A Coupled Model for Fractured Shale Reservoirs with Characteristics of Continuum Media and Fractal Geometry

Wei, Yunsheng; He, Dengfa; Wang, Junlei; Qi, Yue

doi:10.2118/176843-ms

Cited by 8 publications

(3 citation statements)

References 56 publications

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“…It can be noted that instead of fractal derivatives, fractal definitions of the petrophysical properties are used in the derivation of this equation, following a similar path to that proposed in References [11][12][13][14][15][16][17]. Some applications of the use of fractional derivatives on the fluid flow in porous media are presented elsewhere [18][19][20][21].…”

Section: Problem Statementmentioning

confidence: 99%

Partially Penetrated Well Solution of Fractal Single-Porosity Naturally Fractured Reservoirs

Posadas-Mondragón

Camacho-Velázquez

2019

Fractal Fract

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In the oil industry, many reservoirs produce from partially penetrated wells, either to postpone the arrival of undesirable fluids or to avoid problems during drilling operations. The majority of these reservoirs are heterogeneous and anisotropic, such as naturally fractured reservoirs. The analysis of pressure-transient tests is a very useful method to dynamically characterize both the heterogeneity and anisotropy existing in the reservoir. In this paper, a new analytical solution for a partially penetrated well based on a fractal approach to capture the distribution and connectivity of the fracture network is presented. This solution represents the complexity of the flow lines better than the traditional Euclidean flow models for single-porosity fractured reservoirs, i.e., for a tight matrix. The proposed solution takes into consideration the variations in fracture density throughout the reservoir, which have a direct influence on the porosity, permeability, and the size distribution of the matrix blocks as a result of the fracturing process. This solution generalizes previous solutions to model the pressure-transient behavior of partially penetrated wells as proposed in the technical literature for the classical Euclidean formulation, which considers a uniform distribution of fractures that are fully connected. Several synthetic cases obtained with the proposed solution are shown to illustrate the influence of different variables, including fractal parameters.

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Section: Problem Statementmentioning

confidence: 99%

Partially Penetrated Well Solution of Fractal Single-Porosity Naturally Fractured Reservoirs

Posadas-Mondragón

Camacho-Velázquez

2019

Fractal Fract

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“…The correctness of the model was verified by comparing it with the semi-analytical solutions obtained by Medeiros et al (2007). Thereafter, the trilinear flow model has been widely used to investigative the dynamic characteristics of MFHWs in unconventional reservoirs (Ozcan et al 2014;Gao 2014;Wei et al 2015;Wang et al 2015;Chen et al 2016;Wang et al 2016aWang et al , 2016b. Aside from the trilinear flow model, other multi-linear models such as five- (Zhang et al 2016) and seven-region flow models (Yuan et al 2015) have been proposed by some scholars.…”

Section: Introductionmentioning

confidence: 99%

Analytical model for pressure and rate analysis of multi-fractured horizontal wells in tight gas reservoirs

Huang

Yao

et al. 2018

J Petrol Explor Prod Technol

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Multi-fractured horizontal wells (MFHWs) are effective for developing unconventional reservoirs. A complex fracture network around the well and hydraulic fractures form during fracturing. Hydraulic fractures and fracture network are sensitive to the effective stress. However, most existing models do not consider the effects of stress sensitivity. In this study, a new analytical model was established for an MFHW in tight gas reservoirs based on the trilinear flow model. Fractal porosity and permeability were employed to describe the heterogeneous distribution of the complex fracture network. The stress sensitivity of fractures was also considered in the model. Pedrosa substitution and perturbation method were applied to eliminate the nonlinearity of the model. Analytical solutions in the Laplace domain were obtained using Laplace transformation. The model was then validated and applied. Finally, sensitivity analyses of pressure and rate were discussed. The presented model provides a new approach to estimate the effect of fracturing. It can also be utilized to recognize formation properties and forecast the dynamics of pressure and the production of tight gas reservoirs. Keywords Tight gas · Multi-fractured horizontal wells · Complex fracture network · Stress sensitivity List of symbolsGas compressibility (1/MPa) c Pore compressibility (1/MPa) c t Total compressibility (1/MPa) b 3 , b 2 Apparent permeability coefficient in region 3 and region 2 k Permeability (mD) k 3aApparent permeability in region 3 (mD) k 2aApparent permeability in matrix in region 2 (mD) k 2frefFracture permeability in region 2 at the boundary of the hydraulic fracture (mD) k 1refPermeability of region 1 at initial condition (mD) Porosity 2fref Fracture porosity in region 2 at the boundary of the hydraulic fracture Λ Λ= c ti 2m + c ti 2frefStorativity ratio = c ti 2fref Λ, Inter-porosity coefficient = The spacing from the wellbore to the boundary (m) y eHalf fracture spacing (m)

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“…The horizontal wellbore and multiple hydraulic fractures in the target formation constitute a complex flow system, mainly composed of the fluid flow in the surrounding formation, the fluid flow within hydraulic fractures, and the fluid flow along the wellbore. Multi-stage fractured horizontal wells have wellbore lengths typically ranging from 1000 m to 3000 m as well as 10 to 40 stages of hydraulic fractures (Yuan, 2023;Wei et al, 2015;Grieser et al, 2009;Song et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Modeling of Fractured Horizontal Wells in Heterogeneous Formations Considering the Interference between Hydraulic Fractures

Zhou,

Yu,

Cao

et al. 2023

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In this study, a semi-analytical model is developed for the pressure and rate transient analysis of multi-stage fractured horizontal wells. This model simulates the fluid flow towards a fractured horizontal well centered in an unconventional formation with considering the interferences between hydraulic fractures under various heterogeneity conditions. In this proposed model, the formation is divided into sub-systems, and each sub-system is further composed of linear flow regions. Boundaries of the linear flow regions are being updated in real-time response to the interferences between hydraulic fractures. Applicability of the proposed model in heterogeneous reservoirs is demonstrated by the comparison with the five-region model published in literature. The proposed model is applicable to the heterogeneity conditions including a fractured horizontal well having heterogeneous completions and/or the formation being heterogeneous in reservoir properties. Furthermore, the proposed model is utilized to analyze field data from fractured horizontal wells in heterogeneous conditions.

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A Coupled Model for Fractured Shale Reservoirs with Characteristics of Continuum Media and Fractal Geometry

Cited by 8 publications

References 56 publications

Partially Penetrated Well Solution of Fractal Single-Porosity Naturally Fractured Reservoirs

Partially Penetrated Well Solution of Fractal Single-Porosity Naturally Fractured Reservoirs

Analytical model for pressure and rate analysis of multi-fractured horizontal wells in tight gas reservoirs

Semi-Analytical Modeling of Fractured Horizontal Wells in Heterogeneous Formations Considering the Interference between Hydraulic Fractures

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