Justification for the Selection of a Relative Permeability Model in the Task of Predicting Drilling Fluid Filtrate Invasion into the Formation

Modeling the impact of drilling fluid filtrates is a relevant method for selecting the most effective fluid for penetrating the reservoir formation. The use of relative permeability models enables the most accurate prediction of the drilling fluid filtrate invasion process into the productive formation. The objective of this study is to analyze existing methods for approximating experimental data using relative permeability functions and to substantiate the selection of the most effective method. Relative permeabilities are applied in the theory of two-phase filtration to predict the saturation and penetration depth of drilling fluid filtrates. The methodology involves analyzing the forms of nonlinear paired regression equations for approximating relative permeabilities in modeling two-phase filtration in the near-wellbore zone of a productive reservoir. The experimental part includes conducting a filtration experiment on natural core samples of a terrigenous reservoir using drilling fluid filtrates and oil. Equations were chosen to approximate the filtration experiment data points. The least squares method, implemented in Wolfram Language, was used to determine the coefficients of the regression models. Graphs of the Buckley-Leverett function and its derivative with respect to saturation were constructed and verified for compliance with the requirements for further application in modeling the reservoir penetration process. Recommendations for selecting types of equations to describe relative permeability models were substantiated. Examples of calculating saturation and filtrate penetration depth were provided, along with the rationale for selecting the penetration fluid based on these calculations. The results were compared using model and empirical functions.