1 Center for Energy Resources Engineering, Center, Technical University of Denmark2 CERE – Center for Energy Ressources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark3 Department of Chemical and Biochemical Engineering, Technical University of Denmark4 Department of Chemistry, Technical University of Denmark
Stochastic Modeling of Polydisperse Transport
Colloid flow, filtration, and migration in porous media are widely observed in importantnatural and industrial processes, such as pathogen (bacteria) spreading in aquifers, colloid-facilitated migration of heavy metal in soils, mud filtration during drilling wells, injectivity decline during water injection, and deep bed filtration during waste water treatment. The current thesis aims at better understanding the transport and fate of colloids in porous media. A number of methodologies have been applied in this study, such as developing new mathematical models for colloid filtration, comparing the modeling results to experimental observations, uncertainty and sensitivity analysis of the new models, and realizing the pore-scale physics in network models. This thesis has been compiled in such a way that each chapter arises from a selfcontained study targeting a particular problem of colloid filtration: (1) Recent advances in colloids filtration theory; (2) Non-Fickian Transport and heterogeneous attachment of colloids; (3) Uncertainty and sensitivity analysis of models for non-Fickian transport and heterogeneous attachment; (4)Prediction of injectivity decline during waterflooding; (5)Colloid migration and recapture; (6) Induced colloid migration for enhanced oil recovery; (7) Estimating filtration coefficients for straining. These studies have been spearately published as journal papers, conference papers and book chapters. Nevertheless, they are not independent of one another but logically connected. The connections and main findings can be summarized as follows: 1. The discrepancies between the classical colloid filtration theory and experimental observations have been overviewed in Chapter 1. Many of them are observed under unfavorable attachment conditions, such as hyperexponential and non-monotonic deposition profiles. Such behavior of colloids is attributed to the heterogeneous attachment (Chapters 2 and 3) and the migration of colloids (Chapter 5), respectively. 2. A second reason for the deposition hyperexponentiality is the non-Fickian transport due to the heterogeneity of porous media. It also explains the dispersed and asymmetrical breakthrough curves of tracers in natural porous media (Chapters 2 and 3). Chapter 2 shows that the elliptic equation can be applied to capture the non-Fickian behaviors of colloids and tracers in porous media. It is closely followed by Chapter 3, the uncertainty and sensitivity analysis of the model predictions and the parameter estimation. Suggestions for experimental design for accurate determination of the model parameters are also provided. 3. Chapters 2 and 3 form a thorough study of the integral model for colloid filtration with non-Fickian transport and heterogeneous attachment. They are followed by the study of applying of such a model in the petroleum industry to predict injectivity decline during waterflooding in Chapter 4. However, the non-Fickian behavior of particles around the injection well is shown not to be significant. The reasons are that the temporal dispersion term is inverse proportional to the particle velocity and that the particle velocity is higher close to the well than that far away from the well. 4. The criterion of an attached colloid particle to be re-entrained by the hydrodynamic drag into the bulk fluid is the torques of detachment exceeding those of attachment. Bearing such a criterion in mind, the erosion of external cake, the migration of surface-associated colloids during one phase flow, and the migration of reservoir fines during two-phase flow are studied in similar fashions (Chapters 4, 5, 6). The erosion of external cakes in the injection wells gives rise to the steady stage of the injectivity and filling rat holes in the well (Chapter 4). The migration of surfaceassociated colloids gives rise to non-monotonic deposition profiles (Chapter 5). Migration and straining of reservoir fines may enhance oil receovery by increasing the sweep efficiency (Chapter 6). 5. Another important mechanism for particle capture is straining or size exclusion of colloids. Such phenomena are closely tied to the migration of colloids under unfavorable attachment conditions: surface-associated colloids rolling to straining sites (grain-grain contacts, pore throats) in Chapter 5, and the straining of released reservoir fines at pore throats in Chapter 6. However, the straining mechanism is described by nothing more than a straining rate coefficient in these studies. Finally in Chapter 7, a much better understanding of straining is achieved by the study of pore scale physics in a network model. The filtration coefficient for straining is estimated from the particle size and the pore size distributions. A new capture scheme of straining (minimum capture) is proposed to explain the large penentration depths of colloids in porous media and the power law dependencies of filtration coefficients in the experiments.