Modification of Radiogenic Heat Production (RHP) Equation due to Radioactive Disequilibrium in Rock Samples from Gamma-Ray Spectrometry

Abstract

Many factors complicate the estimation of radiogenic heat production (RHP) which may lead to radionuclide concentrations which does not characterize the RHP being produced by rocks. One of this is the Uranium disequilibrium effect. We modified an existing model to minimize this effect. A revised data from gamma-ray spectrometry was used to compute the Beta and Alpha energies (Eβmax) of decay schemes, mass defect (EΔm)of radioelements, total absorbed energy (Eabs) per atom, numerical constants (Ai) and converted to the accepted RHP unit (µWm-3). The modified RHP model (A3) was evaluated and validated using error metrics and radiometric data from seven regions of Nigeria and India. The data was normalized to transform features to be on a similar scale to attain a normal distribution of the data. The modified model (A3) was compared with Birch’s (A1) and Rybach’s (A2) RHP models. All these processes were implemented in Python environment. The RHP constants is several percent higher (6.2% for U; 11.5% for Th) than the values of A1 and A2 RHP models except for Potassium which is higher (74.3%). The A3 RHP model gotten is: A(µWm-3) = ρ(0.103CU + 0.29CTh + 0.061CK). The contributing percentages of the radioelements were in the order of 40K > 238U > 232Th for the Southwest, Southeast and Northcentral regions of Nigeria while the order is 238U > 232Th > 40K for the Southsouth, Northeast and Northwest regions and in order 232Th > 238U > 40K for the Indian region. The A3 model returned a higher R2 value and lower SSE/RMSE/MAE values compared to A1 and A2 models. The R2 values ranged from 42–72% while RMSE ranged from 0.790–1.127. The A3 has the best performance in all metrics for all the regions. The coefficient of determination (R2) for the proportion of variance of the contribution of the radioelements placed K-40 as most dependent variable with a good correlation with the total RHP in the order of use of A1 < A2 < A3. In general A3 return the highest RHP values across all regions. The A3 RHP model gave a higher R2 value and lower RMSE, MAE, SSE values than A1 and A3 RHP models which is an indicator of best performance. The A3 RHP model performed well in all the regions in Nigeria and outside Nigeria. This shows that the A3 RHP model is not geological-formation dependent.