Effect of Temperature on the Thermal Conductivity of Rocks and Its Implication for In Situ Correction
Chi Chen, Chuanqing Zhu, Baoshou Zhang, Boning Tang, Kunyu Li, Wenzheng Li, Xiaodong Fu
Abstract
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.