Thermal Stresses Around a Wellbore and Their Small Effect on Velocity Logging
- V.S. Tuman
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- December 1962
- Document Type
- Journal Paper
- 303 - 308
- 1962. Original copyright American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Copyright has expired.
- 1.11 Drilling Fluids and Materials, 1.6 Drilling Operations, 4.1.2 Separation and Treating
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- 204 since 2007
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TUMAN, V.S., MEMBER AIME, U. OF ILLINOIS, URBANA, ILL.
In the first part of this paper, an estimate is made of the magnitude and extent of the thermal stresses which result from mud circulation. Our study is made for the period of relaxation, i.e., when the drilling operations are terminated and mud circulation is discontinued. In the second part, we have shown how the thermal stress can affect the wave propagation. An example is worked out for a Carbondale sandstone (Illinois basin). It is concluded that, in extreme cases when differential temperature is about 100 degrees F, the travel time will be affected by about 2 microsec/ft. For more refined permeability studies, such corrections would be desirable.
MAGNITUDE AND EXTENT OF THERMAL STRESSES RESULTING FROM MUD CIRCULATION
When geological beds are penetrated by boreholes, it is observed that the formation temperatures increase with depth; however, the temperature profile varies considerably from place to place. During drilling operations, mud pumped from a pit at atmospheric temperature absorbs heat from the lower beds. As a result, the drilling fluid returning to the surface is at a higher temperature than the surrounding beds. The temperature gradient in a well depends on the rate of mud circulation and other factors; normally, this temperature gradient is smaller than the natural gradient in the formations. (See Fig. 1.) The temperature difference between the mud column and the surrounding beds gives rise to thermal stresses (which are also important in the phenomenon of fracturing), and it is expected that they will affect the transit time of the sonic front in velocity logging. It is evident that beds near the surface will undergo various cycles and will have a complicated dynamical and thermal-stress history. A limestone bed which is just penetrated will act as a source of heat, warming up the cold mud pumped down a few minutes earlier from the surface pit. The same limestone bed a week later will act as a sink, absorbing heat from the drilling mud which has already warmed up sufficiently to be at a higher temperature than the bed in question. No doubt a large section of the hole will undergo a heat treatment, which will make the calculation of the exact magnitude of the thermal stresses very difficult. In the solution of wellbore thermal equation, it is assumed that the rock around the wellbore is elastic and isotropic, and that the system is radially symmetrical. A complete dynamical solution of the thermal stresses set up at different horizons during the drilling operations would require a comprehensive history of the mud circulation, the surface temperature of the pit and the number of hours in which mud was not circulated.
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