This paper presents results of an investigation of various criteria that can be used for decisions related to reducing the number of layers needed to represent a reservoir in reservoir simulation. One of the approaches towards reducing the number of grid-blocks needed in simulation study is to combine thinner layers represented by scaled petrophysical properties. The Gypsy formation was used to develop three different geological models 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. It is observed from the results that the use of lithofacies as a criterion provided the closest match to fine-scale results. Also, results based on three criteria differed significantly only during the early phase of flow. Strategies of geological modeling have a significant impact on scale-up. The channel model and the lithofacies model produce similar results, but flow unit model provides inferior results. Comparing the scale-up results for nine-spot drive, line-drive, and five-spot drive, the line-drive scenario produced the best matches for both water production and reservoir pressure. Comparing the scale-up results obtained for three different boundary conditions, no-flow boundary condition obtained a better results compared to open boundary conditions.
Various scale-up techniques have been developed in recent years, such as average methods (arithmetic, geometric, harmonic)1,2, tensor method3,4,5,6, transmissibility scale-up7,8, renormalization technique 9,10,11,12, and pressure-solver method 2,13. A limitation of these scale-up methods is that they concentrate only on the mathematics of combining petrophysical properties of finer grid-blocks, while giving little consideration to the heterogeneity of geological and structural details. These methods choose coarse-grid cell boundaries independent of the distribution of reservoir properties, i.e., averaging reservoir properties within layers or channels without considering the effect of heterogeneity on fluid flow and scale-up. Such 'layer or channel scale-up' may average out the effects of extreme values of reservoir properties, such as thin continuous communicating layers, large flow barriers, or partially communicating faults. Therefore, in order to obtain reliable results in scale-up for reservoir simulation, not only is it very important to use a reliable mathematical method for the calculation of average value of reservoir properties for the upscaled grid blocks, but also to find an effective method to determine the boundaries of upscaled grid blocks. Successful scale-up result can be obtained with the combination of reliable mathematical scale-up methodology and detailed description of formation heterogeneity. One of the objectives of the study is to study the effects of different modeling strategies on scale-up.
In an analytical approach, permeability values are averaged or scaled up by using selected mathematical averaging method. The scale-up results obtained from these methods depend only on the distribution of permeability values in reservoir model. In a numerical approach, the average permeability is obtained by first running reservoir simulation on fine-scale model, and then calculating average permeability using the simulation results. For this approach, scale-up results are sensitive to the flow conditions, such as production scenario and boundary condition.
