Fines detachment is an important component of methane production from Coal Bed Methane reservoirs. Production of coal fines is widely observed during dewatering and simultaneous gas-water production. The theory for fines detachment by drag against electrostatic attraction, model of the transport of those detrital fines, and their validation by laboratory test is widely used for planning and design of Coal Seam Gas developments. However, clay particles that naturally grow on coal grains and asperous parts of coal surfaces (authigenic and potential coal fines) are detached by breakage. To the best of our knowledge, the analytical theory for detachment of authigenic and potential coal fines is not available. The present paper fills the gap. Based on Timoshenko's beam theory, we derive failure conditions for breakage of authigenic and potential coal fines of the rock surface. It allows defining maximum retention function for fines breakage. The maximum retention is incorporated into transport equation of mobilized fines, allowing developing analytical models for linear flow of core flooding and radial flow of well inflow performance. Matching of laboratory coreflood data from four laboratory studies show high agreement. The model coefficients obtained by treatment of laboratory data allow predicting skin growth in production wells under fines migration.