Publications
96 results found
Salinas P, Pavlidis D, Jacquemyn C, et al., 2017, Simulation of geothermal water extraction in heterogeneous reservoirs using dynamic unstructured mesh optimisation, AGU FALL
Salinas P, Pavlidis D, Xie Z, et al., 2017, A robust control volume finite element method for high aspect ratio domains with dynamic mesh optimisation, American Physical Society Division of Fluid Dynamics meeting
Salinas P, Pavlidis D, Xie Z, et al., 2017, A Discontinuous Control Volume Finite Element Method for Multi-Phase Flow in Heterogeneous Porous Media, Journal of Computational Physics, Vol: 352, Pages: 602-614, ISSN: 0021-9991
We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.
Xie Z, Lu L, Stoesser T, et al., 2017, Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder, JOURNAL OF HYDRODYNAMICS, Vol: 29, Pages: 800-804, ISSN: 1001-6058
Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a “volume of fluid” type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.
Salinas P, Pavlidis D, Jacquemyn C, et al., 2017, A Robust Control Volume Finite Element Method for Highly Distorted meshes, SIAM Conference on Mathematical and Computational Issues in the Geosciences
Debbabi Y, Jackson MD, Hampson GJ, et al., 2017, Capillary Heterogeneity Trapping and Crossflow in Layered Porous Media, Transport in Porous Media, Vol: 120, Pages: 183-206, ISSN: 0169-3913
We examine the effect of capillary and viscous forces on the displacement of one fluid by a second, immiscible fluid across and along parallel layers of contrasting porosity, and relative permeability, as well as previously explored contrasts in absolute permeability and capillary pressure. We consider displacements with wetting, intermediate-wetting and non-wetting injected phases. Flow is characterized using six independent dimensionless numbers and a dimensionless storage efficiency, which is numerically equivalent to the recovery efficiency. Results are directly applicable to geologic carbon storage and hydrocarbon production. We predict how the capillary–viscous force balance influences storage efficiency as a function of a small number of key dimensionless parameters, and provide a framework to support mechanistic interpretations of complex field or experimental data, and numerical model predictions, through the use of simple dimensionless models. When flow is directed across layers, we find that capillary heterogeneity traps the non-wetting phase, regardless of whether it is the injected or displaced phase. However, minimal trapping occurs when the injected phase is intermediate-wetting or when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. A dimensionless capillary-to-viscous number defined using the layer thickness rather than the more commonly used system length is most relevant to predict capillary heterogeneity trapping. When flow is directed along layers, we show that, regardless of wettability, increasing capillary crossflow reduces the distance between the leading edges of the injected phase in each layer and increases storage efficiency. This may be counter-intuitive when the injected phase is non-wetting. Crossflow has a significant impact on storage efficiency only when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. In that case, capillary he
Xie Z, Hewitt G, Pavlidis D, et al., 2017, Numerical study of three-dimensional droplet impact on a flowing liquid film in annular two-phase flow, Chemical Engineering Science, Vol: 166, Pages: 303-312, ISSN: 0009-2509
Annular flow with liquid entrainment occurs in a wide variety of two-phase flow system. A novel control volume finite element method with adaptive unstructured meshes is employed here to study three-dimensional droplet deposition process in annular two-phase flow. The numerical framework consists of a ‘volume of fluid’ type method for the interface capturing and a force-balanced continuum surface force model for the surface tension on adaptive unstructured meshes. The numerical framework is validated against experimental measurements of a droplet impact problem and is then used to study the droplet deposition onto a flowing liquid film at atmospheric and high pressure conditions. Detailed complex interfacial structures during droplet impact are captured during the simulation, which agree with the experimental observations, demonstrating the capability of the present method. It is found that the effect of the ambient pressure on the fluid properties and interfacial tension plays an important role in the droplet deposition process and the associated interfacial phenomena.
Salinas P, Pavlidis D, Xie Z, et al., 2017, Improving the robustness of the control volume finite element method with application to multiphase porous media flow, International Journal for Numerical Methods in Fluids, Vol: 85, Pages: 235-246, ISSN: 1097-0363
Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.
Latham J-P, Yang P, Lei Q, et al., 2017, Blast fragmentation in rock with discontinuities using an equation of state gas model coupled to a transient dynamics fracturing and fragmenting FEMDEM code, 51st US Rock Mechanics/Geomechanics Symposium
Obeysekara, Lei Q, Salinas P, et al., 2017, Modelling the evolution of a fracture network under excavation-induced unloading and seepage effects based on a fully coupled fluid-solid simulation, 51st US Rock Mechanics/Geomechanics Symposium
Salinas P, Pavlidis D, Xie Z, et al., 2017, A Double Control Volume Finite Element Method with Dynamic Unstructured Mesh Optimization, SPE Reservoir Simulation Conference 2017
Salinas P, Pavlidis D, Xie Z, et al., 2017, A Double Control Volume Finite Element Method with Dynamic Unstructured Mesh Optimization, Reservoir SImulation Conference
Debbabi Y, Jackson MD, Hampson GJ, et al., 2017, Viscous crossflow in layered porous media, Transport in Porous Media, Vol: 117, Pages: 281-309, ISSN: 1573-1634
We examine the effect of viscous forces on the displacement of one fluid by a second, immiscible fluid along parallel layers of contrasting porosity, absolute permeability and relative permeability. Flow is characterized using five dimensionless numbers and the dimensionless storage efficiency, so results are directly applicable, regardless of scale, to geologic carbon storage. The storage efficiency is numerically equivalent to the recovery efficiency, applicable to hydrocarbon production. We quantify the shock-front velocities at the leading edge of the displacing phase using asymptotic flow solutions obtained in the limits of no crossflow and equilibrium crossflow. The shock-front velocities can be used to identify a fast layer and a slow layer, although in some cases the shock-front velocities are identical even though the layers have contrasting properties. Three crossflow regimes are identified and defined with respect to the fast and slow shock-front mobility ratios, using both theoretical predictions and confirmation from numerical flow simulations. Previous studies have identified only two crossflow regimes. Contrasts in porosity and relative permeability exert a significant influence on contrasts in the shock-front velocities and on storage efficiency, in addition to previously examined contrasts in absolute permeability. Previous studies concluded that the maximum storage efficiency is obtained for unit permeability ratio; this is true only if there are no contrasts in porosity and relative permeability. The impact of crossflow on storage efficiency depends on the mobility ratio evaluated across the fast shock-front and on the time at which the efficiency is measured.
Latham J, Xiang J, Obeysekara A, et al., 2017, Modelling hydro-geomechanical behaviour of fractured and fracturing rock masses: application to tunnel excavation-induced damage, 16th Conference on the Mechanics and Engineering of Rock, MIR
Adam A, Pavlidis D, Percival JR, et al., 2017, Dynamic Mesh Adaptivity for Immiscible Viscous Fingering, Pages: 788-802
The unstable displacement of one fluid by another in a porous medium occurs frequently in various branches of enhanced oil recovery. It is now well known that when the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive, particularly in 3D. We use IC-FERST, a novel control volume finite element (CVFE) code that uses dynamic mesh adaptivity on unstructured meshes to simulate 2D and 3D viscous fingering with higher accuracy and lower computational cost than conventional methods. We provide evidence that these unstructured mesh simulations in fact yield better results that are less influenced by grid orientation error than their structured counterparts. We also include the effect of capillary pressure and show three examples that are very challenging to simulate using more conventional approaches.
Latham, Obeysekara, Xiang J, et al., 2016, Modelling hydro-geomechanical behaviour of fractured and fracturing rock masses: application to tunnel excavation-induced damage, Conferenze di Meccanica e Ingegneria delle Rocce
Salinas P, Pavlidis D, xie Z, et al., 2016, Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media, International Journal for Numerical Methods in Fluids, Vol: 84, Pages: 466-476, ISSN: 1097-0363
A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented.The governing equations are discretised in time using an adaptive -method. However, the use of implicitdiscretisations does not guarantee convergence of the non-linear solver for large Courant numbers. In thiswork, a double-fixed point iteration method with backtracking is presented that improves both convergenceand convergence rate. Moreover, acceleration techniques are presented to yield a more robust non-linearsolver with increased effective convergence rate. The new method reduces the computational effort bystrengthening the coupling between saturation and velocity, obtaining an efficient backtracking parameter,using a modified version of Anderson’s acceleration and adding vanishing artificial diffusion.
Xie Z, Pavlidis D, Salinas P, et al., 2016, A balanced-force control volume finite element method for interfacial flows with surface tension using adaptive anisotropic unstructured meshes, Computers and Fluids, Vol: 138, Pages: 38-50, ISSN: 0045-7930
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.
Salinas P, Pavlidis D, Xie Z, et al., 2016, Dynamic unstructured mesh adaptivity for improved simulation of nearwellbore flow in reservoir scale models, 15th European Conference on the Mathematics of Oil Recovery, Publisher: EAGE
It is well known that the pressure gradient into a production well increases with decreasing distanceto the well and may cause downwards coning of the gaswater interface, or upwards coning ofwateroil interface, into oil production wells; it can also cause downwards coning of the water table,or upwards coning of a saline interface, into water abstraction wells. To properly capture the localpressure drawdown into the well, and its effect on coning, requires high grid or mesh resolution innumerical models; moreover, the location of the well must be captured accurately. In conventionalsimulation models, the user must interact with the model to modify grid resolution around wells ofinterest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of nearwellbore flow in reservoirscale modelsthrough the use of dynamic unstructured adaptive meshing. The method is novel for two reasons.First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of thewell is specified via a line vector. Mesh nodes are placed along the line vector, so the geometry ofthe mesh conforms to the well trajectory. The well location is therefore accurately captured, and theapproach allows complex well trajectories and wells with many laterals to be modelled. Second,the mesh automatically adapts during a simulation to key solution fields of interest such as pressureand/or saturation, placing higher resolution where required to reduce an error metric based on theHessian of the field. This allows the local pressure drawdown and associated coning to be capturedwithout userdriven modification of the mesh. We demonstrate that the method has wideapplication in reservoirscale models of oil and gas fields, and regional models of groundwaterresources.
Gomes JLMA, Pavlidis D, Salinas P, et al., 2016, A force-balanced control volume finite element method for multi-phase porous media flow modelling, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 431-445, ISSN: 1097-0363
A novel method for simulating multi-phase flow in porous media is presented. The approach is based on acontrol volume finite element mixed formulation and new force-balanced finite element pairs. The novelty ofthe method lies in: (a) permitting both continuous and discontinuous description of pressure and saturationbetween elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocityand (c) the use of high-order flux-limited methods in space and to time avoid introducing non-physicaloscillations while achieving high-order accuracy where and when possible. The model is initially validatedfor two-phase flow. Results are in good agreement with analytically obtained solutions and experimentalresults. The potential of this method is demonstrated by simulating flow in a realistic geometry composed ofhighly permeable meandering channels.
Obeysekara A, Lei Q, Salinas P, et al., 2016, A fluid-solid coupled approach for numerical modeling of near-wellbore hydraulic fracturing and flow dynamics with adaptive mesh refinement, 50th US Rock Mechanics/Geomechanics Symposium
Xiao D, Lin Z, Fang F, et al., 2016, Non-intrusive reduced order modeling for multiphase porous media flows using smolyak sparse grids, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 205-219, ISSN: 0271-2091
In this article, we describe a non-intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non-intrusive reduced-order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non-intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced-porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high-fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude.
Adam A, Pavlidis D, Percival J, et al., 2016, Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity, Journal of Computational Physics, Vol: 321, Pages: 512-531, ISSN: 1090-2716
A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
Debbabi Y, Jackson MD, Hampson GJ, et al., 2016, The interplay of capillary and viscous forces driving flow through layered porous media
We examine the impact of viscous and capillary forces on immiscible, two-phase flow parallel and perpendicular to continuous layers of contrasting material properties. We consider layers of contrasting porosity and relative permeability, in addition to the contrasts in absolute permeability investigated previously. We define a set of dimensionless numbers which characterize flow. Some of these are common to flow both parallel and perpendicular to layering, such as the longitudinal permeability ratio σ and the ratio Rs of the moveable pore volumes (MPV) in each layer. Others are specific to a given flow direction, such as the dimensionless capillary to viscous ratio Ncv, and the effective aspect ratio RL that quantifies crossflow for layer-parallel flow. We examine how variations in the dimensionless numbers affect the trapping/recovery efficiency, defined as the fraction of the model MPV occupied by the injected phase after 1 MPV injected, and which is numerically equivalent to the fraction of the displaced phase recovered from the model after 1 MPV injected. The results are directly applicable to geological carbon storage and hydrocarbon production. We find that the trapping efficiency is clearly controlled by the dimensionless numbers. When flow is perpendicular to layering, heterogeneity only influences flow when capillary forces are significant (Ncv>0). As Ncv is increased, a larger fraction of the non-wetting phase is trapped if the layers have contrasting capillary pressure curves. When flow is parallel to layering, both viscous and capillary forces are important. In the viscous limit (Ncv=0), heterogeneity reduces trapping efficiency if σ≠Rs. As capillary forces become more significant (Ncv increases) and if crossflow between layers can occur (RL>0), the trapping efficiency also increases in response to capillary crossflow and reaches a maximum at a given Ncv. At higher Ncv, the benefit of crossflow is outweighed by along layer diffusion
Adam AG, Pavlidis D, Percival JR, et al., 2016, Simulation of immiscible viscous fingering using adaptive unstructured meshes and controlvolume galerkin interpolation
Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability. Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as collocation interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.
Melnikova Y, Jacquemyn C, Osman H, et al., 2016, Reservoir modelling using parametric surfaces and dynamically adaptive fully unstructured grids
Geologic heterogeneities play a key role in reservoir performance. Surface based geologic modeling (SBGM) offers an alternative approach to conventional grid-based methods and allows multi-scale geologic features to be captured throughout the modeling process. In SBGM, all geologic features that impact the distribution of material properties, such as porosity and permeability, are modeled as a set of volumes bounded by surfaces. Within these volumes, the material properties are constant. The surfaces have parametric, grid-free representation, which, in principle, allows for unlimited complexity, since no resolution is implied at the stage of modeling and features of any scale can be included. Surface based models are discretized only when required for numerical analysis. We report here a new automated and integrated workflow for creating and meshing stochastic, surfacebased models. Surfaces are represented through non-uniform rational B-splines (NURBS). Multiple relations between surfaces are captured through geologic rules that are translated into Boolean operations (intersection, union, subtraction). Finally, models are discretized using fully unstructured tetrahedral meshes coupled with a geometry-Adaptive sizing function that efficiently approximate complex geometries. We demonstrate the new workflow via examples of multiple erosional channelized geobodies, fault models and a fracture network. We also show finite element flow simulations of the resulting geologic models, using the Imperial College Finite Element Reservoir Simulator (IC-FERST) that features dynamic adaptive mesh optimization. Mesh adaptivity allows us to focus computational effort on the areas of interest, such as the location of water saturation front. The new approach has broad application in modeling subsurface flow.
Adam AG, Pavlidis D, Percival JR, et al., 2016, Simulation of immiscible viscous fingering using adaptive unstructured meshes and controlvolume galerkin interpolation
Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability. Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as collocation interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.
Debbabi Y, Jackson MD, Hampson GJ, et al., 2016, The interplay of capillary and viscous forces driving flow through layered porous media
We examine the impact of viscous and capillary forces on immiscible, two-phase flow parallel and perpendicular to continuous layers of contrasting material properties. We consider layers of contrasting porosity and relative permeability, in addition to the contrasts in absolute permeability investigated previously. We define a set of dimensionless numbers which characterize flow. Some of these are common to flow both parallel and perpendicular to layering, such as the longitudinal permeability ratio σ and the ratio Rs of the moveable pore volumes (MPV) in each layer. Others are specific to a given flow direction, such as the dimensionless capillary to viscous ratio Ncv, and the effective aspect ratio RL that quantifies crossflow for layer-parallel flow. We examine how variations in the dimensionless numbers affect the trapping/recovery efficiency, defined as the fraction of the model MPV occupied by the injected phase after 1 MPV injected, and which is numerically equivalent to the fraction of the displaced phase recovered from the model after 1 MPV injected. The results are directly applicable to geological carbon storage and hydrocarbon production. We find that the trapping efficiency is clearly controlled by the dimensionless numbers. When flow is perpendicular to layering, heterogeneity only influences flow when capillary forces are significant (Ncv>0). As Ncv is increased, a larger fraction of the non-wetting phase is trapped if the layers have contrasting capillary pressure curves. When flow is parallel to layering, both viscous and capillary forces are important. In the viscous limit (Ncv=0), heterogeneity reduces trapping efficiency if σ≠Rs. As capillary forces become more significant (Ncv increases) and if crossflow between layers can occur (RL>0), the trapping efficiency also increases in response to capillary crossflow and reaches a maximum at a given Ncv. At higher Ncv, the benefit of crossflow is outweighed by along layer diffusion
Melnikova Y, Jacquemyn C, Osman H, et al., 2016, Reservoir modelling using parametric surfaces and dynamically adaptive fully unstructured grids
Geologic heterogeneities play a key role in reservoir performance. Surface based geologic modeling (SBGM) offers an alternative approach to conventional grid-based methods and allows multi-scale geologic features to be captured throughout the modeling process. In SBGM, all geologic features that impact the distribution of material properties, such as porosity and permeability, are modeled as a set of volumes bounded by surfaces. Within these volumes, the material properties are constant. The surfaces have parametric, grid-free representation, which, in principle, allows for unlimited complexity, since no resolution is implied at the stage of modeling and features of any scale can be included. Surface based models are discretized only when required for numerical analysis. We report here a new automated and integrated workflow for creating and meshing stochastic, surfacebased models. Surfaces are represented through non-uniform rational B-splines (NURBS). Multiple relations between surfaces are captured through geologic rules that are translated into Boolean operations (intersection, union, subtraction). Finally, models are discretized using fully unstructured tetrahedral meshes coupled with a geometry-Adaptive sizing function that efficiently approximate complex geometries. We demonstrate the new workflow via examples of multiple erosional channelized geobodies, fault models and a fracture network. We also show finite element flow simulations of the resulting geologic models, using the Imperial College Finite Element Reservoir Simulator (IC-FERST) that features dynamic adaptive mesh optimization. Mesh adaptivity allows us to focus computational effort on the areas of interest, such as the location of water saturation front. The new approach has broad application in modeling subsurface flow.
Jackson MD, Percival JR, Mostaghiml P, et al., 2015, Reservoir modeling for flow simulation by use of surfaces, adaptive unstructured meshes, and an overlapping-control-volume finite-element method, SPE Reservoir Evaluation and Engineering, Vol: 18, Pages: 115-132, ISSN: 1094-6470
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 valid
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