An Interpretable Method for Formation Pressure Calculation with Embedding Mechanism
Authors: Zhang R. , Li G. S. , Yao X. Z. , Shi J. G. , Guo Y. , Song X. Z. , Zhu Z. P. , Li B. Y. 
Published: September 2023

ABSTRACT
Formation pressure is a key parameter in the process of oilfield exploration and development. In this study, a novel deep learning model is proposed for accurate calculation of formation pressure. Particularly, making use of the long short-term memory (LSTM) network in solving sequential-data based regression problems, this paper considers the specific domain knowledge of logging and develops a self-interpretable LSTM (SI-LSTM) to calculate the formation pressure. It can dynamically capture the potential correlation between the formation pressure and input variables, and interpretability analysis is conducted for weighting coefficient of characteristics and temporal. Field logging datasets are adopted to evaluate the accuracy and effectiveness of the proposed models. The results indicate that the model embedded mechanism knowledge has greatly improved the prediction accuracy and stability with a mean absolute percentage error of 1.223%. The interpretation results show that the formation pressure has short-term auto-correlation. The proposed method provides a new idea for field calculation of formation pressure, and can be a useful and high-precision scientific alternative to the traditional methods.

INTRODUCTION
Formation pore pressure is a crucial parameter in the process of exploring and developing oilfields, and accurate prediction of this parameter is essential to reduce the occurrence of wellbore instability, such as overflow (Song et al., 2022). Currently, formation pore pressure prediction methods can be broadly classified into four categories: (1) under-compaction theory-based methods, such as the equivalent depth method (Hottman and Johnson, 1965; Walter and George, 1988; Song et al., 2011) and the Eaton method (Bektas et al., 2015; Ernanda et al., 2018; Yi et al., 2019), which construct the normal compaction trend equation through the mud shale layer and consider only the under-compaction effect; (2) rock mechanics theory-based methods, such as the effective stress method (Sun et al., 2011; Wang et al., 2019) the Bowers formula method (Bowers, 1995; Etminan et al., 2012; Qiang et al., 2020). These methods require a large amount of logging data, experimental data, and statistical regression analysis to determine the empirical coefficients; (3) empirical statistical model methods, such as multiple regression method (Deng et al., 2015) which involves more empirical parameters. The errors of each parameter are superimposed on each other, making the calculation accuracy of formation pore pressure limited; (4) artificial intelligence prediction methods, which have been a hot research topic in recent years, such as the gray prediction model with drilling (Zhang and Gao, 2005; He et al., 2008), artificial neural networks (S et al., 2018; Rashidi and Asadi, 2018; Hadi et al., 2019; Hutomo et al., 2019), support vector machines (Wei et al., 2007). Although these intelligent methods effectively improve the prediction accuracy, they do not integrate with empirical knowledge, which leads to the instability of the prediction results. Moreover, the black-box nature of the internal decision making of the model also makes the results weakly interpretable.