Treatment of unphysical numerical oscillations via local grid refinement

2021 ◽  
Vol 33 (7) ◽  
pp. 077104
Author(s):  
Haosen H. A. Xu ◽  
Xiang I. A. Yang
Keyword(s):  
Grid Refinement ◽  
Local Grid Refinement ◽  
Numerical Oscillations ◽  
Local Grid

Improved Calculation of Wellblock Pressures for Numerical Simulation of Non-Newtonian Polymer Injection

SPE Journal ◽  
2021 ◽  
pp. 1-12
Author(s):  
Irfan Tai ◽  
Marie Ann Giddins ◽  
Ann Muggeridge
Keyword(s):  
Numerical Simulation ◽  
Oil Recovery ◽  
Polymer Solutions ◽  
Shear Thinning ◽  
Injection Well ◽  
Solution Viscosity ◽  
Grid Refinement ◽  
Equivalent Radius ◽  
Local Grid Refinement ◽  
Local Grid

Summary The viability of any enhanced-oil-recovery project depends on the ability to inject the displacing fluid at an economic rate. This is typically evaluated using finite-volume numerical simulation. These simulators calculate injectivity using the Peaceman method (Peaceman 1978), which assumes that flow is Newtonian. Most polymer solutions exhibit some degree of non-Newtonian behavior resulting in a changing polymer viscosity with distance from the injection well. For shear-thinning polymer solutions, conventional simulations can overpredict injection-well bottomhole pressure (BHP) by several hundred psi, unless a computationally costly local grid refinement is used in the near-wellboreregion. We show theoretically and numerically that the Peaceman pressure-equivalent radius, based on Darcy flow, is not correct when fluids are shear thinning, and derive an analytical expression for calculating the correct radius. The expression does not depend on any particular functional relationship between polymer-solution viscosity and velocity. We test it using the relationship described by the Meter equation (Meter and Bird 1964) and the Cannella et al. (1988) correlation. Numerical tests indicate that the solution provides a significant improvement in the accuracy of BHP calculations for conventional numerical simulation, reducing or removing the need for expensive local grid refinement around the well when simulating the injection of fluids with shear-thinningnon-Newtonianrheology.

A local grid refinement scheme for B‐spline material point method

2020 ◽  
Vol 121 (11) ◽  
pp. 2398-2417
Author(s):  
Zheng Sun ◽  
Yong Gan ◽  
Zhilong Huang ◽  
Xiaomin Zhou
Keyword(s):  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Grid Refinement ◽  
B Spline ◽  
Local Grid Refinement ◽  
Local Grid
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