Use of a Multiple Regression Model in the Estimation of Water Borehole Flows in the Middle of Cracked Basement in Côte d’Ivoire

Abstract

The objective of this study was to propose a mathematical regression model to estimate the exploitation flow rate of a water borehole from geophysical parameters in the midst of a fissured basement in the central-eastern part of C?te d’Ivoire. The data of the study are both hydrogeological and geophysical parameters from one hundred and eleven (111) data sheets of (111) water and geophysical boreholes. Two methods were used. The Normal Principal Component Analysis (NPCA) method applied to the data made it possible to select the explanatory variables (geophysical parameters) for borehole productivity. The multiple linear regression method subsequently made it possible to propose a mathematical model capable of estimating the exploitation rate from the geophysical parameters. The results indicate a very strong correlation (0.87) between longitudinal conductivity and flow rate, with flow rate and apparent resistivity negatively correlated. The multiple linear regression method highlighted two relevant explanatory variables, longitudinal conductivity and apparent resistivity. These two geophysical parameters contributed to a mathematical model in the form Q = C1X1 + C2X2 + ... + CnXn + C0. the real model obtained in this work is Q = 0.82Cl - 0.12Rho.app + 2.5. The resulting model is efficient with a correlation of 86% in calibration and 95% in validation. A bias of 0.37 in calibration and 0.82 in validation is observed. Finally, the square root mean square error (RMSE) is 3.10 to 3.38 respectively in calibration and validation.