Rate of penetration (ROP) is a critical parameter affecting the total cost of drilling an oil well. This study introduces an empirical equation developed based on the optimized artificial neural networks (ANNs) for estimation of the rate of penetration (ROP) in real-time while horizontally drilling natural gas-bearing sandstone reservoirs based on the surface measurable drilling parameters of the mud injection rate, drillstring rotation speed (DSR), standpipe pressure, torque, and weight on bit (WOB) in combination with ROP_c, which is a new parameter developed in this study based on regression analysis. The ANN model was learned and optimized using 1154 data points; the training parameters were collected while horizontally drilling natural gas-bearing sandstone formations in Well-A. An empirical equation for ROP estimation was developed based on the optimized ANN model. Moreover, 495 unseen data points from Well-A were used to test the developed ROP equation, which was finally validated on 2213 data points from Well-B. The predictability of the new ROP equation was compared with the available correlations. The results showed that, without considering ROP_c, the optimized ANN model estimated the ROP for the training dataset with an average absolute percentage error (AAPE) of 42.6% and correlation coefficient (R) of 0.424, while when ROP_c was considered as an input, the AAPE decreased to 5.11% and R increased to 0.991. The new empirical equation estimated the ROP for the testing data of Well-A with AAPE and R of 5.39% and 0.989 and for the validation data of Well-B with AAPE and R of 8.85% and 0.954, respectively. The new empirical equation overperformed all the available empirical correlations for ROP estimation.

渗透率（ROP）是影响钻探油井总成本的关键参数。这项研究引入了一个基于优化人工神经网络（ANN）开发的经验方程式，用于根据泥浆的表面可测量钻井参数实时水平钻探含天然气砂岩储层时的渗透率（ROP）注入速率，钻柱转速（DSR），竖管压力，扭矩和钻压（WOB）结合ROP _c，这是本研究基于回归分析开发的新参数。使用1154个数据点学习和优化了ANN模型；在A井水平钻探含天然气砂岩地层时收集了训练参数。在优化的神经网络模型的基础上，建立了ROP估计的经验方程。此外，使用了来自Well-A的495个看不见的数据点来测试开发的ROP方程，该方程最终在Well-B的2213个数据点上得到了验证。将新的ROP方程的可预测性与可用的相关性进行了比较。结果表明，在不考虑ROP _{c的情况下}，优化的ANN模型估计的训练数据集的ROP具有42.6％的平均绝对百分比误差（AAPE）和相关系数（R）为0.424，而当将ROP _c作为输入时，AAPE降低至5.11％，R升高至0.991。新的经验方程式估算出AAPE和R分别为5.39％和0.989的Well-A井测试数据和AAPE和R分别为8.85％和0.954的B井验证数据的ROP 。新的经验公式优于所有可用的经验相关性，可用于ROP估计。