The Flow Model Of Multistagefractured Horizontal Well Based On Tree-Shaped Fractal Theory

As an indispensible member of the world's oil and gas resource family, low permeability oil and gas reservoirs are promising to serve as the bellwether for the exploitation of unconventional oil and gas resources. However, jeopardized by the undesirable special geological features and percolation theories, oil and gas reservoirs with low permeability are generally characterized by lower reserve abundances and faster production decline than other conventional reservoirs, entailing higher difficulties as well as technical requirements. Therefore, it is rather vital for petroleum engineers to study and explore the geological characteristics, percolation theories and wells'productivities for such unconventional reservoirs.Based on the sufficient investigation for the productivity theories of multi-stage fractured horizontal wells and the basic geological features of low permeability oil and gas reservoirs, the unified capillary bundle was introduced into the description of the matrixes in low permeability oil and gas reservoirs. In order to simulate the real porous media, multi-scale percolation and stress sensitivity were also taken into consideration with discussion of threshold pressure gradient. While for the fracture system, tree-like fractal fracture network was utilized for simulating the artificial fractures induced by hydraulic fracturing. By establishing the theories related to the generation methods for tree-like fractal fracture network and the numbering rules for fractures and nodes, flowing features for such network were analyzed, leading to the formation of flowing model for multi-stage fractured horizontal wells among fracture networks. Furthermore, with the aid of single fracture's potential function as well as the potential superposition principle, the seepage flow model for such well was further derived, which lays a sound foundation for establishing the matrix-fracture coupled seepage flow model. At last, the accuracy of productivity models derived in this paper was certified by instance data. For detailed considerations for those productivity models, factors influencing productivities and their influencing degrees for such wells were also analyzed in this paper. The main conclusions and understandings drawn in this paper can be summarized as follows:(1) Based on the basic principle of percolation in capillary, a unified capillary bundle model was established for porous media where the flux, lengths as well as the probability density distribution functions of capillaries were introduced. By means of contrasting the novel capillary bundle model with conventional ones, the unified model proposed in this paper tend to get satisfactory relevance with previous research achievements.Moreover, the accuracy and practicality of the unified capillary model for porous media were also be certified by comparing with experimental data.(2) In order to simulate the real matrixes in low permeability oil and gas reservoirs, the unified capillary bundle model for porous media was utilized. During the process of deriving, multi-scale percolation and stress sensitivity were explained based on the microcosmic capillary percolation model. In addition, threshold pressure gradient was discussed, providing a deeper understanding for fluid flow mechanism in porous media.(3) Generation methods and numbering rules for tree-like fractal fracture networks were established by pinpointing basic parameters and their constraints based on the physical model for tree-like fractal fracture networks. Taking percolation features under multi-scale conditions in the single fracture into consideration, the flowing characteristics in the tree-like fractal fracture networks were obtained by analyzing the special structures for such networks.(4) As for the single fracture, the potential distribution was studied by taking it as the three dimensional line sources. Thus, the potential distribution law for the single fracture under steady production in the boundless formation was derived. Based on the said law, with the aid of the method of mirror and superposition theory, the potential distribution law for single fracture underproduction in several common types of reservoirs was derived, leading to the foundation of pressure distribution law in the formation. Based on the assumption that the multi-stage fractured horizontal wells' tree-like fractal fracture networks were comprised by a plurality of such element networks, the semi-analytical model for calculating the productivity of multi-stage fractured horizontal well was derived. Furthermore, based on the research of potential distribution laws for such fractured wells, the potential distribution function for single fracture in the networks was achieved. Considering the percolation features in multi-staged fractured horizontal well's fracture network and the interaction between fluids percolation theory in reservoirs and fracture networks, a productivity model for such wells and the pressure distribution function for fracture networks were respectively obtained by coupling the matrix and fracture network percolation models with semi-analytical calculation method.