Planimeter

From a top reservoir map (Fig. 6.2) the area within a selected depth interval is measured. This is done using a planimeter, a hand operated device that measures areas. 

The stylus of the planimeter is guided around the depth to be measured and the respective area contained within this contour can then be read off. The area is now plotted for each depth as shown in Figure 6.2 and entered onto the area - depth graph. Since the structure is basically cut into slices of increasing depth the area measured for each depth will also increase. 

We can now planimeter the thickness of the different NOS contours, plot thickness versus area and then integrate both with the planimeter. The resulting value is the volume of net oil sand (4) and not the GRV ... 

Figure 9-71 is a summation of steps indicated, or the area can be circumscribed witli a planimeter and evaluated. 

Planimetry. The planimeter is a mechanical device which enables the peak area to be measured by tracing the perimeter of the peak. The method is slow but can give accurate results with experience in manipulation of the planimeter. Accuracy and precision, however, decrease as peak area diminishes. 

The amount of BrOnsted sites was evaluated by measuring the surface of the characteristic band at 1540 cm . Corrections have been made to take into account the differences in weight and surface of the wafers. After each test, the wafer was weighted and its cross section was measured with a planimeter. The results were corrected to represent those of a "standard wafer" (Ag) of 5 mg and 25 units of area, according to the following expression ... 

If the area under the curve in Figure A.3 needs to be determined without access to a computer, graphical integration can be used. Once the curve has been plotted, the area under the curve can be measured with a planimeter, or by cutting out the desired area, weighing the paper, and comparing the weight to that of a sample of the same paper of known area. 

Differential thermal analysis was performed with the DuPont 900 differential thermal analyzer the heating rate was usually 10°C. per minute. To determine heats of reaction, the calorimeter attachment to the Du Pont instrument was employed. Planimeter determinations of peak areas were converted to heat values by using standard calibration curves. For the infrared spectra either a Beckman IR5A instrument or a Perkin Elmer 521 spectrophotometer with a Barnes Engineering temperature-controlled chamber, maintained dry, was used. Specimens for infrared were examined, respectively, as Nujol mulls on a NaCl prism or as finely divided powders, sandwiched between two AgCl plates. For x-ray diffraction studies, the acid-soap samples were enclosed in a fine capillary. Exposures were 1.5 hours in standard Norelco equipment with Cu Ko radiation. For powder patterns the specimen-to-film distance was 57.3 mm. and, for long-spacing determinations, 156 mm. 

As the cut and weigh method above, the planimeter method is a perimeter method that makes use of a surveyor s or draftsman s instrument called a planimeter. Using this technique the baseline is drawn as usual. The perimeter of the peak is then traced using the eyepiece containing cross-hairs of the planimeter. 

When the starting point is reached the dial reads a number proportional to the area. On some planimeters the number is proportional to area via a settable scale factor. On other instruments the factor must be determined by measuring a known area. The major advantage of the technique is the ability to handle distorted and tailing peaks to produce a true area. The major problems are the painstaking nature of tracing the peak and the use of a tool not normally found in a laboratory. 

A final point of consideration is the measurement time required. Certainly electronic integration is by far the fastest and the ball and disc integrator would also be considered fast. The manual methods in increasing slowness would be peak height, height and width, triangulation, planimeter, and finally cut and weigh technique. 

Two methods used to find the area under the photometer trace are peak-height-times-half-width approximations and actual measurements with a polar planimeter. Both methods are time consuming and offer little increase in total accuracy over the peak center method. Another method involves computer fitting an assumed scattering function, usually a Gaussian or Lorentzian (though more exotic functions have also been used) to the scan data. The integrated area under the mathematical curve is then calculated. 

The GPC curves in Figure 6 show asphaltene or "large molecule" exclusion at the nominal temperatures of 200, 400 and 600°F. The effect decreases with increasing temperature planimeter areas fall in the ratio of 1.00, 0.65, and 0.40. 

The x-ray diffraction patterns were made with a Picker diffractometer, using Ni-filtered CuK radiation and glass-slide mounts. To derive accurate unit cell constants, slow-scan x-ray patterns were internally standardized with NaCl, KC1, or Si. The integrated intensities were obtained by measuring the area under each peak with a planimeter. 

The animals are sacrificed and the thoracic aorta is removed, cleaned of surrounding tissues, and longitudinally cut and opened for fixation with formaldehyde. The tissue is stained with oil red. The percentage of the intimal surface covered by the oil red positive lesions is calculated with a computerized planimeter. In animals fed a normal diet, the aorta does not show any staining, whereas in cholesterol-fed rabbits the aorta shows severe atherogenic lesions. 

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