A semi-analytical model for multilateral horizontal wells in low-permeability naturally fractured reservoirs

Multilateral horizontal wells (MLHWs) can significantly increase the reservoir exposure as well as connect high permeability areas (natural fractures), and thus have been widely adopted in petroleum industry as an effective technique for efficient development of low-permeability reservoirs. Compared to vertical wells and horizontal wells, the flowing problems caused by MLHWs are more complex. In addition, extensive study has revealed that stress sensitivity of permeability in low-permeability reservoirs is obvious which cannot be ignored, especially for naturally fractured dual-porosity reservoirs. The non-linearity caused by stress sensitivity of permeability further complicates the flowing problems of MLHWs; however, so far, little work has been done in literature to simulate pressure transient dynamics of MLHWs with consideration of stress-sensitivity effect of permeability in low-permeability reservoirs. In this paper, a more rigorous analytical model for MLHWs in low-permeability naturally fractured reservoirs is presented. The model can not only consider different combinations of multiple branches, it can also consider the stress-sensitivity effect of reservoir permeability. The non-linear mathematical model can be linearized by Pedrosa transform and perturbation technique, and the final solution thus can be obtained by Laplace transformation method, finite cosine transform, element discretization and matrix theory. The presented model and corresponding solution are first validated by comparison with transient pressure responses calculated with a 'commercial numerical simulator for a simple case. Then the transient pressure responses are calculated, and flowing patterns and characteristic flowing periods caused by MLHWs are analyzed. A parametric analysis is also conducted to screen the critical parameters affecting the performance of multilateral horizontal wells. Analysis results suggest that stress-sensitivity of reservoir permeability has significant influence on the performance of MLHWs in low-permeability reservoirs; the parameters related to the shape of MLHWs, such as branch length, branch spacing, the angles between branch and horizontal wellbore, also can obviously affect the transient pressure dynamics of MLHWs. The proposed model in this paper can accurately simulate the transient pressure behaviors of MLHWs. It can help better understand the flowing characteristics of MLHWs, provide more accurate dynamic parameters for reservoir development, and give some insight into the design of MLHWs to obtain higher recovery.