A new method in predicting productivity of multi-stage fractured horizontal well in tight gas reservoirs

摘要

The generally accomplished technique for horizontal wells in tight gas reservoirs is by multi-stage hydraulic fracturing, not to mention, the flow characteristics of a horizontal well with multiple transverse fractures are very intricate. Conventional methods, well as an evaluation unit, are difficult to accurately predict production capacity of each fracture and productivity differences between wells with a different number of fractures. Thus, a single fracture sets the minimum evaluation unit, matrix, fractures, and lateral wellbore model that are then combined integrally to approximate horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. This paper presents a new semi-analytical methodology for predicting the production capacity of a horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. Firstly, a mathematical flow model used as a medium, which is disturbed by finite conductivity vertical fractures and rectangular shaped boundaries, is established and explained by the Fourier integral transform. Then the idea of a single stage fracture analysis is incorporated to establish linear flow model within a single fracture with a variable rate. The Fredholm integral numerical solution is applicable for the fracture conductivity function. Finally, the pipe flow model along the lateral wellbore is adapted to couple multi-stages fracture mathematical models, and the equation group of predicting productivity of a multi-stage fractured horizontal well. The whole flow process from the matrix to bottom-hole and production interference between adjacent fractures is also established. Meanwhile, the corresponding iterative algorithm of the equations is given. In this case analysis, the productions of each well and fracture are calculated under the different bottom-hole flowing pressure, and this method also contributes to obtaining the distribution of pressure drop and production for every horizontal segment and its changes with effective fracture half-length and conductivity. Application of this technology will provide gas reservoir engineers a better tool to predict well and fracture productivity, besides optimizing transverse hydraulic fractures configuration and conductivity along the lateral wellbore.