A straightforward mathematical procedure allows the calculation of the isogeothermal pattern in and about a salt intrusion. Temperature anomalies are controlled not only by the thermal properties of the media, but also are indicative of the geometry and history of the system. As a simple example, an axially symmetrical structure was chosen to illustrate the kind of inferences one can make from the temperature data, such as discrimination between connected and disconnected domes, and the estimation of the vertical velocity of the intrusion. The numerical results confirm and extend the observations in electrolytic scale models (Hubert Guyod, 1946), and augment W. Heroy’s comments on thermal properties of salt, given at the International Conference on Saline Deposits, Houston, 1962.
Z. F. Daneš’s mathematical formulation of salt dome dynamics was modified to the extent that explicit solutions can be obtained. For both the two‐dimensional and three‐dimensional model, a formula is derived relating the rate of growth and the wavenumber of a fundamental mode with the physical and geometrical parameters. It is shown that there exists one wavenumber for which the rate of growth reaches a maximum. In time this component will dominate and control the final pattern.
If two fluids of different densities are superposed one over the other, the plane interface between the two fluids becomes unstable if the heavy fluid overlays the lighter one. This type of hydrodynamic instability is called Rayleigh‐Taylor instability. The theory of Rayleigh‐Taylor instability is a useful tool to study the distribution of salt domes in the coastal region of the Gulf Coastal Province. In spite of a drastic simplification of the geologic situation, the model shows: a) that the spacing of salt domes about an initial disturtbance depends upon the thickness of the mother salt and viscosity ratio of overlying sediment to salt; b) that domes not only grow upward from the initial disturbance, but domes are also triggered in the vicinity of the primary disturbance, forming a family of incipient domes with a regular pattern; c) that the family of incipient domes develops out of the initial disturbance starting at the location of maximal instability and spreading radially. Several numerical examples provide a framework for examining the disturbance of Gulf Coastal salt domes.
A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable.From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells.
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