Calculation of water influx into petroleum reservoir is a tedious evaluation with significant reservoir engineering applications. The classical approach developed by van Everdingen–Hurst (vEH) based on diffusivity equation solution had been the fulcrum for water influx calculation in both finite and infinite-acting aquifers. The vEH model for edge-water drive reservoirs was modified by Allard and Chen for bottom-water drive reservoirs. Regrettably, these models solution variables: dimensionless influx (\(W_{{{\text{eD}}}}\)) and dimensionless pressure (\(P_{D}\)) were presented in tabular form. In most cases, table look-up and interpolation between time entries are necessary to determine these variables, which makes the vEH approach tedious for water influx estimation. In this study, artificial neural network (ANN) models to predict the reservoir-aquifer variables \(W_{{{\text{eD}}}}\) and \(P_{D}\) was developed based on the vEH datasets for the edge- and bottom-water finite and infinite-acting aquifers. The overall performance of the developed ANN models correlation coefficients (R) was 0.99983 and 0.99978 for the edge- and bottom-water finite aquifer, while edge- and bottom-water infinite-acting aquifer was 0.99992 and 0.99997, respectively. With new datasets, the generalization capacities of the developed models were evaluated using statistical tools: coefficient of determination (R²), R, mean square error (MSE), root-mean-square error (RMSE) and absolute average relative error (AARE). Comparing the developed finite aquifer models predicted \(W_{{{\text{eD}}}}\) with Lagrangian interpolation approach resulted in R², R, MSE, RMSE and AARE of 0.9984, 0.9992, 0.3496, 0.5913 and 0.2414 for edge-water drive and 0.9993, 0.9996, 0.1863, 0.4316 and 0.2215 for bottom-water drive. Also, infinite-acting aquifer models (Model-1) resulted in R², R, MSE, RMSE and AARE of 0.9999, 0.9999, 0.5447, 0.7380 and 0.2329 for edge-water drive, while bottom-water drive had 0.9999, 0.9999, 0.2299, 0.4795 and 0.1282. Again, the edge-water infinite-acting model predicted \(W_{{{\text{eD}}}}\) and Edwardson et al. polynomial estimated \(W_{eD}\) resulted in the R² value of 0.9996, R of 0.9998, MSE of 4.740 × 10^–4, RMSE of 0.0218 and AARE of 0.0147. Furthermore, the developed ANN models generalization performance was compared with some models for estimating \(P_{D}\). The results obtained for finite aquifer model showed the statistical measures: R², R, MSE, RMSE and AARE of 0.9985, 0.9993, 0.0125, 0.1117 and 0.0678 with Chatas model and 0.9863, 0.9931, 0.1411, 0.3756 and 0.2310 with Fanchi equation. The infinite-acting aquifer model had 0.9999, 0.9999, 0.1750, 0.0133 and 7.333 × 10^–3 with Edwardson et al. polynomial, then 0.9865, 09,933, 0.0143, 0.1194 and 0.0831 with Lee model and 0.9991, 0.9996, 1.079 × 10^–3, 0.0328 and 0.0282 with Fanchi model. Therefore, the developed ANN models can predict \(W_{{{\text{eD}}}}\) and \(P_{D}\) for the various aquifer sizes provided by vEH datasets for water influx calculation.

渗入石油储层的水量的计算是一项繁琐的评估，具有重要的储层工程应用程序。van Everdingen-Hurst（vEH）基于扩散方程解开发的经典方法一直是有限和无限作用含水层中涌水量计算的支点。边缘水驱油藏的vEH模型由Allard和Chen修改了底部水驱油藏。遗憾的是，这些模型解决了以下变量：无量纲流入（\（W _ {{{text {eD}}}} \））和无量纲压力（\（P_ {D} \））以表格形式呈现。在大多数情况下，需要通过表查找和时间条目之间的插值来确定这些变量，这使得vEH方法对于水流量的估算很繁琐。在这项研究中，基于vEH数据集，开发了用于预测储层含水量\（W _ {{{text {eD}}}}}和\（P_ {D} \）的人工神经网络（ANN）模型用于边缘和底部水有限和无限作用的含水层。所开发的ANN的整体性能可建立相关系数（R），对于边缘和底部水有限作用含水层来说，其值为0.99983和0.99978，而对于边缘和底部水作用有限的含水层分别是0.99992和0.99997。对于新的数据集，使用统计工具评估了开发模型的泛化能力：确定系数（R ²），R，均方误差（MSE），均方根误差（RMSE）和绝对平均相对误差（AARE） ）。用拉格朗日插值方法比较预测的发展的有限含水层模型\（W _ {{{\ text {eD}}}} \）与拉格朗日插值法得出R ²，R，水边驱动的MSE，RMSE和AARE为0.9984、0.9992、0.3496、0.5913和0.2414，底水驱动为0.9993、0.9996、0.1863、0.4316和0.2215。此外，无限作用含水层模型（模型1）对于边缘水驱，R ²，R，MSE，RMSE和AARE分别为0.9999、0.9999、0.5447、0.7380和0.2329，而底部水驱分别为0.9999、0.9999， 0.2299、0.4795和0.1282。再次，边缘水无限作用模型预测了\（W _ {{{\ text {eD}}}} \）和Edwardson等人。多项式估计\（W_ {eD} \）得出R ²值为0.9996，R为0.9998，MSE为4.740×10 ^–4，RMSE为0.0218，AARE为0.0147。此外，将已开发的ANN模型泛化性能与某些模型进行了比较，以估计\（P_ {D} \）。Chatas模型的有限含水层模型结果显示了统计量度：R ²，R，MSE，RMSE和AARE为0.9985、0.9993、0.0125、0.1117和0.0678，Fanchi方程为0.9863、0.9931、0.1411、0.3756和0.2310。Edwardson等人的无限作用含水层模型具有0.9999，0.9999，0.1750，0.0133和7.333×10 ^-3。多项式，则0.9865，09933，0.0143，0.1194和0.0831与李模型和0.9991，0.9996，1.079×10 ^-3，和0.0328 0.0282与Fanchi模型。因此，开发的神经网络模型可以预测\（W _ {{{\ text {eD}}}} \）和\（P_ {D} \）表示由vEH数据集提供的各种含水层尺寸，用于计算水的涌入量。