N-phasic finite element method for calculating a fully coupled response of multiphase compositional fluid flow and a system for uncertainty estimation of the calculated reservoir response

A system for modeling subterranean formations and deriving responses in zones of interest in the subterranean formations based on the modeling, the system comprising:

• a display device;
• central processing unit;
• a memory in communication with the central processing unit;
• a data input device in communication with the central processing unit;
• and
• an interface in communication with the central processing unit, wherein the interface is configured to communicate with external or remote processors or databases, wherein the central processing unit is configured to execute software instructions stored on the memory, and wherein the software instructions, when executed by the central processing unit, cause the central processing unit to control operations for modeling a subterranean formation in three spatial dimensions and one temporal dimension and for deriving a response in a zone of interest in the subterranean formation based on the modeling, the operations comprising:
• constructing a multi-scale or multi-grid finite element mesh from a formation geometry included in raw data on the subterranean formation;
• generating multiple realizations of a static coarse or fine scale petrophysical and geomechanical property model based on the multi-scale or multi-grid finite element mesh;
• generating a multi-scale or multi-grid finite element dynamic simulation model of the subterranean formation for each realization of the static coarse or fine scale petrophysical and geomechanical property model;
• deriving the response in the zone of interest in the subterranean formation from at least one of realizations of the multi-scale or multi-grid finite element dynamic simulation model, wherein the response is derived in the form of one or more displacement fields for solid phases and one or more pressure fields for fluid phases in the zone of interest in the subterranean formation;
• and
• applying information representative of the response in the zone of interest in the subterranean formation to model the subterranean formation.

A non-transitory computer-readable medium storing a program that, when executed by one or more microprocessors, causes one or more microprocessors to perform operations for modeling a subterranean formation and deriving a response in a zone of interest in the subterranean formation based on the modeling, the operations comprising:

• receiving raw data representative of a four dimensional subterranean formation, wherein the raw data comprises data associated with a formation geometry of the subterranean formation;
• storing the raw data in an electronic database;
• constructing a multi-scale or multi-grid finite element mesh from the formation geometry;
• generating multiple realizations of a static coarse or fine scale petrophysical and geomechanical property model based on the finite element mesh;
• generating a multi-scale or multi-grid finite element dynamic simulation model of the subterranean formation for each realization of the static coarse or fine scale petrophysical and geomechanical property model,
• wherein the multi-scale or multi-grid finite element dynamic simulation model comprises a parallelized preconditioner and a matrix free solver to simultaneously derive the response in the zone of interest in the subterranean formation, wherein the response is derived in the form of one or more displacement fields for solid phases and one or more pressure fields for fluid phases in the zone of interest in the subterranean formation;
• and
• applying information representative of response derived from at least one of the realizations for the finite element dynamic simulation models of the subterranean formation to model the subterranean formation.

A method for modeling a subterranean formation and deriving a response in a zone of interest in the subterranean formation based on the modeling, the method comprising:

• collecting, by a processor, raw data on the subterranean formation, wherein the raw data comprises data associated with a formation geometry of the subterranean formation;
• storing, by the processor, the raw data in an electronic database;
• generating, by the processor, multiple realizations of a static coarse or fine scale petrophysical and geomechanical property model by electronically processing the raw data;
• generating, by the processor, a multi-scale or multi-grid finite element dynamic simulation model of the subterranean formation for each realization of the static coarse or fine scale petrophysical and geomechanical property model, wherein generating the multi-scale or multi-grid finite element dynamic simulation model includes simultaneously calculating statistical bounds of:
• at least one of flow and pressure formation fluids;
• and
• displacement of rock material and any derived quantities thereof;
• deriving, by the processor, the response in the zone of interest in the subterranean formation from at least one of the realizations of the multi-scale or multi-grid finite element dynamic simulation model, wherein the response is derived in the form of one or more displacement fields for solid phases and one or more pressure fields for fluid phases in the zone of interest in the subterranean formation;
• and
• displaying, by the processor, information representative of the response in the zone of interest in the subterranean formation derived from the at least one realization of the multi-scale or multi-grid finite element dynamic simulation model of the subterranean formation at a display device.