This paper presents an analytical method for determining wellbore heat transmission during liquid or gas flow along the tubing. The mathematical model describes the heat transfer of the flowing fluid in the wellbore and in the surrounding formation as one whole physical system. The transient heat transfer equations in the two regions with coupling at the sandface are solved simultaneously. Previous treatments of wellbore heat transmission are improved upon in several aspects. Non-homogeneous formations are treated which consist of several layers with different physical properties and arbitrary initial temperature distributions in the vertical direction. Closed form analytical solutions are obtained in real space and in Laplace space, which can be used to calculate the temperature distribution along the wellbore and in the formation, and to evaluate heat transfer rate and cumulative heat exchange between wellbore and formation. A more accurate formula is given for the widely-used transient heat conduction function f(t/sub D/) of thermal resistance. This is shown to differ from Ramey's approximate solution at early time, while approaching it at late time. 14 refs., 10 figs., 1 tab.

/pdf/an-analytical-solution-for-wellbore-heat-transmission-in-1wp0grje7n.pdf

An analytical solution for wellbore heat transmission in layered formations

The petroleum system; status of research and methods, 1990

During two shallow thermal drilling programs, thermal measurements were obtained in 56 shallow (76.2 m) and one intermediate (457.3 m) depth holes located both onshore and offshore along the southern margin of the Salton Sea in the Imperial Valley, California. These data complete the surficial coverage of the thermal anomaly, revealing the shape and lateral extent of the hydrothermal system. The thermal data show the region of high thermal gradients to extend only a short distance offshore to the north of the Quaternary volcanic domes which are exposed along the southern shore of the Salton Sea. The central thermal anomaly has an arcuate shape, about 4 km wide and 12 km long. Across the center of the anomaly, the transition zone between locations exhibiting high thermal gradients and those exhibiting regional thermal gradients is quite narrow. Thermal gradients rise from near regional (0.09°C/m) to extreme (0.83°C/m) in only 2.4 km. The heat flow in the central part of the anomaly is greater than 600 mW/m2 and in the two local anomalies exceeds 1200 mW/m2. The shape of the thermal anomaly is asymmetric with respect to the line of volcanoes previously thought to represent the center of the field, with its center line offset south of the volcanic buttes. There is no broad thermal anomaly associated with the magnetic high that extends offshore to the northeast from the volcanic domes. The Salton Sea thermal anomaly can be described as three nested thermal features superimposed on the regional Salton Trough heat flux: a broad region of elevated conductive heat flow with constant temperature gradients of about 0.1° C/m, a central anomaly of high (0.4°C/m) near-surface gradients observed through a conductive thermal cap underlain by a nearly isothermal zone of hydrothermal circulation, and two local anomalies with shallow temperature gradients as high as 0.8°C/m superimposed on the central geothermal system. These observations of the thermal anomaly provide important constraints for models of the circulation of the hydrothermal system. Thermal budgets based on a simple model for this hydrothermal system indicate that the heat influx rate for local “hot spots” in the region may be large enough to account for the rate of heat flux from the entire Salton Trough.

/pdf/shallow-drilling-in-the-salton-sea-region-the-thermal-hsgzum3yzy.pdf

Shallow drilling in the Salton Sea region: The thermal anomaly

A two-phase flow model for geothermal wells in the presence of non-condensable gas

STATIC_TEMP: a useful computer code for calculating static formation temperatures in geothermal wells

A new method for evaluating formation equilibrium temperature in holes during drilling

Construction of a probe for measuring temperature and pressure in deep wells

On some computation methods of unit response functions from varying-rate data

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A new method for evaluating formation equilibrium temperature in holes during drilling

Construction of a probe for measuring temperature and pressure in deep wells

On some computation methods of unit response functions from varying-rate data