Developing a new mathematical model between formation permeability and invasion radius using deep learning and genetic algorithm

Permeability has significant effects on the fluid production of oil and gas reservoirs, and it can cause various consequences during drilling. In particular, high permeability in fractured formations can lead to issues like lost circulation, which can be costly and risky. Lost circulation is a significant issue in drilling operations that needs to be addressed. The invasion radius is a crucial factor that determines the extent of the invaded zone and the permeability of the formation. Therefore, it is essential to analyze the relationship between permeability and invasion radius parameters and develop a mathematical model that describes their relationship accurately to prevent potential problems and risks. To do this, these parameters have been predicted and genetic algorithm has been used to establish an innovative empirical equation between them. For the first time, this study examines the relationship between formation permeability and invasion radius of drilling fluid within that formation. In this study, two distinct multi-layer perceptron (MLP) networks were employed to forecast the permeability and invasion radius. Data from 73 wells drilled in one of the largest Iranian oil fields were used that include 42,912 data points. The neural networks provided high R (correlation coefficient) of 0.9985 and 0.9936 for prediction of permeability and invasion radius, respectively. Then, a combination of curve fitting, regression, and genetic algorithm techniques has been used to establish the best model between the predicted data of permeability and drilling mud invasion radius. Finally, an equation of Power-Law type has been executed with an R value of 0.975. The findings of this research facilitate easier access to data and allow for the evaluation of the formation and its radius of influence related to lost circulation. Additionally, this research significantly reduces costs and helps prevent risks.