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Abstract

Summary

Multi-stage hydraulic fracturing has received considerable attention for production from unconventional resources. One of the key technologies that made development of unconventional shale formations possible is the creation of complex fracture network systems via interaction of hydraulic fractures, natural and induced fractures. Currently, most modeling approaches for multi-stage hydraulically fractured wells are based on diffusivity flow in several distinct scales (matrix/fracture), in which the network of fractures is assumed to be connected and equivalent to a homogeneous medium of Euclidean geometry. In this paper we incorporate a more detailed description of complex fracture networks to improve the pressure transient analysis of hydraulically fractured shale formations. Specifically, we employ a Fractal Diffusivity approach in which characteristics of flow in a dual-continuum porous medium is taken into consideration using fractal theory. In our dual-mechanism Fractal Diffusivity approach, we represent the average porosity and permeability of the fracture network using the fractal porosity-permeability relations. We use a trilinear flow mathematical model to represent the flow in hydraulic fractures, in the formation between the fractures, and in the formation away from the hydraulic fractures. To solve the equations at different regions, we prescribe proper boundary conditions and use Laplace transformation and numerical inversion from Laplace domain to time domain. Using numerical simulation, we validate the new semi-analytical solutions (Fractal Fracture Diffusivity solution) for flow in finite-conductivity multi-staged fractured reservoirs. We perform sensitivity analysis and show that the solution mostly depends on the value of the fractal parameters chosen. Moreover, we generate type curves for well bore pressure and pressure derivatives for multiple transverse fractures for a variety of external boundary conditions and show that the proposed mathematical model is more general than the dual porosity trilinear flow models. We also show applications of the proposed model in flow regime diagnostics.

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/content/papers/10.3997/2214-4609.20141796
2014-09-08
2024-04-20

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References

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A Mathematical Model for Flow in Multi-stage Hydraulic Fracture Systems Using Fractal Theory
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141796
/content/papers/10.3997/2214-4609.20141796
/content/papers/10.3997/2214-4609.20141796
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