Petrophysical interpretation of borehole geophysical measurements in the presence of deep mud-filtrate invasion remains a challenge in formation evaluation. Traditional interpretation methods often assume a piston-like radial resistivity model to estimate the radial length of invasion, resistivities in the flushed and virgin zones, and the corresponding fluid saturations from apparent resistivity logs. Such assumptions often introduce notable inaccuracies, especially when the radial distribution of formation resistivity exhibits a deep and smooth radial front. Numerical simulation of mud-filtrate invasion and well logs combined with inversion methods can improve the estimation accuracy of petrophysical properties from borehole geophysical measurements affected by the presence of mud-filtrate invasion.

We develop a new method to quantify water saturation in the virgin zone, residual hydrocarbon saturation, and permeability from borehole geophysical measurements. This method combines the numerical simulation of well logs with the physics of mud-filtrate invasion to quantify the effect of petrophysical properties and drilling parameters on nuclear and resistivity logs. Our approach explicitly considers the different volumes of investigation associated with the borehole geophysical measurements included in the interpretation. The new method is successfully applied to a tight-gas sandstone formation invaded with water-base mud (WBM). Petrophysical properties were estimated in three closely spaced vertical wells that exhibited different invasion conditions (i.e., different times of invasion and different overbalance pressures). Available rock-core laboratory measurements were used to calibrate the petrophysical models and obtain realistic spatial distributions of petrophysical properties around the borehole. This approach assumes that initial water saturation is equal to irreducible water saturation. Based on the calibrated petrophysical models, thousands of invasion conditions were numerically simulated for a wide range of petrophysical properties, including porosity and permeability. Based on the large data set of numerical simulations, analytical and machine-learning (ML) models were combined to infer unknown rock properties in each well. Mean-absolute-percent errors (MAPE) of the analytical and ML models for the estimation of water saturation in the virgin zone are 5% and 2%, respectively, while the MAPE of the analytical models for the estimation of residual hydrocarbon saturation is 10%. Synthetic and field examples are examined to benchmark the successful application and verification of the new interpretation method. Estimates of water saturation in the virgin zone using the new method are in good agreement with core-based models.

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