Correlation of experimental data

This has the advantage that the expressions for the adsotbed-phase concentration ate simple and expHcit, and, as in the Langmuir expression, the effect of competition between sorbates is accounted for. However, the expression does not reduce to Henry s law in the low concentration limit and therefore violates the requirements of thermodynamic consistency. Whereas it may be useful as a basis for the correlation of experimental data, it should be treated with caution and should not be used as a basis for extrapolation beyond the experimental range. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

This method for vertical thermosiphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients 30 percent, which is about the same range of accuracy for most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. See Figures 10-110 and 10-111. 

Two equations have been proposed for correlation of experimental data on pentane isomerizaton the single-site Langmuir-Hinshelwood expression ... 

The choice of capacity is sometimes a problem, and may change according to the particular circumstance. Sometimes using a definition of time constant, based on the above equations, is not very helpful and other means must be employed. For example, mixing time is a very important time constant relating to liquid mixing, and this is best obtained directly from empirical correlations of experimental data. 

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

Fig. 6.16 Comparison of Heywood correlation with experimental results for cylinders of — 2, 4 and 10. and Re are based on Dashed lines are calculated from the correlations of experimental data given in Table 6,1. Light solid lines are the corresponding Heywood predictions.

However, simple kinetic models, especially of the Langmuir—Hinshel-wood type, can serve with advantage for correlation of experimental data in spite of simplifying assumptions which are necessary for their derivation. Experience shows that heterogeneous acid—base catalysis is the very field where they fit best. Their most frequent general form... 

Figure 4.20 shows the correlation of experimental data of Hammerschmidt (1939) with five inhibitors with the pressure and temperature axes reversed from their normal position. The striking feature of Figure 4.20 is the parallel nature of all experimental lines, for the inhibition effect of both alcohols and salts relative to pure water. The parallel solid lines provide some indication of the molecular nature of the inhibition. Normally a phase transformation is considered relative to the change in Gibbs free energy defined as ... 

In 2001, Mirodatos et al. [89] stressed the importance of transient studies as an alternative to steady continuous reactor operations. A combination of microkinetic analysis together with transient experiments should allow the determination of the global catalytic conversion from elementary reaction steps. Prerequisite for such analysis is the correlation of experimental data with the data of a model. Compliance between the data helps to derive the reaction mechanism. 

The convective heat transfer coefficients hi and h0 must be calculated from equations that involve the geometry of the system, the physical properties of the fluid, and the velocity with which it is flowing. These equations are obtained variously by more or less fundamental analysis of the heat transfer and fluid flow mechanisms, or by correlation of experimental data, or by combinations of these methods. A few typical values of the film coefficients are... 

With turbulent flows we normally have to resort to the correlation of experimental data. Friction between fluids and surfaces are normally characterised by friction factors. Different flow situations give rise to different friction factors. 

Turbulent flow, Re > 5000. In turbulent flow, one has to rely on correlation of experimental data... 

Fluid flow is often turbulent, and so heat transfer by convection is often complex and normally we have to resort to correlations of experimental data. Dimensional analysis will give us insight into the pertinent dimensionless groups see Chapter 6, Scale-Up in Chemical Engineering, Section 6.7.4. 

Correlation of Experimental Data - Formation of Gas Bubbles at an Orifice... 

Correlation of experimental data with fundamental parameters... 

The above sections have presented models that link the process of diffusion of small penetrants in polymers to microscopic features of the penetrant polymer system. Strictly speaking the type of diffusion models presented above are not truly microscopic because they actually describe average and not truly local - microscopic - properties of the penetrant polymer system. Sometimes even excellent correlations of experimental data offered by these models are due to the fact that the experimental methods used to determine the diffusion coefficients are in turn probing the penetrant polymer system over non-microscopic distances and comparatively long times. 

The purpose of the foregoing discussion has not been to emphasize or even to imply any new method for solving problems, but rather to indicate the necessity of applying intuitive physical reasoning to a difficult problem and to point out the obvious advantage of using any and all information which may be available. When the problem of correlation of experimental data for a previously unsolved situation is encountered, one must frequently adopt devious methods to accomplish the task. 

An interesting peak heat-flux phenomenon is observed when liquid droplets impinge on hot surfaces. Experiments with water, acetone, alcohol, and some of the Freons indicate that the maximum heat transfer is observed for temperature excesses of about 165°C, for all the fluids. The peak flux is a function of the fluid properties and the normal component of the impact velocity. A correlation of experimental data is given in Ref. 30 as... 

Solubility data of biological compounds taken from literature are considered in this work. Different thermodynamic models based on cubic equations of state and UNIFAC are used in the correlation of experimental data. Interaction parameters are obtained by group contribution approach in order to establish correlations suitable for the prediction of the solid solubility. 

Nonequilibrium conditions may occur with respect to disturbances in the interior of a system, or between a system and its surroundings. As a result, the local stress, strain, temperature, concentration, and energy density may vary at each instance in time. This may lead to instability in space and time. Constantly changing properties cannot be described properly by referring to the system as a whole. Some averaging of the properties in space and time is necessary. Such averages need to be clearly stated in the utilization and correlation of experimental data, especially when their interpretations are associated with theories that are valid at equilibrium. Components of the generalized flows and the thermodynamic forces can be used to define the trajectories of the behavior of systems in time. A trajectory specifies the curve represented by the flow and force components as functions of time in the flow-force space. 

Here, we note that under extensive creep conditions, C is also proportional to PV, but the proportionality factor is different from that which applies in Eqn. (9). In some specimens, the proportionality factor for C, in SSC is not appreciably different than that for the extensive creep parameter C, so that apparent correlations of experimental data in terms of C are actually correlations in terms of Ct. The important distinction arises when an attempt is made to calculate the value of the fracture parameter for use in design or life estimation. Under SSC conditions, C, can be much greater than C so that predictions based upon C in SSC will be nonconservative. 

Figure 4-20 Correlation of experimental data (36 percent KATB feed) by the axial dispersion model.

One of the goals of the experimental research is to analyze the systems in order to make them as widely applicable as possible. To achieve this, the concept of similitude is often used. For example, the measurements taken on one system (for example in a laboratory unit) could be used to describe the behaviour of other similar systems (e.g. industrial units). The laboratory systems are usually thought of as models and are used to study the phenomenon of interest under carefully controlled conditions. Empirical formulations can be developed, or specific predictions of one or more characteristics of some other similar systems can be made from the study of these models. The establishment of systematic and well-defined relationships between the laboratory model and the other systems is necessary to succeed with this approach. The correlation of experimental data based on dimensional analysis and similitude produces models, which have the same qualities as the transfer based, stochastic or statistical models described in the previous chapters. However, dimensional analysis and similitude do not have a theoretical basis, as is the case for the models studied previously. 

For a chemical engineering problem, the concrete activity of the correlation of experimental data shows the following two particularities ... 

Fariss, R. H., and V. J. Law, An efficient computational technique for generalized application of maximum likelihood to improve correlation of experimental data, Comput. Chem. Eng., 3, 95-104 (1979). 

Correlations of experimental data have shown that relative activity of the catalyst for cracking gas oil also decreases exponentially with time, the exponent in this case being remarkably close to the exponent m — 1 in the formula for rate of coke deposition (73,290). The activity at the shortest times investigated, on the order of 1 to 5 seconds, is roughly 100 times that noted after one hour of use (73). Synthetic silica-alumina shows a slower rate of decline in activity with time than activated clay. Thus, although the initial activities of the two are about equal, the synthetic catalyst is three to four times as active as activated clay after two hours of exposure to oil vapors at identical cracking conditions. 

Equality constraints arise from conservation equations (mass, mole, energy, and momentum balances) and constitutive relations (the laws of chemistry and physics, correlations of experimental data, design equations, etc.). Any equation that is introduced into the optimization model that contains an equal (=) sign will become an equality constraint. Many examples of such equations can be found throughout this book. 

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