Problem of measuring thermal conductivity in heterogeneous rocks

Thermal conductivity is a critical component in the
evaluation of source rocks and reservoir rocks in petroleum
geoscience. However, rock heterogeneity provides a daunting
task with regards to estimating thermal conductivity on such
materials. Essentially, the main problem in thermal conductivity
estimations measurements is to get a reliable representative
estimate. Therefore, the objective of this study was to determine
if it were feasible to determine a representative value for the
thermal conductivity of a heterogeneous rock. The study was also
carried out to determine the optimum number of readings and
samples required to get a statistically viable estimation of the
thermal conductivity for such rocks. The thermal conductivity of
twelve granite block samples from Lata Kinjang, Perak, was
estimated using the needle probe method at 40o C. Each face on
the granite blocks (0.1 x 0.15 x 0.05m) were subdivided into
parallel lines of 0.01m apart. The thermal conductivity was
estimated along these lines. Statistical means for each face tended
to be different within each block. The standard deviations
differed as well, implying that the thermal conductivity
estimations were anisotropic between faces and within the faces.
The study showed that there were significant variations along
each face, between different faces and different blocks. The mean
thermal conductivity estimated for 9 samples was 2.37 Wm-1k-1
with standard deviation of 0.20 and standard mean of error
0.067. The confidence interval taken was 95% with lower and
upper intervals values of 2.22 and 2.53 respectively. The
comparison of means at the face level, sample specimen level and
collectively all samples, showed that the means are significantly
different. Therefore, in order to get a statistically reliable
representative value, a minimum number of 3 lines per block
face, 3 faces per sample, and 4 samples per rock type are
required.
Keywords- thermal conductivity, Heat flow, Granitic rocks.