reservoir models with many grid blocks suffer from long run time; it is hence important to deliberatea method to remedy this drawback. usual upscaling methods are proved to fail to reproduce fine gridmodel behaviors in coarse grid models in well proximity. this is attributed to rapid pressure changesin the near-well region. standard permeability upscaling methods are limited to systems with lin...

Reservoir models with many grid blocks suffer from long run time; it is hence important to deliberate a method to remedy this drawback. Usual upscaling methods are proved to fail to reproduce fine grid model behaviors in coarse grid models in well proximity. This is attributed to rapid pressure changes in the near-well region. Standard permeability upscaling methods are limited to systems with ...

In this work, we incorporated the effects of slippage and adsorption into transient productivity index to determine pressure in horizontal wells simulation natural gas reservoirs. We modeled by introducing an apparent permeability, a function Knudsen number, while is using Langmuir isotherm. As for index, included one classic Peaceman reservoir-coupling models, which integral exponential polyno...

The Peaceman-Rachford splitting method is very efficient for minimizing sum of two functions each depends on its variable, and the constraint is a linear equality. However, its convergence was not guaranteed without extra requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a ...

Numerical simulation of uid ow in a hydrocarbon reservoir has to ac count for the presence of wells The pressure of a grid cell containing a well is di erent from the average pressure in that cell and di erent from the bottomhole pressure for the well Peaceman This paper presents a study of grid pressures obtained from the simulation of single phase ow through an isotropic porous medium using d...

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 fo...

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...

We propose and study a domain decomposition method which treats the constraint of displacement continuity at the interfaces by augmented Lagrangian techniques and solves the resulting problem by a parallel version of the Peaceman-Rachford algorithm. We prove that this algorithm is equivalent to the fictitious overlapping method introduced by P.L. Lions. We also prove its linear convergence inde...