure 4.9 shows a plot of Eq. (4.12). As the purge fraction a is increased, the flow rate of purge increases, but the concentration of methane in the purge and recycle decreases. This variation (along with reactor conversion) is an important degree of freedom in the optimization of reaction and separation systems, as we shall see later. 

Rgure 8.2 A plot of economic potential versus conversion shows where the optimum is, but why does the optimum occur where it is ... 

Now using a hydrocarbon component, say ethane, as an example, let us consider the other parameter, volume, using a plot of pressure versus specific volume (i.e. volume per unit mass of the component, the inverse of the density). The process to be described could be performed physically by placing the liquid sample into a closed cell (PVT cell), and then reducing the pressure of the sample by withdrawing the piston of the cell and increasing the volume contained by the sample. 

The primary drive mechanism for gas field production is the expansion of the gas contained in the reservoir. Relative to oil reservoirs, the material balance calculations for gas reservoirs is rather simple the recovery factor is linked to the drop in reservoir pressure in an almost linear manner. The non-linearity is due to the changing z-factor (introduced in Section 5.2.4) as the pressure drops. A plot of (P/ z) against the recovery factor is linear if aquifer influx and pore compaction are negligible. The material balance may therefore be represented by the following plot (often called the P over z plot). 

Routine production tests are performed, approximately once per month on each producing well, by diverting the production through the test separator on surface to measure the liquid flowrate, water cut, and gas production rate. The wellhead pressure (also called the flowing tubing head pressure, FTHP) is recorded at the time of the production test, and a plot of production rate against FTHP is made. The FTHP is also recorded continuously and used to estimate the well s production rate on a daily basis by reference to the FTHP vs production rate plot for the well. 

Fig. Ill-13. (a) Plots of molecular density versus distance normal to the interface a is molecular diameter. Upper plot a dielectric liquid. Lower plot as calculated for liquid mercury. (From Ref. 122.) (b) Equilibrium density profiles for atoms A and B in a rare-gas-like mixmre for which o,bb/ o,aa = 0.4 and q,ab is given by Eq. III-56. Atoms A and B have the same a (of Eq. m-46) and the same molecular weight of SO g/mol the solution mole fraction is jcb = 0.047. Note the strong adsorption of B at the interface. [Reprinted with permission from D. J. Lee, M. M. Telo de Gama, and K. E. Gubbins, J. Phys. Chem., 89, 1514 (1985) (Ref. 88). Copyright 1985, American Chemical Society.]...

A plot of G x versus composition is shown in Fig. IV-22 for condensed films of octadecanol with docosyl sulfate. Gaines [241] and Cadenhead and Demchak [242] have extended the above approach, and the subject has been extended and reviewed by Barnes and co-workers (see Ref. 243). 

Barnes and Hunter [290] have measured the evaporation resistance across octadecanol monolayers as a function of temperature to test the appropriateness of several models. The experimental results agreed with three theories the energy barrier theory, the density fluctuation theory, and the accessible area theory. A plot of the resistance times the square root of the temperature against the area per molecule should collapse the data for all temperatures and pressures as shown in Fig. IV-25. A similar temperature study on octadecylurea monolayers showed agreement with only the accessible area model [291]. 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

Thus a plot of Ci/n versus Ci should give a straight line of slope 1/n and intercept /n b. 

The CMC for sodium dodecylbenzenesulfonate is about lO Af at 25°C. Calculate K for the preceding reaction, assuming that it is the only process that occurs in micelle formation. Calculate enough points to make your own quantitative plot corresponding to Fig. Xni-13. Include in your graph a plot of (Na )(R ). Note It is worthwhile to invest the time for a little reflection on how to proceed before launching into your calculation ... 

A surfactant solution is a mixture of DTAC (dodecyltrimethylammonium chloride) and CPC (cetyl pyridinium chloride) the respective CMCs of the pure surfactants are 2 X lO M and 9 x IO M (Ref. 140). Make a plot of the CMC for mixtures of these surfactants versus the mole fraction of DTAC. 

Emulsion A has a droplet size distribution that obeys the ordinary Gaussian error curve. The most probable droplet size is 5 iim. Make a plot of p/p(max), where p(max) is the maximum probability, versus size if the width at p/p(max) = j corresponds to... 

A plot of P/n versus P should give a straight line, and the two constants and b may be evaluated from the slope and intercept. In turn, n may be related to the area of the solid ... 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

Make a plot of Eq. XVII-69 as 6 versus P, and, for comparison, one of a Langmuir adsorption isotherm of same limiting or Henry s law slope. Comment on the comparison. 

Convert the upper curve of Fig. XVII-31a to an adsorption isotherm, that is, to a plot of V versus P/I. ... 

Show whether a plot of d versus log t should be linear (a form of the Elovich equation). 

If Langmuir adsorption occurs, then a plot of 9 versus p for a particular isothenn will display the fonn of equation (Al.7.3). Measurements of isothenns are routinely employed in this manner in order to detennine adsorption kinetics. 

If adsorption occurs via a physisorbed precursor, then the sticking probability at low coverages will be enhanced due to the ability of the precursor to diflfiise and find a lattice site [30]. The details depend on parameters such as strength of the lateral interactions between the adsorbates and the relative rates of desorption and reaction of the precursor. In figure Al.7,8 an example of a plot of S versus 0 for precursor mediated adsorption is presented. 

Figure Bl.19.21. A plot of cantilever displacement as a function of tip sample separation during approach and retraction with an AFM. Note the adliesive forces upon retraction from the surface.

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