Fines migration is a common cause of permeability and, consequently, injectivity and productivity decline in subterranean reservoirs. Many practitioners implement prevention or remediation strategies to reduce the impact of fines migration on field productivity and injectivity. These efforts rely on careful modelling of the underlying physical processes. Existing works have demonstrated the ability to predict productivity decline by quantifying the extent of particle decline at different fluid velocities. Fluid flows in porous media often involve multiple phases, which has been shown in laboratory experiments to influence the extent of particle detachment. However, no theory has directly accounted for this in a particle detachment model. In this work, a new model for fine particle detachment, expressed through the critical retention function, is presented, explicitly accounting for the immobile fines trapped within the irreducible water phase. The new model utilises the pore size distribution to allow for the prediction of particle detachment at different velocities. Further, an analytical model is presented for fines migration during radial flow into a production well. The model accounts for single-phase production in the presence of irreducible water, which has been shown to affect the extent of fines migration significantly. Combining these two models allows for the revealing of the effects of connate water saturation on well impedance (skin factor growth) under fines migration. It is shown that the higher the connate water saturation, the less the effect of fines migration. The appropriateness of the model for analyzing production well data is verified by the successful matching of 10 field cases. The model presented in this study is an effective tool for predicting the rate of skin growth, its stabilization time and final value, as well as the areal distribution of strained particles, allowing for more intelligent well remediation design. Further, the findings of this study can help for a better understanding of the distribution of fines within porous media and how their detachment might be influenced by pore structure and the presence of a secondary immobile phase.