Comparison Of Discretization Methods For Modelling Near-Well Phenomena In Thermal Processes
Authors: Hiebert A.D. , Fung L.S.K. , Oballa V.V. , Mourits F.M. 
Published: March 2010

Abstract
The treatment of near-wellbore flow phenomena has a strong influence on reservoir simulation results for thermal processes. Using large well gridblocks can result in high predicted injection pressures, and inaccurate predictions of override and coning behaviours.
Several new discretization methods have been proposed to efficiently provide more accurate modelling of the near-wellbore region. These methods, Cartesian hybrid grids, control-volume finite-element (CVFE) grids, and CVFE hybrid grids, have been implemented in a general purpose thermal reservoir simulator. In this paper, they are compared for the modelling of three thermal processes; single well cyclic steam stimulation, multi-well cyclic steam stimulation, and steam drive.
Results show that Cartesian hybrid grids and CVFE hybrid grids provide an efficient means of accurately modelling near-well phenomena. In multi-well cyclic steam stimulation processes, the hybrid grids allow the use of cylindrical grids to accurately and efficiently mode/the near-wellbore region, while including the influence of adjacent wells with offset steaming. For steam drive processes, the hybrid grids predict earlier steam override and breakthrough times than a standard Cartesian or CVFE grid. The CVFE hybrid grid has the advantages of providing more geometric flexibility and a more consistent discretization at the boundary between the CVFE and cylindrical grid than the Cartesian hybrid grid.

Introduction
The treatment of near-wellbore flow phenomena has a strong influence on reservoir simulation results. In the current practice for field-scale simulation with communicating wells, a coarse Cartesian grid system is used to represent the reservoir, and wells are represented as sources or sinks within the coarse gridblock. This representation of wells is usually nor adequate, especially in thermal processes. For example, the ability to inject steam depends on the viscosity reduction of oil or bitumen by heat conduction and convection in the vicinity), of the wellbore. Thus, because the well is located within a coarse gridblock, an artificially high well injectivity has to be used to allow steam injection. Similarly, for producers, the coning behaviour is not properly handled in coarse gridblocks and empirical pseudo-functions, which are not always accurate, are normally used. For horizontal wells, the near-well phenomena have even a stronger effect on the simulation results because of the longer completion lengths.
Accurate simulation of a field-scale thermal project with a Cartesian grid would be extremely costly due to the large number of gridblocks required to accurately model the phenomena occurring in the field. Small gridblocks are required near the well to model the rapidly changing properties (temperature, pressure, viscosity, saturation, etc.) in this region. To reduce the over-all cost or the simulation, gridblocks with larger volumes may be used away from the wells where changes occur less rapidly and have less impact on simulation results. Typical methods used to vary the volumes of Cartesian gridblocks result in large aspect ratios for many gridblocks which can lead to further discretization errors.
For an accurate simulation of near-well phenomena, the best grid system is the cylindrical grid system because it follows the potential and stream lines near the well.