Publications
96 results found
Hu H, Salinas P, Jackson M, 2023, A 3D finite element magma reservoir simulator
<jats:p>IC-FEMRES (Imperial College Finite Element Magma REservoir Simulator), is a finite-element based numerical code for simulating the 3D dynamic behaviour of a two-phase, multi-component magma reservoir with chemical reaction.&#160; The code is built upon the open-source IC-FERST package (http://multifluids.github.io/) which includes advanced numerical features such as dynamic mesh optimization, to allow fine-scale solution features to be captured while simulating in a large domain.The model solves for velocity using a finite-element approach, and for transport using a control-volume scheme to ensure the conservation of energy, mass, and components.&#160; Solid, melt and volatile phases are modelled as Stokes fluids with very different Newtonian viscosities.&#160; Individual crystals in the solid matrix are incompressible, but the solid phase is compressible to account for changes in melt fraction.&#160; The formulation captures viscous compaction and convection of the solid matrix, and flow of melt and volatiles via a Darcy-type formulation at low melt fraction, and a hindered-settling type approach at high melt fraction. &#160;It also captures heat transport by conduction and advection, and component transport by advection.&#160; A chemical model is used to calculate phase fraction and composition.&#160; The numerical package sequentially solves for: 1. Melt and solid velocity (mass and momentum conservation); 2. Enthalpy and component transport (energy and component conservation); 3. Phase fraction and composition (chemical model). &#160;Material properties such as density and viscosity can be coupled to solution fields such as melt fraction and composition to yield a highly non-linear system of coupled equations that are solved iteratively.We demonstrate here the validation of the formulation against well-constrained test cases, and example results for a magma reservoir in the continental
Al Kubaisy J, Salinas P, Jackson MD, 2023, A hybrid pressure approximation in the control volume finite element method for multiphase flow and transport in heterogeneous porous media, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 475, ISSN: 0021-9991
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- Citations: 1
Kadeethum T, O'Malley D, Ballarin F, et al., 2022, Enhancing high-fidelity nonlinear solver with reduced order model, SCIENTIFIC REPORTS, Vol: 12, ISSN: 2045-2322
Bahlali ML, Salinas P, Jackson MD, 2022, Efficient Numerical Simulation of Density-Driven Flows: Application to the 2-and 3-D Elder Problem, WATER RESOURCES RESEARCH, Vol: 58, ISSN: 0043-1397
Heaney C, Liu X, Go H, et al., 2022, Extending the capabilities of data-driven reduced-order models to make predictions for unseen scenarios: applied to flow around buildings, Frontiers in Physics, Vol: 10, Pages: 1-16, ISSN: 2296-424X
We present a data-driven or non-intrusive reduced-order model (NIROM) which is capable of making predictions for a significantly larger domain than the one used to generate the snapshots or training data. This development relies on the combination of a novel way of sampling the training data (which frees the NIROM from its dependency on the original problem domain) and a domain decomposition approach (which partitions unseen geometries in a manner consistent with the sub-sampling approach). The method extends current capabilities of reduced-order models to generalise, i.e., to make predictions for unseen scenarios. The method is applied to a 2D test case which simulates the chaotic time-dependent flow of air past buildings at a moderate Reynolds number using a computational fluid dynamics (CFD) code. The procedure for 3D problems is similar, however, a 2D test case is considered sufficient here, as a proof-of-concept. The reduced-order model consists of a sampling technique to obtain the snapshots; a convolutional autoencoder for dimensionality reduction; an adversarial network for prediction; all set within a domain decomposition framework. The autoencoder is chosen for dimensionality reduction as it has been demonstrated in the literature that these networks cancompress information more efficiently than traditional (linear) approaches based on singular value decomposition. In order to keep the predictions realistic, properties of adversarial networks are exploited. To demonstrate its ability to generalise, once trained, the method is applied to a larger domain which has a different arrangement of buildings. Statistical properties of the flows from the reduced order model are compared with those from the CFD model in order to establish how realistic the predictions are.
Hamzehloo A, Bahlali ML, Salinas P, et al., 2022, Modelling saline intrusion using dynamic mesh optimization with parallel processing, ADVANCES IN WATER RESOURCES, Vol: 164, ISSN: 0309-1708
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Regnier G, Salinas P, Jacquemyn C, et al., 2022, Numerical simulation of aquifer thermal energy storage using surface-based geologic modelling and dynamic mesh optimisation, HYDROGEOLOGY JOURNAL, Vol: 30, Pages: 1179-1198, ISSN: 1431-2174
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Heaney CE, Wolffs Z, Tómasson JA, et al., 2022, An AI-based non-intrusive reduced-order model for extended domains applied to multiphase flow in pipes, Physics of Fluids, Vol: 34, Pages: 1-22, ISSN: 1070-6631
The modeling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of meters vs a pipe diameter of just a few inches. Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM), which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we compare Proper Orthogonal Decomposition with several types of autoencoder networks, known for their ability to compress information accurately and compactly. The comparison is assessed with two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network, which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce visually realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1 and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Inspection of the predicted liquid volume
Al Kubaisy J, Salinas P, Jackson M, 2022, Discontinuous low order pressure formulation in control volume finite element method for simulating flow and transport in highly heterogeneous porous media
<jats:p>&lt;p&gt;Control volume finite element (CVFE) methods provide flexible framework for modelling flow and transport in complex geological features such as faults and fractures. They combine the finite element method that captures complex flow characteristics with the control volume approach known for its stability and mass conservative properties. The general approach of CVFE methods maps the physical properties of the system onto the element mesh (element-wise properties) while the node centred control volumes span element boundaries. In the presence of abrupt material interfaces between elements which are often encountered in fractured models, the method suffers from non-physical leakage in the saturation solution as the result of control volume discretization used for advancing the transport solution. In this work, we present a discontinuous pressure formulation based on control volume finite element (CVFE) method for modelling coupled flow and transport in highly heterogeneous porous media. We propose the element pair P&lt;sub&gt;(1,DG)&lt;/sub&gt;-P&lt;sub&gt;(0,DG)&lt;/sub&gt;, a discontinuous first order velocity approximation combined with a discontinuous low order pressure approximation. The approach circumvents the non-physical leakage issue by incorporating a discontinuous, element-based approximation of pressure. Hence, the resultant control volume representation directly maps to the element mesh as well as to the projected physical properties of the system. Due to the low order nature of the formulation, low computational requirement per element and the improved control volume discretization, the presented formulation is proven more robust and accurate than classical CVFE methods in the presence of highly heterogeneous domains.&lt;/p&gt;</jats:p>
Silva V, Salinas P, Jackson M, et al., 2022, Nonlinear solver acceleration based on machine learning applied to multiphase porous media flow
<jats:p>&lt;p&gt;We present a machine learning strategy to accelerate the nonlinear solver convergence for multiphase porous media flow problems. The presented approach dynamically controls an acceleration method based on numerical relaxation. The methodology is implemented and demonstrated in a Picard iterative solver; however, it can also be used with other types of nonlinear solvers. The goal of the machine learning acceleration is to reduce the number of iterations required by the nonlinear solver by adjusting the value of the relaxation factor to the complexity/physics of the system. A set of dimensionless parameters is used to train and control the machine learning. In this way, a simple two-dimensional layered reservoir can be used for training while still exploring a large portion of the dimensionless parameter space. As a result, the training process is simplified, and the machine learning model can be applied to any type of reservoir models.&lt;/p&gt;&lt;p&gt;We demonstrate that the presented technique dramatically reduces the number of nonlinear iterations without sacrificing the quality of the results, even for models that are far more complex than the training case. The average reduction in the number of nonlinear iterations obtained due to the presented method is 24% and the reduction in runtime is 37%. It is worth noting that the optimum value of the relaxation factor is not known &lt;em&gt;a-priori &lt;/em&gt;and it is problem specific. Hence, having an acceleration that adapts itself to the complexity/physics of the system throughout the numerical simulation is extremely valuable and has driven several publications in multiple fields.&lt;/p&gt;&lt;p&gt;The method presented here provides an easy way to deal with nonlinear system of equations that does not necessitate as much effort as a custom nonlinear solver while producing outstand
Regnier G, Salinas P, Jacquemyn C, et al., 2022, Numerical modelling of Aquifer Thermal Energy Storage systems with Surface-Based Geologic modelling and Dynamic Mesh Optimisation
<jats:p>&lt;p&gt;Aquifer Thermal Energy Storage (ATES) has significant potential to provide large-scale seasonal cooling and heating in the built environment, offering a low-carbon alternative to fossil fuels. To deliver safe and sustainable ATES deployments, accurate numerical modelling tools must be used to predict flow and heat transport in the targeted aquifers. However, numerical simulation of ATES systems is very challenging, due to the associated high computational cost of capturing fluid flow and heat transport at a high resolution and importance of accurately modelling complex geological heterogeneity.&lt;/p&gt;&lt;p&gt;Here, we present a novel approach to simulate ATES, based on the use of surface-based geologic models (SBGM), a double control-volume finite element method, and unstructured tetrahedral meshes with dynamic mesh optimisation (DMO). Previous use of DMO for a range of porous media flow applications has allowed an important reduction in the cost of numerical simulations. DMO allows the resolution of the mesh to vary over time and space to satisfy a user-defined solution precision for selected fields, refining where the solution fields are complex and coarsening elsewhere. SBGM allows accurate representation of complex geological heterogeneity and efficient application of DMO, essential for accurate simulation of ATES without excessive computational cost.&amp;#160;&lt;/p&gt;&lt;p&gt;We demonstrate application of these methods in two low-temperature ATES scenarios: a homogeneous aquifer, and a heterogeneous fluvial aquifer containing meandering, channelised sandbodies separated by mudstones. For both cases, cold and warm water are injected alternatively over 6-month periods via a well doublet. We demonstrate that DMO reduces the required number of mesh elements by a factor of up to 22 and simulation time by a factor of up to 15, whilst maintaining the sam
Salinas P, Regnier G, Jacquemyn C, et al., 2022, Geothermal reservoir modelling by using dynamic unstructured meshes for improved heat recovery in highly heterogeneous reservoirs
<jats:p>&lt;p&gt;Numerical modelling of fluid flow and heat transport in geothermal reservoirs can be very challenging. One reason is the broad range of length-scales that control the flow behaviour, spanning several orders of magnitude from fractures (millimetre-scale) and wells (metre-scale) to facies architecture and faults (kilometre-scale). The usual approach for modelling geothermal reservoirs is to discretise the equations using the finite-volume method and variants thereof to ensure mass conservation, subdividing space onto a fixed, structured mesh. However, using a fixed mesh resolution across the entire model domain can be very computationally expensive, and prohibitive if the model must resolve many length-scales.&lt;/p&gt;&lt;p&gt;Here we report an efficient method to apply dynamic mesh optimisation (DMO) to model geothermal reservoirs. DMO is widely used in other areas of computational fluid dynamics because it offers significant advantages in providing higher resolution, multi-scale solutions at much lower computational cost. However, application of DMO to geothermal reservoir modelling has so far been very limited.&lt;/p&gt;&lt;p&gt;The method reported here uses a surface-based representation of all geological heterogeneity that should be captured in the model. The numerous surfaces in the model represent geologic features such as faults, fractures, and boundaries between rock types with different material properties. The surfaces bound rock volumes, termed geologic domains, within which material properties are constant. When simulating flow and heat transport, the mesh dynamically adapts to optimize the representation of key solutions metrics of interest such as temperature, pressure, flow velocity or fluid saturation, but the surface architecture is preserved. The advantage of this approach is that up-, cross- or down-scaling of material properties during DMO is no
Bahlali ML, Salinas P, Jackson MD, 2022, Dynamic mesh optimisation for efficient numerical simulation of density-driven flows: Application to the 2- and 3-D Elder problem
<jats:p>&lt;p&gt;Density-driven flows in porous media are frequently encountered in natural systems and arise from the gravitational instabilities introduced by fluid density gradients. They have significant economic and environmental impacts, and numerical modelling is often used to predict the behaviour of these flows for risk assessment, reservoir characterisation or management. However, modelling density-driven flow in porous media is very challenging due to the nonlinear coupling between flow and transport equations, the large domains of interest and the wide range of time and space scales involved. Solving this type of problem numerically using a fixed mesh can be prohibitively expensive. &amp;#160;Here, we apply a dynamic mesh optimisation (DMO) technique along with a control-volume-finite element method to simulate density-driven flows. DMO allows the mesh resolution and geometry to vary during a simulation to minimize an error metric for one or more solution fields of interest, refining where needed and coarsening elsewhere. We apply DMO to the Elder problem for several Rayleigh numbers. We demonstrate that DMO accurately reproduces the unique two-dimensional (2D) solutions for low Rayleigh number cases at significantly lower computational cost compared to an equivalent fixed mesh, with speedup of order x16. For unstable high Rayleigh number cases, multiple steady-state solutions exist, and we show that they are all captured by our approach with high accuracy and significantly reduced computational cost, with speedup of order x6. The lower computational cost of simulations using DMO allows extension of the high Rayleigh number case to a three-dimensional (3D) configuration and we demonstrate new steady-state solutions that have not been observed previously. Early-time, transient 3D patterns represent combinations of the previously observed, steady-state 2D solutions, but all evolve to a single, steady-state finger in the late t
Silva V, Regnier G, Salinas P, et al., 2022, Rapid modelling of reactive transport in porous media using machine learning
Reactive transport in porous media can play an important role in a variety of processes in subsurface reservoirs, such as groundwater flow, geothermal heat production, oil recovery and CO2 storage. However, numerical solution of fluid flow in porous media coupled with chemical reaction is very computationally demanding. Simultaneously, the success of machine learning in different fields has opened up new possibilities in reactive transport simulations. In this project, we focus on using machine learning techniques to replace the geochemical kinetic calculations generated by PHREEQC. PHREEQC is an open-source aqueous geochemical code that can be used in stand-alone mode or as a reaction module coupled with a flow and transport simulator. Here, we apply machine learning approaches to produce a fast proxy model of PHREEQC. This enables us to have a coupling between transport and reaction while minimizing the added computational cost. We focus initially on calcite dissolution during CO2 sequestration. Different machine learning techniques are investigated and compared to see which is more appropriate for the calcite dissolution problem. The proposed machine learning approach is designed to deal with different time-step sizes and unstructured elements. It accelerates the numerical simulation and proves to be practical to replace the reaction model presented in PHREEQC. This considerably reduces the computational cost of reactive transport while ensuring excellent simulation accuracy. The rapid modelling of reactive transport in porous media has a broad potential to replace many other phase equilibrium models across a wide range of reactive transport problems.
Al Kubaisy J, Salinas P, Jackson MD, 2022, Hybrid finite element pressure approximation for multiphase flow and transport in highly heterogeneous porous media
Control volume finite element (CVFE) methods are commonly used for modeling flow and transport in geometrically complex porous media domains with unstructured meshes. The CVFE approach is based on the finite element method to approximate the pressure and velocity fields, and uses the finite volume method to model saturation ensuring mass conservation. Control volumes are constructed by spanning element boundaries, leading to an artificial smearing of the numerical solution in the presence of sharp material interfaces. Recently, a CVFE method based on discontinuous pressure was introduced that enabled the construction of discontinuous control volumes, thus preventing control volumes from spanning element boundaries. This modification of the method provides accurate solutions but is computationally very expensive due to the discontinuous approximation which incorporates additional degrees of freedom per element. In this work, we propose using hybrid finite element pressure approximations to capture flow and transport in highly heterogeneous porous media. The CVFE element pair $P_{0,DG}-P_{1,H}$ denotes a constant, element-wise, discontinuous Galerkin velocity vector approximation and a hybrid (continuous/discontinuous) Galerkin first-order pressure scalar approximation of the flow model. The method exploits the efficient continuous CVFE method in most of the model domain while the discontinuous CVFE approach is applied exclusively along material discontinuities. We demonstrate that this hybrid scheme outperforms the classical CVFE continuous approach as well as the discontinuous Galerkin modification by incorporating the best of both approaches. The presented hybrid approach computational requirements are comparable to the continuous approach while the accuracy of the transport solution corresponds to that of the discontinuous pressure method. We validate the presented hybrid approach and discuss the convergence of the method. The effectiveness of the new scheme is de
Silva VLS, Salinas P, Jackson MD, et al., 2021, Machine learning acceleration for nonlinear solvers applied to multiphase porous media flow, Computer Methods in Applied Mechanics and Engineering, Vol: 384, Pages: 1-17, ISSN: 0045-7825
A machine learning approach to accelerate convergence of the nonlinear solver in multiphase flow problems is presented here. The approach dynamically controls an acceleration method based on numerical relaxation. It is demonstrated in a Picard iterative solver but is applicable to other types of nonlinear solvers. The aim of the machine learning acceleration is to reduce the computational cost of the nonlinear solver by adjusting to the complexity/physics of the system. Using dimensionless parameters to train and control the machine learning enables the use of a simple two-dimensional layered reservoir for training, while also exploring a wide range of the parameter space. Hence, the training process is simplified and it does not need to be rerun when the machine learning acceleration is applied to other reservoir models. We show that the method can significantly reduce the number of nonlinear iterations without compromising the simulation results, including models that are considerably more complex than the training case.
Obeysekara A, Salinas P, Heaney CE, et al., 2021, Prediction of multiphase flows with sharp interfaces using anisotropic mesh optimisation, Advances in Engineering Software, Vol: 160, Pages: 1-16, ISSN: 0965-9978
We propose an integrated, parallelised modelling approach to solve complex multiphase flow problems with sharp interfaces. This approach is based on a finite-element, double control-volume methodology, and employs highly-anisotropic mesh optimisation within a framework of high-order numerical methods and algorithms, which include adaptive time-stepping, metric advection, flux limiting, compressive advection of interfaces, multi-grid solvers and preconditioners. Each method is integral to increasing the fidelity of representing the underlying physics while maximising computational efficiency, and, only in combination, do these methods result in the accurate, reliable, and efficient simulation of complex multiphase flows and associated regime transitions. These methods are applied simultaneously for the first time in this paper, although some of the individual methods have been presented previously. We validate our numerical predictions against standard benchmark results from the literature and demonstrate capabilities of our modelling framework through the simulation of laminar and turbulent two-phase pipe flows. These complex interfacial flows involve the creation of bubbles and slugs, which involve multi-scale physics and arise due to a delicate interplay amongst inertia, viscous, gravitational, and capillary forces. We also comment on the potential use of our integrated approach to simulate large, industrial-scale multiphase pipe flow problems that feature complex topological transitions.
Titus Z, Heaney C, Jacquemyn C, et al., 2021, Conditioning surface-based geological models to well data using artificial neural networks, Computational Geosciences: modeling, simulation and data analysis, Vol: 26, Pages: 779-802, ISSN: 1420-0597
Surface-based modelling provides a computationally efficient approach for generating geometrically realistic representations of heterogeneity in reservoir models. However, conditioning Surface-Based Geological Models (SBGMs) to well data can be challenging because it is an ill-posed inverse problem with spatially distributed parameters. To aid fast and efficient conditioning, we use here SBGMs that model geometries using parametric, grid-free surfaces that require few parameters to represent even realistic geological architectures. A neural network is trained to learn the underlying process of generating SBGMs by learning the relationship between the parametrized SBGM inputs and the resulting facies identified at well locations. To condition the SBGM to these observed data, inverse modelling of the SBGM inputs is achieved by replacing the forward model with the pre-trained neural network and optimizing the network inputs using the back-propagation technique applied in training the neural network. An analysis of the uncertainties associated with the conditioned realisations demonstrates the applicability of the approach for evaluating spatial variations in geological heterogeneity away from control data in reservoir modelling. This approach for generating geologically plausible models that are calibrated with observed well data could also be extended to other geological modelling techniques such as object- and process-based modelling.
Salinas P, Regnier G, Jacquemyn C, et al., 2021, Dynamic mesh optimisation for geothermal reservoir modelling, Geothermics, Vol: 94, Pages: 1-13, ISSN: 0375-6505
Modelling geothermal reservoirs is challenging due to the large domain and wide range of length- and time-scales of interest. Attempting to represent all scales using a fixed computational mesh can be very computationally expensive. Application of dynamic mesh optimisation in other fields of computational fluid dynamics has revolutionised the accuracy and cost of numerical simulations. Here we present a new approach for modelling geothermal reservoirs based on unstructured meshes with dynamic mesh optimisation. The resolution of the mesh varies during a simulation, to minimize an error metric for solution fields of interest such as temperature and pressure. Efficient application of dynamic mesh optimisation in complex subsurface reservoirs requires a new approach to represent geologic heterogeneity and we use parametric spline surfaces to represent key geological features such as faults and lithology boundaries. The resulting 3D surface-based models are mesh free; a mesh is created only when required for numerical computations. Dynamic mesh optimisation preserves the surfaces and hence geologic heterogeneity. The governing equations are discretised using a double control volume finite element method that ensures heat and mass are conserved and provides robust solutions on distorted meshes. We apply the new method to a series of test cases that model sedimentary geothermal reservoirs. We demonstrate that dynamic mesh optimisation yields significant performance gains, reducing run times by up to 8 times whilst capturing flow and heat transport with the same accuracy as fixed meshes.
Lyu Z, Lei Q, Yang L, et al., 2021, A novel approach to optimising well trajectory in heterogeneous reservoirs based on the fast-marching method, Journal of Natural Gas Science and Engineering, Vol: 88, Pages: 1-12, ISSN: 1875-5100
To achieve efficient recovery of subsurface energy resources, a suitable trajectory needs to be identified for the production well. In this study, a new approach is presented for automated identification of optimum well trajectories in heterogeneous oil/gas reservoirs. The optimisation procedures are as follows. First, a productivity potential map is generated based on the site characterisation data of a reservoir (when available). Second, based on the fast-marching method, well paths are generated from a number of entrance positions to a number of exit points at opposite sides of the reservoir. The well trajectory is also locally constrained by a prescribed maximum curvature to ensure that the well trajectory is drillable. Finally, the optimum well trajectory is selected from all the candidate paths based on the calculation of a benefit-to-cost ratio. If required, a straight directional well path, may also be derived through a linear approximation to the optimised non-linear trajectory by least squares analysis. Model performance has been demonstrated in both 2D and 3D. In the 2D example, the benefit-to-cost ratio of the optimised well is much higher than that of a straight well; in the 3D example, laterals of various curvatures are generated. The applicability of the method is tested by exploring different reservoir heterogeneities and curvature constraints. This approach can be applied to determine the entrance/exit positions and the well path for subsurface energy system development, which is useful for field applications.
ViaEstrem L, Salinas P, Xie Z, et al., 2020, Robust control volume finite element methods for numerical wave tanks using extreme adaptive anisotropic meshes, International Journal for Numerical Methods in Fluids, Vol: 92, Pages: 1707-1722, ISSN: 0271-2091
Multiphase inertia‐dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave‐structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality‐related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water‐air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.
Yekta A, Salinas P, Hajirezaie S, et al., 2020, Reactive transport modeling in heterogeneous porous media with dynamic mesh optimization, Computational Geosciences: modeling, simulation and data analysis, Vol: 25, Pages: 357-372, ISSN: 1420-0597
This paper presents a numerical simulator for solving compositional multiphase flow and reactive transport. The simulator was developed by effectively linking IC-FERST (Imperial College Finite Element Reservoir SimulaTor) with PHREEQCRM. IC-FERST is a next-generation three-dimensional reservoir simulator based on the double control volume finite element method and dynamic unstructured mesh optimization and is developed by the Imperial College London. PHREEQCRM is a state-of-the-art geochemical reaction package and is developed by the United States Geological Survey. We present a step-by-step framework on how the coupling is performed. The coupled code is called IC-FERST-REACT and is capable of simulating complex hydrogeological, biological, chemical, and mechanical processes occurring including processes occur during CO2 geological sequestration, CO2 enhanced oil recovery, and geothermal systems among others. In this paper, we present our preliminary work as well as examples related to CO2 geological sequestration. We performed the model coupling through developing an efficient application programming interface (API). IC-FERST-REACT inherits high-order methods and unstructured meshes with dynamic mesh optimization from IC-FERST. This reduces the computational cost by placing the mesh resolution where and when necessary and it can better capture flow instabilities if they occur. This can have a strong impact on reactive transport simulations which usually suffer from computational cost. From PHREEQCRM the code inherits the ability to efficiently model geochemical reactions. Benchmark examples are used to show the capability of IC-FERST-REACT in solving multiphase flow and reactive transport.
Joulin C, Xiang J, Latham J-P, et al., 2020, Capturing heat transfer for complex-shaped multibody contact problems, a new FDEM approach, Computational Particle Mechanics, Vol: 7, Pages: 919-934, ISSN: 2196-4378
This paper presents a new approach for the modelling of heat transfer in 3D discrete particle systems. Using a combined finite–discrete element (FDEM) method, the surface of contact is numerically computed when two discrete meshes of two solids experience a small overlap. Incoming heat flux and heat conduction inside and between solid bodies are linked. In traditional FEM (finite element method) or DEM (discrete element method) approaches, to model heat transfer across contacting bodies, the surface of contact is not directly reconstructed. The approach adopted here uses the number of surface elements from the penetrating boundary meshes to form a polygon of the intersection, resulting in a significant decrease in the mesh dependency of the method. Moreover, this new method is suitable for any sizes or shapes making up the particle system, and heat distribution across particles is an inherent feature of the model. This FDEM approach is validated against two models: a FEM model and a DEM pipe network model. In addition, a multi-particle heat transfer contact problem of complex-shaped particles is presented.
Xie Z, Pavlidis D, Salinas P, et al., 2020, A control volume finite element method for three‐dimensional three‐phase flows, International Journal for Numerical Methods in Fluids, Vol: 92, Pages: 765-784, ISSN: 0271-2091
A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three‐dimensional three‐phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P1DG‐P2 elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second‐order finite element methods. A force‐balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three‐dimensional three‐phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.
Lei Q, Jackson MD, Muggeridge AH, et al., 2020, Modelling the reservoir-to-tubing pressure drop imposed by multiple autonomous inflow control devices installed in a single completion joint in a horizontal well, Journal of Petroleum Science and Engineering, Vol: 189, Pages: 1-16, ISSN: 0920-4105
Autonomous inflow control devices (AICDs) are used to introduce an additional pressure drop between the reservoir and the tubing of a production well that depends on the fluid phase flowing into the device: a larger pressure drop is introduced when unwanted phases such as water or gas enter the AICD. The additional pressure drop is typically represented in reservoir simulation models using empirical relationships fitted to experimental data for a single AICD. This approach may not be correct if each completion joint is equipped with multiple AICDs as the flow at different AICDs may be different. We use high-resolution numerical modelling to determine the total additional pressure drop introduced by two AICDs installed in a single completion joint in a horizontal well. The model captures the multiphase flow of oil and water through the inner annulus into each AICD. We explore a number of relevant oil-water inflow scenarios with different flow rates and water cuts. Our results show that if only one AICD is installed, the additional pressure drop is consistent with the experimentalzly-derived empirical formulation. However, if two AICDs are present, there is a significant discrepancy between the additional pressure drop predicted by the simulator and the empirical relationship. This discrepancy occurs because each AICD has a different total and individual phase flow rate, and the final steady-state flow results from a self-organising mechanism emerging from the system. We report the discrepancy as a water cut-dependent correction to the empirical equation, which can be used in reservoir simulation models to better capture the pressure drop across a single completion containing two AICDs. Our findings highlight the importance of understanding how AICDs modify flow into production wells, and have important consequences for improving the representation of advanced wells in reservoir simulation models.
Kampitsis AE, Adam A, Salinas P, et al., 2020, Dynamic adaptive mesh optimisation for immiscible viscous fingering, COMPUTATIONAL GEOSCIENCES, Vol: 24, Pages: 1221-1237, ISSN: 1420-0597
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Salinas P, Pain C, Osman H, et al., 2020, Vanishing artifficial diffusion as a mechanism to accelerate convergence for multiphase porous media flow, Computer Methods in Applied Mechanics and Engineering, Vol: 359, Pages: 1-15, ISSN: 0045-7825
Numerical solution of the equations governing multiphase porous media flow is challenging. A common approach to improve the performance of iterative non-linear solvers for these problems is to introduce artificial diffusion. Here, we present a mass conservative artificial diffusion that accelerates the non-linear solver but vanishes when the solution is converged. The vanishing artificial diffusion term is saturation dependent and is larger in regions of the solution domain where there are steep saturation gradients. The non-linear solver converges more slowly in these regions because of the highly non-linear nature of the solution. The new method provides accurate results while significantly reducing the number of iterations required by the non-linear solver. It is particularly valuable in reducing the computational cost of highly challenging numerical simulations, such as those where physical capillary pressure effects are dominant. Moreover, the method allows converged solutions to be obtained for Courant numbers that are at least two orders of magnitude larger than would otherwise be possible.
Silva VLS, Salinas P, Pain CC, et al., 2020, Non-linear solver optimisation for multiphase porous media flow based on machine learning
Numerical simulation of multiphase flow in porous media is of paramount importance to understand, predict and manage subsurface reservoirs with applications to hydrocarbon recovery, geothermal energy resources, CO2 geological sequestration, groundwater sources and magma reservoirs. However, the numerical solution of the governing equations is very challenging due to the non-linear nature of the problem and the strong coupling between the different equations. Newton methods have been traditionally used to solve the non-linear system of equations, although, the Picard iterative method has been gaining ground in recent years. The Picard method is attractive because the multiphysics problem can be subdivided and each subproblem solved separately, which gives wide flexibility and extensibility. Rapid convergence of the non-linear solver is of vital importance as it strongly affects the overall computational time. Therefore, a great deal of effort has been put on obtaining robust and stable convergence rates. At the same time, machine learning (ML) is gaining more and more attention with revolutionary results in areas such as computer vision, self-driving cars and natural language processing. The success of ML in different fields has inspired recent applications in reservoir engineering and geosciences. Here, we present a Picard non-linear solver with convergence parameters dynamically controlled by ML. The ML is trained based on the parameters of the reservoir model scaled to a dimensionless space. In the approach reported here, data for the ML training is generated using simulation results obtained for multiphase flow in a two-layered reservoir model which captures many of the flow features observed in models of natural reservoirs. The presented method significantly reduces the computational effort required by the non-linear solver as it can adjust itself to the complexity/physics of the system. We demonstrate its efficiency under a variety of numerical tests cases, inc
Al Kubaisy J, Osman H, Salinas P, et al., 2020, Discontinuous control volume finite element method for multiphase flow in porous media on challenging meshes
Control volume finite element methods (CVFEM) are gaining increasing popularity for modeling multi-phase flow in porous media due to their inherited geometric flexibility for modeling complex shapes. Nonetheless, classical CVFEM suffer from two key problems; first, mass conservation is enforced by the use of control volumes that span element boundaries. Consequently, when modeling flow in regions with discontinuous material properties, control volumes that span geologic domain boundaries result in non-physical leakage that degrades the numerical solution accuracy. Another challenge is to provide an accurate solution for distorted elements; elements with high aspect ratio that are part of the discretized heterogeneous domain. In fact, most numerical methods struggle to provide a converged pressure solution for high aspect ratio elements of the domain. Here, we introduce a numerical scheme that removes non-physical leakage across geologic domains and addresses the accuracy of classical control volume finite element method (CVFEM) in high aspect ratio elements. The scheme utilizes the frameworks of double-CVFEM (DCVFEM) where pressure is discretized CV-wise rather than element-wise. In addition, it introduces discontinuous control volumes by allowing pressure to be discontinuous between elements. The resultant finite element pair has an equal-order of velocity and pressure, with discontinuous linear elements for both the pressure and velocity fields P1DG-P1DG. This type of element pair is LBB unstable. The instability issue is circumvented by global enrichment of the finite element velocity interpolation space with an interior bubble function, given by the new element pair P1(BL)DG-P1DG. This element pair resolves both issues addressed earlier. We demonstrate that the developed numerical method is mass conservative, and it accurately preserves sharp saturation changes across different material properties or discontinuous permeability fields as well as improves converge
Salinas P, Jacquemyn C, Heaney C, et al., 2020, Well location optimisation by using surface-based modelling and dynamic mesh optimisation
Predictions of production obtained by numerical simulation often depend on grid resolution as fine resolution is required to resolve key aspects of flow. Moreover, the controls on flow can depend on well location in a model. In some cases, it may be key to capture coning or cusping; in others, it might be the location of specific high permeability thief zones or low permeability flow barriers. Thus, models with a suitable grid resolution for one particular set of well locations may fail to properly capture key aspects of flow if the wells are moved. During well optimisation, it is impossible to predict a-priori which well locations will be tested in a given model. Thus, it is unlikely to know a-priori if the grid resolution is suitable for all possible locations tested during a well optimisation procedure on a single model, and the problem is even more profound if well optimisation is tested over a range of different models. Here, we report an optimisation methodology based on Dynamic Mesh Optimisation (DMO). DMO will produce optimised meshes for a given model, set of well locations, pressure (and other key fields) distribution and timelevel. Grid-free Surface-Based Modelling (SBM) models are automatically generated in which well trajectories are introduced (also not constrained by a mesh), respected by DMO. For the optimization of the well location a Genetic Algorithm (GA) approach is used, more specifically the open-source software package DEAP. DMO ensures that all the models automatically generated and simulated in the optimisation process are modelled with an equivalent mesh resolution without user interaction, in this way, the local pressure drawdown and associated physical effects (such as coning or cusping) can be properly captured if they appear in any of the many scenarios that are studied . We demonstrate that the method has wide application in reservoir-scale models of oil and gas fields, and regional models of groundwater resources.
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