Abstract
Accuracy and efficiency of reservoir simulators in complex systems depend highly upon a proper grid selection. Grids based on a cartesian coordinate system have been widely used, but have some disadventages: (a) Flexibility in description of faults, pinchouts, hydraulic fractures, horizontal wells and general discontinuities presented in reservoirs, (b) inflexibility in representing well locations; and (c) suffer of grid orientation effects1,6 .
Local grid refinement2 , nine-point3,4 , and thirteen point5 schemes were introduced to enhance the performance of cartesian grids. Research has covered other techniques to reduce grid orientation effects, starting from the development of a uniform hexagonal grid block pattern until the application until the application of Voronoi or PEBI grids. However, the experience on PEBI grids is very limited since their application and development are still in their childhood, as far as the oil industry is concerned. PEBI grids have been applied to the oil industry for about a decade. Besides, last applications are being introduced during the last three years. On the other hand, generation and construction of PEBI grids are not as easy as cartesian grids. The construction of a PEBI grid for a reservoir is feasible only if it is done by a numerical grid generation procedure. A PEBI (PErpendicular BIsection) grid or Voronoi6,7 grid is defined as the region of the space that is closer to its gridpoint than to any other gridpoints. The PEBI is locally orthogonal. It means the block boundaries are normal to lines joining the nodes on the two sides of each boundary. This allows a reasonable accurate computation of interblock transmissibility for heterogeneous but isotropic permeability distribution.
Currently, five types of PEBI grids–namely: hexagonal, elliptical, rectangular, circular and varieable – are being applied, but there is no evidence of their limitations and/or applicability to simulate well transient behavior. Therefore, the point of this paper is to establish and recommend their use for simulation of transient pressure behavior horizontal wells, vertical wells and vertical hydraulic fractured wells. The effectiveness of the PEBI grids was tested by matching numerical to analytical results.
It was found and shown though simualtion experiments that any PEBI grid describes very well the transient behavior of a horizontal well, however, it is not the same for vertical wells. For instance, it is shown that only the elliptical PEBI grid describes transient behavior of hydraulically fractured vertical wells. Circular PEBI grids are good to simulate vertical unfractured wells. Additionally, it is also demonstrated through different simulated experiments the power of PEBI grids to handle non-orthogonal systems8 .
