Mathematical models for oil reservoir simulation

Petroleum resources are found within sedimentary rocks that have a sufficient interconnected void space to store and transmit fluids. The actual flow of liquid and gas phases occurs on a micrometer scale in the void space between rock grains. On the other hand, the hydrocarbon is typically carried in rock zones that are a few tens of meters thick but extend several kilometers in the lateral directions. The rock formations are typically heterogeneous at all length scales in between and phenomena at all length scales can have a profound impact on flow, making flow in subsurface reservoirs a true multiscale problem. Observing dynamic fluid behavior and measuring the pertinent parameters of a subsurface reservoir is difficult. Predicting reservoir performance therefore has a large degree of uncertainty attached. Simulation studies are usually performed to quantify this uncertainty. Reservoir simulation is the means by which one uses a numerical model of the geological and petrophysical characteristics of a hydrocarbon reservoir to analyze and predict fluid behavior in the reservoir over time. In its basic form, a reservoir simulation model consists of three parts: (i) a geological model in the form of a volumetric grid with cell/face properties that describes the given porous rock formation; (ii) a flow model that describes how fluids flow in a porous medium, typically given as a set of partial differential equations expressing conservation of mass or volumes together with appropriate closure relations; and (iii) a well model that describes the flow in and out of the reservoir, including a model for flow within the well bore and any coupling to flow control devices or surface facilities. Reservoir simulation is used for two main purposes: (i) to optimize development plans for new fields; and (ii) assist with operational and investment decisions.. In particular, simulation is used in inverse modeling to integrate static and dynamic (production) data. The role and need for simulation depends greatly depend on the geological setting, the production environment (onshore versus offshore), and field maturity.