Numerical Multiphase Flow Model Research Articles

Augmenting Deep Residual Surrogates with Fourier Neural Operators for Rapid Two-Phase Flow and Transport Simulations

Summary Accurate numerical modeling of multiphase flow and transport mechanisms is essential to study varied, complex physical phenomena including flow in subsurface oil and gas reservoirs and subsurface aquifers subject to CO2 sequestration. State-of-the-art complete physics-based solvers suffer from many computational challenges. High-fidelity data-driven surrogate models that solve the governing partial differential equations (PDEs) have the potential to optimize the time to solution and increase confidence in critical business and engineering decisions through better quantification of solution statistics. We leverage the recently proposed Fourier neural operators (FNOs) with quasilinear time complexity to capture the spectral information from feature maps to solve the coupled porous flow and transport PDEs. Embedding Fourier layers within the residual blocks results in a highly effective structure that, while achieving competitive accuracy, also enables efficient training of deeper networks with a dramatically reduced number of trainable parameters. The resulting novel deep-learning (DL) architecture is coined as FResNet++. FResNet++ uses squeeze and excitation blocks, atrous spatial pyramid pooling (ASPP), and attention blocks to increase its sensitivity to the relevant features and capture multiscale information, and it is specifically tuned to operate optimally to learn from and predict numerically simulated flow (pressure and saturation) fields. We demonstrate the ability of FResNet++ to generalize over multiple high-dimensional input parameter spaces that describe subsurface permeability and porosity heterogeneity. The resulting DL architecture accurately captures the complex interplay between viscous forces and highly heterogeneous permeability and porosity fields. We investigate two-phase flow in porous media, which is the archetypal problem for reservoir simulation giving rise to a system of nonlinearly coupled PDEs with highly heterogeneous coefficients. We show in blind tests that FResNet++ predicts saturation fields more accurately compared to ResU-Net and original FNO with fully connected linear layers. We additionally investigate the effects of using alternative loss functions and an alternative way of utilizing FResNet++ to increase its effectiveness. For the first time in the literature, we show that the spatiotemporal evolution of pressure and saturation fields can be jointly predicted with good accuracy using a single FResNet++ network over long time horizons in response to previously unseen permeability and porosity fields. After a moderate training investment on graphics processing units (GPUs), FResNet++ yields a speedup of at least four orders of magnitude compared to a conventional numerical PDE solver and operates with notably fewer trainable parameters compared to the original FNO. Our numerical experiments validate that FNOs can be utilized in various convolutional neural network-based architectures and can effectively substitute for repetitive physics-based forward simulations for scenario testing.

Numerical Modeling of Hydrothermal System Circulation Beneath Asal Rift, Republic of Djibouti

Asal rift is an aerial rift segment resulting from the westward propagation of the Aden ridge into the Afar Depression. Geothermal manifestations such as hot springs and fumaroles, fault creep, conductivity anomaly, and high geothermal gradient were observed both at the surface and in the subsurface. Despite many scientific works conducted in Asal to understand the rifting mechanisms, the hydrothermal fluid circulation still needs to be evaluated since it is based on simplified conceptual models. To further contribute and progress toward a quantitative evaluation of fluid circulation, a 2D numerical model perpendicular to the rift axis was developed with the objective of better understanding the role of subsurface anisotropy in fluid flow and heat transfer in the Asal rift. Numerical modeling of multiphase flow and heat transfer was carried out with an equivalent porous medium intersected by fault zones having greater permeability. Horizontal anisotropic permeability and magmatic fluid release were taken into account with different simulation scenarios. The results indicate that fault zones act as recharge/discharge areas depending on their location, permeability, and number. Simulations considering horizontal anisotropic permeability allowed the reproduction of the thermal state observed in geothermal wells with the expected general pattern of fluid circulation in the Asal rift. Comparing our result with a recent study made with a 2D numerical modeling parallel to the rift axis, we suggest the presence of a saddle point where fluid flow is both to the northeast and to the southwest direction of the rift. Moreover, magmatic fluid release assumed in two simulation scenarios showed to have an impact on the hydrological behavior of fault zones and facilitate the development of super-critical flow at the center of the rift.

Research on characteristics of deep-sea implosion based on Eulerian finite element method

Marine structures operating in the deep-sea, such as submersibles and photomultiplier tubes, bear enormous hydrostatic pressure of deep-sea, which may cause structural damage and implosion. And a pressure wave will emit from the collapse of the cavity and pose a threat to nearby structures. On the basis of the Eulerian finite element method, the numerical model of multiphase flow for deep-sea implosion is established in this paper. The numerical method is verified by comparing the results with those from Keller equation and literature. The physical process under the spherical simplification is firstly analyzed in our work. The basic phenomena are studied, and the pressure changes under different distances and Mach numbers are given. Subsequently, the basic physical process and pressure distribution under cylindrical simplification are introduced. Then, the bubble evolutions under different Mach numbers and initial aspect ratios are given. In the early stage of bubble movement, a rarefaction wave will radiate to the surrounding. The multi-peak phenomenon will occur in the cylindrical model because of the bubble sides breakage and the bubble pulsation. Finally, asymmetric three-dimensional cylindrical bubble implosion near the solid wall with different standoff distances are present in this paper, where the typical oblique jet is observed and analyzed.

The Numerical modeling of multiphase flow in the oil and gas gathering pipeline from wellhead platform of X field to central processing platform of Y field

The main objective of this research is to investigate the characteristics of slug flow inside the riser which is a 68-meter vertical pipe segment reaching from the seabed to the central processing platform of the Y field. The oil and gas mixture flows into the riser from the wellhead platform of the X field through a 25-km horizontal subsea pipeline. In this study, an integrated modeling approach is used to take into account major physical phenomena associated with the multiphase flow in the gathering system that might have strong influences on slug flow characteristics. The phase behavior model of oil and gas in the gathering pipeline were first built on the basis of Peng-Robinson equation of state to determine the multiphase equilibria and estimate fluid properties at various pressure and temperature conditions. The multiphase flow was then modeled by Beggs & Brill method for pressure drops and Hasan & Kabir for temperature distribution along the pipeline. In particular, the pressure drop calculation is based on empirical correlations from which the flow regimes can be identified and pressure drop is determined accordingly. The heat transfer calculation, on the other hand, is based on the mechanistic approach from which the temperature distribution along the pipeline system can be estimated. Finally, the slug-tracking model was developed to characterize the slug flow with essential properties such as slug frequency, length and surge volume. This helps identify slug flow existence inside the riser segment and predict potential consequences it may cause to surface facilities. The results from this work show that the integrated modeling approach is suitable to the multiphysics nature of the flow assurance problem under consideration. The slug flow might exist in the 68-m riser where more than 20 slugs of 2-m length might occur after every 1.5 hours.

Numerical modeling of multiphase flow inside aeromixture channel and low emission burner of boiler OB-650

Determination of multiphase flow inside PC boiler plant is of particular importance for the process control of the boiler and its efficient operation. Nowadays numerical modeling is used as an advanced tool in improvement of this or similar process. Separation of coal particle in aero-mixture channel, after pulverization, represent an important process which has a big effect on boiler efficiency, and its determination represents an important step. In this paper, numerical modeling of multiphase flow inside aero-mixture channel and low emission burner of boiler OB-650 are exposed in several steps from 3D modeling, discretization of fluid domain, setting the physical and mathematical model to validation of same model. Main goals of the same process is to obtain valid numerical model of observed problematic, that will give us data about model parameters that can be used for modeling of the same process with different inlet boundary conditions, and also to obtain appropriate specific process parameters that can be used for rising of level of efficiency and utility of boiler plant in some steady operating modes.

Analysis of multiphase flow characteristics in a deepwater riser

Oil and gas mixed transportation is an important technology in oil and gas production. Multiphase fluid is transported from the wellhead to the floating platform through a riser system. Based on computational fluid dynamics, a numerical model of multiphase flow in a deepwater riser by considering hydrate phase transformation and sand production was established, which was then solved by the finite-difference method. The results show that under constant inlet pressure, the pressure drop decreases with increasing gas–liquid two-phase flow rate, and increases with increasing sand production rate. Furthermore, the hydrate phase transition decreases the pressure. The effect of liquid on the temperature in the riser is apparent: the heat transfer between the fluid and seawater is mitigated by the insulation layer, thus raising the critical point of the hydrate phase transition. Finally, the velocity and volume fraction of the gas phase increase from the inlet to the outlet of the riser. At the same time, the velocity of the liquid–solid phase increases, whereas the volume fraction decreases.

Numerical modelling of multiphase FLOW and calcination process in an industrial calciner with fuel of heavy oil

In a calciner for cement production, limestone (CaCO3) particles are decomposed into quicklime (CaO) and carbon dioxide (CO2) during the calcination process. The complex flow and temperature distribution caused by fuel combustion and calcination reaction of limestone are essential to calciner performance. This paper presents a method by coupling the calcination model and combustion into multiphase flow simulation. In this approach, flue gases, CaCO3, and CaO particles are defined as multiple continuous phases, and heavy oil droplets are defined as discrete phase. This simulation is based on the Euler multiphase model for continuous phase and discrete phase model for the oil phase.The transport of heat, mass, momentum, species and energy among these different phases are calculated by solving the governing equations of each phase with phase-interacting coefficients and models. To verify the accuracy of this modeling approach, numerical predictions were compared with measurement data collected from cement production lines, which yielded satisfactory results. This modeling approach can help optimize calciner design, performance, and process parameters in actual industrial applications.

Geophysical response to simulated methane migration in groundwater based on a controlled injection experiment in a sandy unconfined aquifer

Geophysical methods have the capacity to detect and characterize gas-phase dynamics in groundwater. Suitable methods can be deployed at surface or within boreholes depending on the required depth of investigation, spatial/temporal resolution, and geologic conditions. While the application of geophysical methods to monitor immiscible phase contaminants in the subsurface has been extensively documented, the effects of hydraulic properties and flow system conditions on the nature of the geophysical responses used to elucidate multi-phase fluid flow remains underdeveloped. A series of numerical 2-dimensional multi-phase flow and geophysical model simulations based on a controlled methane release experiment in the Borden unconfined sand aquifer was carried out to assess the influence of porous media hydraulic properties and flow system conditions on geophysical signatures associated with transient gas-phase saturation and gas migration behaviour. Specifically, the utility of electrical resistivity tomography (ERT) and ground-penetrating radar (GPR) to monitor gas-phase plume dynamics in shallow groundwater flow systems is examined. ERT and GPR responses to gas-phase distribution and migration during a 72-day methane gas injection and subsequent recovery period was calculated using a numerical multi-phase flow model (CFbio) simulating four distinct parameterizations of the sandy aquifer system. Geophysical models showed that ERT was effective at imaging the central position of the plume but was less effective at detecting thinner lateral migration pathways extending beyond the primary high gas saturation bulb. Conversely, GPR was able to detect thin gas pools emanating from the primary gas bulb and small-scale vertical preferential pathways arising from capillary boundaries with contrasting saturations; however, gradational boundaries proved to be more difficult to resolve using GPR. This study demonstrates that ERT and GPR can be very useful tools in combination for longer-term monitoring of stray gas leakage from decommissioned hydrocarbon wells in shallow granular media freshwater aquifers, especially given the likelihood of strong lateral migration.

Grid design and numerical modeling of multiphase flow in complex reservoirs using orthogonal collocation schemes

An advanced grid system design was developed to capture accurately the effects of geometrically complex features such as geological features (faults, pinch outs and inclined beddings) and well-related phenomenon (multilateral wells of general orientation) in triangular coordinates. Modeling these effects can have significant impact on the accuracy of the simulation and prediction of reservoir performance as well as reservoir fluid flow using conventional grid designs. The finite difference method provides additional difficulty in capturing geological features in typical reservoir flow and grid model simulators. Hence, the orthogonal collocation method was used for simulating multiphase reservoir flow equations in triangular curvilinear coordinates left[ {xi left( r right),xi left( theta right),xi left( z right)} right] of domain [0,1] that were derived from Cartesian coordinates left( {x,y,z} right). This was to accommodate general three-dimensional deviated wells and complex reservoir geometry for multiphase flow of hydrocarbon in complex reservoir formations. Based on preliminary field data obtained from multinational oil and gas operator in Nigeria, the proposed model was used to predict saturation, production and petroleum productivity with time and distance in a MATLAB environment. The simulated plots revealed that pressure is parabolic at the center of the reservoir with coordinates xi (r) =0.4257, reflecting the impact of geological features in the pressure and production flow performance.

Numerical modelling of multiphase flow and heat transfer within an induction skull melting furnace

A numerical and experimental study of free surface motion and heat transfer within an induction skull melting furnace is discussed in this paper. The developed computational domain was three-dimensional with defined periodic boundary conditions, which correspond to the segmented geometry of an actual cold crucible. An electromagnetically driven flow and temperature field within the numerical domain was simulated on the basis of two-way coupling of electromagnetic and fluid dynamic fields. To predict the electromagnetic field, a set of Maxwell’s equations was solved. Then, the information regarding the Lorentz force and Joule heat distributions was transferred to a fluid dynamics submodel. These fields appeared as source terms in the momentum conservation and energy equations, respectively. The multiphase flow was considered turbulent with a free surface. It was simulated using a realizable k-ε model and a volume of fluid approach. Moreover, to consider the radiation heat transfer, the discrete ordinates method was applied. The proposed coupled mathematical model was compared with experimental results obtained from an industry induction skull melting furnace. The model validation clearly showed high accuracy in the discussed numerical model despite the applied simplifications. The shape of the free surface obtained from the computational model was within the standard deviation of the measurements, with a relative error under 4%. The charge temperature, after achieving steady state, was predicted with very high accuracy; however, the heating process was slightly underestimated. Finally, a qualitative comparison for the lower part of the meniscus was also performed. In that region, characteristic tooth-shaped peaks in the connection between the charge and crucible walls were identified for both experimental and numerical analyses.

Numerical simulation of gasoline evaporation in refueling process

A numerical model of multiphase flow was developed to investigate the heat and mass transfer mechanisms in refueling process. The two-dimensional model takes into account the effects of surface ten...

Modified sequential fully implicit scheme for compositional flow simulation

The fully implicit (FI) method is widely used for numerical modeling of multiphase flow and transport in porous media. The FI method is unconditionally stable, but that comes at the cost of a low-order approximation and high computational cost. The FI method entails iterative linearization and solution of fully-coupled linear systems with mixed elliptic/hyperbolic character. However, in methods that treat the near-elliptic (flow) and hyperbolic (transport) separately, such as multiscale formulations, sequential solution strategies are used to couple the flow (pressures and velocities) and the transport (saturations/compositions). The most common sequential schemes are: the implicit pressure explicit saturation (IMPES), and the sequential fully implicit (SFI) schemes. Problems of practical interest often involve tightly coupled nonlinear interactions between the multiphase flow and the multi-component transport. For such problems, the IMPES approach usually suffers from prohibitively small timesteps in order to obtain stable numerical solutions. The SFI method, on the other hand, does not suffer from a temporal stability limit, but the convergence rate can be extremely slow. This slow convergence rate of SFI can offset the gains obtained from separate and specialized treatments of the flow and transport problems. In this paper, we analyze the nonlinear coupling between flow and transport for compressible, compositional systems with complex interphase mass transfer. We isolate the nonlinear effects related to transmissibility and compressibility from those due to interphase mass transfer, and we propose a modified SFI (m-SFI) method. The new scheme involves enriching the ‘standard’ pressure equation with coupling between the pressure and the saturations/compositions. The modification resolves the convergence problems associated with SFI and provides a strong basis for using sequential formulations for general-purpose simulation. For a wide parameter range, we show that the proposed m-SFI algorithm is as robust as the FI method with a comparable convergence rate.

Decision analysis for robust CO2 injection: Application of Bayesian-Information-Gap Decision Theory

Care must be taken when choosing a site for geological CO2 sequestration to ensure that the CO2 remains sequestered for many years, and that the environment is not harmed. Making a decision between sites for sequestration is not without its challenges because, as in the case of many subsurface problems, there are a lot of uncertainties. A method for making decisions under various types and severities of uncertainties, Bayesian-Information-Gap Decision Theory (BIG DT), is coupled with a numerical multiphase flow model for CO2 injection. The framework is used to make a decision between two CO2 sequestration sites; data are collected during a test injection and are used by the framework to assess the robustness of each site against failure by either leakage or induced seismic activity. A discussion of how the data are used to decide on a site follows. The results show that at the two synthetic sites examined here, the one with the less leakage potential is preferred. This indicates that the potential for leakage is more prone to violate decision goals at these sites than the potential for overpressurization.

Numerical modelling of multiphase flow in unsaturated deforming porous media

The aim of this paper is to address a number of significant challenges in the analysis of multiphase unsaturated soils when subjected to both static and dynamic loading. These challenges include the non-linear behaviour of the solid skeleton of the soil as well as the means by which the unsaturated nature of the multi-phase soil is dealt with. A review of some fundamental issues in partially saturated soils as well as the governing equations are presented and then the application of the generalised-α algorithm for time integration of the global equations of motion for unsaturated soils is demonstrated. Solutions to these equations obtained by the finite element method are validated by recently presented analytical solutions. A description of the selected constitutive model and its integration is also presented, together with a strategy to verify the numerical implementation. Finally, solutions for the classic problem of static loading of a rigid footing resting on a partially saturated (three-phase) soil and a fully saturated (two-phase) soil are presented.

Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs

Variance-based global sensitivity analysis (GSA) is a powerful procedure for importance ranking of the uncertain input parameters of a given flow model. The application of GSA is made possible for long-running flow simulators (computation (CPU) time more than several hours) by relying on meta-modeling techniques. However, such flow models can involve one or several spatial inputs, for instance, the permeability field of a reservoir and of a caprock formation in the context of CO2 geological storage. Studying the sensitivity to each of these spatial inputs motivated the present work. In this view, we propose a strategy which combines (1) a categorical indicator (i.e., a pointer variable taking discrete values) assigned to the set of stochastic realizations associated with each spatial input (spatial maps) and (2) meta-modeling techniques, which jointly handle continuous and categorical inputs. In a first application case, a costless-to-evaluate numerical multiphase flow model was used to estimate the sensitivity indices. Comparisons with results obtained using the meta-model showed good agreement using a two-to-three ratio of the number of learning samples to the number of spatial maps. On this basis, the strategy can be recommended for cases where the number of maps remains tractable (i.e., a few hundred), for example, for moderately complex geological settings, or where a set of such maps can be selected in a preliminary stage using ranking procedures. Finally, the strategy was applied to a more complex multiphase flow model (CPU time of a few hours) to analyze the sensitivity of CO2 saturation and injection-induced pressure build-up to seven homogeneous rock properties and two spatial inputs.

Numerical Simulation of Droplets Impacting on a Liquid Film with a Vapor Bubble Growing

A numerical model of multiphase flow is developed to investigate the relative contributions of droplet parameters to spray cooling heat transfer. The 2-D model takes into account the effects of surface tension, gravity and viscosity. The heat and mass exchanges of free surface are defined to study vapor bubble behavior in liquid films. The multiphase flow and heat transfer are discussed for the three droplet parameters: initial droplet position, initial droplet temperature, and droplet impact frequency. The heat transfer mechanisms of the three cases are discussed in detail.

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

Dynamic saturation curve measurement for resin flow in glass fibre reinforcement

A methodology is presented to determine the saturation curve of a resin/glass fabric system, during infiltration in a transparent mould under constant flow rate. Video acquisitions are transformed by image analysis into saturation level versus position and time, and coupled to inlet pressure measurements. A numerical multiphase flow model is then used to simulate the infiltration for various combinations of drainage curve parameters. The numerical parameters to describe the saturation and relative permeability are determined by response surface optimization. The drainage curve and relative permeability equations determined at one time are shown to adequately describe the entire injection process, and to be flow-rate dependent.

Gas tracer transport in a heterogeneous fracture in two-phase flow conditions. Experimental and modeling results

Large amounts of gas can result from anaerobic corrosion of metals and from chemical and biological degradation of organic substances in underground repositories for radioactive waste. Gas generation may lead to the formation of a buoyant gas phase bubble (i.e. zone with increased gas saturation surrounded by water) and to the migration of radioactive gaseous species. In this situation, gaseous species migration is controlled by (1) advection, dispersion and diffusion within the gas bubble, and (2) dissolution in the water surrounding the gas bubble and diffusion of the dissolved species away from the interface. A number of gas tracer tests were performed in the framework of the GAs Migration (GAM) project to study the role played by dissolution/diffusion phenomena in gas transport. Tracers were selected to display a large range of solubility and diffusion coefficients, which should have led to significant chromatographic separation in the breakthrough curves (BTCs) of the tracers. However, measured BTCs displayed much smaller chromatographic separation than expected. These curves were interpreted using (1) a numerical model of multiphase flow and tracer transport in the fracture plane and diffusion into the immobile water, and (2) a simple two box model. Results showed that dissolution/diffusion into immobile water regions played a small role, and tailing appears to have been largely controlled by diffusion into dead gas volumes, such as boreholes.

Estimation of Fracture–Matrix Transport Properties from Saturation Profiles Using a Multivariate Automatic History Matching Method

This study focuses on the development and implementation of a numerical model of multiphase flow in a fractured core sample by describing the capillary pressure–relative permeability characteristics. An automated history matching approach is proposed to determine relative permeability and capillary pressure curves simultaneously for both matrix and fracture consistent with a core flood reservoir model performance, which relies on a commercial reservoir simulator coupled with an optimization protocol. The results indicate that the proposed approach successfully predicts relative permeability and capillary pressure curves of a fractured core sample and provides a foundation for field-scale history matching with simultaneous estimation of transport properties.