Petrophysical parameter estimation using a rock-physics model and collaborative sparse representation

The estimation of petrophysical parameters is key in the identification of underground reservoirs. Current petrophysical parameter estimation methods are typically constrained by the choice of particular rock-physics models, necessitating the use of distinct models for various reservoirs. Furthermore, the inherent pronounced nonlinearity of these models presents significant challenges to the solution process in reservoir parameter inversion. Although linearized petrophysical inversion methods can simplify the solving process, they can introduce errors due to linearization. To address these limitations, we develop a petrophysical parameter estimation method driven by a rock-physics model and collaborative sparse representation (CSR). In this approach, the rock-physics model governs the fundamental pattern of the petrophysical parameters, with the CSR introducing perturbations to minimize model errors. Our method maximizes the use of well-log data and the rock-physics model, thereby reducing errors associated with linearized rock-physics (LRP) models and enhancing the method’s adaptability. We use the joint dictionary method to learn features and correlations among multiple parameters from the existing well-log data. This learned dictionary is then used as a CSR regularization constraint and applied to refine the LRP inversion objective function. Finally, the objective function is minimized using the block coordinate descent method to predict the petrophysical parameters. The effectiveness of this method in enhancing the adaptability and accuracy of petrophysical parameter estimation is confirmed through synthetic and field data tests.