This paper presents the results of a study on the development of efficient methods for scaling of petrophysical properties from high resolution geological models to the resolution of reservoir simulation. These methods were evaluated using the data for Gypsy field located in northeastern Oklahoma near Lake Keystone. In this study, transmissibility between two grid blocks is the property that is scaled. After conducting the linear flow scale-up of transmissibility between two grid blocks, a scale-up of productivity index (PI) was found to be important and necessary in order to account for the radial flow around the wellbore. Special consideration was also needed for the pinch-out grid blocks in the system. Validity of the proposed approach was evaluated by comparing the performance prediction for various reservoir flow scenarios using finescale and coarse-scale reservoir models.
Numerous methods of scale-up for single phase flow have been developed, including average method (arithmetic/ geometric/ harmonic),1,2 tensor method,3,4,5,6 transmissibility scale-up,7,8 renormalization technique, 9,10,11,12 and pressuresolver method.2,13
The simplest method for scaling permeability of a reservoir formation is the average method. Begg et al.2 determined that harmonic and arithmetic methods gave the lowest and highest values, respectively, of average permeability and the geometric method provided results between the values from harmonic and arithmetic methods. White and Horne7 demonstrated that the general tensor scaling procedure can give accurate, efficient production estimate on a coarse grid. Uniform pressures are applied at two opposite faces and no-flow boundary conditions are applied at the other four faces when solving the finitedifference equation. Tensor method is significantly more accurate than other scale-up methods, but it greatly increases the computation time needed for simulation. Therefore, it still cannot be directly incorporated into a commercial reservoir simulator without significantly slowing down computation time.
Several authors have proposed methods for scale-up at the wellbore or in the vicinity of wells that consider the characteristics of radial flow. Soeriawinata and Kelkar16 presented an analytical method in which the wellblock was divided into many sectors. The permeability for each layer was calculated as the weighted arithmetic average and the permeability of the wellblock was determined using a thickness averaging method. Ding17 proposed a scale-up procedure to calculate the equivalent coarse grid transmissibility for the linear flow region based on the results of simulation on fine grid. For radial flow in the vicinity of a well, the transmissibility, or productivity index (PI), was scaled by using an imposed well condition. The methodology was tested by conducting scale-up including both the standard procedure for linear flow pattern and the procedure for radial flow pattern. The errors between fine scale and coarse scale caused by the new scale-up procedure including a radial flow region are much lower than the error caused by standard procedure.
The purpose of permeability scale-up is to preserve the key features of flow on a coarse grid and to match them to a fine gird in reservoir simulation.
