Determining model parameters for non-linear deep-bed filtration using laboratory pressure measurements

The mathematical model for suspension-colloidal transport in natural reservoirs contains two empirical functions of retained particle concentration. The filtration function expresses the particle capture rate. The formation-damage function determines the permeability decline due to particle capture and retention. Previous works developed an inverse-problem solution to recover both functions from breakthrough concentration and the pressure drop. The present paper develops a new method that determines the filtration and formation-damage functions from pressure measurements only. The method uses pressure data at an intermediate point of the porous column (core), which supplements pressure measurements at the core inlet and outlet. The proposed method furnishes two retained-concentration functions for filtration and formation-damage. The method is validated by comparison with laboratory experiments. A high fit with the pressure data at three core points was observed. Moreover, the fitted model predicts the pressure measured at other core points with high precision.