Artificial neural network models for reservoir-aquifer dimensionless variables: influx and pressure prediction for water influx calculation

Abstract Calculation of water influx into petroleum reservoir is a tedious evaluation with significant engineering applications. The classical approach developed by van Everdingen–Hurst (vEH) based on diffusivity equation solution had been the fulcrum for calculation in both finite and infinite-acting aquifers. vEH model edge-water drive reservoirs was modified Allard Chen bottom-water reservoirs. Regrettably, these models variables: dimensionless ( $$W_{{{\text{eD}}}}$$ WeD ) pressure $$P_{D}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">PD were presented tabular form. In most cases, table look-up interpolation between time entries are necessary to determine variables, which makes estimation. this study, artificial neural network (ANN) predict reservoir-aquifer variables datasets edge- overall performance ANN correlation coefficients R 0.99983 0.99978 aquifer, while aquifer 0.99992 0.99997, respectively. With new datasets, generalization capacities evaluated using statistical tools: coefficient determination 2 ), , mean square error (MSE), root-mean-square (RMSE) absolute average relative (AARE). Comparing predicted Lagrangian resulted MSE, RMSE AARE 0.9984, 0.9992, 0.3496, 0.5913 0.2414 0.9993, 0.9996, 0.1863, 0.4316 0.2215 drive. Also, (Model-1) 0.9999, 0.5447, 0.7380 0.2329 drive, 0.2299, 0.4795 0.1282. Again, Edwardson et al. polynomial estimated $$W_{eD}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">WeD value 0.9998, MSE 4.740 × 10 –4 0.0218 0.0147. Furthermore, compared some estimating . results obtained showed measures: 0.9985, 0.0125, 0.1117 0.0678 Chatas 0.9863, 0.9931, 0.1411, 0.3756 0.2310 Fanchi equation. 0.1750, 0.0133 7.333 –3 polynomial, then 0.9865, 09,933, 0.0143, 0.1194 0.0831 Lee 0.9991, 1.079 0.0328 0.0282 model. Therefore, can various sizes provided calculation.