Index of content:
Volume 16, Issue 3, 01 March 1945
16(1945); http://dx.doi.org/10.1063/1.1707562View Description Hide Description
16(1945); http://dx.doi.org/10.1063/1.1707563View Description Hide Description
16(1945); http://dx.doi.org/10.1063/1.1707564View Description Hide Description
In this paper a transmission type electron microscope with magnetic lenses is described. The electron speed can be varied between 30 ekv and 100 ekv. The magnification of the instrument is produced in three stages. The instrument has improved air locks, hydraulically operated stage movement, and a stage tilting device up to ±15½°. It is also provided with means for bright and dark field illumination and for conversion into a diffraction camera. Improved electrical circuits provide the necessary stability of the power supplies.
16(1945); http://dx.doi.org/10.1063/1.1707565View Description Hide Description
The diffusion equation is transformed to a set of coordinates moving with the pearlite interface and a solution applicable to the problem obtained in the form of an infinite series of terms. Using the first three terms, the edgewise velocity of pearlite growth is calculated for a plain carbon eutectoid steel using data most of which are obtained by extrapolation. The values obtained show reasonable agreement with values for the rate of pearlite nodule growth determined by Hull, Colton, and Mehl. The velocity increases with decreasing temperature, as expected, and it is shown that this is caused by the change in the solubilities of ferrite and cementite in austenite with temperature. The theory predicts curved ferrite‐austenite and cementite‐austenite interfaces and the carbon concentration in austenite is shown to vary across each of these interfaces.
16(1945); http://dx.doi.org/10.1063/1.1707566View Description Hide Description
A theory has been developed for predicting the behavior of solution gas‐drive oil producing reservoirs, on the basis of previously established empirical laws on the flow of heterogeneous fluids through porous media. Treatments are given both for the simple pressure depletion history without gas injection, and those for systems in which gas is injected during the course of oil production. The specific results provided by the theoretical analysis include the ultimate oil recovery, and the pressure decline, gas‐oil ratio, and productivity factor histories. Two types of gas injection have been considered, namely: (1) that in which the returned gas is supposed to diffuse through and be produced continuously with the oil zone; and (2) that in which the injected gas remains locked in the gas cap, which merely expands as oil production and gas injection proceed. In the latter case the rate of growth of the gas cap is also obtained as a function of the cumulative oil recovery.
The theory is illustrated by numerical application to a hypothetical virgin oil reservoir with an original pressure of 2500 p.s.i. producing by gas‐drive, and with no initial gas cap. It is so found that if no gas is injected into the system the physical ultimate oil recovery will be 14.5 percent of the pore space, or 27.1 percent of the original stock tank oil content, assuming that the formation initially has a connate water saturation of 30 percent. The gas‐oil ratio first declines as production is started, then rises sharply to a maximum of 4400 cu. ft./bbl., and finally falls steeply as the pressure is depleted to atmospheric. If there is no gas segregation and 60 percent of the produced gas is returned to the formation, the ultimate oil recovery will be increased by 27.6 percent. The gas‐oil ratio history will be similar to that with no gas injection, but will rise to a maximum of 10,300 cu. ft./bbl. If 80 percent of the gas is returned, the recovery increase will be 48.8 percent, the maximum in the gas‐oil ratio history reaching a value of 19,450 cu. ft./bbl. If all the gas is returned, the gas‐oil ratio rise will be so rapid that by the time 20,000 cu. ft./bbl. is reached only 23.5 percent additional oil will be recovered. During these operations the productive capacities of the wells will fall by factors of the order of 10, because of the increasing viscosities of the oil and decreasing permeabilities to the oil, as the pressure declines and the oil saturation decreases.
For the case where the gas remains trapped in the gas cap, the ultimate oil recovery will be 163 percent greater than by direct pressure depletion, if the residual oil after gravity drainage is 15 percent of the pore space. This recovery will be essentially independent of the amount of gas return, although the final reservoir pressure at the time of complete gas cap expansion will be greater as more gas is returned. The increased oilviscosity and decreased permeability to the oil will here reduce the specific production capacities of the wells to ¼ or ⅓ of their initial values.
16(1945); http://dx.doi.org/10.1063/1.1707567View Description Hide Description
Apparatus by means of which tire cords may be conditioned and tested at elevated humidities (1.6–65 percent R. H.) and temperatures (20–165°C) is described. The apparatus consists of a portable conditioning unit which is used with a standard tensile testing machine. Equipment for measuringcreep of tire cords under dead load at elevated temperatures is also described. Five representative types of tire cord were employed in the experiments, medium stretch cotton, low stretch cotton, viscose rayon, Fortisan, and Nylon. Tenacity, ``10 pound‐stretch,'' and ultimate stretch are studied as functions of relative humidity, temperature, and moisture regain. It is shown that the tensile properties are best represented as functions of temperature at constant regain. The tenacity of viscose rayon cords decreases with increasing temperature at constant regain in the range of regains 0–5 percent. The tenacity of the medium stretch cotton cords at constant regain falls off with increasing temperature in the range of 20–100°C and then changes very little up to 165°C. That of the low stretch cotton cords, however, decreases in a manner similar to that found for rayon. The Fortisan cords show a decrease of tenacity in the range 20–100°C and then a slight increase for higher temperatures. The cotton, rayon, and Fortisan cords give nearly linear creep curves (elongation vs. log time) in the range of creep times 0.002 to 20 hours. The creep curves for Nylon show a tendency to increase in slope at extended creep times. The creep data are analyzed in terms of two arbitrarily defined indices, ``initial compliance'' and ``weighted creep.'' Both the tensile and creepcharacteristics are discussed from the viewpoint of current theories of structure and also in the light of their relations to serviceability in tires.
16(1945); http://dx.doi.org/10.1063/1.1707568View Description Hide Description
Numerical methods are developed to solve certain types of linear and nonlinear partial differential equations to any desired degree of accuracy with the aid of equivalent electrical networks. The methods of solution of ordinary differential equations, both linear and nonlinear, follow as special cases. Three types of problems are considered:
1. Initial‐value problems. If the field quantities are known along a surface, the networks may be solved by a straight‐forward step‐by‐step calculation. The networks may also be looked upon as supplying a ``schedule'' of operations that can be put on a digital calculating machine.
For time‐varying problems new types of networks are developed in which time appears as an extra spatial variable. Examples of new networks for the elastic field and for the general nonlinear waveequation are given. Sample calculations and theoretical checks of a transient heat flow problem and of an ordinary differential equation are also included.
2. Boundary‐value problems. Four methods of solution are given, the first three being cut and try processes. (a) The method of weighted averages; (b) The method of unbalanced currents and voltages; (c) The ``relaxation'' method; (d) The ``diffusion'' method, that changes the boundary‐value problem into an initial‐value problem by adding to the original partial differential equation a time variable of the form A∂φ/∂t, allowing the unbalanced currents to ``diffuse'' in time.
These numerical methods may also be used to improve the accuracy of the results found on the Network Analyzer. Examples of calculations are given for the electromagnetic and the elastic fields.
3. Characteristic‐value problems. Their methods of solution are similar to those of boundary‐value problems. An additional method of unbalanced admittances is also indicated. It is shown that by calculating the power in the network, the characteristic value of the assumed function is found.
An improved characteristic value of the linear harmonic oscillator, solved initially on a Network Analyzer, is calculated as an example.
In general the electrical networks may be used to check the consistency and correctness of solutions arrived at by other methods, approximate or exact. The unbalanced currents at the junctions (easily calculated) give a quantitative measure of the deviation from the correct solution.
16(1945); http://dx.doi.org/10.1063/1.1707569View Description Hide Description