Integrated Geological Modelling and Transmissibility Scale-Up for Improved Accuracy in Reservoir Simulation
Authors: Wang W. , Gupta A. 
Published: March 2010

Abstract
This paper presents a study on the development of efficient methods for scaling petrophysical properties from high-resolution geological models to the resolution of reservoir simulation models. These methods were evaluated using data for the Gypsy field located in northeastern Oklahoma near Lake Keystone. Various criteria that may be used to reduce the number of layers to represent a reservoir in simulation studies were investigated.
The approach attempts to reduce the number of grid blocks needed by combining thinner layers and representing them by scaled petrophysical properties assigned to the resulting thicker layers. Three different geological models were developed based on channel identifiers, lithofacies, and flow units, respectively. The effect of the criteria used for combining layers on simulation results was studied by conducting scale-up for three different geological models, three different production scenarios, and three different boundary conditions.
In addition to the linear flow scale-up of transmissibility between two grid blocks, a scale-up of the 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. The validity of the proposed approach was evaluated by comparing the performance prediction for various reservoir flow scenarios using fine-scale and coarse-scale reservoir models.
Strategies of geological modelling were found to have a significant impact on simulation results, especially during the early phase of flow. The use of lithofacies as a criterion provided the closest match to fine-scale results. Amongst various drive mechanisms compared, the best matches for both water production and reservoir pressure were achieved for the line-drive scenario. A better match was obtained for no-flow boundary conditions compared to an open boundary conditions scenario.

Introduction
Various scale-up techniques have been developed in recent years, such as the averaging method(1, 2), the tensor method(3–6), transmissibility scale-up(7, 8), renormalization technique(9–12), and the pressure-solver method(2, 13). White and Horne(7) showed that the general tensor scaling procedure can give estimates on a coarse grid that are significantly more accurate than other scale-up methods, but greatly increases the computation effort.
It is important that the scale-up near wells includes the characteristics of radial flow. Soeriawinata and Kelkar(16) presented an analytical method in which the well block was divided into sectors. The permeability of the well block in the upscaled layers, was determined using a thickness averaging method. Ding(17) calculated the equivalent coarse grid transmissibility based on fine grid simulations and scaled the productivity index using an imposed well condition for radial flow near a well. It was reported that the errors between fine and coarse-scale results, using a scaleup procedure including a radial flow region, are much lower than using a standard procedure.
Many scale-up methods concentrate on the mathematics of combining petrophysical properties, but ignore the geological heterogeneity and structural details.