Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Wang, Wendong; Su, Yuliang; Wang, Kai; Cao, Xiaopeng

doi:10.3390/en11020286

Cited by 23 publications

(9 citation statements)

References 31 publications

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“…Pressure depletion easily causes the deformation of the pores across different scales. When affected by the failure of the propellant, the artificial fracture is deformed or even completely closed [28,29]. The relation of permeability stress sensitivity because of matrix pore throat deformation is as follows [30]:…”

Section: Stress Sensitivity Effectmentioning

confidence: 99%

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An Analytical Solution for Transient Productivity Prediction of Multi-Fractured Horizontal Wells in Tight Gas Reservoirs Considering Nonlinear Porous Flow Mechanisms

Wang

Wan

et al. 2020

Energies

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Multi-fractured horizontal wells (MFHW) is one of the most effective technologies to develop tight gas reservoirs. The gas seepage from tight formations in MFHW can be divided into three stages: early stage with high productivity, transitional stage with declined productivity, and final stage with stable productivity. Considering the characteristics and mechanisms of porous flows in different regions and at different stages, we derive three coupled equations, namely the equations of porous flow from matrix to fracture, from fracture to near wellbore region, and from new wellbore region to wellbore then an unstable productivity prediction model for a MFHW in a tight gas reservoir is well established. Then, the reliability of this new model, which considers the multi-fracture interference, is verified using a commercial simulator (CMG). Finally, using this transient productivity prediction model, the sensitivity of horizontal well's productivity to several relevant factors is analyzed. The results illustrate that threshold pressure gradient has the most significant influence on well productivity, followed by stress sensitivity, turbulence flow, and slippage flow. To summarize, the proposed model has demonstrated a potential practical usage to predict the productivity of multi-stage fractured horizontal wells and to analyze the effects of certain factors on gas production in tight gas reservoirs.Energies 2020, 13, 1066 2 of 20 of tight gas reservoirs has made considerable breakthrough and become the primary growth point for oil and gas production [1][2][3][4][5][6]. Because of its strong heterogeneity, complicated microscopic pore structure, and poor connectivity of the effective sand bodies, the porous flow mechanism of tight gas reservoirs is obviously distinct from those of conventional reservoirs. Moreover, because of poor reservoir physical properties, small discharging radius, lack of or low natural productivity, high development difficulty, and some other potential disadvantages, a MFHW with hydraulic stimulations is extensively used for developing tight gas reservoirs [7][8][9][10][11][12][13][14][15][16].To date, many scholars are dedicated to the transient productivity of fractured wells in unconventional hydrocarbon reservoirs, considering the different characteristics of nonlinear flows compared to multi-scale flows. The methods to calculate the transient productivity of fractured horizontal wells primarily include analytical and numerical solutions, among which the analytical solution includes the complex potential theory, conformal transformation, and the equivalent flow resistance method [14,17,18]. Research on the transient productivity of tight gas reservoirs is increasingly wide. Through an iterative algorithm, Zheng et al. [19] quantified the correlation between saturation and pressure of the infinitesimal coal. They used the Corey relative permeability model to describe relative gas/water permeability as a function of the pressure. By applying the inter-porosity flow equation based on a pseudo-pr...

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Section: Stress Sensitivity Effectmentioning

confidence: 99%

“…Considering the slippage effect, pressure sensitive effect, threshold pressure gradient, and high-speed non-Darcy turbulence effect, the productivity equation can be expressed by Combining Equations (25), (29), and (31).…”

Section: Productivity Model Of a Single Fracture In Horizontal Wellsmentioning

confidence: 99%

An Analytical Solution for Transient Productivity Prediction of Multi-Fractured Horizontal Wells in Tight Gas Reservoirs Considering Nonlinear Porous Flow Mechanisms

Wang

Wan

et al. 2020

Energies

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“…On the basis of models, such as Khristianovich-Geertsma-DeKlerk (KGD) model [2], Perkins-Kern-Nordgren (PKN) model [3], penny-shaped fracture model [4], pseudo 3D model [5] and fully 3D hydraulic fracture model [6], the numerical simulation of hydraulic fracturing technology has developed vigorously. Recent researches have expanded the complexity of hydraulic fracturing modeling and improved the mathematical model in simulation in three folds, including: (1) three-dimensional fractures developed near the wellbore [7][8][9]; (2) the interaction between a hydraulic fracture (HF) and natural fracture (NF) [10][11][12]; (3) the stimulated reservoir volume (SRV) of fractured formations [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of Factors Influencing Stimulated Fracture Volume in Layered Formation

et al. 2019

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Hydraulic fracture dimension is one of the key parameters affecting stimulated porous media. In actual fracturing, plentiful uncertain parameters increase the difficulty of fracture dimension prediction, resulting in the difficulty in the monitoring of reservoir productivity. In this paper, we established a three-dimensional model to analyze the key factors on the stimulated reservoir volume (SRV), with the response surface method (RSM). Considering the rock properties and fracturing parameters, we established a multivariate quadratic prediction equation. Simulation results show that the interactions of injection rate (Q), Young’s modulus (E) and permeability coefficient (K), and Poisson’s ratio (μ) play a relatively significant role on SRV. The reservoir with a high Young’s modulus typically generates high pressure, leading to longer fractures and larger SRV. SRV reaches the maximum value when E1 and E2 are high. SRV is negatively correlated with K1. Moreover, maintaining a high injection rate in this layered formation with high E1 and E2, relatively low K1, and μ1 at about 0.25 would be beneficial to form a larger SRV. These results offer new perceptions on the optimization of SRV, helping to improve the productivity in hydraulic fracturing.

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“…For the complex fracture network intermingled with natural fractures and artificial fractures near the wellbore [24][25][26], Min et al [27] used the cubic law to calculate the permeability of complex fracture networks, and fracture closure and shear failure of complex fracture networks under different stresses are considered. In a study of the unsteady productivity prediction of shale gas, Stalgorova et al [28] divided the seepage area of shale reservoir into stimulated region and un-stimulated region, and a pressure transient model based on tri-line flow model was established.…”

Section: Introductionmentioning

confidence: 99%

A Transient Productivity Model of Fractured Wells in Shale Reservoirs Based on the Succession Pseudo-Steady State Method

et al. 2018

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After volume fracturing, shale reservoirs can be divided into nonlinear seepage areas controlled by micro- or nanoporous media and Darcy seepage areas controlled by complex fracture networks. In this paper, firstly, on the basis of calculating complex fracture network permeability in a stimulated zone, the steady-state productivity model is established by comprehensively considering the multi-scale flowing states, shale gas desorption and diffusion after shale fracturing coupling flows in matrix and stimulated region. Then, according to the principle of material balance, a transient productivity calculation model is established with the succession pseudo-steady state (SPSS) method, which considers the unstable propagation of pressure waves, and the factors affecting the transient productivity of fractured wells in shale gas areas are analyzed. The numerical model simulation results verify the reliability of the transient productivity model. The results show that: (1) the productivity prediction model based on the SPSS method provides a theoretical basis for the transient productivity calculation of shale fractured horizontal well, and it has the characteristics of simple solution process, fast computation speed and good agreement with numerical simulation results; (2) the pressure wave propagates from the bottom of the well to the outer boundary of the volume fracturing zone, and then propagates from the outer boundary of the fracturing zone to the reservoir boundary; (3) with the increase of fracturing zone radius, the initial average aperture of fractures, maximum fracture length, the productivity of shale gas increases, and the increase rate gradually decreases. When the fracturing zone radius is 150 m, the daily output is approximately twice as much as that of 75 m. If the initial average aperture of fractures is 50 μm, the daily output is about half of that when the initial average aperture is 100 μm. When the maximum fracture length increases from 50 m to 100 m, the daily output only increases about by 25%. (4) When the Langmuir volume is relatively large, the daily outputs of different Langmuir volumes are almost identical, and the effect of Langmuir volume on the desorption output can almost be ignored.

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Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Cited by 23 publications

References 31 publications

An Analytical Solution for Transient Productivity Prediction of Multi-Fractured Horizontal Wells in Tight Gas Reservoirs Considering Nonlinear Porous Flow Mechanisms

An Analytical Solution for Transient Productivity Prediction of Multi-Fractured Horizontal Wells in Tight Gas Reservoirs Considering Nonlinear Porous Flow Mechanisms

Uncertainty Analysis of Factors Influencing Stimulated Fracture Volume in Layered Formation

A Transient Productivity Model of Fractured Wells in Shale Reservoirs Based on the Succession Pseudo-Steady State Method

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