The Impact of Compaction and Sand Migration on Permeability and Non-Darcy Coefficient from Pore-Scale Simulations

  • Sultan Anbar
  • Karsten E. Thompson
  • Mayank Tyagi


Compaction and sand migration are important problems in loosely consolidated and unconsolidated high-rate gas reservoirs, and proppants in the hydraulic fractures. Their impacts on permeability and non-Darcy flow are important for accurate estimation of well productivity. In this paper, we quantified changes in flow parameters due to simulated compaction and sand migration for computer-generated sphere packing and presented the results in the context of correlations for permeability and non-Darcy coefficient that can be used in reservoir simulations. Compaction effects were simulated by increasing grain diameter in a sphere packing. Permeability and non-Darcy coefficients were calculated using the lattice Boltzmann method (LBM). Findings indicated that the permeability decrease was not directional for compaction simulated by simple grain growth and the change in permeability could be estimated from the porosity change with a power-law relation with an exponent equal to 3.28. An analogous power-law relation between non-Darcy coefficient and permeability was found with the exponent equal to − 1.32. For reservoirs that undergo these compaction-like processes during production, estimation of the inertial effects from traditional correlations developed as a function of permeability and porosity may lead to underestimation of the inertial effects. Sand migration causes pore-throat plugging, which leads to significant permeability reduction. We simulated sand particle-plugged pore-throat locations from network simulations for different values of pore volume reduction, and the corresponding permeability and non-Darcy coefficients were calculated from LBM. It was found that permeability change from sand plugging was directional; permeability decrease in the flow direction was approximately double the other directions. A power-law relation between permeability and porosity could be used to estimate the permeability with a much larger exponent: approximately 10 in the flow direction in the range of plugging studied in this work. Because porosity reduction can depend on other factors besides pore-throat plugging (e.g., compaction or pore surface deposition), a correlation was developed to estimate permeability dependence on the pore-throat sand concentration. Even though permeability change was directional, the permeability and non-Darcy coefficient trends collapsed onto a single power-law relation. The exponent on a power-law relation was greater in magnitude (approximately − 1.84) compared to compaction.


Sand migration Compaction Lattice Boltzmann method Kozeny–Carman relationship Permeability and non-Darcy coefficient 



Authors would like to thank Shell E&P Co. for funding this research. LBM was developed by the PALABOS group ( We thank the LSU Center for Computation and Technology (CCT) and the Louisiana Optical Network Initiative (LONI) for providing high-performance computing resources. We thank Dongxing Liu for the help with the algorithm that identified sand plugging locations in network modeling simulations.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Sultan Anbar
    • 1
  • Karsten E. Thompson
    • 1
  • Mayank Tyagi
    • 1
  1. 1.Louisiana State UniversityBaton RougeUSA

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