Chevron U.s.a. Inc.

Schlumberger Technology Corporation

Eth Zurich

Other

Schlumberger Technology Company

Schlumberger Canada Limited

Seong H. Lee

Hamdi a. Tchelpi

Jenny Patrick

Seong H Lee

Hamdi A Tchelepi

Patrick Jenny

Ivan Fabrizio Lunati

Hui Zhou

Liyong Li

Christian Wolfsteiner

Yalchin Efendiev

Manav Tyagi

Clair Jensen

A method can include receiving information associated with a geologic environment; based at least in part on the information, computing values associated with multiphase fluid flow in the geologic environment using a viscous flow upwind scheme and a buoyancy flow upwind scheme; and outputting at least a portion of the computed values.

Multiphase flow in porous media

A Multiscale Finite Volume (MSFV) method is provided to efficiently solve large heterogeneous problems; it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. It relies on the hypothesis that the fine-scale problem can be described by a set of local solutions coupled by a conservative coarse-scale problem. In numerically challenging cases, a more accurate localization approximation is used to obtain a good approximation of the fine-scale solution. According to an embodiment, a method is provided to iteratively improve the boundary conditions of the local problems, and is responsive to the data structure of the underlying MSFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. In one embodiment the MSFV operator is used. Alternately, the MSFV operator is combined with an operator derived from the problem solved to construct the conservative flux field.

Multiscale finite volume method for reservoir simulation

Computer-implemented systems and methods are provided for an upscaling approach based on dynamic simulation of a given model. A system and method can be configured such that the accuracy of the upscaled model is continuously monitored via indirect error measures. If the indirect error measures are bigger than a specified tolerance, the upscaled model is dynamically updated with approximate fine-scale information that is reconstructed by a multi-scale finite volume method. Upscaling of multi-phase flow can include flow information in the underlying fine-scale. Adaptive prolongation and restriction operators are applied for flow and transport equations in constructing an approximate fine-scale solution.

Indirect-error-based, dynamic upscaling of multi-phase flow in porous media

A multi-scale method to efficiently determine the fine-scale saturation arising from multi-phase flow in a subsurface reservoir is disclosed. The method includes providing a simulation model that includes a fine-scale grid defining a plurality of fine-scale cells, and a coarse-scale grid defining a plurality of coarse-scale cells that are aggregates of the fine-scale cells. The coarse-scale cells are partitioned into saturation regions responsive to velocity and/or saturation changes from the saturation front. A fine-scale saturation is determined for each region and the saturation regions are assembled to obtain a fine-scale saturation distribution. A visual display can be output responsive to the fine-scale saturation distribution.

Multi-scale method for multi-phase 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 three-dimensional hybrid reservoir model representative of a fractured subterranean reservoir is created for simulating fluid flow. The model includes porous matrix blocks and a network of long fractures, which include two-dimensional fracture blocks, that ideally overly and are fluidly connected to the matrix blocks. To simulate fluid flow, matrix and fracture flow equations are obtained and effective fluid flow transmissibilities are determined. The matrix and fracture flow equations are then coupled via the effective fluid flow transmissibilities, such that they can be solved simultaneously for flow responses. The long fractures can be in direct fluid communication with one or more intersecting wells or other fractures. These intersections can be modeled as a point source to enhance numerical stability during simulation. The fracture characteristics, such as orientation, fracture aperture, fracture length, and fracture height, are more realistically modeled using this approach compared to previously known reservoir models.

Method, system and apparatus for simulating fluid flow in a fractured reservoir utilizing a combination of discrete fracture networks and homogenization of small fractures

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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Emeryville, CA, United States of America

Seong H Lee