Unsteady Flow Research Of Partially Penetrated Vertical Well In Double-Layer Oil Reservoir

Duing to the gradual improvement of oil and gas technology and drilling technology,we have discoverd variety of oil and gas reservoir.For the different types of oil and gas reservoir that we have found,including offshore oil and gas reservoir,bottom water into the cone severely,oil and gas reservoir with high anisotropy,low permeability oil and gas reservoir,old oil reservoir of high water content and high recovery and so on,vertical well mining program is limited to many factors.The effect is not obvious,resulting in the more and more application of directional wells and partially penetrated wells.There are many practical examples of using drilling directional wells methods to develop special types of oil and gas reservoir in field.On the one hand,the flow area of oil and gas flow can be greatly increased by drilling the directional well,thus the oil and gas field production is increased.On the other hand,we have found a lot of reservoir with the different thickness,permeability and other flow physical conditions under different geological conditions and storage conditions.As the small circular solution of single-layer oil reservoir space is closer to the actual field production than the point source solution.The laplace transform and the fourier finite cosine integral transform are used to obtain the pressure distribution of the small circular.Then,the stehfest numerical inversion method is used to obtain the pressure solution of small circular in the time space.The solution can provide a theoretical basis for solving the line distribution sinks involved in partially penetrated vertical wells and directional wells.Basing on the solution of the small circle,the flow mathematical model of unlimited extension of single-layer reservoir is established and the pressure solution and the productivity solution of the single-layer reservoir are obtained by laplace and fourier transform.I have carried out a case of comparing pressure acting on shaft wall with the numerical simulation results calculated by the finite difference methods which Bilhartz has given.With the base of the analytic solution of infinite extended single-layer reservoir,a well model of infinite extended double-layer reservoir is established.The non-dimensional pressure and production of partially penetrated wells of the double-layer reservoir in the infinite extension boundary are obtained and calculated.We validates the calculated results with the Intepreter software's unstable experimental data of partially penetrated well.Then the non-dimensional pressure and production of partially penetrated wells of the double-layer reservoir in the round closed boundary are obtained and calculated.The problem of reference point is solved by the integral average and the speed of the calculation is accelerated.I have analyzed the production decline and the characteristics of late quasi-steady-state flow.Finally,basing on sink solution of the small circle in the partially penetrated wells,the pressure solution of inclined wells with the angle is obtained by integrating.The influence of well angle,length of partially penetrated and different formation thickness on the inclined well pressure of acting on shaft wall were analyzed.