Compaction and sand migration are some of the main problems for the loosely consolidated and unconsolidated high rate gas reservoirs. A reliable estimation of the well productivity depends on accurate modeling of permeability and inertial effects. Therefore, the key objective of this paper is to quantify the flow parameters change in the case of compaction and sand migration, and the development of permeability and the non-Darcy coefficient correlations that can be used in reservoir simulations. The compaction effects are simulated by increasing grains diameters with the same ratio. Permeability and the non-Darcy coefficients are calculated from lattice Boltzmann method (LBM). Results indicate that permeability decrease is not directional and the change in permeability can be estimated from porosity change with a Kozeny-Carman type relation with an exponent of 3.2. A Kozeny-Carman type relation between the non-Darcy coefficient and permeability is also found with an exponent −1.303. For high compressibility reservoirs, estimation of the inertial effects from the correlations developed as a function of permeability and porosity may also lead to underestimation of the inertial effects.
Sand migration causes pore-throat plugging that leads to significant reduction in permeability. Permeability impairment due to sand or fines migration is usually estimated from Kozeny-Carman type relation based on porosity. There is no study in the literature on how the inertial effects are changed with permeability impairment due to sand or fines migration. Sand particle plugging locations are found from the network simulations for different pore volume reduction, and corresponding permeability and the non-Darcy coefficient are calculated from LBM. It is found that permeability change with sand plugging is direction dependent: permeability reduction in the flow direction is twice compared to other directions. Porosity reduction does not depend on only pore-throat plugging, porosity can be decrease due to compaction and pore-surface deposition. Therefore, a correlation is developed to estimate permeability from pore-throat sand concentration. Even though permeability change is directional, the trend between permeability and the non-Darcy coefficient is similar and the magnitude of exponent in Kozeny-Carman type relation is larger, −1.803, compared to that of compaction.