For the past ten years or so, a number of so-called multiscale methods have been developed as an alternative approach to upscaling and to accelerate reservoir simulation. The key idea of all these methods is to construct a set of prolongation operators that map between unknowns associated with cells in a fine grid holding the petrophysical properties of the geological reservoir model and unknowns on a coarser grid used for dynamic simulation. The prolongation operators are computed numerically by solving localized flow problems, much in the same way as for flow-based upscaling methods, and can be used to construct a reduced coarse-scale system of flow equations that describe the macro-scale displacement driven by global forces. Unlike effective parameters, the multiscale basis functions have subscale resolution, which ensures that fine-scale heterogeneity is correctly accounted for in a systematic manner. Among all multiscale formulations discussed in the literature, the multiscale restriction-smoothed basis (MsRSB) method has proved to be particularly promising. This method has been implemented in a commercially available simulator and has three main advantages. First, the input grid and its coarse partition can have general polyhedral geometry and unstructured topology. Secondly, MsRSB is accurate and robust when used as an approximate solver and converges relatively fast when used as an iterative fine-scale solver. Finally, the method is formulated on top of a cell-centered, conservative, finitevolume method and is applicable to any flow model for which one can isolate a pressure equation. We discuss numerical challenges posed by contemporary geomodels and report a number of validation cases showing that the MsRSB method is an efficient, robust, and versatile method for simulating complex models of real reservoirs.
Streamline methods as a reservoir simulation tool have generated a great deal of interest in petroleum engineering because of the capability to calculate fluid flow in multi-million cell geological models with reasonable CPU times. Recently, streamline simulation has been applied to fractured reservoirs at the geo-scale. However, these simulations have been limited to two-phase incompressible systems. Commercial application of streamline methods to fractured reservoirs often requires the modeling of at least three compressible fluid phases. Flow simulation of fractured reservoirs is commonly performed using a dual porosity model. The dual porosity system is modeled by using two coupled grids: one for matrix and one for fracture. The interaction between the two continua is modeled using matrix-fracture transfer functions. Until now, there were no mathematical models of dual porosity three-phase compressible flow for streamline simulators. To realize this model it was necessary to reformulate the matrix and fracture pressure equations. Conventional transfer function has been incorporated as a source/sink term, not only in the streamline saturation equations (as it was in incompressible case), but also in the pressure equation. The dual porosity model has been implemented into a streamline simulator. This tool has its main application in the high resolution reservoir modeling domain for analyzing geological uncertainty, model ranking and screening, and dynamic model calibration using production data. This paper describes the mathematical model for three-phase compressible dual porosity model for a streamline simulator and compares the results and run times of the streamline-based approach with a conventional dual porosity grid-based commercial simulator. The results from the streamline simulator for dual porosity show good agreement with those produced by a commercial finite difference simulator with order of magnitude improvement in simulation time. Introduction Streamline methods have been used for fluid flow analysis since the nineteenth century (Helmoltz [,10] and Muskat [19]). Improvement of the method and application to reservoir simulation were published by a number of authors (LeBlanc [16], Higgins [11]), but streamline methods were not considered a general purpose reservoir simulation technology. During the 1960–1990's, the reservoir simulation community mainly focused on the finite difference/finite volume computational schemes. This approach has certain limitations for flow simulation at the geo-scale. There are many complicated geological multiwell models that require a large number of grid cells, and therefore require either very large (parallel) computing effort, or coarsening the model through upscaling. Time step length has to satisfy CFL condition for the explicit case. The convergence of the non-linear equations for the implicit approach may also require short time step length. Simulation of geological scale reservoir models with finite difference/finite volume methods may be impractical due to time constraints. Coarse models can result in numerical smearing of flood fronts, and grid orientation effects may also be observed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.