Analysis of the Correlations between Thermal Neutron Absorption Cross-Section and K, U, Th Concentrations for Miocene Rocks from Carpathian Piemont in Poland.
Jerzy Łoskiewicz, Jan Swakoń
The H.Niewodniczański Institute of Nuclear Physics
31-342 Krakуw, POLAND
ul. Radzikowskiego 152
In the paper are analysed the data from radiometric analysis for K, U, Th concentrations and neutron absorption cross-section E a of rock samples obtained from coring. The cores are from wellbores located on gas producing Miocene formations in the Carpathian foreland area of Southern Poland. The E a values are used currently in rock porosity estimation and are helpful for specification of perspective gas producing zones.
The values of correlation coefficients for the interdependence of neutron absorption cross-section (E a) on K, U, Th concentrations are presented. They are R(E a-K) = 0.90, R(E a-U) = 0.86, R(E a-Th) = 0.92. They do not differ conspicuously from previously analysed data for Jordanуw-Sucha region and older geological formations where the values are R(E a-K) = 0.83, R(E a-U) = 0.62, R(E a-Th) = 0.85. Therefore probably these dependencies may have more general character.
A neural network representation of the function E a = f(K, U, Th) is obtained and can be later used for E a estimation on the basis of spectrometric probe results from uncored wells of the region.
The work was partially funded by Komitet Badań Naukowych of Poland with grant No. 6P04D 046 11
The concentration of natural radioactive elements in rocks is depending on their mineralogical composition as well as on how they were formed, but also on process which has enriched the rocks in rare elements.
The primary source of radioactive materials is formed by magmatic rocks as granite, syenite etc. The radioactive elements are also present in the form of many minerals e.g. monazite, uraninite, coffinite, sylvine, orthoclase, etc. During the weathering processes these elements may be released from the rocks and transported on important distances. Then sedimentation processes intervene forming sedimentary rocks. Otherwise the thorium, uranium and potassium minerals may fill cavities as cracks, fissures or simply be deposited between rock matrix grains of many types of rocks. They are also abundant in clays and rocks lithified from clays e.g. mudstones and shales.
In our research samples from two geological regions of Southern Poland were analyzed. Samples are coming from 11 boreholes in Carpathian Mountains and 6 boreholes located in Carpathian Piemont (see Fig.1.). The Carpathian samples are showing various lithologies (sands, mudstones, limestones, shales etc.). The samples from Miocene formations in Carpathian foreland were gradual changing from shaly sandstone to silted shale. Thermal neutron absorption cross-section was measured by two different methods, what is representing an additional complication.
The K, U, Th concentrations were measured using gamma ray spectrometer with N 3"x3" scintillation crystal and crushed rock samples. The concentrations were calculated from the measured spectra using energy window method. The typical cross-plot potassium and thorium is presented in Fig.2. Small picture in the upper left corner is presenting data both for Carpathian region and Miocene formation (foreland). The correlation coefficient between K and Th for Miocene samples is 0.98. But for Carpathian region the correlation between parameters is nonlinear.
Thermal neutron absorption cross-section S a is depending mainly on rock microconstituents and in a lesser degree on the concentrations of main rock forming elements. The elements which strongly influence the value of neutron absorption cross-section are some rare earth elements as gadolinium, europium, samarium. Also boron has an important cross-section value for thermal neutrons.
Therefore both groups of elements - radioactive and with high neutron cross-section - have something in common i.e. they are low concentration admixtures to main rock forming elements (silicon, magnesium, aluminum, calcium). Having remarked this fact, we tried to make correlation plots of S a versus concentrations of potassium uranium and thorium.
An attempt to seek these correlations has been performed at 82 rock samples from deep drilling in Sucha region in Carpathian mountains (Southern Poland) and 53 samples from drillings in Miocene rocks in Carpathian Piemont.
The thermal neutron absorption cross-sections were measured on samples using Czubek's method (in the Institute of Nuclear Physics) and Kreft's method (in the University of Mining and Metallurgy).
Fig.3. presents cross-plot between K and G a for samples of Miocene. The dependency is linear. The correlation coefficient is 0.90. In upper left corner is presented cross-plot between K and G a for samples from Carpathian region (blue squares) and samples from Miocene (orange squares). The correlation coefficient for Carpathian samples is 0.83.
Fig.4. presents cross - plot between U and G a for Miocene formation. The dependence is linear too. The correlation coefficient is 0.86. The small picture in the right down side presents similar cross-plot for all analyzed samples. The blue squares show Carpathian samples and orange squares – samples from Miocene formations.
Fig.5. presents dependencies between Th concentration and G a values for Miocene formation. The correlation coefficient is 0.92. Small picture shows the same dependence for Carpathian samples (blue squares) and for Miocene (orange samples).
All dependencies for Carpathian samples were nonlinear. The results of multivariate nonlinear correlation were not good. In this situation we tried to use neural network backpropagation methods for retrieving the functional dependence G a = f(K, U, Th). For Carpathian samples thermal neutron absorption cross-sections were measured using two methods (Czubek’s method and Kreft’s method) and the lithology of rocks was known. Assuming that the problem is a complex one we have used the neural network realizing the function G a = f(K, U, Th, Methode, Lithology). We have fixed number of 5 input neurons, 11 neurons in first hidden layer, 3 neurons in second hidden layer and one neuron in output layer. The net is presented in Fig.6. The data were normalized into the interval (0.1- 0.9). Fig.6. presents the results of training (navy blue solid squares) and generalization (red solid squares). The total sum of squares of differences (TSS) for generalization set is 0.0456. The correlation coefficient for learning set (CML) is 0.970 and for generalization set (CMT) is 0.949. The RMS for learning set is 0.083. The mean distance (SY) for learning set is 0.050.
For samples from Carpathian Piemont we used a net that is presented in Fig.7. The net has only three input neurons and one neuron in output layer. It realizes the function G a = f(K, U, Th). The lithology of samples from Carpathian Piemont is very complicated, but dependencies between G a and particular concentrations of natural radioactive elements are more linear then for the samples from Carpathian mountains. The net, which we have prepared, is similar to the net presented in Fig.6 but a little smaller. It has 10 neurons in first hidden layer and three neurons in second hidden layer. Fig.7. presents the results of learning and generalization of the net. The navy blue solid squares present the results of learning and red solid squares present the results of generalization. The TSS for generalization set is 0.0755. The CML for learning set is 0.988 and for generalization set - CMT is 0.946. The RMS for learning set is 0.129. The mean distance (SY) for learning set is 0.0785 and SY for generalization set is 0.0648
CONCLUSIONS
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