Volume 28: Closing Carbon Cycles – A Transformation Process Involving Technology, Economy, and Society: Part III

A semi-analytical model for pressure transient analysis of partially penetrating inclined fracture networks for multi-stage fractured horizontal well Zhikai Wang, LinSong Cheng, Renyi Cao, Pin Jia

Abstract

There are some partially penetrating inclined fractures (PPIFs) due to stress interference between fracture networks in multi-stage fractured horizontal wells (MFHWs). It would take tremendous computation time to make flow behavior analysis and well production optimization in numerical simulators. Therefore, it is an extremely urgent task to establish efficient and rigorous models of PPIF networks. In this paper, triangular elements were introduced to characterize the geometry and intersection of PPIFs. Control volume method is adopted to model the fracture flow numerically and the star-delta transformation is used to solve the interconnected fractures more accurately. The fluid flow in the matrix is analytical modeled by source function. The transient flow between PPIFs and matrix is coupled on the surface of fractures. By introduce spatial triangle numerical integral technology in source function calculation, the model efficiency can be greatly increased. Finally, the pressure transient analysis (PTA) of PPIFs can be modelled with high accuracy and less calculation time. With the aid of proposed PPIFs model, the transient pressure behaviors of different MFHWs were analyzed. The hydraulic and natural fractures in these MFHWs have different inclinations, trends, and heights. The flow regimes of PPIFs with finite conductivity are analyzed in detail. Flow regimes analysis indicates that eight flow regimes can be observed, including the wellbore storage flow, fracture linear flow, bilinear flow, formation linear flow, early radial flow, compound linear flow, pseudo-radial flow, and boundary-dominated flow. The results indicate that the formation linear flow and early radial flow would be influenced by the geometry of nature fractures, which is quite different from that of vertical penetration fractures. The introduction of numerical integral method greatly reduces the calculation time (less than 2 minutes) with high accuracy, which make it possible to analysis the fracture parameters more efficiently. The result of typical well test curves analyses shows that the duration of flow regimes will be influenced the parameters of fractures. When the penetration ratio (> 0.6) or the incline angle (>60°) is large enough, the bilinear flow will last longer, and the early radial flow will be absent.

Keywords Fracture networks, Pressure-transient behavior, Finite conductivity, Semi-analytical model, Source function