Temperature-time data

The function 7(f) can be chosen for the whole reaction time interval, or two or three subsequent temperature-time data points 7(fi-i), 7(fi), and 7(fi+i) can be approximated by polynomials of second or third order 7,(f), respectively. These polynomials will then be used in a procedure for numerical integration in each integration step i. This method has been successfully applied in a kinetic study of the partial oxidation of hydrocarbons (Skrzypek et al., 1975, Krajewski etai, 1975, 1976, 1977). 

The values of k,, 7), and Tf can be obtained from the temperature-time data... 

Therefore, by using equation 7.64 it is possible to automatically include the energy of rotation in the calculation of Arcorr. As indicated in section 7.1, it is frequently observed that the temperature of the calorimeter proper during the initial and final periods is, to a good approximation, a linear function of time. In this case, the values of gj and gf in equation 7.64 are derived from a linear least squares fit to the experimental temperature-time data obtained during those periods. When significant departures from linearity are observed, T0Cj and Tx,f... 

The results of the calibration and reaction experiments are shown in table 8.1 [142]. In this table, t is the time during which a current of intensity /flows through the calibration resistance, V the measured potential drop across the resistance, and m the mass of sample. The values of ATad for the calibration and reaction experiments were determined from the corresponding temperature-time data, using the Regnault-Pfaundler method with 7], Tf, k, and Tc0 calculated from equations 7.12-7.15 (section 7.1). 

A rather simple model can be developed to fit temperature-time data such as those of Figures 2 and 5, and to predict the total catalyst life. Consider the fixed-bed deactivation of the Hopcalite catalyst as an example. If ve assume that the deactivation rate is a function of current activity alone, then... 

Figure 7. comparison of temperature time data, Hopcalite catalyst, with equation (6). 

Temperature Time-Data Series Indicating Effective Flow Velocities... 

The following temperature time data were obtained for two different critical concentrations of acetic anhydride under adiabatic operation. The heating rate was 2 C/rain. 

P9-19, The following temperature-time data was taken on the ARSST. Deienninc the heat of reaction and the activation energy. Heat capacitv of the solution Cf ... 

Heat the water in the beaker sufficiently to cause all of the naphthalene to melt. Be sure that the bulb of the thermometer dips completely below the surface of the molten naphthalene and that all of the naphthalene is below the level of the water in the beaker. Stop heating the water, and allow the apparatus to cool slowly while you stir the naphthalene continuously with a slow up-and-down motion of the wire stirrer. The stirrer must not touch the thermometer. When the thermometer reading has dropped to 82°C, start reading and recording the temperature to the nearest 0.1° every half-minute. Continue to take readings until it becomes impossible to stir. Record your temperature-time data in TABLE 20.1. 

TABLE 20.2 Temperature-time data for cooling pure naphthalene. 

Three and one-half turns of 0.001-in. platinum wire wound on two Jia-in.-diameter copper wire supports spaced in. apart were used as the probe and connected into a bridge circuit. The temperature-time data are displayed on an oscilloscope and photographed. 

Plastic deformation is commonly measured by measuring the strain as a function of time at a constant load and temperature. The data is usually plotted as strain versus time. Deformation strain can be measured under many possible loading configurations. Because of problems associated with the preparation and gripping of tensile specimens, plastic deformation data are often collected using bend and compression tests. 

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

The evaluation of ehemieal reaetion hazards involves establishing exothermie aetivity and/or gas evolution that eould give rise to inei-dents. Flowever, sueh evaluation eannot be earried out in isolation or by some simple sequenee of testing. The teehniques employed and the results obtained need to simulate large-seale plant behavior. Adiabatie ealorimeters ean be used to measure the temperature time eurve of selfheating and the induetion time of thermal explosions. The pertinent experimental parameters, whieh allow the data to be determined under speeified eonditions, ean be used to simulate plant situations. 

Thus all the different temperature related data in Fig. 2.58 could be shifted to a single master curve at the reference temperature (7 ). Alternatively if the properties are known at Tref then it is possible to determine the property at any desired temperature. It is important to note that the shift factor cannot be applied to a single value of modulus. This is because the shift factor is on the horizontal time-scale, not the vertical, modulus scale. If a single value of modulus 7, is known as well as the shift factor ar it is not possible to... 

Both of the sources above contain tWo types of failure rate data used in CPQRAs time-related failure rates and demand-related failure rates. Time-related failure rates, presented as failures per 10 hours, are for equipment that is normally functioning, for example, a running pump, or a temperature transmitter. Data are collected to reflect the number of equipment failures per operating hour or per calendar hour. 

Kinetic studies at several temperatures followed by application of the Arrhenius equation as described constitutes the usual procedure for the measurement of activation parameters, but other methods have been described. Bunce et al. eliminate the rate constant between the Arrhenius equation and the integrated rate equation, obtaining an equation relating concentration to time and temperature. This is analyzed by nonlinear regression to extract the activation energy. Another approach is to program temperature as a function of time and to analyze the concentration-time data for the activation energy. This nonisothermal method is attractive because it is efficient, but its use is not widespread. ... 

The tests are performed under carefully controlled stress (load), temperature, time, and creep (elongation) conditions. To save time, tests for different constant loads are performed simultaneously on different specimens of the same material. Creep tests may be rather extensively conducted, as for example when developing creep data prior to the design and fabrication of the first all-plastic airplane (41). The usual procedure is to plot the creep versus time curve, but other combinations are possible. 

The minimum number of postulates of the model of a desorption process with no explicit analytical expression of the heating schedule are required if the primary output data are treated according to Eqs. (10) and (12), viz. by numerical or graphical derivations and integrations of the recorded pressure data. After an adaptation of the analyzer, these operations can be performed by means of electrical circuits. The known temperature-time relationship (either in the form of an analytical function or established... 

Data to demonstrate the stability characteristics of both the drug substance and the drug product must be collected. Studies using three different batches of both substance and product in their respective containers/packaging must be conducted. Real-time data should be collected under conditions of temperature and relative humidity in line with the recommended storage. Conditions in different world climatic zones must be taken into consideration for cases where normal environmental... 

Storage conditions will be used. Standard conditions to simulate normal storage are temperatures of 25 or 30 °C and relative humidity of 60 or 65%. A minimum of 12 months real-time data is required for a marketing authorisation application. Real-time data should be supported by accelerated and intermediate stress testing at higher temperature/relative humidity. Photostability should be verified using a single batch. 

Continuous Polymerizations As previously mentioned, fifteen continuous polymerizations in the tubular reactor were performed at different flow rates (i.e. (Nj g) ) with twelve runs using identical formulations and three runs having different emulsifier and initiator concentrations. A summary of the experimental runs is presented in Table IV and the styrene conversion vs reaction time data are presented graphically in Figures 7 to 9. It is important to note that the measurements of pressure and temperature profiles, flow rate and the latex properties indicated that steady state operation was reached after a period corresponding to twice the residence time in the tubular reactor. This agrees with Ghosh s results ). 

These results have been fit to experimental data obtained for the reaction between a diisocyanate and a trifunctional polyester polyol, catalyzed by dibutyltindilaurate, in our laboratory RIM machine (Figure 2). No phase separation occurs during this reaction. Reaction order, n, activation energy, Ea, and the preexponential factor. A, were taken as adjustable parameters to fit adiabatic temperature rise data. Typical comparison between the experimental and numerical results are shown in Figure 7. The fit is quite satisfactory and gives reasonable values for the fit parameters. Figure 8 shows how fractional conversion of diisocyanate is predicted to vary as a function of time at the centerline and at the mold wall (remember that molecular diffusion has been assumed to be negligible). 

Experimental conversion-time data, obtained from the literature, on the bulk free radical polymerization of MMA initiated by AIBN at several temperatures and initiator concentrations, were described by the model. However, the expressions for the rate of conversion and gel effect index were first simplified and rearranged. ... 

Figure 4.27. Arrhenius analysis The right-hand panel shows the assay-vs.-time data for an aqueous solution of a peptide. The regression lines are for storage temperatures of 80°, 73°, 60°, 50°, 40°, and 30°C. The left-hand panel gives the ln(-slope)-vs.-l/T Arrhenius plot.

Obtaining Kinetic Samples for Reactive Extrusion. To develop and test kinetic models, homogeneous samples with a well defined temperature-time history are required. Temperature history does not necessarily need to be isothermal. In fact, well defined nonisothermal histories can provide very good test data for models. However, isothermal data is very desirable at the initial stages of model building to simplify both model selection and parameter estimation problems. 

Adiabatic calorimetry. Dewar tests are carried out at atmospheric and elevated pressure. Sealed ampoules, Dewars with mixing, isothermal calorimeters, etc. can be used. Temperature and pressure are measured as a function of time. From these data rates of temperature and pressure rises as well as the adiabatic temperature ri.se may be determined. If the log p versus UT graph is a straight line, this is likely to be the vapour pressure. If the graph is curved, decomposition reactions should be considered. Typical temperature-time curves obtained from Dewar flask experiments are shown in Fig. 5.4-60. The adiabatic induction time can be evaluated as a function of the initial temperature and as a function of the temperature at which the induction time, tmi, exceeds a specified value. 

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