Single-phase Flow Model Research Articles

A guideline for appropriate application of vertically-integrated modeling approaches for geologic carbon storage modeling

Mathematical modeling is an essential tool for answering questions related to geologic carbon storage (GCS). The choice of modeling approach depends on the type of questions being asked. In this paper we discuss a series of approaches with a hierarchical complexity including vertically-integrated single-phase flow approaches, vertically-integrated multi-phase flow approaches (with and without vertical equilibrium assumption), three-dimensional multi-phase flow approaches, and fully-coupled multi-phase flow approaches that couple flow with geochemistry and/or geomechanics. Three spatial scales are used to categorize the questions to be addressed by modeling: regional scale (encompasses CO2 plume extent and majority of area of pressure impact of one or more injection operations), site scale (includes the CO2 plume extent and some of the area impacted by the pressure increase of a single injection site), and well scale (the immediate vicinity of an injection well). A set of guidelines is developed to help modelers choose the most appropriate modeling approach, and show when simpler modeling approaches may be the better choice. Vertically-integrated single-phase flow models are the most appropriate choice at both the site and regional scales, if the pressure impact outside of the CO2 plume is of interest. Vertically-integrated multi-phase flow models should be chosen at the regional scale, if the locations of CO2 plumes are of interest, and at the site scale if vertical segregation of CO2 and brine is fast or vertical heterogeneity in properties can be presented by distinct, continuous layers. Three-dimensional multi-phase flow models are the appropriate choice at the well and site scales for cases with significant vertical flow components of CO2 and brine. Fully-coupled multi-phase flow models should only be chosen if pore-space alteration through geochemistry or geomechanics feeds back to fluid flow.

Automatic differentiation using operator overloading (ADOO) for implicit resolution of hyperbolic single phase and two-phase flow models

Implicit time integration schemes are widely used in computational fluid dynamics to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit counterpart. The derivation of an implicit scheme is however a challenging and time-consuming task, increasing substantially with the model equations complexity since this method usually requires fairly accurate evaluation of the spatial scheme's matrix Jacobian. This article presents a flexible method to overcome the difficulties associated to the computation of the derivatives, based on the forward mode of automatic differentiation using operator overloading (ADOO). Flexibility and simplicity of the method are illustrated through implicit resolution of various flow models of increasing complexity such as the compressible Euler equations, a two-phase flow model in full equilibrium [28] and a symmetric variant [44] of the two-phase flow model of Baer and Nunziato [2] dealing with mixtures in total disequilibrium.

3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers

This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the applied finite element Lagrange multiplier spaces show good performance. The method is further evaluated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the variational transfer approach, is capable of modeling single-phase flow through realistic 3D fracture networks.

A block preconditioner for non-isothermal flow in porous media

In petroleum reservoir simulation, the industry standard preconditioner, the Constrained Pressure Residual method (CPR), is a two-stage process which involves solving a restricted pressure system with Algebraic Multigrid (AMG). Initially designed for isothermal models, this approach is often used in the thermal case. However, it does not have a specific treatment of the additional energy conservation equation and temperature variable. We seek to develop preconditioners which better capture thermal effects such as heat diffusion. In order to study the effects of both pressure and temperature on fluid and heat flow, we consider a model of non-isothermal single phase flow through porous media. For this model, we develop a block preconditioner with an efficient Schur complement approximation. Both the pressure block and the approximate Schur complement are approximately inverted using an AMG V-cycle. The resulting solver is scalable with respect to problem size and parallelization.

Liquid impingement cooling of cold plate heat sink with different fin configurations: High heat flux applications

The objective of this study is to investigate the cooling performance of the liquid jet impingement of a cold plate heat sink with different fin geometries using water and nanofluids as working fluids. In experiments, the monitored parameters mainly focus on the effects of different heat flux, the water mass flow rate, and heat source area on its thermal resistance. In the numerical study, a three-dimensional of a single-phase and two-phase Eulerian turbulent flow models are used to visualize the temperature and fluid flow behaviors of the cold plate heat sinks. The initial and the boundary conditions of the model based on the experimental conditions. It indicated from the experiments that the increasing of Reynolds number, heat source area, and power input results in decreased thermal resistance. Using nanofluids as working fluid gives the thermal resistance lower than de-ionized water as the working fluid. Additionally, the predicted results have verified with the measured data. It found that good agreement is obtained and gives an average error of 2.69%, 11.77% for CP base temperature and thermal resistance, respectively.

CFD Modeling and Simulation of Oil-Water Flows in Oil Reservoir

Understanding fluid flow in porous media is of tremendous importance for many industrial and environmental applications at various spatial and temporal scales. The present study consequently focuses on CFD 2D modeling of single-phase flow in steady mode, and unsteady mode oil-water flows by the Volume-of-Fluid method (VOF) in oil reservoir using ANSYS Fluent while meshing has been done on Gambit. The effects of temperature and permeability on water flow in porous medium, which was considered as a reservoir have been studied in this work, velocity and pressure distributions, also have been presented. In oil-water flow simulation, total pressure and oil volume fraction distributions have been visualized. Besides, the study of pressure gradient and permeability effects on the breakthrough time and on the recoverable oil has been carried out.

Construction of locally conservative fluxes for high order continuous Galerkin finite element methods

Despite their robustness, it is known that standard continuous Galerkin Finite Element Methods (CGFEMs) do not produce a locally conservative flux field. As a result, their application to solving model problems that are derived from conservation laws can be limited. To remedy this issue some form of post-processing must be performed on the CGFEM solution. In this work, a simple post-processing technique is proposed to obtain a locally conservative flux field from a CGFEM solution. One distinct advantage of the proposed method is that it produces continuous normal flux at the element’s boundary. The post-processing is implemented on nodal-centered control volumes that are constructed from the original finite element mesh. The post-processing method is performed by solving an independent set of low dimensional problems posed on each element. The associated linear algebra systems are of dimension 1 2 ( k + 1 ) ( k + 2 ) where k is the polynomial degree of CGFEM basis on a triangular mesh. A theoretical investigation is conducted to confirm that the post-processed solution converges in an optimal fashion to the true solution in the H 1 semi-norm. Various numerical examples that demonstrate the performance of technique are given. Specifically, a simulation of a model for single-phase flow in a heterogeneous system is presented to show the necessity of the local conservation as well as the effective performance of the post-processing technique.

Experimental and numerical study on thermoelectric liquid cooling module performance with different heat sink configurations

In the present study, the cooling performance of thermoelectric cooling module with different heat sink configurations has been investigated. In experiments, 0.015 kg/s cold water flow rate and hot water temperature are test in the range of 32-50 °C. Effects of heat sink configurations and hot side temperature on cooling performance of the thermoelectric cooling module are considered. For numerical study, a three-dimensional single-phase flow model is used to analyze the heat transfer and flow characteristics of the problem. The predicted results are verified with the measured data and good agreement is obtained. It can be found that the heat sink configurations have a significant effect on the velocity and temperature distributions of coolant which results in cooling performance of thermoelectric cooling module. The heat sink model C gives the highest cooling performance as compared with others models. While the higher hot water temperature results in increasing temperature different between hot and cold sides of thermoelectric plate. Therefore, cooling performance tends to decrease with increasing hot water temperature. The results from this study are expected to lead to guidelines that will allow designing the thermoelectric cooling module embedded with the heat sink to maximize cooling performance.

Integrated deterministic approaches for productivity index of reservoirs depleted by horizontal wells and undergone multiphase flow conditions

This paper introduces new integrated approaches for estimating pseudo-steady state productivity index (PI) and shape factor of oil and gas reservoirs drained by horizontal wells and dominated by multiphase flow conditions. These approaches couple PVT data, relative permeability curves, and pressure distribution models during pseudo-steady state flow (PSS). The objective is eliminating the uncertainties of applying single phase flow models and substantially comprising the realistic parameters that govern multiphase flow conditions. The importance of this study is represented by introducing the impact of multiphase flow (Gas, Oil, Water) to the productivity index and inflow performance relationship of reservoirs depleted by horizontal wellbores.This study is conducted throughout three tasks. The first includes reviewing currently used techniques for calculating pseudo-steady state PI and shape factor of bounded oil and gas reservoirs assuming single phase flow is the dominant flow pattern in the porous media. The second introduces new deterministic models for reservoir mobility and compressibility and new multiphase flow pressure function [f(P)mp]. While the third focuses on calculating PI and shape factor of reservoirs depleted by horizontal wellbores and predicting inflow performance relationship (IPR) considering multiphase flow conditions.The outcomes of this study can be summarized as: 1) Developing deterministic models by multi-regression analysis for reservoir mobility and compressibility using PVT data and relative permeability curves. 2) Generating multiphase flow reservoir pressure function [f(P)mp] that introduces the impact of multiphase flow conditions to PI model. 3) Applying the new approaches for calculating multiphase flow PI and shape factor and thereafter generating multiphase flow IPR. The study has pointed out: 1) The fact that the PI of constant Sandface flow rate is greater than constant wellbore pressure is confirmed for single and multiphase flow conditions. 2) PI and shape factor are time invariant at late production time and depends only on reservoir geometry and wellbore type. 3) PI of multiphase flow is less than the index of single phase flow while shape factor exhibits higher value for multiphase flow compared to the one for single phase flow. 4) Multiphase flow negatively changes the IPR either by increasing the pressure drop or by declining the flow rate. 5) Most of the deterministic models developed in this study show high accuracy (high R-squared value, R2≥90% ) for the changes in fluid properties with reservoir pressure.

CFD modelling of friction stir welding (FSW) process of AZ31 magnesium alloy using volume of fluid method

In this work, a validate couple-thermo flow model of the FSW process is generated using the CFD software FLUENT, with this model, then being developed to model the flash formation phenomena that occur during the FSW process using the volume of fluid method. From both models, pressure distribution on the tool surface was predicted at different radial positions. A comparison was made between single and multiple phase flow models. A significant reduction of the pressure values was seen when using a two-phase flow model. Volume fraction contour showed the changing in the metal phase when increased the welding time steps. A modelling procedure of this work is presented in details to utilize it in the further numerical investigation as a guide. This work could be used to afford more understanding of surface flash formation phenomena. Moreover, the outcome of this study can be a useful technique to aid the tool failure and increase the tool life during the FSW process.

Development of a dynamics model for graphite-moderated channel-type molten salt reactor

A molten salt reactor (MSR) is one of the six advanced reactor concepts selected by the generation IV international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model (3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent. With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.

Nonlinear model predictive control of gas kick in a managed pressure drilling system

Managed pressure drilling (MPD) operation utilizes a fully automated control system to manage kicks during drilling which typically utilizes a proportional-integral (PI) controller and a single-phase flow model. This study proposes an MPD control system that uses a nonlinear model predictive controller (NMPC) and a two-phase flow model for computing annular pressure and choke valve dynamics during kick control operation. The performance of the proposed model is demonstrated by simulating kick control operation and compared their results with a single-phase linear model. The results confirm that the single-phase model underestimates key well control parameters (including kick size, bottomhole pressure and choke pressure), which may be due to ignoring gas-phase flow behaviour on mud density and the choke valve performance. Additionally, the performance of the proposed model is tested by validating the gas kick simulation results from a lab-scale MPD setup and a gas kick event from a field's case study based on North Sea drilling operation. The comparison of the control performance between the proposed NMPC model against the PI controller utilized in the field study confirms that the NMPC response more swiftly to disturbance, such as kick than the PI controller.

Effect of vacuum deterioration on thermal performance of coaxial evacuated tube solar collector considering single and two phase flow modelling: A numerical study

Boiling and condensation play an important role in heat transfer in evacuated tube solar collectors (ETC), especially for low flow rates. Another factor that influences the efficiency of an ETC is deterioration of vacuum inside the ETC. The present study investigates numerically the effect of deteriorating vacuum during single and two phase flows inside an ETC to analyze its thermal performance. A steady-state one-dimensional model is developed which can simulate the steady-state thermal performance of the Evacuated tube solar collector (ETC) with single and two-phase flows under saturation conditions considering effects of vacuum deterioration to simulate a more real-life situation of solar collectors. The rise in pressure inside the ETC has a significant effect on the suppression of boiling and condensation due to rise in overall heat loss coefficient. The radiative, convective and conductive heat loss coefficients from the collector are studied for gradual pressure rise inside the ETC. The two phase model also indicates that if boiling starts inside the ETC in a particular inlet flow condition, consideration of two phase flow along with the effect of vacuum deterioration shows significant deviation of efficiency and temperature profile from those of single phase flow models and predicts more accurate results. Inducing of two-phase heat transfer in ETC, with all the fluid condensing again within the collector tube, will result in improved efficiency for that range of mass flow rates. It also helps in maintaining uniform temperature and equal heat gain throughout the collector absorber plate. The efficiency of the collector for higher inlet temperatures is seen to be effected more significantly by vacuum deterioration than at lower inlet temperatures in single phase flows. However, in two phase flows for a fixed saturation temperature of the fluid, vacuum deterioration has negligible effect on the efficiency at higher inlet temperatures (Tfi ≥ 85 °C).

Revisiting the single-phase flow model for liquid steel ladle stirred by gas

Ladle stirring is an important step of the steelmaking process to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions before casting. Gas is injected from the bottom of the bath to induce a turbulent flow of the liquid steel. Multiphase modeling of ladle stirring can become computationally expensive, especially when used within optimal flow control problems. This paper focuses therefore on single-phase flow models. It aims at improving the existing models from the literature. Simulations in a 2d axial-symmetrical configuration, as well as, in a real 3d laboratory-scale ladle, are performed. The results obtained with the present model are in a relative good agreement with experimental data and suggest that it can be used as an efficient model in optimal flow control problems.

Adaptive mesh refinement with an enhanced velocity mixed finite element method on semi-structured grids using a fully coupled solver

We describe a novel approach for performing adaptive mesh refinement using mixed finite elements for flow in porous media applications. The enhanced velocity (EV) mixed finite element method is used to construct a strongly flux-continuous velocity approximation between non-matching subdomain grids. In this work, the original EV implementation was generalized to allow interfaces in the interior of subdomains adjacent to inactive cells and to allow dynamic adaptive mesh refinement (AMR). In the new implementation, subdomains with different spatial resolutions are stacked on top of each other to produce a very general semi-structured grid. The decomposition is non-overlapping, but now the subdomains can have holes, have ragged edges, and be nested within each other. Several examples with adaptive mesh refinement are demonstrated in two and three spatial dimensions; a priori indicators are used to adapt the grid for a multiphase compositional flow model, and a posteriori indicators are used to adapt the grid for a single-phase flow model. Moreover, a new fully coupled linear solver for the EV method is also implemented in this work, which shows a dramatic reduction in the number of Newton iterations versus the previously implemented nonlinear block Jacobi solver, especially when systems have a strong elliptic component.

PRESSURE DROP MODELS FOR PARAFFINIC OIL FLOW

Wax deposition is a common phenomenon that occurs when crude oil flows in a pipeline. It is one of the main problems related to flow maintenance, because it leads to flux limitation and pressure drop increase. In addition, it can produce major damage to equipment, creating high-risk in operation or even a complete shutdown of production, impacting profitability negatively. Thus, this research aims to show pressure drop models based on Darcy-Weisbach and Power Fluid model for single-phase flow of paraffinic oils in horizontal lines. It will investigate aspects such as different flows, outdoor temperatures, and the BSW (Basic Sediments and Water) values observing their influence on flow pressure. Experimental data from paraffinic oil wells were used to validate the models. The results showed good fit of the models to the data of the eight experiments, with high values of adequacy coefficient (R2) above 0.97. Experiments with higher BSW content and lower ambient temperature had a greater impact on the pressure drop, being well represented by the two models.

Long runout mechanism of the Shenzhen 2015 landslide: insights from a two-phase flow viewpoint

A catastrophic landslide occurred at Hongao dumpsite in Guangming New District of Shenzhen, South China, on December 20, 2015. An estimated total volume of 2.73x10(6) m(3) of construction spoils was mobilized during this event. The landslide traveled a long distance on a low-relief terrain. The affected area was approximately 1100 m in length and 630 m in width. This landslide made 33 buildings destroyed, 73 people died and 4 people lost. Due to the special dumping history and other factors, soil in this landfill is of high initial water content. To identify the major factors that attribute to the long runout character, a two-phase flow model of Iverson and George was used to simulate the dynamics of this landslide. The influence of initial hydraulic permeability, initial dilatancy, and earth pressure coefficient was examined through numerical simulations. We found that pore pressure has the most significant effect on the dynamic characteristics of Shenzhen landslides. Average pore pressure ratio of the whole basal surface was used to evaluate the degree of liquefaction for the sliding material. The evolution and influence factors of this ratio were analyzed based on the computational results. An exponential function was proposed to fit the evolution curve of the average pore pressure ratio, which can be used as a reasonable and simplified evaluation of the pore pressure. This fitting function can be utilized to improve the single-phase flow model.

A Cartesian grid based multiphase flow model for water impact of an arbitrary complex body

A Cartesian grid based multiphase flow model is developed to simulate water impact problems. This model is capable of simulating complex moving bodies interacting with a highly non-linear free surface such as jet flow or air cushion. A radial basis function based ghost cell method (RBFGCM) is developed to treat the arbitrary moving body on a fixed Cartesian grid. The complex moving boundary is tracked with the RBF and ghost cells are identified based on the signed function property of the RBF. To capture large deformation of the free surface, a gradient-augmented level set (GALS) method is used. Sub-grid resolution is obtained by simultaneously evolving both the level set (LS) function and its gradient information. Also, a simple distance function assignment method is developed to treat the contact boundary between the free surface and the solid surface. The accuracies of the ghost cell method (GCM) and the GALS method are validated by inline oscillation of a cylinder and horizontal sloshing cases, respectively. Then, the water impact of an arbitrary body is simulated. The cases include the water entry of a free falling multihull and the water entry of a bow-flare ship section with various roll angles. The accuracy of the proposed multiphase flow model and its capability are examined by comparing the present results to experimental and numerical results. Also, the results show that the present method can more accurately predict the slamming load in the presence of flow separation and air cushion than the smoothed particle hydrodynamics (SPH) based single-phase flow model and the boundary element method (BEM). Furthermore, the influence of roll angles on the slamming load and the free surface are studied.

An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test

In this work an equivalent single-phase flow model is proposed based on the oil-water two-phase flow equation with saturation-dependent parameters such as equivalent viscosity and equivalent formation volume factor. The equivalent viscosity is calculated from the oil-water relative permeability curves and oil-water viscosity. The equivalent formation volume factor is obtained by the fractional flow of the water phase. In the equivalent single-phase flow model, the equivalent viscosity and phase saturation are interdependent when the relative permeability curves are known. Four numerical experiments based on PEBI grids show that equivalent single-phase flow has a good agreement with the oil-water two-phase flow, which shows that the equivalent single-phase flow model can be used to interpret oil-water two-phase pressure data measured in the wellbore during the buildup period. Because numerical solution of single-phase flow model is several times faster than that of the two-phase flow model, whether the new model interprets the pressure data directly or offers good initial values for the true oil-water two-phase pressure data interpretation, it will obviously improve the efficiency of the interpretation of oil-water pressure data and decrease the burden of engineers.

Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model.