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Proppant transportation and placement in fractures by water and liquid nitrogen: a numerical simulation

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Abstract

Hydraulic fracturing, a highly efficient well-stimulation technique, can be utilised to significantly increase production from unconventional low-permeability rocks like shale. This is achieved through creating fractures in the formation by injecting a solution of water, sand, and chemicals. These fractures may make it easier for the hydrocarbons to enter the wellbore. Proppant is essential in the hydraulic fracturing technique since it is employed to maintain the fractures open. Therefore, the movement and placement of the proppant are crucial elements that determine the conductivity and efficiency of the propped fracture. In this study, the efficacy of water and liquid nitrogen (LN) as fracturing fluids is examined. In order to analyse elucidate the factors controlling the phenomenon of proppant transportation, volume percent of sand (proppant), proppant density, fluid viscosity, fluid velocity, and proppant diameter have been examined in this study. The concepts of proppant volume fraction (V.F.) contour, equilibrium dune height (EDH, in mm) and equilibrium dune level (EDL, in %) have been established in this study. Water was observed to have higher proppant carrying capacity than LN. The developed model was validated against published information. Reduction in proppant density was found to have a significant impact on its placement. Major findings of this study shall assist in comprehending the proppant movement and placement during the course of fracturing and ultimately in improving the job performance.

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Abbreviations

\(\dot{m}\) :

Interphase mass transfer

\(\overrightarrow{F}\) :

Body forces on solid-phase

\(\overrightarrow{\tau }\) :

Phase stress–strain tensor

\(\overrightarrow{u}\) :

Velocity vector

k:

Interphase exchange coefficient

ρ:

Density in kg/m3

α:

Volume fraction

V.F.:

Proppant volume fraction

R:

Interaction forces between phases

P:

Pressure

V:

Velocity in m/s

D:

Diameter of the proppant in mm

η:

Viscosity in Pa.s

EDH:

Equilibrium Dune Height in mm

EDL:

Equilibrium Dune Level in %

ft. /min:

Feet-per-minute

m/s:

Meter-per-second

LN:

Liquid Nitrogen

EGT:

Eulerian-Granular Technique

s:

Solid-phase

f:

Fluid-phase

q:

Phase (particle or gas)

fs:

Interphase between solid and fluid phase

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Drilling, Cementing and Stimulation (DCS) Research Centre, Department of Petroleum Engineering (DPE), School of Energy Technology (SoET), Pandit Deendayal Energy University (PDEU), Knowledge Corridor, Raysan, Gandhinagar, Gujarat, 382 426, India

    Sanket Patel, Isaac Wilson, Hari Sreenivasan, Paul Naveen & Shanker Krishna

  2. Department of Petroleum Engineering, Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, Jharkhand, 826 004, India

    Pawan Gupta

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  1. Sanket Patel
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Contributions

SP: Conceptualization, Software and Visualization. IW: Software and Visualization. HS: Formal Analysis and Data Curation. PN: Formal Analysis and Validation. PG: Formal Analysis and Validation. SK: Methodology, Writing—Original Draft Preparation, Reviewing and Editing. All authors have read and approved the manuscript.

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Correspondence to Shanker Krishna.

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Patel, S., Wilson, I., Sreenivasan, H. et al. Proppant transportation and placement in fractures by water and liquid nitrogen: a numerical simulation. Comp. Part. Mech. 11, 721–743 (2024). https://doi.org/10.1007/s40571-023-00649-z

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