Chevron U.s.a. Inc.

Schlumberger Technology Corporation

Eth Zurich

Other

Schlumberger Technology Company

Schlumberger Canada Limited

Patrick Jenny

Hamdi A Tchelepi

Seong H Lee

Hadi Hajibeygi

Ivan Fabrizio Lunati

Christian Wolfsteiner

Giuseppe Bonfigli

Dimitrios Karvounis

Marc Andre Hesse

A method, system and computer program product are disclosed for simulating fluid flow in a fractured subterranean reservoir. A reservoir model representative of a fractured subterranean reservoir is provided. The reservoir model includes porous matrix control volumes and a network of fractures, which define fracture control volumes, overlying the porous matrix control volumes. A system of equations based on scale separation is constructed for fluid flow in the porous matrix control volumes and the fracture control volumes. The system of equations can include fracture equations having a pressure vector for each network of fractures that is split into an average pressure value and remainder pressure value. The system of equations based on scale separation is sequentially solved, such as by using an iterative Multi-Scale Finite Volume (MSFV) method.

System and method for simulating fluid flow in a fractured reservoir

Computer-implemented iterative multi-scale methods and systems are provided for handling simulation of complex, highly anisotropic, heterogeneous domains. A system and method can be configured to achieve simulation of structures where accurate localization assumptions do not exist. The iterative system and method smoothes the solution field by applying line relaxation in all spatial directions. The smoother is unconditionally stable and leads to sets of tri-diagonal linear systems that can be solved efficiently, such as by the Thomas algorithm. Furthermore, the iterative smoothing procedure, for the improvement of the localization assumptions, does not need to be applied in every time step of the computation.

Iterative multi-scale method for flow in porous media

A multi-scale finite-volume (MSFV) method simulates nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces. Consistent with the MSFV framework, flow and transport are treated separately and differently using a fully implicit sequential algorithm. The pressure field is solved using an operator splitting algorithm. The general solution of the pressure is decomposed into an elliptic part, a buoyancy/capillary force dominant part, and an inhomogeneous part with source/sink and accumulation. A MSFV method is used to compute the basis functions of the elliptic component, capturing long range interactions in the pressure field. Direct construction of the velocity field and solution of the transport problem on the primal coarse grid provides flexibility in accommodating physical mechanisms. A MSFV method computes an approximate pressure field, including a solution of a course-scale pressure equation; constructs fine-scale fluxes; and computes a phase-transport equation.

Method, apparatus and system for reservoir simulation using a multi-scale finite volume method including black oil modeling

A multi-scale finite-volume (MSFV) method to solve elliptic problems with a plurality of spatial scales arising from single or multi-phase flows in porous media is provided. Two sets of locally computed basis functions are employed. A first set of basis functions captures the small-scale heterogeneity of the underlying permeability field, and it is computed to construct the effective coarse-scale transmissibilities. A second set of basis functions is required to construct a conservative fine-scale velocity field. The method efficiently captures the effects of small scales on a coarse grid, is conservative, and treats tensor permeabilities correctly. The underlying idea is to construct transmissibilities that capture the local properties of a differential operator. This leads to a multi-point discretization scheme for a finite-volume solution algorithm. Transmissibilities for the MSFV method are preferably constructed only once as a preprocessing step and can be computed locally. Therefore, this step is well suited for massively parallel computers. Furthermore, a conservative fine-scale velocity field can be constructed from a coarse-scale pressure solution which also satisfies the proper mass balance on the fine scale. A transport problem is ideally solved iteratively in two stages. In the first stage, a fine scale velocity field is obtained from solving a pressure equation. In the second stage, the transport problem is solved on the fine cells using the fine-scale velocity field. A solution may be computed on the coarse cells at an incremental time and properties, such as a mobility coefficient, may be generated for the fine cells at the incremental time. If a predetermined condition is not met for all fine cells inside a dual coarse control volume, then the dual and fine scale basis functions in that dual coarse control volume are reconstructed.

Multi-scale finite-volume method for use in subsurface flow simulation

An apparatus and method are provided for solving a non-linear S-shaped function F=&#x192;(S) which is representative of a property S in a physical system, such saturation in a reservoir simulation. A Newton iteration (T) is performed on the function &#x192;(S) at Sto determine a next iterative value S. It is then determined whether Sis located on the opposite side of the inflection point Sfrom S. If Sis located on the opposite side of the inflection point from S, then Sis set to S, a modified new estimate. The modified new estimate, S, is preferably set to either the inflection point, S, or to an average value between Sand S, i.e., S=0.5(S+S). The above steps are repeated until Sis within the predetermined convergence criteria. Also, solution algorithms are described for two-phase and three-phase flow with gravity and capillary pressure.

Stable method and apparatus for solving S-shaped non-linear functions utilizing modified Newton-Raphson algorithms

A multi-scale finite-volume (MSFV) method to solve elliptic problems with a plurality of spatial scales arising from single or multi-phase flows in porous media is provided. The method efficiently captures the effects of small scales on a coarse grid, is conservative, and treats tensor permeabilities correctly. The underlying idea is to construct transmissibilities that capture the local properties of a differential operator. This leads to a multi-point discretization scheme for a finite-volume solution algorithm. Transmissibilities for the MSFV method are preferably constructed only once as a preprocessing step and can be computed locally.

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Patrick Jenny