The numerical asymptotic solution to initial condition problem of preexisting plane-strain hydraulic fracture with fluid lag

Li, Kairui; Смирнов, Н.Н.; Qi, Chengzhi; Kiselev, Arthemy V.; Pestov, D.A.

doi:10.1016/j.engfracmech.2020.107296

Cited by 4 publications

(4 citation statements)

References 29 publications

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“…Li et al, 2023 developed a planar three-dimensional model to study the influence of rock fracture toughness heterogeneity on hydraulic fracture propagation [16]. Zvyagin et al, 2021 proposed a numerical method for solving spatial problems in fracture mechanics, which performed well in both quantitative and qualitative display [17]. Pestov et al, 2023 conducted a comparative study on cracks in one matrix and two matrices, and defined the influence coefficient as the research object [18].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation of Hydraulic Fracture Propagation on Multilayered Formation Using Limited Entry Fracturing Technique

Liu,

Ji,

Huang

et al. 2024

Processes

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Hydraulic fracturing is one of the most effective stimulation methods for unconsolidated sandstone reservoirs. However, the design of hydraulic fracturing must take into account the mechanical and stress properties of different geological formations between layers. In this paper, a three-dimensional coupled fluid-solid model using the finite element method is developed to investigate multiple vertical fractures at different depths along a vertical wellbore under different geological and geomechanical conditions. The finite element model does not require further refinement of any new cracks, requiring much smaller degrees of freedom and higher computational efficiency. In addition, new elements were used to account for local pressure drop due to perforation entry friction along the vertical wellbore. Numerical simulation results indicate that hydraulic fracture connections are observed from adjacent layers. Furthermore, the low stress contrast and high Young’s modulus between the layers increases the likelihood of multiple fracture connections. Higher fluid leakage rates increase the likelihood of fracture branching, but decrease the area of fracture coverage near the wellbore. Increasing fluid viscosity is effective in improving the area of fracture coverage near the wellbore. These findings are useful for the design of hydraulic fracturing in multi-layered formations in unconsolidated sandstone formations.

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Section: Introductionmentioning

confidence: 99%

“…obtained numerical asymptotic solutions for the initial condition problem (early solution) of plane strain hydraulic fractures with fluid hysteresis. And complete the planar three-dimensional simulation of fluid flow [20,21].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Hydraulic Fracture Propagation on Multilayered Formation Using Limited Entry Fracturing Technique

Liu,

Ji,

Huang

et al. 2024

Processes

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“…Therefore, in order to overcome the above-mentioned drawbacks, we tried to establish a planar-3D model for studying the effect of heterogeneous fracture toughness on hydraulic fracture propagation in the early-time stage based on the methods developed by us in previous studies [54][55][56]. In this model, the whole evolution process including the stage before propagation and the stage of early-time propagation were considered.…”

Section: Introductionmentioning

confidence: 99%

A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation

Смирнов

et al. 2023

Mathematics

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Among the studies of the effect of rock’s heterogeneity on hydraulic fracture propagation, very little information on the effects of the heterogeneity of rock’s fracture toughness is available. The objective of the present paper is to develop a planar-3D model for studying the effect of the heterogeneity of rock’s fracture toughness on hydraulic fracture propagation. Not only the stage of fracture propagation, but also the stage before the fracture propagation is considered in this model. Based on the proposed model, the evolution of hydraulic fracture propagation under a typical heterogeneous distribution of rock’s fracture toughness and the solution at the stage before fracture propagation are analyzed in detail. Furthermore, a series of numerical comparison experiments including five different distributions of rock’s fracture toughness are made in order to study the effect of the heterogeneity of rock’s toughness. The results indicate that the minimum fracture radius and the contrast of rock’s fracture toughness between adjacent layers are important parameters for determining the size and location of the maximum fracture opening. Most importantly, the fracture contour is greatly affected by the heterogeneity of rock’s fracture toughness.

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“…In the hydraulic fracturing design fracture geometry (length, width and height) is a critical target, which is determined by two "controllable" variables: hydraulic fluid viscosity and wellbore pumping rate, and four "natural" variables: in situ stress, reservoir's stiffness (Young's modulus and Poisson's ratio), fluid loss (porosity and permeability) and fracture toughness [6]. Hydraulic fluid viscosity and wellbore pumping rate are controlled artificially [7][8][9], so they can be easily studied and their working mechanism is relatively clear. The remaining four "natural" variables are mainly controlled by geological conditions, which have strong randomness and complexity.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Hydraulic Fracture Formation and Cleaning Processes

Смирнов

Скрылева

et al. 2022

Energies

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The effectiveness of the hydraulic fracturing procedure is crucially dependent on the stage of fracture planning and design. Forecasting fracture behavior in rock formations characterized by non-uniform toughness is a serious challenge. In the present paper, a planar-3D model considering the rock’s non-uniform fracture toughness has been developed for the uneven propagation of a hydraulic fracture. The series of numerical experiments were designed to study the effect of inhomogenous fracture toughness. The results show that the fracture toughness contract significantly controls the overall direction of fracture propagation, and a combination of toughness contrast and the proportion between the pay zone and barrier zone determine the fracture profile: from almost circular with or without a pair of narrow wedges when the proportion is small to almost rectangular otherwise. This paper also discusses the process of cleaning a fracture from hydraulic fracturing fluid by oil. Using numerical modeling on the basis of the constructed mathematical model, a relationship is established between the quality of hydraulic fracture cleaning and the geometrical parameters of the fracture and the region filled with the hydraulic fracturing fluid. The results of numerical experiments show that while fracturing fluid is more viscous than oil, the length of the fracture has a greater influence on the cleaning process than the viscosity of the fracturing fluid.

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The numerical asymptotic solution to initial condition problem of preexisting plane-strain hydraulic fracture with fluid lag

Cited by 4 publications

References 29 publications

Numerical Simulation of Hydraulic Fracture Propagation on Multilayered Formation Using Limited Entry Fracturing Technique

Numerical Simulation of Hydraulic Fracture Propagation on Multilayered Formation Using Limited Entry Fracturing Technique

A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation

Mathematical Modeling of Hydraulic Fracture Formation and Cleaning Processes

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