An Approximate Analytical Solution for Damage Radius Prediction in Water Injection Wells Based on Langmuirian Blocking: Derivation, Comparison and Field Applications

Water flooding is extensively used in the industry to develop the mature oilfields. However, after several years’ of injection, the injectivity usually declines and the injection pressure increases. This is because the solid or liquid particles in the injected water are retained in the pores and block the flow channel in the near wellbore region. The prediction of the particle retention and permeability damage is important for the design of damage removal methods like acidizing. Previous researchers including M. Nunes, P. Bedrikovetsky, Feike J. Leij, et al. have done some work on the analytical solutions of the flow of particulate suspension in porous media with particle retention and consequent permeability reduction. However, they either assumed one-dimensional linear flow in the porous media or took the filtration coefficient as a constant. These are not always true because the flow of the injected water near the wellbore is radial and the filtration coefficient tends to decline with more and more particles being retained in the pores and ultimately reaches zero when all channels are blocked. In this paper, we established a near-wellbore axisymmetric suspension flow and particle retention model based on Langmuirian blocking, obtained the approximate analytical solution and compared it with the numerical solution. The results showed that the error of our approximate solution for the retained particle concentration is within 5%. Then we incorporated the analytical expression into the Darcy's law equation and derived the expression of pressure drop as well as skin factor caused by particle retention. Damaged zone radius was also defined so as to estimate the acid volume needed to remove the damage. We also checked our models and solutions using field cases of water injection and acidizing from Tarim Oilfields, western China. The results showed that the injection pressure drop due to particle retention and the injection pressure recover after acidizing calculated from our models are basically consistent with the actual situation. Our models can be further used to predict the damage zone radius and design the acid volume for damage removal. The analytical solution can also be used to perform sensitivity analysis for the parameters involved.