The behavior of a power-law fluid flowing through a sudden expansion: Part I. A numerical solution

AIChE Journal ◽  
1975 ◽  
Vol 21 (3) ◽  
pp. 540-549 ◽  
Author(s):  
A. L. Halmos ◽  
D. V. Boger ◽  
A. Cabelli
Keyword(s):  
Numerical Solution ◽  
Power Law ◽  
Sudden Expansion ◽  
Power Law Fluid

The Equation of the Limit Replacement Width of Non-Newton Fluid in Eccentric Annulus

2013 ◽  
Vol 807-809 ◽  
pp. 2616-2619
Author(s):  
Yin Qing Liu ◽  
Mei Wei Wang ◽  
Hai Qing Cui
Keyword(s):  
Numerical Solution ◽  
Rheological Properties ◽  
Power Law ◽  
Solution Method ◽  
Cement Slurry ◽  
Power Law Fluid ◽  
Two Phase ◽  
Numerical Solution Method ◽  
Eccentric Annulus ◽  
The One

The equation of the limit replacement width of the one-dimension two-phase flow of Bingham fluid replacing Power law fluid in eccentric annulus was established, the numerical solution method of the equation mentioned above was given and taking the 3 wells, such as the He 104-27 well etc for examples, the limit replacement widths of cement slurry displacing mud, whose rheological properties can be described as Bingham and Power law modles respectively, were calculated, by using the equation and the numerical solution method mentioned above, and compared with those of cement slurry displacing mud, whose rheological properties are all described as Binghanm modle.

A semi-infinite hydraulic fracture with leak-off driven by a power-law fluid

2017 ◽  
Vol 837 ◽  
pp. 210-229 ◽  
Author(s):  
E. V. Dontsov ◽  
O. Kresse
Keyword(s):  
Numerical Solution ◽  
Power Law ◽  
Hydraulic Fracture ◽  
Closed Form Solution ◽  
Analytic Solutions ◽  
Form Solution ◽  
Rapid Evaluation ◽  
Power Law Fluid ◽  
Parametric Space ◽  
Fluid Rheology

This study investigates the problem of a semi-infinite hydraulic fracture that propagates steadily in a permeable formation. The fracturing fluid rheology is assumed to follow a power-law behaviour, while the leak-off is modelled by Carter’s model. A non-singular formulation is employed to effectively analyse the problem and to construct a numerical solution. The problem under consideration features three limiting analytic solutions that are associated with dominance of either toughness, leak-off or viscosity. Transitions between all the limiting cases are analysed and the boundaries of applicability of all these limiting solutions are quantified. These bounds allow us to determine the regions in the parametric space, in which these limiting solutions can be used. The problem of a semi-infinite fracture, which is considered in this study, provides the solution for the tip region of a hydraulic fracture and can be used in hydraulic fracturing simulators to facilitate solving the moving fracture boundary problem. To cater for such applications, for which rapid evaluation of the solution is necessary, the last part of this paper constructs an approximate closed form solution for the problem and evaluates its accuracy against the numerical solution inside the parametric space.

scholarly journals Unsteady natural convective power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of a homogeneous chemical reaction

2010 ◽  
Vol 15 (2) ◽  
pp. 139-154 ◽  
Author(s):  
A. J. Chamkha ◽  
A. M. Aly ◽  
M. A. Mansour
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Numerical Solution ◽  
Chemical Reaction ◽  
Power Law ◽  
Vertical Plate ◽  
Graphical Form ◽  
Power Law Fluid ◽  
Time Step ◽  
Flow Past

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a non-Newtonian power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction effects. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in tabular and graphical form to show the effects of material parameters of the problem on the solution.

Free Convective Heat and Mass Transfer in a Doubly Stratified Porous Medium Saturated with a Power-Law Fluid

2009 ◽  
Vol 36 (6) ◽  
pp. 524-537 ◽  
Author(s):  
P. A. Lakshmi Narayana ◽  
P. V. S. N. Murthy ◽  
P. V. S. S. S. R. Krishna ◽  
Adrian Postelnicu
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Power Law ◽  
Power Law Fluid
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