Estimating fluid flow in a reservoir

A method to manage a subsurface reservoir, comprising:

• determining fluid flow in the subsurface reservoir by:
• dividing the reservoir into discrete volume elements;
• determining, for one or more fluid phases comprising the fluid, the potential for each volume element;
• ordering, for one or more of the fluid phases, the volume elements according to their potentials;
• determining a local, fully coupled time-step sequence using a local conservation solution based on the potential ordering of one or more of the fluid phases;
• determining the fluid flow using a global conservation solution based on the local, fully coupled time-step sequence;
• and
• determining one or more injection and/or production sites based on the determined fluid flow.

A system to determine fluid flow in a subsurface reservoir, comprising:

• a computer system comprising a central processing unit, an input device, and an output device;
• input data that can be read by the input device, the input data comprising known values of state variables characterizing the fluid flow at some time;
• a computer program that can be run on the central processing unit to:
• divide the reservoir into discrete volume elements;
• determine, for one or more fluid phases comprising the fluid, the potential for each volume element;
• order, for one or more of the fluid phases, the volume elements according to their potentials;
• determine a local, fully coupled time-step sequence using a local conservation solution based on the potential ordering of one or more of the fluid phases;
• determine the fluid flow using a global conservation solution based on the local, fully coupled time-step sequence;
• and
• output the determined fluid flow to the output device.