Exact Solution and Typical Curve for Two Layers Constant Pressure Boundary Reservoir with Crossflow
Sun hedong(1), Liu Lei(1), Qin Huanqun(1), Zhou Fangde(1), Gao Chengtai(2)
(1,State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University, Xi'an 710049, China)
(2,Department of Petroleum Engineering, Xi'an Petroleum Institute, Xi'an 710065, China)

Abstract: The skin factor is usually caused by improper drilling, completion technology, acidization or stimulation. The skin factor of different layers is probably different for multilayered reservoir. The maximum effective hole-diameter mathematical model describing flow of slightly compressible fluid through a two -layer reservoir with crossflow is solved rigorously with consideration of well bore storage and different skin factors. The exact solutions obtained for a well producing at a constant rate from a radial drainage area constant pressure outer boundary condition are expressed in terms of ordinary Bessel functions. The numerical computation of these solutions is made by the Crump numerical inversion method and the behavior of the systems is studied as a function of various reservoir parameters. The new model is numerically stable. The Bourdet model is numerically stable only when the skin is positive. Because the curves explicitly include skin factor and other reservoir parameters, the techniques is expected to be more accurate than the Bourdet technique.
Keywods: well-testing, mathematical model, crossflow, effective hole diameter, inversion of laplace transform, layered reservoir.