Estimate of Saturation Pressures of Crude Oil by Using Ensemble-Smoother-Assisted Equation of State

The equation of state (EOS) has been extensively used to evaluate the saturation pressures of petroleum fluids. However, the accurate determination of empirical parameters in the EOS is challenging and time-consuming, especially when multiple measurements are involved in the regression process. In this work, an ensemble smoother (ES) -assisted EOS method has been proposed to compute the saturation pressure by intelligently optimizing the to-be-tuned parameters. To be specific, the to-be-tuned parameters for the Peng–Robinson EOS (PR EOS) are integrated into a model input matrix and the measured saturation pressures are collected into a model output matrix. The model input matrix is then integrally and iteratively updated with respect to the model output matrix by using the iterative ES algorithm. For convenience, an in-house module is compiled to implement the ES-assisted EOS for determining the saturation pressures of crude oils. Subsequently, the experimentally measured saturation pressures of 45 mixtures of heavy oil and solvents are used to validate the performance of the in-house module. In addition, 130 measured saturation pressures of worldwide light oil samples are collected to verify the applicability of the developed ES-assisted EOS method. The in-house module is found to be competent by not only matching 45 measured saturation pressures with a better agreement than a commercial simulator but also providing a quantitative means to analyze the uncertainties associated with the estimated model parameters and the saturation pressure. Moreover, the application of the ES-assisted EOS to 130 light oil samples distinctly demonstrates that the new method greatly improves the accuracy and reliability of the EOS regression. Consequently, the in-house module representing the ES-assisted EOS is proven as an efficient and flexible tool to determine the saturation pressure under various conditions and implement uncertain analyses associated with the saturation pressure.