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Journal ArticleDOI

Fluid Mechanics of Hydraulic Fracturing: a Review

TL;DR: A review of the state of the art in multiphase fluid mechanics modeling of hydraulic fracturing, highlighting gaps in the body of knowledge and clarifying the questions that are still open.
About: This article is published in Journal of Petroleum Science and Engineering.The article was published on 2017-07-01. It has received 195 citations till now. The article focuses on the topics: Hydraulic fracturing.
Citations
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Journal ArticleDOI
TL;DR: A review of the basic approaches for hydraulic fracture simulation can be found in this article, where the authors discuss both continuum and meso-scales numerical methods as well as engineering models which typically make use of additional assumptions to reduce computational cost.

280 citations


Cites background from "Fluid Mechanics of Hydraulic Fractu..."

  • ...We refer to Osiptsov (2017); Hormozi and Frigaard (2017) for a recent discussion of a wide range of issues related to the modeling of proppant transport in hydraulic fracturing....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a 2D model is presented to model the evolution of the residual aperture profile and conductivity of fractures partially/fully filled with proppant packs, and the model accommodates the mechanical response of proppers in response to closure of arbitrarily rough fractures.

71 citations


Cites background from "Fluid Mechanics of Hydraulic Fractu..."

  • ...…(D. Elswor February 2018; Accepted 7 March 2 solid mechanics aspects of hydraulic fracturing has been comprehensively reviewed by Adachi et al. (2007), Rahman and Rahman (2010), and Detournay (2016), among others, while reviews of the fluid mechanics aspects can be found in Osiptsov (2017)....

    [...]

Journal ArticleDOI
TL;DR: A method of pressure drop calculation in the pipeline based on well segmentation and calculation of the pressure gradient in each segment using three surrogate models based on Machine Learning (ML) algorithms trained on a representative lab data set from the open literature.

51 citations


Cites background from "Fluid Mechanics of Hydraulic Fractu..."

  • ...Multiphase flows in pipes of a circular cross-section are encountered in many industrial applications, such as drilling of oil wells [1], [2], multistage fracturing and cleanup of oil or gas wells [3], transport of hydrocarbons over surface [4]....

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  • ...Excessive drawdown (flowing the well at excessively high flow rates) may be dangerous to the wellfracture system, resulting in undesired geomechanics events, such as proppant flowback, tensile rock failure and fracture pinch-out in the near wellbore [3]....

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Journal ArticleDOI
TL;DR: In this article, a multi-discharge CO2 fracturing system (Multi CO2 Frac) was proposed and tested in Changping coal mine, which can effectively improve coal seam permeability and further enhance gas drainage efficiency.

40 citations

01 Jan 1988
TL;DR: In this article, it has been shown that suspension by fluid turbulence of mineral solids larger than those of medium sands does not become appreciable until the bed shear stress is increased to a value exceeding 12 times its threshold value for the bed material considered.
Abstract: Owing to observational difficulties the distinction between a ‘suspended’ load of solids transported by a stream and a ‘ bed-load ’ has long remained undefined. Recently, however, certain critical experiments have thrown much light on the nature of bed-load transport. In particular, it has been shown that bed-load transport, by saltation, occurs in the absence of fluid turbulence and must therefore be due to a separate dynamic process from that of transport in suspension by the internal eddy motion of a turbulent fluid. It has been further shown that the forward motion of saltating solids is opposed by a frictional force of the same order as the immersed weight of the solids, the friction coefficient approximating to that given by the angle of slip. The maintenance of steady motion therefore requires a predictable rate of energy dissipation by the transporting fluid. The fluid thrust necessary to maintain the motion is shown to be exerted by virtue of a mean slip velocity which is predictable in the same way as, and approxim ates to, the terminal fall velocity of the solid. The mean thrust, and therefore the transport rate of saltating solids, are therefore predictable in terms of the fluid velocity close to the bed, at a distance from it, within the saltation zone, of a ‘centre of fluid thrust’ analogous to the ‘centre of pressure’. This velocity, which is not directly measurable in water streams, can be got from a knowledge of stream depth and mean flow velocity. Thus a basic energy equation is obtained relating the rate of transporting work done to available fluid transporting power. This is shown to be applicable to the transport both of wind-blown sand, and of water-driven solids of all sizes and larger than that of medium sand. Though the mean flow velocity is itself unpredictable, the total stream power, which is the product of this quantity times the bed shear stress, is readily measurable. But since the mean flow velocity is an increasing function of flow depth, the transport of solids expressed in terms of total stream power must decrease with increasing flow depth/grain size ratio. This considerable variation with flow depth has not been previously recognised. It explains the gross inconsistencies found in the existing experimental data. The theoretical variation is shown to approximate very closely to that found in recent critical experiments in which transport rates were measured at different constant flow depths. The theory, which is largely confirmed by these and other earlier experiments, indicates that suspension by fluid turbulence of mineral solids larger than those of medium sands does not become appreciable until the bed shear stress is increased to a value exceeding 12 times its threshold value for the bed material considered. This range of unsuspended transport decreases rapidly, however, as the grain size is reduced till, at a certain critical size, suspension should occur at the threshold of bed movement.

39 citations

References
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Book
01 Jan 1941
TL;DR: The physics of blown sand and desert dunes, The physics of windblown sand and sand dunes, this paper, and the physics of dunes in the Middle East and Africa.
Abstract: The physics of blown sand and desert dunes , The physics of blown sand and desert dunes , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

3,315 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamline moving in the direction opposite to V.
Abstract: It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segree & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

2,912 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a flow is possible in which equally spaced fingers advance steadily at very slow speeds, such that behind the tips of the advancing fingers the widths of the two columns of fluid are equal.
Abstract: When a viscous fluid filling the voids in a porous medium is driven forwards by the pressure of another driving fluid, the interface between them is liable to be unstable if the driving fluid is the less viscous of the two. This condition occurs in oil fields. To describe the normal modes of small disturbances from a plane interface and their rate of growth, it is necessary to know, or to assume one knows, the conditions which must be satisfied at the interface. The simplest assumption, that the fluids remain completely separated along a definite interface, leads to formulae which are analogous to known expressions developed by scientists working in the oil industry, and also analogous to expressions representing the instability of accelerated interfaces between fluids of different densities. In the latter case the instability develops into round-ended fingers of less dense fluid penetrating into the more dense one. Experiments in which a viscous fluid confined between closely spaced parallel sheets of glass, a Hele-Shaw cell, is driven out by a less viscous one reveal a similar state. The motion in a Hele-Shaw cell is mathematically analogous to two-dimensional flow in a porous medium. Analysis which assumes continuity of pressure through the interface shows that a flow is possible in which equally spaced fingers advance steadily. The ratio λ = (width of finger)/(spacing of fingers) appears as the parameter in a singly infinite set of such motions, all of which appear equally possible. Experiments in which various fluids were forced into a narrow Hele-Shaw cell showed that single fingers can be produced, and that unless the flow is very slow λ = (width of finger)/(width of channel) is close to , so that behind the tips of the advancing fingers the widths of the two columns of fluid are equal. When λ = 1/2 the calculated form of the fingers is very close to that which is registered photographically in the Hele-Shaw cell, but at very slow speeds where the measured value of λ increased from 1/2 to the limit 1.0 as the speed decreased to zero, there were considerable differences. Assuming that these might be due to surface tension, experiments were made in which a fluid of small viscosity, air or water, displaced a much more viscous oil. It is to be expected in that case that λ would be a function of μU/T only, where μ is the viscosity, U the speed of advance and T the interfacial tension. This was verified using air as the less viscous fluid penetrating two oils of viscosities 0.30 and 4.5 poises.

2,634 citations

Book
27 Oct 2012
TL;DR: In this article, the origin of Bubbles is discussed, and the theory of Granular Mixtures is presented, along with the application of Kinetic Theory in the field of Continuum Problems.
Abstract: (Chapter Headings): Transport Equations. One-Dimensional Steady Gas Solid Flow. Drift Flux. Critical Granular Flow. The Fluidized State. On the Origin of Bubbles. Inviscid Multiphase Flows: Bubbling Beds. Viscous Flow and Circulating Fluidized Beds. Kinetic Theory Approach. Applications of Kinetic Theory. Kinetic Theory of Granular Mixtures. Sedimentation and Consolidation. Appendices: Formulation of Continuum Problems: Introduction. Appendices: The Method of Characteristics: Introduction. Chapter References. Index.

2,421 citations