A scheme for conservative interpolation on overlapping grids
SIAM Journal on Scientific Computing
Pointwise localized error estimates for parabolic finite element equations
Numerische Mathematik
On Multigrid for Overlapping Grids
SIAM Journal on Scientific Computing
Simulation of lognormal random fields with varying resolution scale and local average for Darcy flow
Computing and Visualization in Science
Numerical Transform Inversion Using Gaussian Quadrature
Probability in the Engineering and Informational Sciences
| Hi-index | 31.45 |
Accurate computation of time-dependent well bore pressure is important in well test analysis - a branch of petroleum engineering where reservoir properties are estimated by comparing measured pressure responses at an oil well to results from a mathematical model. Similar methods are also used in groundwater engineering. In this paper we present the new approach of decoupled overlapping grids for accurately computing time-dependent pressure at the oil well. Our method is implemented in two stages: a global stage with a simple point or line source well approximation, and a local post-process stage with the well modeled correctly as an internal boundary. We investigate the accuracy of our method for a representative 2D problem in both homogeneous and heterogeneous isotropic domains, and compare our results with the widely used Peaceman well index solution (in the homogeneous case), and the approximate solution on locally refined grids. We also present a theoretical analysis that explains the observed O(h^2) behavior of the error in our method for the homogeneous case.