A two dimensional finite element model is proposed to predict the effectivee thermal conductivity of rock sample. The heterogeneity of rock is taking into account in the numerical model at mesoscopic level by employ the statistical method. Finite element models simulated a steady-state thermal conductivity measurement device performing measurements on numerical samples with varying heterogeneity. The results obtained by numerical model agree well with that of theoretical serial and parallel model, and seems more accurate to predict effective thermal conductivity of the disordered structure. The simulations of different heterogeneity samples show the relationship between effective thermal conductivity and heterogeneity. For specimens with same geometry and heterogeneity, although the distribution of thermal parameters in each sample are different because of random distribution, numerical results show that they are almost the same effective thermal conductivity. The results also indicate that different heterogeneity of the specimen will get different effective thermal conductivity, more homogeneous of the sample, smaller difference with the input thermal conductivity. The heat flux vector of relatively heterogeneous sample is more disordered than that of homogeneous one. It deems that the microfractures in rock have the resistance effect on heat conduction. All of the results reveal that the proposed numerical model efficiently predicting the effective thermal conductivity of the heterogeneity rock.
It is essential that heat transfer properties be estimated in engineering such as nuclear waste deposition, hot dry rock exploitation and energy saving of building(Brodsky et al. 1997; Kohl et al. 1995; Thomas et al. 1999; Hasan 1999; Özkahraman et al. 2004). Thermal conductivity is the most important parameter to evaluate the thermal conduction of the body. Thus, precise and accurate thermal conductivity measurements of rocks are necessary for the calculation of heat flow in both fundamental and applied geothermal studies, and for petrophysical studies of geological materials (Popov et al. 1999). The thermal conductivity of rocks indicate that the effective thermal conductivity, keff, is primarily depending on thermal conductivities of its mineralogy, microcracks, liquid phase of water, etc (Görguelue et al. 2008; Gruescu et al. 2007). In the last two decades, the evolution of measurement techniques for effective thermal conductivity has been guided by the available technology. There are three in situ methods be used, i.e. Divided-Bar Method(DB), Line-Source Method(LS) and Optical Scanning Method (OS). The compare of the results tested by the three methods indicate that they are interchangeable within their combined errors. However, rock heterogeneity at a sample scale may affect the measured effective thermal conductivity (Popov 1999). For the thermo-mechanical-hydrogeological computer codes, correct input parameter of thermal conductivity in numerical sample is most important to get reliable results. Nevertheless, Although the effect of cracks that form an effective barrier for heat flow when dry but have a negligible effect when the rock is saturated is discussed by Walsh (Walsh et al. 1996) for stress relief dilatancy and by Pribnow (Pribnow et al. 1996) for thermally-induced cracks, it is difficult to model the influence of multi-existing microcracks and heterogeneous of rocks on thermal conduction.