The Performance of Pseudofunctions in the Upscaling Process

Abstract

To obtain a reliable characterization of complex reservoirs, geoscientists and petroleum engineers commonly build geologic or geostatistical reservoir models which contain more than a million grid cells. However, for flow simulation such a detailed description demands a great deal of information and processing time. Therefore, less complex models are usually preferred where the number of grid cells must be reduced by a factor of 10 or more. Such scaling up necessarily involves the loss of information that must be captured through upscaling porosity, permeability and the use of pseudofunctions. The main objective of this paper is to determine a general method for using pseudofunctions for upscaling multiphase flow in 3D anisotropic heterogeneous reservoirs with different capillary and gravity numbers and applying the method to a real field case "Hassi Messaoud Field - Algeria". The performance of different types of pseudofunctions is evaluated under different capillary and gravity numbers, and upscaling levels. As a part of this research study a software package to calculate pseudofunctions has been developed. It includes:the input option from ECLIPSE restart filesgenerates pseudo curves for three phase three-dimensional problems using Kyte and Berry, Pore Volume, Stone, and Transmissibility Weighted methods, andgenerates output file format which can be read by ECLIPSE 100ä. A variety of homogeneous fine grid models representing different flow regimes were considered in this study and the performance of several pseudofunction methods was compared. All the pseudo function methods succeeded in reproducing the fine grid watercut and maintained oil production for the capillary dominated, equilibrium, viscous dominated flows, however, for the gravity dominated flow they failed to match the fine grid curve exactly. Although this shortcoming of the pseudofunction curves gives better results than the rock curves. Next in this study, the results of the waterflood of a heterogeneous 3-D model of HMD Zone 17 are presented. This real field model confirmed the homogeneous case results: for high flow rates the pseudofunctions can be applied successfully to upscale from fine to coarse grid simulation. Introduction As the clock is ticking geostatistical model scales are becoming finer and finer. Unfortunately, the development of reservoir flow simulators is not moving at the same pace to handle such a large fine scale model. A revolution in the computational hardware or modification to the way the simulation is done is therefore necessary. A typical grid block size is 100 m areally and 1–10 m vertically. Such a large grid block may include a lot of heterogeneity. If we use rock curves for simulation with such large grid blocks, the important effects of heterogeneity will be omitted. Large simulation grid blocks will also cause large numerical dispersion. So, under such circumstances, dynamic pseudo functions are needed to replace the rock curves. Through the use of dynamic pseudo functions, one attempts to capture the effects of heterogeneity below the scale of a simulation grid block, and reduce the effects of numerical dispersion. One common use of pseudo functions is to reduce the number of grid blocks used in the simulation, and sometimes even reduce the dimension of the problem such as reducing a 3-D field case model to a 2-D cross-sectional model. By doing so, we hope to retain fine grid information while performing coarse grid simulations. Theory Pseudofunctions Methods Full-field models may not use simulation layers that are on the same scale as the core samples. Consequently, scaleup of relative permeability and capillary pressure often is required for coarse-grid reservoir simulation. This scaleup is accomplished with relative permeability and capillary pressure inter-block pseudo functions. Two types of inter-block pseudofunctions are available to the engineer working on a reservoir study:analytical (1) anddynamic pseudo functions. This study is mainly concerned with the use of dynamic pseudo functions. Well Pseudofunctions: Inter-block pseudofunctions describe the flow of fluids form one gridblock to adjacent gridblocks. These pseudofunctions, however, do not necessarily describe flow from the gridblock to the wellbore. Well pseudofunctions are used to describe flow to the wellbore.

The Impact of Reservoir Properties on Pseudo Functions: Upscaling of Relative Permeability

“…Because the weighting factor should reflect the relative importance of each fine grid cell, so is taken as the transmissibility value across the interface to the upstream cell. Thus the pseudo relative permeability value is calculated from the following equation (Azoug and Tiab, 2003):…”