Modelling of time-dependent proppant embedment and its influence on tight gas production

Ding, Xiang; Zhang, Fan; Zhang, Guangqing

doi:10.1016/j.jngse.2020.103519

Cited by 14 publications

(11 citation statements)

References 28 publications

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“…In this study, only the instantaneous embedment depth is considered; however, the embedment due to the creep behavior of reservoir rocks may also be significant. 39 …”

Section: Discussionmentioning

confidence: 99%

Influence of Proppant Size on the Proppant Embedment Depth

et al. 2022

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Hydraulic fracturing is a well stimulation technique involving the fracturing of bedrock formations by a pressurized liquid, in which proppants are added to keep the fracture open after the fracturing operation. The scale discrepancy between the rock specimen and the proppant may bring deviations in the analysis of proppant embedment depth if the fluid-deteriorated formation is treated as an isotropic medium. This study tries to uncover the origins of these deviations through numerical and analytical analyses. The fluid-deteriorated formation is first modeled as a layered rock to obtain equivalent elastic parameters under isotropic conditions. Then, the equivalent parameters are used in the numerical modeling of proppant embedment. The numerical simulations indicate that the simplification of the fluid-deteriorated formation into an isotropic rock results in an underestimation of the proppant embedment depth, and this deviation increases with the scale contrast between rock specimens and proppants. Hertz contact theory is utilized to explain this deviation. As a promising technique, the nano/micro-indentation is also proposed to depict the fluid-deterioration effect along the depth. This study provides methods for the calibration of mechanical parameters of fluid-deteriorated rocks in the analysis of proppant embedment.

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“…In this study, only the instantaneous embedment depth is considered; however, the embedment due to the creep behavior of reservoir rocks may also be significant. 39 …”

Section: Discussionmentioning

confidence: 99%

Influence of Proppant Size on the Proppant Embedment Depth

et al. 2022

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Section: Methodsmentioning

confidence: 99%

Numerical Modeling of Proppant Embedment in Viscoelastic Formations with the Fractional Maxwell Model

et al. 2021

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Hydraulic fracturing is often used to exploit unconventional hydrocarbons, and proppants are usually added during hydraulic fracturing to keep the fractures induced open. Nevertheless, time-dependent proppant embedment has often been neglected in previous studies. In this survey, the fractional Maxwell model is first proposed to describe the viscoelastic deformation of tight sandstones. Then, the fractional rheological model is incorporated into the finite element framework in ABAQUS to establish a numerical model to investigate the time-dependent embedment of proppants in viscoelastic formations. Parameter sensitivity studies are also performed to investigate the influences of the mechanical characteristics of proppants and formation on the embedment depth. Several factors that influence proppant embedment are also discussed.

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“…The application of fractional calculus in rheology has been verified to be successful and various fractional rheological models have been proposed to describe the time-dependent phenomena [18]. Among these fractional models, due to its simplicity, the fractional Maxwell model has often been adopted to depict the rheological dynamics for polymers [19], foods [20], fluids [21] and geomaterials [22][23][24]. As fractional modelling is still unfamiliar to non-mathematicians, the constitutive equation for the fractional Maxwell model is presented briefly in the following section.…”

Section: Methodsmentioning

confidence: 99%

Analytical and Numerical Modelling of Creep Deformation of Viscoelastic Thick-Walled Cylinder with Fractional Maxwell Model

et al. 2021

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The deformation of a thick-walled cylinder under pressure is a classic elastic mechanics problem with various engineering applications. In this study, the displacement of a viscoelastic thick-walled cylinder under internal pressure is investigated via analytical as well as numerical modelling. The fractional Maxwell model is initially introduced to describe the creep deformation of high-strength Q460 steel. Subsequently, an analytical solution to the creep deformation of the thick-walled cylinder under both internal and external pressures is deduced with the corresponding principle. The analytical solution is examined with a numerical simulation that incorporates the fractional Maxwell model by a user-defined subroutine. The numerical simulation agrees well with the analytical solution. The limitations of the current study are also discussed.

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Modelling of time-dependent proppant embedment and its influence on tight gas production

Cited by 14 publications

References 28 publications

Influence of Proppant Size on the Proppant Embedment Depth

Influence of Proppant Size on the Proppant Embedment Depth

Numerical Modeling of Proppant Embedment in Viscoelastic Formations with the Fractional Maxwell Model

Analytical and Numerical Modelling of Creep Deformation of Viscoelastic Thick-Walled Cylinder with Fractional Maxwell Model

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