Mathematical models for foam-diverted acidizing and their applications

Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing.Based on gas trapping theory and the mass conservation equation,mathematical models were developed for foam-diverted acidizing,which can be achieved by a foam slug followed by acid injection or by continuous injection of foamed acid.The design method for foam-diverted acidizing was also given.The mathematical models were solved by a computer program.Computed results show that the total formation skin factor,wellhead pressure and bottomhole pressure increase with foam injection,but decrease with acid injection.Volume flow rate in a highpermeability layer decreases,while that in a low-permeability layer increases,thus diverting acid to the low-permeability layer from the high-permeability layer.Under the same formation conditions,for foamed acid treatment the operation was longer,and wellhead and bottomhole pressures are higher.Field application shows that foam slug can effectively block high permeability layers,and improve intake profile noticeably.