ABSTRACT
CONTENTS Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 11.2 Improved Plugging-Nonplugging Parallel Pathways
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 11.2.1 Plugging and Nonplugging Pathways with Exchange
Model of Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 11.2.2 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 11.2.3 Fractions of Porous Media Containing the Plugging and
Nonplugging Pathways. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 11.2.4 Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 11.2.5 Volumetric Flux of the Particle-Carrier Fluid Suspension . . . . 462 11.2.6 Particle Deposition Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 11.2.7 Particle Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 11.2.8 Average Particle Deposition and Overall Pressure
Difference in a Core Plug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 11.3 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 11.4 Experimental Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 11.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 11.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 11.7 Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Appendix — Evaluation of Spatial Derivatives and Integrals . . . . . . . . . . . . . . 481 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
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An improved microscopic phenomenological model and its numerical solution, and experimental validation for fine particle migration and deposition in porous media are presented. The mathematical model of Gruesbeck and Collins (“Entrainment and Deposition of Fine Particles in Porous Media,” SPEJ, 22(6), 847-856, 1982) with the modifications and improvements made here and proposed by Civan (Reservoir Formation Damage — Fundamentals, Modeling, Assessment, and Mitigation, Gulf Pub. Co., Houston, TX, and Butterworth-Heinemann, Woburn, MA, 742 pp. 2000) is facilitated and applied. A bundle of plugging and nonplugging parallel capillary pathways with
exchange model of porous media is developed in order to represent the particle andfluid transferprocesses associatedwith theflowofaparticle-fluid suspension throughporousmedia. Relatively smootherflowpathshaving larger cross-sectional areas are classified as the nonplugging pathways, which primarily undergo surface deposition and sweeping processes. Highly tortuous flow paths having significantly varying cross-sectional areas are called the plugging pathways, along which the particle bridges formed across the pore throats may interrupt the particle migration and limit the flow of the carrier fluid. Simultaneously, particle transfer between the plugging and nonplugging pathways is allowed bymeans of cross-flow. Thismodel is used to simulate the porosity and permeability reduction, and the evolution of the plugging and nonplugging pathways by particle deposition in porousmedia. The model is solved numerically bymeans of the method of lines approach
and the results are shown to compare favorably with experimental data involving typical laboratory core tests undergoing suspension injection. The values of the various phenomenological parameters are determined by matching the simulation results to the measured data. The improved model provides an accurate representation of the phenomena resulting from the fine particle deposition and provides valuable insights into the consequences of fine particle migration through the plugging and nonplugging pathways in porous media.
