Upscaling and Permeability and Porosity for a Sandstone and a Carbonate Reservoirs

Various upscaling techniques are used to reduce the number of grid blocks in geologic models to produce simulation models. Nevertheless, the number of grid blocks still amounts to hundreds of thousands of grid blocks, thereby incurring high computing costs. Some upscaling techniques require major programming changes to a simulator. The main objective of this study is to reduce the number of grid blocks in a reservoir simulator by using simple averaging methods on porosity and permeability. Since porosity and permeability proportionally are related, the effects of using different averaging techniques on the two properties were investigated. In this study, the black oil, three–phase–three–dimension option of the Eclipse simulator was used. The reservoirs simulated were a heterogeneous sandstone model that consisted of 43,200 grid blocks (60X40X18) and a heterogeneous carbonate model (60X22X16) with dead oil as the reservoir fluid system. Simulation was repeated on the sandstone model using live oil system. The optimum number of grid blocks was defined as the minimum number of grid blocks that produced errors less than 10% in field oil rate, field gas rate, field water cut, field average pressure and field gas–oil ratio. Sensitivity analysis was conducted to find the optimum condition and two averaging techniques were tested, arithmetic averaging and geometric averaging. For both techniques, permeability showed more influence than porosity. The analysis also shows that geometric averaged permeability and arithmetic averaged porosity gave smaller errors. The optimized sandstone model was 15X40X18, a reduction of 75% from the original model, with 3.48% error. The carbonate model managed to achieve up to 50% reduction (30X22X16) with 3.89% error. Simulation using live oil also resulted in the same number of grid blocks for sandstone but caused a higher error that is 5.1%