A coupled finite element method for the numerical simulation of hydraulic fracturing with a condensation technique

Bao, Jin; Fathi, Ebrahim; Ameri, S.

doi:10.1016/j.engfracmech.2014.08.002

Cited by 47 publications

(29 citation statements)

References 44 publications

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“…It is noted that the leak‐off flow q l was integrated analytically since its dependency on time is known. It is emphasized that some authors do not carry this integration analytically . Instead, q l is taken as discrete values in time.…”

Section: Formulationmentioning

confidence: 99%

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Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

Shauer

Duarte

2019

Num Anal Meth Geomechanics

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Summary This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak‐off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples.

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Section: Formulationmentioning

confidence: 99%

“…Since the time dependency of this term is known, it can be integrated analytically between time steps. Some authors, however, handle this term as discrete values in time . An analysis of the errors associated with this strategy is presented in Section .…”

Section: Introductionmentioning

confidence: 99%

Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

Shauer

Duarte

2019

Num Anal Meth Geomechanics

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“…In this paper, an in-house numerical simulator (HFWVU) based on PKN model and the finite element method is used to simulate hydraulic fracturing in a unified way where no additional effort is needed to track the fluid front explicitly when a fluid lag exists or occurs (Bao et al, 2014a;Bao et al, 2014b). The simulation results of HFWVU have been confirmed with asymptotic solutions in different hydraulic fracturing regimes (Bao et al, 2014b).…”

Section: Fracture Geometry and Permeabilitymentioning

confidence: 61%

Coupled 3-D numerical simulation of proppant distribution and hydraulic fracturing performance optimization in Marcellus shale reservoirs

Kong

Fathi

Ameri

2015

International Journal of Coal Geology

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“…Both large propped fracture area and fracture conductivity are desired to optimize the fracture and well after-stimulation performance. Previous work has been focused on simulating hydraulic fracture propagation and fluid/proppant transport in fractures (Bao, Fathi, & Ameri, 2014;Barree & Conway, 1995;Daneshy, 1978;Gadde, Yajun, Jay, Roger, & Sharma, 2004;B. Kong, Fathi, & Ameri, 2015;Novotny, 1977;Smith, Bale, Britt, Hainey, & Klein, 2001;A.…”

Section: Introductionmentioning

confidence: 99%

Proppant Transport Simulation in Hydraulic Fractures and Fracture Productivity Optimization

et al. 2015

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The success of hydraulic fracturing stimulation is highly reliant on the flow area and permeability of the induced fractures. The flow area can be significantly affected by proppant distribution while fracture permeability is mainly governed by proppant sizes. To create a fracture with a large flow area, small proppants are essential to maintain a minimum proppant settling velocity; on the other hand, large proppant sizes provide higher proppant pack permeability (i.e., fracture permeability). Therefore, it is critical to study the effect of proppant on the efficiency of hydraulic fracturing stimulation.In this paper, a 3-D numerical simulator is developed to simulate proppant distribution profile, calculate fracture geometry based on the proppant distribution and forecast productivity through each fracture. More specifically, finite difference method is applied to calculate proppant distribution profile during the hydraulic fracturing and flow back processes for different settings such as proppant size and relative density. Both single-proppant and multi-proppant size combination are investigated and their after-stimulation productivities are compared. Proppant slippage velocity is considered over a wide range of fracturing fluid viscosity and density. Fracture geometry is firstly determined through the hydraulic fracturing operating parameters and then recalculated based on simulated proppant concentration profile. The adjusted fracture geometry is then used to simulate fluid flow from reservoir matrix to the fracture with non-uniform proppant distribution and non-Darcy flow of compressible fluid.Results show that, among all parameters, reservoir permeability mostly affects proppant size selection and pumping scheduling in order to achieve an optimum fracturing performance. Multi-proppant size combination simulation results indicate that properly designed multi-proppant combination treatment can increase after-stimulation productivity and improve fracture performance. There exists an optimum combination of proppants size and their volume portion exists for a specific reservoir. The approach presented here can help further understand proppant transport and settling, fracture geometry variation and fracture production performance.

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A coupled finite element method for the numerical simulation of hydraulic fracturing with a condensation technique

Cited by 47 publications

References 44 publications

Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

Coupled 3-D numerical simulation of proppant distribution and hydraulic fracturing performance optimization in Marcellus shale reservoirs

Proppant Transport Simulation in Hydraulic Fractures and Fracture Productivity Optimization

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