Method Of Production Performance Analysis For Partially Penetrated Fractured Well In Naturally Fractured Gas Reservoir

Naturally fractured gas reservoirs(NFGRs)have great potential resources and a wide distribution in China.However,most of them are low permeable and tight,which can only be developed efficiently by the utility of fracturing technology.The vertical fractures formed by fracturing usually cannot penetrate the whole reservoir in the longitudinal direction.Especially,when fracturing technology is conducted in the thick layer,partially penetrated fractures are usually formed.Therefore,it is of great significance to establish the production performance analysis method of partial penetrated fractured well in this kind of gas reservoir.In this paper,the basic seepage characteristics of NFGRs are overviewed firstly.Then,based on the dual-porosity model,the control equation of NFGR considering permeability anisotropy and stress sensitivity is derived by defining the pseudo pressure function of matrix system and fracture system respectively and pseudo time factor.In addition,based on the theory of material balance,the material balance equations of fractured dual-porosity and fractured vuggy triple-porosity gas reservoirs are established.On this basis,the point and line sink solutions of partially penetrated vertical well in a single NFGR are obtained by Laplace transform and finite Fourier cosine transform.The out boundary is considered as infinite,circular constant pressure and circular closed respectively.Flow segments of pressure and pressure derivative curve are divided.In order to describe the difference of properties between the near well zone and the far well zone of NFR,the unsteady seepage model of partially penetrated vertical well in a circular composite gas reservoir is established,the effect of key parameters on production curve is analyzed,and the main factors which control production rate are defined.Based on the point sink solution of partially penetrated vertical well in single circular and circular composite NFGRs,the pressure solution of partially penetrated fractured well with infinite conductivity in Laplace domain is obtained by superposition principle.Then,pressure solution of partially penetrated fractured well with finite conductivity is obtained with the aid of the influence function of artificial fracture conductivity.Taking the partially penetrated fractured well in a circular closed radial composite NFGR as an example,the pressure and pressure derivative curves are plotted,and the characteristic flow segments are divided.The effect of various parameters on pressure and production rate curves is discussed.The analysis shows that for partially penetrated fractured well,the vertical penetration ratio of fracture should be greater than 0.5 in actual fracturing,and the optimal half-length and permeability of artificial fracture should be determined according to geological characteristics,operation conditions and other factors.Besides,the area of SRV should be increased as soon as possible.Finally,production performance analysis is carried out combining with the actual production data of a gas well,and the applicability of the model is demonstrated.In this paper,the production performance analysis method of partial penetrated well in NFGRs has provided theoretical basis for the production performance prediction and recoverable reserves evaluation of this kind of gas reservoir,and laid a foundation for the development plan and adjustment plan of gas reservoir.