Schlumberger Technology Corporation

Chevron U.s.a. Inc.

Eth Zurich

Other

Total Sa

Schlumberger Technology Company

Schlumberger Canada Limited

Hamdi A Tchelepi

Seong H Lee

Patrick Jenny

John R Wallis

Hui Zhou

Arthur Regis Catherin Moncorgé

Ivan Fabrizio Lunati

Hui Cao

Christian Wolfsteiner

Yalchin Efendiev

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

The invention relates to a method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein. The method includes determining a time-step for simulating the reservoir, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations, calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions of the reservoir model corresponding to the time-step, the plurality of CFL conditions comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, simulating a first cell of the plurality of gridded cells with an Implicit Pressure, Explicit Saturations (IMPES) system, and simulating a second cell of the plurality of gridded cells with a Fully Implicit Method (FIM) system.

System and method for performing oilfield simulation operations

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 method, system, a program storage device and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a region of interest, wherein the region of interest has been gridded into cells. Each cell has one or more unknown variable. Each cell has a node. A graph of the nodes is represented by a sparse matrix. The graph is an initially decomposed into a pre-specified number of domains, such that each cell exists in at least one domain. The cells and domains are numbered. Each cell has a key, the key of each cell is the set of domain numbers to which the cell belongs. Each cell has a class, the class of each cell being the number of elements in the cell. The cells are grouped into connectors, each connector being the set of cells that share the same key. Each connector having a connector class, the connector class being the number of elements in the key of the connector. Each connector having only one higher-order neighbor connector is merged with such higher-order neighbor connector. The class of all locally maximum class connectors is reset to the maximum class of held by any connector. The maximum class connector is forced to contain only one cell. The connectors are ordered in increasing order of class. Interpolation operator and restriction operator are constructed from the ordered connectors. The interpolation operator and restriction operator are used to construct a coarse grid. The coarse grid may be used to determine the unknown variables of the cells.

Apparatus, method and system for improved reservoir simulation using an algebraic cascading class linear solver

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

A method, system and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a gridded region of interest. The grid of the region of interest includes one or more types of cells, the type of cell being distinguished by the number of unknown variables representing properties of the cells. The cells share a common variable as an unknown variable. The method includes the steps of identifying different cell types for the grid; constructing an overall matrix for the reservoir model based on the different cell types; at least partially decoupling the common variable from the other unknown variables in the matrix by using a reduction process to yield a reduced matrix; mathematically breaking up the variables in the reduced matrix into k subsets by cell types; applying an overlapping multiplicative Schwartz procedure to the reduced matrix to obtain a preconditioner and using the preconditioner to solve for the unknown variables.

Apparatus, method and system for improved reservoir simulation using a multiplicative overlapping Schwarz preconditioning for adaptive implicit linear systems

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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San Mateo, CA, United States of America

Hamdi A Tchelepi