Simulation of oil down-coning in a single well scenario using finite element analysis

When an oil reservoir is underlain by an aquifer, oil production draws the water from the aquifer upward, forming a water cone, which under adverse conditions enters in the production well leading to high water cuts. An alternative option is to produce above the critical rate from the aquifer, i.e., at such a rate that the oil cone is drawn into the well. Analytical models, such as derived by Muskat et al. allow to determine the critical rate in terms of simple expressions for interface models that thus ignore relative permeability and capillary pressure effects. Including these effects requires numerical modeling. The numerical modeling of this process is a challenge, because of the occurrence of steep water-oil fronts in the flow direction and the small width of the cone near the production well, which coincides with high production rates. This thesis investigates the possibility of using finite elements for the simulation of oil down-coning. The advantage of finite elements is that it allows grid refinement in regions where large variations occur. A diffusion coefficient is introduced in the saturation equation to smoothen the numerical solution, hereby decreasing the occurrence of flow singularities and allowing larger element sizes, thus decreasing the computation time. The computer model is then used to simulate coning of the oil-water interface, towards a single production well situated at the bottom of a reservoir. The considered reservoir geometry is radially symmetric, so that calculations can be done for a two-dimensional section. The model includes relative permeabilities, capillary pressure and gravity effects. To avoid infinite capillary pressure at connate water saturation, we use a fractal model for continuation of the capillary pressure below a defined critical water saturation. The height of the oil-water interface is not kept constant at the external radius, so that all oil is free to move through the reservoir. Simulations are done for scenarios with different fluid parameters, and variating drawdown rates. For certain drawdown rates, a stationary profile of the interface occurs. If this does, the height of the cone is within the range of values given by the interface model. However, critical rates provided by the derived interface model is not satisfied in the numerical model, since breakthrough does occur in simulations with rates below this critical rate. This is due to the neglecting of capillary force and relative permeabilities in the interface model. The numerical model in this study represents a reservoir where the initial oil cap is of limited radial extend, because the height of the oil column at the external radius decreases and is not kept fixed at a certain height, and is therefore not representative for a reservoir with larger interface size.Section Petroleum EngineeringGeoscience & EngineeringCivil Engineering and Geoscience