Apply Navier-Stokes Equation in Naturally Fractured Reservoirs

In highly consolidated rocks where grain packing is relatively tight like carbonates rock, natural fractures play a vital role in enhancing production rate. There are lot of uncertainties involved in understanding the architecture and properties of fractures which lead to reservoir modeling. Very often reservoir simulationsoftware don’t account for complex geometry of real fracture system. The reason is very simple that no such technology has been developed to image the micro fractures. Fractures are considered to be highly conductive channels foe flow among all type of porous- permeable formations. This article presents mathematical models that govern fluid flow from porous media to a fracture in the formation. The model shows how much fluid can flow from porous medium to a fracture in a practical reservoir situation. It is also established a model which determines the change of fluid volume with the change of pressure gradient within the system. To develop the models, Navier- Stokes equation in the fracture (channel flow) and Darcy’s law in porous media are considered. The proposed models provide more flexible tools in matching the geological variations and to avoid unrealistic predictions of reservoir flow and storage. The models can be used in reservoir simulation and enhanced oil recovery scheme. It can also be used to measure the volume flow rate in a fracture system

کلیدواژه ها:

Fracture flow ، mathematical model ، porous media ، Navier -Stokes equation ، Darcy’s law