Analysis of the transient flow of non-Newtonian power-law fluids in homogeneous reservoirs with the elastic outer boundary

2021 ◽  
Author(s):  
Chaochao Zhao ◽  
Chao Min
Keyword(s):  
Power Law ◽  
Transient Flow ◽  
Outer Boundary ◽  
Power Law Fluids

Wellbore Storage and Skin Effects During the Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

1980 ◽  
Vol 20 (01) ◽  
pp. 25-38 ◽  
Author(s):  
Chi U. Ikoku ◽  
Henry J. Ramey
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Transient Flow ◽  
Constant Pressure ◽  
Outer Boundary ◽  
Petroleum Reservoirs ◽  
Storage Effect ◽  
Well Test ◽  
Wellbore Storage ◽  
Power Law Fluids

Abstract A model recently presented by Ikoku and Ramey for non-Newtonian power-law flow in porous media was extended to flow in finite circular reservoirs. A constant flow rate was stipulated at the wellbore, and two boundary conditions were considered: no-flow outer boundary and constant-pressure outer boundary. The results were used to derive a new expression for the stabilization time for power-law flow in porous media.Wellbore storage and skin effects always distort the transient pressure behavior of wells in petroleum reservoirs. It is important to investigate the consequences of these phenomena and be able to interpret real well test information. This paper considers the effects of skin and wellbore storage on the transient flow of non-Newtonian power-law fluids in petroleum reservoirs. petroleum reservoirs. A new numerical wellbore storage simulator was used to study the effects of skin and wellbore storage during the transient flow of power-law fluids in infinitely large and finite circular reservoirs. Results are presented both in tabular form and as log-log graphs of dimensionless pressures vs dimensionless times. The log-log graphs may be used in a type-Curve matching procedure to analyze short-time well test data.The early period is dominated by wellbore storage effect. A new expression was obtained for the duration of wellbore storage effect when skin exists for infinitely large reservoirs. This criterion is not valid for finite circular reservoirs with no-flow outer boundary or constant-pressure outer boundary. Results indicate that there is no apparent end of wellbore storage effect for the no-flow outer boundary condition for the values of external radius presented. New relationships were derived for skin presented. New relationships were derived for skin factor and "effective well radius" for power-law flow. Introduction Many papers in the petroleum engineering, chemical engineering, and rheology literature have addressed the subject of non-Newtonian flow in porous media. These studies have represented non-Newtonian flow with power-law models. Most of the results are similar. The main differences in the final expressions lie in the type of power-law model used.In the basic papers on the transient flow of non-Newtonian power-law fluids in porous media, wellbore storage effect was not considered. Ikoku and Ramey and Odeh and Yang presented techniques for calculating the skin factor from injection well test data. However, wellbore storage and skin effects always distort the transient pressure behavior of wells in petroleum reservoirs. It is important to investigate the consequences of these phenomena to be able to interpret real well test information properly.The flow geometries of interest to petroleum engineers in well test analysis usually involve bounded reservoirs. In most cases, a constant flow rate is stipulated at the well along with one of these outer boundary conditions: no flow across the outer boundary, or constant pressure at the outer boundary. Reservoirs with rectangular and other polygonal shapes often are encountered. Transient polygonal shapes often are encountered. Transient pressure behavior for these shapes may be obtained pressure behavior for these shapes may be obtained by applying the principle of superposition in space to the solutions of the infinitely large reservoir cases.In this paper we seek solutions for constant-rate injection into finite circular reservoirs with no-flow and constant-pressure outer boundaries. SPEJ P. 25

Forced convection heat transfer study of a blunt-headed cylinder in non-Newtonian power-law fluids

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jaspinder Kaur ◽  
Roderick Melnik ◽  
Anurag Kumar Tiwari
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Power Law ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Total Drag ◽  
Shear Thinning Fluids ◽  
Power Law Fluids

Abstract In this present work, forced convection heat transfer from a heated blunt-headed cylinder in power-law fluids has been investigated numerically over the range of parameters, namely, Reynolds number (Re): 1–40, Prandtl number (Pr): 10–100 and power-law index (n): 0.3–1.8. The results are expressed in terms of local parameters, like streamline, isotherm, pressure coefficient, and local Nusselt number and global parameters, like wake length, drag coefficient, and average Nusselt number. The length of the recirculation zone on the rear side of the cylinder increases with the increasing value of Re and n. The effect of the total drag coefficient acting on the cylinder is seen to be higher at the low value of Re and its effect significant in shear-thinning fluids (n < 1). On the heat transfer aspect, the rate of heat transfer in fluids is increased by increasing the value of Re and Pr. The effect of heat transfer is enhanced in shear-thinning fluids up to ∼ 40% and it impedes it’s to ∼20% shear-thickening fluids. In the end, the numerical results of the total drag coefficient and average Nusselt number (in terms of J H −factor) have been correlated by simple expression to estimate the intermediate value for the new application.

The Analysis Approach of Boundary Layer Equations of Power-Law Fluids of Second Grade

2008 ◽  
Vol 63 (9) ◽  
pp. 564-570 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Muhammet Yürüsoy ◽  
Mehmet Pakdemirli
Keyword(s):  
Power Law ◽  
Homotopy Analysis Method ◽  
Nonlinear Problems ◽  
Analytic Solutions ◽  
Second Grade ◽  
Analysis Method ◽  
Boundary Layer Equations ◽  
Power Law Fluids ◽  
Homotopy Analysis ◽  
Constant Coefficients

A powerful analytic technique for nonlinear problems, the homotopy analysis method (HAM), is employed to give analytic solutions of power-law fluids of second grade. For the so-called secondorder power-law fluids, the explicit analytic solutions are given by recursive formulas with constant coefficients. Also, for the real power-law index in a quite large range an analytic approach is proposed. It is demonstrated that the approximate solution agrees well with the finite difference solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear equations of the power-law fluids of second grade.

Sign in / Sign up

Export Citation Format

Share Document