Bi-power law correlations for sediment transport in pressure driven channel flows

Wang, Jing; Joseph, Daniel D.; Patankar, Neelesh A.; Conway, M.W.; Barree, R.D.

doi:10.1016/s0301-9322(02)00152-0

Cited by 108 publications

(54 citation statements)

References 6 publications

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“…The prediction of power laws from numerical data suggests that the same type correlations could be obtained from experimental data as was done by Patankar, Joseph, Wang, Barree, Conway, and Asadi 13 and Wang, Joseph, Patankar, Conway, and Barree. 14 The existence of such power laws is an expression of selfsimilarity, which has not yet been predicted from analysis or physics. The flow of dispersed matter appears to obey those self-similar rules to a large degree ͑Barenblatt 15 ͒.…”

Section: Introductionmentioning

confidence: 99%

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Wang

Joseph

2003

Physics of Fluids

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Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow Phys. Fluids 21, 053302 (2009); 10.1063/1.3119802 Plane Poiseuille flow of a sedimenting suspension of Brownian hard-sphere particles: Hydrodynamic stability and direct numerical simulationsLift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids are investigated by direct numerical simulation. Previous works on this topic for Newtonian fluids show that the two-dimensional channel can be divided into alternating regions defined by the stability of the particle's equilibrium. We observe stability regions with the same pattern in flows of shear thinning fluids and study the effects of shear thinning properties on the distribution of the stability regions. Joseph and Ocando ͓J. Fluid Mech. 454, 263 ͑2002͔͒ analyzed the role of the slip velocity U s ϭU f ϪU p and the angular slip velocity ⍀ s ϭ⍀ p Ϫ⍀ f on migration and lift in plane Poiseuille flow of Newtonian fluids. They concluded that the discrepancy ⍀ s Ϫ⍀ se , where ⍀ se is the angular slip velocity at equilibrium, changes sign across the equilibrium position. In this paper we verify that this conclusion holds in shear thinning fluids. Correlations for lift forces may be constructed by analogy with the classical lift formula LϭCU⌫ of aerodynamics and the proper analogs of U and ⌫ in the present context are U s and ⍀ s Ϫ⍀ se . Using dimensionless parameters, the correlation is a power law near the wall and a linear relation ͑which can be taken as a power law with the power of one͒ near the centerline. The correlations are compared to analytical expressions for lift forces in the literature and we believe that the correlations capture the essence of the mechanism of the lift force. Our correlations for lift forces can be made completely explicit provided that the correlations relating U s and ⍀ s to prescribed parameters are obtained.

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Section: Introductionmentioning

confidence: 99%

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Wang

Joseph

2003

Physics of Fluids

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“…Two power law correlations for sediment transport have been studied by Wang et al (2003) and for friction factors in turbulent gas-liquid flows by Garcia et al (2003Garcia et al ( , 2005. Correlations of families of bi-power laws depending on a third parameter have been constructed by Viana et al (2003) who correlated data for the rise velocity of Taylor bubbles in round vertical pipes as a family of bi-power laws of the Froude number vs. Reynolds number indexed by the Eotvos number.…”

Section: Classical Logistic Dose Response Curvementioning

confidence: 99%

Friction factor correlations for laminar, transition and turbulent flow in smooth pipes

Joseph

Yang

2010

Physica D: Nonlinear Phenomena

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In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose curve algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds number but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data Marusic and Perry 1995 for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse 1932 andMcKeon et al. 2004 on friction factors for flow in smooth pipes and to the data of Nikuradse 1933 for effectively smooth pipes.

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“…Patankar's theory on sediment transport in pressure-driven channel flows (Patankar, 2002;Wang et al, 2002) can be depicted by Figure 5. Patankar's experiment resembles the proppant transportation at steady pumping rate in a typical frac job.…”

Section: Why the Pdg Is A Key Factor Influencing Sand Screen Out?mentioning

confidence: 99%

Using Prefrac Test Information to Predict and Avoid Screenout Associated with Slickwater Frac in Tight Gas Sands at the Wattenberg Field in the Denver-Julesburg Basin

Yang

Kremer

2008

SPE Annual Technical Conference and Exhibition

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Slick water hydraulic fracturing is becoming more attractive as more tight formations and economically marginal reservoirs are developed. However, its economic advantage can not cajole us to ignore sand screen-out problem largely caused by its poor sand carrying capability. By studying pressure declining characteristics of leak-off tests and the corresponding frac job results, the authors have successfully correlated the pressure declining gradient of leak-off tests with the likeliness of sand screen-out. This method has been effectively applied to predict the likeliness of sand screen-out at the beginning of frac jobs, and avoid sand screen-out during frac jobs.As the first step, we selected 96 fracs that share the same frac design and implementation, such as the same pumping rate,

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Bi-power law correlations for sediment transport in pressure driven channel flows

Cited by 108 publications

References 6 publications

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Friction factor correlations for laminar, transition and turbulent flow in smooth pipes

Using Prefrac Test Information to Predict and Avoid Screenout Associated with Slickwater Frac in Tight Gas Sands at the Wattenberg Field in the Denver-Julesburg Basin

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