Summary We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation. Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional corner-point or unstructured grids. Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N +1) representation for pressure. This method exactly represents Darcy-force balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptive-mesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required. After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.
The city of London, UK, has seen in recent years an increase in the number of high-rise/multi-storey buildings ("skyscrapers") with roof heights reaching 150 m and more, with the Shard being a prime example with a height of ∼310 m. This changing cityscape together with recent plans of local authorities of introducing Combined Heat and Power Plant (CHP) led to a detailed study in which CFD and wind tunnel studies were carried out to assess the effect of such high-rise buildings on the dispersion of air pollution in their vicinity. A new, open-source simulator, FLUIDITY, which incorporates the Large Eddy Simulation (LES) method, was implemented; the simulated results were subsequently validated against experimental measurements from the EnFlo wind tunnel. The novelty of the LES methodology within FLUIDITY is based on the combination of an adaptive, unstructured, mesh with an eddy-viscosity tensor (for the sub-grid scales) that is anisotropic. The simulated normalised mean concentrations results were compared to the corresponding wind tunnel measurements, showing for most detector locations good correlations, with differences ranging from 3% to 37%. The validation procedure was followed by the simulation of two further hypothetical scenarios, in which the heights of buildings surrounding the source building were increased. The results showed clearly how the high-rise buildings affected the surrounding air flows and dispersion patterns, with the generation of "dead-zones" and high-concentration "hotspots" in areas where these did not previously exist. The work clearly showed that complex CFD modelling can provide useful information to urban planners when changes to cityscapes are considered, so that design options can be tested against environmental quality criteria.
A balanced-force control volume finite element method is presented for three-dimensional interfacial flows with surface tension on adaptive anisotropic unstructured meshes. A new balanced-force algorithm for the continuum surface tension model on unstructured meshes is proposed within an interface capturing framework based on the volume of fluid method, which ensures that the surface tension force and the resulting pressure gradient are exactly balanced. Two approaches are developed for accurate curvature approximation based on the volume fraction on unstructured meshes. The numerical framework also features an anisotropic adaptive mesh algorithm, which can modify unstructured meshes to better represent the underlying physics of interfacial problems and reduce computational effort without sacrificing accuracy. The numerical framework is validated with several benchmark problems for interface advection, surface tension test for equilibrium droplet, and dynamic fluid flow problems (fluid films, bubbles and droplets) in two and three dimensions
SUMMARYA novel method for simulating multi-phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in (i) permitting both continuous and discontinuous description of pressure and saturation between elements; (ii) the use of arbitrarily high-order polynomial representation for pressure and velocity and (iii) the use of high-order flux-limited methods in space and time to avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. The model is initially validated for two-phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels.
SUMMARYThis paper develops methods for interface-capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi-component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P 1 DG-P 2 (linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface-capturing scheme based on compressive control volume advection methods and high-order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many-material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows.
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.