Reservoir Simulation

A method for simulating pressures and saturations of oil, gas, and water in an oil reservoir with at least one production or injection well, the method comprising:

• dividing the reservoir into a fine grid array of grid blocks, each block with a permeability and porosity;
• defining a coarse grid array with fewer cells than the fine array, wherein the fine grid array is nested within the coarse grid with cell centers points of the coarse grid corresponding to cell center points of the fine grid,
• calculating pressure for each cell of the coarse grid array,
• fixing the pressure value of fine grid array cells to the solution of corresponding-center-point coarse grid cells,
• calculating pressures for cells of the fine grid by an iterative method where the cell pressure values solved by the coarse grid are fixed and not recalculated.

A method for simulating pressures and saturations of oil, gas, and water in an oil reservoir with at least one production or injection well, the method comprising:

• executing a time-step (n) comprising
• dividing the reservoir into an array of grid blocks, each block with a permeability and porosity,
• the center points of each block positioned on-constant saturation contours, with the saturation contours being at predetermined intervals;
• generating an approximating set of linear algebraic equations (finite difference equations) to represent a partial differential equation governing flow in the reservoir, one equation for each block,
• solving the set of linear algebraic equations to calculate a pressure for each block,
• calculating the location of the bulkflow streamlines for each block based on the calculated pressures,
• calculating the position on the streamline for each block center point were the streamline intersects with a constant saturation contour, and calculating a time (τn−1), associated with the intersection, where the time (τn−1) is the travel time within the reservoir from the position of the center point to the intersection position, where τ0=0,
• displacing each center point to a position along the streamline to a new time location and thereby displacing saturation contours, the new time (τn) consistent with the relationship
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