Modeling of Unsteady-State Cake Formation on a Fracture in Produced Water Re-Injection Process (PWRI)

In petroleum production, produced water re-injection (pwri) has earned much interestamong disposal methods of the produced water. however, presence of the contaminantsin the produced waters usually results in formation damage in well bores and their surroundingfracture systems. in the present study, modeling of external cake formation on a fracture inunsteady-state conditions is discussed. the existing force vectors of different nature are analyzedin detail at first, as the second step force and fluid mass balances specific to the case are derived.finally, by solving the formulated governing equations, cake thickness, permeate velocity andcross flow velocity profiles in unsteady-state conditions are obtained.