Predicting Thermal Conductivities of Formations From Other Known Properties

Measuring the thermal properties of rocks and rock-fluid systems is difficult and time consuming and the results from such measurements are of limited value unless complete descriptions of the rock and fluids are given. A need exists for a method of predicting thermal behavior from other more easily measurable properties. Presented here are correlations developed for predicting the thermal conductivity of consolidated sandstones from a knowledge of density, porosity, permeability, and formation resistivity factor. Values for all these properties are available from well logs or core properties are available from well logs or core analysis data. Also obtained were correlations for estimating the thermal conductivity of liquid-saturated sandstones from a knowledge of the conductivities of dry sandstone. The thermal conductivity of most rocks decreases with increasing temperature and a method of estimating this effect is presented. The effect of pressure on conductivities is generally small, but may be predicted from a knowledge of the bulk predicted from a knowledge of the bulk compressibility of the rock. Introduction Although thermal recovery processes have been applied in the petroleum industry for many years, there is still a lack of basic thermal data with which predict the performance of these processes. Much of the thermal conductivity work reported in the literature lacks a complete description of the physical properties of the rocks used, and in physical properties of the rocks used, and in addition, most of the thermal conductivity measurements have been made at room temperature and at atmospheric pressure. The work reported in this paper deals with the thermal conductivity of typical porous rocks at simulated subsurface conditions of temperature, pressure, and saturation. Because thermal conductivity is difficult to measure, emphasis has been placed here on methods of predicting thermal conductivity from other more easily measured properties as well as on methods of predicting the effects of temperature, pressure, and liquid saturation on thermal properties. pressure, and liquid saturation on thermal properties. RELATIONSHIP OF THERMAL CONDUCTIVITY TO OTHER PHYSICAL PROPERTIES The thermal conductivities of dry rocks have been shown to be functions of density, porosity, grain size and shape, cementation, and mineral composition. The first two properties are easy to measure and precise values may, be assigned for correlation purposes. Grain size and shape and cementation are difficult to quantify. There are, however, other related properties that can be used to characterize these properties for use in correlations. Permeability and formation resistivity factors are probably most closely related to these properties and are readily measurable as unique properties and are readily measurable as unique values. Precise mineral composition values are generally not available, and even A they were, it would be difficult to introduce them into correlations. The high thermal conductivity of quartz seems to have a predominating influence, and thus for most sandstones containing quartz in moderate amounts, the effects of other minerals can be ignored. Many efforts have been made to relate thermal conductivity to the physical properties of porous rocks. These efforts have been reviewed in rather complete detail by Scorer and Anand. Unfortunately, most of the correlations developed require a knowledge of the thermal conductivity of the rock matrix or the dry rock at some known porosity. Although some simple correlations have porosity. Although some simple correlations have been obtained, these are for specific systems and are not applicable generally. Probably the most useful work in this area is that reported by Zierfuss and Van der Vliet. Basing their analysis on 36 sandstones having a wide range in measured properties, they obtained a correlation between properties, they obtained a correlation between effective porosity and the product of thermal conductivity and formation resistivity factor. A fourth-order polynomial fit of thermal conductivity and fractional porosity was obtained by regression analysis. Their data also seemed to indicate that thermal conducting increases with permeability, this being attributed to conduction with permeability. SPEJ P. 267