Effect of Temperature on the Thermal Conductivity of Rocks and Its Implication for In Situ Correction

Detailed knowledge of the effects of temperature on the thermal conductivity ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>λ</a:mi> </a:math> ) of rocks is essential for investigating the geothermal regime of basins and their thermal evolution. In this study, the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>λ</c:mi> </c:math> of four rock types (carbonate, clastic, intrusive, and volcanic rocks) were measured at temperatures of 25°C, 50°C, 100°C, 150°C, 200°C, 250°C, and 300°C using the Transient Plane Source (TPS) approach, which is accurate to ±3%. Experimental results demonstrate that the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi>λ</e:mi> </e:math> of carbonate and clastic specimens decrease strongly with increasing temperature. In contrast, the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"> <g:mi>λ</g:mi> </g:math> of intrusive and volcanic rocks are relatively insensitive to temperature. The temperature ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M5"> <i:mi>T</i:mi> </i:math> ) dependence of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M6"> <k:mi>λ</k:mi> </k:math> can be classified into three groups in terms of the value of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M7"> <m:mi>λ</m:mi> </m:math> at 25°C. The first group is composed of rocks characterized by high <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M8"> <o:mi>λ</o:mi> </o:math> (>4.5 W/m·K) at room temperature, for which the curves of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M9"> <q:mi>λ</q:mi> <q:mo>−</q:mo> <q:mi>T</q:mi> </q:math> exhibit a concave pattern. The second group consists of rocks with a moderate <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" id="M10"> <s:mi>λ</s:mi> </s:math> (2.5~3.5 W/m·K), in which the curves tend to be a straight line. The last group comprises rocks with a low <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M11"> <u:mi>λ</u:mi> </u:math> (<2.5 W/m·K), exhibiting convex curves. There exists a close relationship between the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" id="M12"> <w:mi>λ</w:mi> </w:math> at 25°C and its rate of decrease ( <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" id="M13"> <y:mi>α</y:mi> </y:math> ). The absolute value of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" id="M14"> <ab:mi>α</ab:mi> </ab:math> increases with the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" id="M15"> <cb:mi>λ</cb:mi> </cb:math> at 25°C rising. The relationship between the two values can be fitted by the equation <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M16"> <eb:mi>y</eb:mi> <eb:mo>=</eb:mo> <eb:mi>a</eb:mi> <eb:mi>x</eb:mi> <eb:mo>+</eb:mo> <eb:mi>b</eb:mi> <eb:mfenced open="(" close=")"> <eb:mrow> <eb:mn>1</eb:mn> <eb:mo>/</eb:mo> <eb:mi>x</eb:mi> </eb:mrow> </eb:mfenced> <eb:mo>+</eb:mo> <eb:mi>c</eb:mi> </eb:math> to derive the fitting parameters <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" id="M17"> <ib:mi>a</ib:mi> </ib:math> , <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" id="M18"> <kb:mi>b</kb:mi> </kb:math> , and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" id="M19"> <mb:mi>c</mb:mi> </mb:math> ; by this equation with known fitting parameters, the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" id="M20"> <ob:mi>λ</ob:mi> </ob:math> of the deep carbonate rocks of the Tarim Basin have been estimated.