Drift-flux Approach Research Articles

A Novel Geothermal Wellbore Model Based on the Drift-Flux Approach

Geothermal energy, being a clean energy source, has immense potential, and accurate wellbore modeling is crucial for optimizing the drilling process and ensuring safety. This paper presents a novel geothermal wellbore model based on the drift-flux approach, tested under three different temperature and pressure well conditions. The proposed model integrates the conservation equations of mass, momentum, and energy, incorporating the gas–liquid two-phase flow drift-flux model and heat transfer model. The key features include handling the heat transfer between the formation and the wellbore, addressing the slip relationship between the gas and liquid phases, and accounting for wellbore friction. The nonlinear equations are discretized using the finite difference method, and the highly nonlinear system is solved using the Newton–Raphson method. The numerical simulation, validation, and comparison with existing models demonstrate the enhanced accuracy of this model. In our tests, the model achieved a high accuracy in calculating the bottom-hole pressure and temperature, with mean relative errors (MREs) significantly lower than those of other models. For example, the MREs for the bottom-hole pressure and temperature of the Rongxi area well in Xiongan, calculated by this model, are 1.491% and 1.323%, respectively. These results offer valuable insights for optimizing drilling parameters and ensuring drilling safety. Comparisons indicate that this approach significantly outperforms others in capturing the complex dynamics of geothermal wellbores, making it a superior tool for geothermal energy development.

Modeling Approach Estimates Temperatures in Growing High-Temperature Wells

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 214836, “Downhole Temperature Estimation of a Growing High-Temperature Wellbore Using a Modified Drift-Flux Modeling Approach,” by Ningyu Wang, SPE, Mohamed S. Khaled, and Anthony Luu, The University of Texas at Austin, et al. The paper has not been peer reviewed. _ Downhole temperature (DHT) estimation is very important for heat management while drilling high-pressure/high-temperature (HP/HT) and geothermal wells. Existing transient models neglect the effect of wellbore growth or deepening on the downhole temperature. The complete paper provides a new modeling tool to estimate and manage the DHT in higher-temperature oil, gas, and geothermal wells. The model, which has the potential to run in real time and thereby digitally twin the drilling operation, may contribute to preventing premature temperature-related failures of bits and downhole tools while drilling future wells in high-temperature environments. Introduction Analytical and numerical modeling are the two main approaches discussed in the literature to estimate the mud temperature inside the drillstring and the annulus. Although these models provide valuable insights on selecting optimal heat-management techniques during circulation, none consider the effect of drilling rate of penetration (ROP) on downhole temperature, and all consider the wellbore as having fixed and static dimensions. On the other hand, the effect of ROP in an arbitrarily growing wellbore on other aspects of drilling has been modeled and studied. In this work, the authors present a validated thermohydraulic model based on the drift-flux approach to simulate the transient behavior of downhole temperature during drilling. This model can predict the effect of different cooling-strategy techniques based on real-time operational changes and can predict temperature-sensor measurements. It thereby establishes a foundation for active managed-temperature drilling of HP/HT and geothermal wells. Methodology The drift-flux model is a well-studied model for 1D flow in a flow channel with static geometry. Conservation equations, and their discretization, are detailed in the complete paper, as are equations regarding heat transfer in the solid. Assumptions. To lay the foundation for a thermohydraulics model that considers the effect of the growth of the wellbore, the following key assumptions are made: - The ROP is much slower than the mud-flow velocity. - The cuttings are assumed to be perfectly integrated into the mud and to share the physical properties of the drilling mud. Therefore, the added mud volume equals the volume of the cuttings. The complete paper focuses on laying the foundation for a solver that accounts for the wellbore growth. - The transient temperature distribution in the drillstring is neglected because the authors are primarily interested in temperature behavior on larger time scales. - The growth of the wellbore trajectory is an external input and is to be updated in a timely manner if the solver is run in real-time mode. - The drillpipe entering the well has constant cross-sectional geometry. - The formation temperature ahead of the bit is considered to not yet be disturbed as drilling proceeds.

An OpenFOAM solver for computing suspended particles in water currents

Abstract A new OpenFOAM solver has been developed for computing the spatial variation of particle concentrations in flowing water. The new solver was programmed in C ++ using OpenFOAM libraries, and the source code has been made openly available. The current article describes the coding of how the water flow and particle movements are computed. The solver is based on a Eulearian approach, where the particles are computed as concentrations in cells of a grid that resolves the computational domain. The Reynolds-averaged Navier–Stokes equations are solved by simpleFoam, using the k-ε turbulence model. The new solver uses a drift-flux approach to take the fall or rise velocity of the particles into account in a convection-diffusion equation. The model is therefore called sediDriftFoam. The results from the solver were tested on two cases with different types of particles. The first case was a sand trap with sand particles. The geometry was three-dimensional with a recirculation zone. The computed sediment concentrations in three vertical profiles compared well with earlier numerical studies and laboratory measurements. The second case was a straight channel flume with plastic particles that had a positive rise velocity. In this case, the results also compared well with the laboratory measurements.

Numerical modeling of transient cuttings transport in deviated wellbores

Hole-cleaning optimization is one of the major challenges while drilling long-reach horizontal wells. Accumulation of cuttings can affect the equivalent circulating density (ECD) by decreasing the open flow area and increasing the average density of the drilling fluid. The transient development or removal of cuttings bed due to variation of operating parameters are often ignored in the majority of prior numerical studies. In this paper, it is aimed to develop a transient cutting transport model to predict ECD while drilling. A one-dimensional transient two-phase hydraulic model based on the drift-flux approach is developed to predict the cuttings transport considering cuttings deposition and entrainment. The numerical method employs an upwind scheme to discretize the governing equations. To account for the effect of operating parameters on the cuttings bed, two empirical correlations were employed from the literature. A new empirical correlation is also developed for the prediction of cuttings bed hold-up through regression analysis of the experimental results of a published study. A computer program is developed to solve the governing equations and predict the ECD taking into account the effect of suspended cuttings and cuttings bed along the wellbore trajectory. The numerical model is validated by comparing the predicted return weight of cuttings with measured data in the literature for the cases of no pipe rotation and pipe rotation. The effects of employed empirical correlations on predicted ECD profiles are also examined for a hypothetical well. It is realized that the predicted cuttings bed area of the proposed correlation falls between the predictions of the existing empirical correlations. It is concluded that the most conservative prediction in terms of cutting accumulation in the wellbore cannot necessarily yield a conservative prediction in terms of ECD for early times.

Door to diuretics time is longer among heart failure patients with atrial fibrillation

Hole-cleaning optimization is one of the major challenges while drilling long-reach horizontal wells. Accumulation of cuttings can affect the equivalent circulating density (ECD) by decreasing the open flow area and increasing the average density of the drilling fluid. The transient development or removal of cuttings bed due to variation of operating parameters are often ignored in the majority of prior numerical studies. In this paper, it is aimed to develop a transient cutting transport model to predict ECD while drilling. A one-dimensional transient two-phase hydraulic model based on the drift-flux approach is developed to predict the cuttings transport considering cuttings deposition and entrainment. The numerical method employs an upwind scheme to discretize the governing equations. To account for the effect of operating parameters on the cuttings bed, two empirical correlations were employed from the literature. A new empirical correlation is also developed for the prediction of cuttings bed hold-up through regression analysis of the experimental results of a published study. A computer program is developed to solve the governing equations and predict the ECD taking into account the effect of suspended cuttings and cuttings bed along the wellbore trajectory. The numerical model is validated by comparing the predicted return weight of cuttings with measured data in the literature for the cases of no pipe rotation and pipe rotation. The effects of employed empirical correlations on predicted ECD profiles are also examined for a hypothetical well. It is realized that the predicted cuttings bed area of the proposed correlation falls between the predictions of the existing empirical correlations. It is concluded that the most conservative prediction in terms of cutting accumulation in the wellbore cannot necessarily yield a conservative prediction in terms of ECD for early times.

Entropy Generation Minimization for Boiling Flow Inside Evaporator Tube With R32 and R410A Refrigerants: A Comparison of Different Two-Phase Flow Models

AbstractThe objective of the present work is to find out the optimal mass flux of two common refrigerants, R32 and R410A, undergoing boiling in an evaporator tube based on the entropy generation minimization approach. An entropy generation model is developed for two-phase boiling flow based on the drift flux approach. The distinct terms for entropy generation due to heat transfer and pressure drop are developed. The optimal solutions of the present model under a practical range of parametric conditions are compared with that obtained from the existing homogeneous and separated flow-based model. Analysis reveals that increasing the evaporator diameter and heat flux increases the optimal mass flux at minimum entropy generation for both refrigerants. On the other hand, increasing the evaporator length decreases the optimal mass flux. It is observed that the optimal mass flux data for all parametric conditions deviate within 10–15% on the positive and negative sides for drift flux and homogeneous models, respectively, compared to separate flow model. The present analysis also reveals that the overall deviation of data of the drift flux model and homogeneous flow model indicates a standard deviation of 1.95–1.98%, respectively.

A model for investigating wellbore hydraulics of thermo-thixotropic drilling fluids

In high-temperature drilling environments, accurate management of wellbore hydraulics is made more difficult due to complex fluid viscosity-temperature profiles. Although most of the fluid samples reported in the literature have monotonically decreasing viscosity with temperature, several studies have found the relationship much more complicated. This study investigates thermal effects on annular pressure loss and cuttings transport for fluids with non-monotonic viscosity-temperature profiles while modeling the thixotropic behavior of the drilling fluid. To this end, three fluid samples have been studied that have distinctly different viscosity-temperature profiles: monotonically decreasing, parabolic and inverted parabola. The mathematical framework is based on the drift flux approach and is numerically solved using the computational fluid dynamics (CFD) methodology. The recently proposed rheological algorithm by the authors has been extended to model thixotropy. The results are presented for different inclinations and eccentricities. It is observed that for fluids with parabolic or inverted parabolic viscosity-temperature profiles, annular pressure loss is highly non-linear, and a single equivalent density value cannot be ascribed to the wellbore. The annular pressure loss near the inlet is significantly higher than that near the outlet. The fluid with a monotonic decrease in viscosity yields the lowest pressure loss but worst cuttings transport whereas, the fluid with a parabolic viscosity-temperature profile has best cuttings transport but causes extremely high-pressure loss.

A 3D numerical simulation-based methodology for assessment of landslide-generated impulse waves: a case study of the Tersun Dam reservoir (NE Turkey)

This paper focuses on the evaluation of temporal and spatial propagations of impulse waves using 3D numerical simulation-based models for a potential landslide area in the Tersun Dam reservoir, Northeast Turkey. The topographical model was created using Stereo Lithography files, and a drift-flux model was used to simulate the landslides. The wave generation was simulated using the Reynolds-averaged Navier–Stokes equations. The Drift-Flux approach was selected, and a renormalization group-based k-e turbulence model was used to create a fluid–solid coupled model. The results show that a 16.5-m impulse wave is created as a result of sliding material hitting the water at a velocity of 16.4 m/s. The wave will reach the opposite shore in 27.4 s, and the run-up height will reach up to 48.8 m. As the wave, with an average velocity of 11.6 m/s in the reservoir, propagates toward the dam body, its height will decrease, and a 3.7-m-high wave will hit the dam in 155 s. A validation analysis performed using empirical equations and laboratory model tests indicates small differences in the results. The main reason for these differences is that the evaluation of wave properties is independent of the type of mass movement in empirical methods. A proper stability analysis is required to have a better estimation of the volume and the velocity of the sliding mass.

Research of two‐phase density wave instability in reactor core channels with rolling motion

In this study, two-phase density wave instability in parallel-twin rectangular channels was investigated with axially nonuniform heat profiles in the reactor core combined with static and rolling conditions. A parallel-channel thermal-hydraulic model was built using the method of two-phase homogeneous flow developed in previous work, while the drift-flux approach for void fraction and profile-fit model for subcooled boiling were implemented. Although the rolling condition was chosen as the typical motion in this work, the additional force caused by the motion with six degrees of freedom was derived. The theoretical analysis was performed based on the method of small power perturbation for parallel-twin rectangular channels. The flow oscillation caused by rolling was studied for different system parameters, including inlet resistance, exit resistance, pressure, and axial heating profile. The influence on flow instability of rolling parameters such as period, amplitude, and distance between channels was analyzed. The results showed that it would destabilize the system if a larger additional force was generated by rolling parameters. The influence of different axial heat profiles on flow instability was also studied under inlet-peaked, cosine-shape, and outlet-peaked heat fluxes. The coupling effect of rolling motion and axial nonuniform heating was finally studied. The stability boundaries under different conditions were compared to the inherent boundary under the static condition with uniform heating. The results indicated that the influence of nonuniform heating was more evident and should be paid more attention to.

A Compositional Thermal Multiphase Wellbore Model for Use in Non-Isothermal Gas Lifting

Abstract In this paper, a new compositional mechanistic wellbore model, including gas lifting parameters, is presented. In the governing equations of this model, new terms for mass transfer between phases and the enthalpy of phase change, which are important in non-isothermal gas lift systems, have been considered. These terms have been ignored in some recent research studies and subsequent results show that by ignoring them, serious errors may arise. In the current research study, using a mechanistic drift-flux approach, the pressure distribution in a wellbore was modeled. To verify the new simulator, the results were compared with those of commercial simulators. They were also verified against the phase behavior analysis of the fluid flowing in the wellbore. In addition, in order to show the novel aspects of the new simulator, the results of the presented simulator were compared with the results of a recently proposed model found in the literature. It was concluded that neglecting phase change effects may cause significant errors in calculating pressure and temperature values along wellbores. This error could be significant, up to 24% depending on conditions when flowing fluid pressure is close to its saturation point or in the case of simulating gas lift operation.

Validation of Selected Cesar Friction Models of the ASTECV21 Code Based on Moby Dick Experiments

In the event of a loss of integrity of the main coolant line, a large mass and energy release from the primary circuit to the containment is to be expected. The temporal evolution of such depressurization is mainly governed by the critical flow, whose correct prediction requires, in first place, a correct description of the different friction terms. Within this work, selected friction models of the CESAR module of the Accident Source Term Evaluation Code (ASTEC) V2.1 integral code are validated against data from the Moby Dick test facility. Simulations are launched using two different numerical schemes: on the one hand, the classical five equation (drift flux) approach, with one momentum conservation equation for an average fluid plus one algebraic equation on the drift between the gas and the liquid; on the other hand, the recently implemented six equation approach, where two differential equations are used to obtain the phase velocities. The main findings are listed hereafter: The use of five equations provides an adequate description of the pressure loss as long as the mass fluxes remain below 1.24 kg/cm2 s and the gas mass fractions below 5.93 × 10 − 4. Beyond those conditions, the hypotheses of the drift flux model are exceeded and the use of an additional momentum equation is required. The use of an additional momentum equation leads to a better agreement with the experimental data for a wider range of mass fluxes and gas mass fractions. However, the qualitative prediction for high gas mass fractions still shows some deviations due to the decrease of the regular friction term at the end of the test section.

Experimental investigation of upward vertical two-phase high-velocity flows in large-diameter pipes

An experimental investigation is carried out to analyze the effect of the diameter and high fluid velocities on two-phase flow in vertical large-diameter pipes. This study generated and gathered experimental data for diameters ranging from 97 to 297 mm. The working fluids for the experimental database are water and air, for superficial liquid velocities ranging from 0.2 to 4.7 m/s; and superficial gas velocities ranging from 0.1 to 30 m/s.From the experimental observations of flow regimes for diameters larger than 97 mm, cap-bubble flow is observed for conditions which slug flow would be expected in smaller diameter pipes. Based on experimental results obtained in this work and available in the literature, it is observed that pressure gradient only varies around 50% for changes of one order of magnitude on the pipe diameter (from 19 to 297 mm), for superficial gas velocities lower than the minimum point in the pressure gradient curve. The measurements of liquid holdup and pressure gradient are compared to a numerical model based on the drift-flux approach, which shows good agreement with the experimental observations.

Multiphase flow models for hydraulic fracturing technology

The technology of hydraulic fracturing of a hydrocarbon-bearing formation is based on pumping a fluid with particles into a well to create fractures in porous medium. After the end of pumping, the fractures filled with closely packed proppant particles create highly conductive channels for hydrocarbon flow from far-field reservoir to the well to surface. The design of the hydraulic fracturing treatment is carried out with a simulator. Those simulators are based on mathematical models, which need to be accurate and close to physical reality. The entire process of fracture placement and flowback/cleanup can be conventionally split into the following four stages: (i) quasi-steady state effectively single-phase suspension flow down the wellbore, (ii) particle transport in an open vertical fracture, (iii) displacement of fracturing fluid by hydrocarbons from the closed fracture filled with a random close pack of proppant particles, and, finally, (iv) highly transient gas-liquid flow in a well during cleanup. The stage (i) is relatively well described by the existing hydralics models, while the models for the other three stages of the process need revisiting and considerable improvement, which was the focus of the author’s research presented in this review paper. For stage (ii), we consider the derivation of a multi-fluid model for suspension flow in a narrow vertical hydraulic fracture at moderate Re on the scale of fracture height and length and also the migration of particles across the flow on the scale of fracture width. At the stage of fracture cleanaup (iii), a novel multi-continua model for suspension filtration is developed. To provide closure relationships for permeability of proppant packings to be used in this model, a 3D direct numerical simulation of single phase flow is carried out using the lattice-Boltzmann method. For wellbore cleanup (iv), we present a combined 1D model for highly-transient gas-liquid flow based on the combination of multi-fluid and drift-flux approaches. The derivation of the drift-flux model from conservation olaws is criticall revisited in order to define the list of underlying assumptions and to mark the applicability margins of the model. All these fundamental problems share the same technological application (hydraulic fracturing) and the same method of research, namely, the multi-fluid approach to multiphase flow modeling and the consistent use of asymptotic methods. Multi-fluid models are then discussed in comparison with semi-empirical (often postulated) models widely used in the industry.

The analysis of density wave oscillation in ocean motions with a density variant drift-flux model

The two-phase flow instability in heated channels is an important phenomenon in industrial facilities. The effect of ocean motions upon the flow instability should be predicted accurately for the heat exchangers in floating platform. The reduced order model with drift-flux approach is developed to analyze the density wave oscillation in a uniformly heated channel in ocean motions. The density variation of coolant flow is considered. The stability maps can be predicted precisely on experimental data. The effect of ocean motions on the stability boundary is investigated quantitatively by the defining of the degree of instability. The subcritical Hopf bifurcation in ocean motions is also studied.

Critical Power and Void Fraction Prediction of Tight Bundle Designs

With the objective of providing long-term energy supply via actinide breeding and burning, the next-generation boiling water reactor (BWR) design, the Hitachi’s resource-renewable BWR (RBWR), has been proposed. Unlike a traditional square lattice BWR fuel bundle, the RBWR bundles are shorter with hexagonal tight lattice arrangement and heterogeneous axial fuel zoning. The RBWR’s different core geometry combined with the higher power-to-flow ratio and void fraction necessitates the reexamination of the standard BWR thermal-hydraulic models.For the prediction of dryout, the previously derived best-estimate empirical correlation showed significant scatter when compared to experimental data within its calibration database. In this work, the correlation is further calibrated and improved by supplementing tight bundle data with relevant critical power data for tubes and annuli to better quantify the effects of various parameters and by incorporating subchannel-level results to account for intra-assembly flow mixing. Another approach using the mechanistic three-field model is also investigated, and the minimum critical power ratio of the RBWR design is evaluated.For the prediction of void fraction, measurements and the three-field model in annular flow regime reveal that the common drift flux approaches tend to overestimate the void fraction at small hydraulic diameters. The void fraction dependence on hydraulic diameter below 10 mm requires further experimentation and high-fidelity mechanistic simulations.

An extension of the drift-flux model for submarine granular flows

To model submarine flows of granular materials we propose an extension of the drift-flux approach. The extended model is able to represent dilute suspensions as well as dense granular flows. The dense granwular flow is modelled as a Herschel–Bulkley fluid, with a yield stress that depends on the dispersed phase pressure. Qualitative numerical experiments show that the model is able to correctly reproduce the stability of submerged sand heaps with different internal angles of friction and initial slopes. When initially starting with heaps with an angle smaller than the internal angle of friction, the heaps are stable. When starting with heaps with angles larger than the internal angle of friction, a flow of solid material is initiated. The flow later stops when the bed is at an angle smaller than the internal angle of friction.

Unified graph-based multi-fluid model for gas–liquid pipeline flows

We present a novel model of transient multiphase flow for gas–liquid mixtures in long pipelines. The study develops a general flexible formulation of a one-dimensional flow for complex multiphase mixtures in the presence of slip and mass exchange. Multi-fluid and drift–flux approaches are combined. The multi-fluid model governs the momentum balance for the fluids, and drift–flux correlations are used for modelling of the slip between individual components. A tree-like graph is introduced to describe the hierarchy of fluids and components within the mixture. The numerical implementation for an arbitrary number of components is based on the extension of the Semi-Implicit Method for Pressure-Linked Equations. Imbalances of equations are selected as criteria for iteration convergence. Specific corrections are discussed, including those proposed for the equilibrium gas-release model.

Applicability of a drift-flux model of aerosol deposition in a test tunnel and an indoor heritage environment

Near-wall turbulence associated with air flows parallel to walls can promote aerosol deposition. In indoor environments, where this kind of flow is frequently present, this results in local deposition gradients near ventilation inlets and outlets. This phenomenon is of special interest to the heritage field, which is often concerned about the spatial distribution of deposition and its links to environmental management. In this paper we investigate the capability of a drift-flux model of particulate matter deposition to describe this mechanism. This model has often been validated using decay rates of particulate matter concentration; however, in several indoor applications the interest is not in concentration but in the spatial distribution of the deposition flux. To test the model, we use untreated atmospheric aerosols in two different cases: an experimental tunnel designed to induce near-wall velocity gradients and an actual indoor room with various ventilation regimes. Both systems exhibit significantly inhomogeneous deposition distributions. While the first system is operated under controlled laboratory conditions, the second yields data collected in-situ during a six-month monitoring campaign. In either case the model reproduces the experimental values with enough accuracy to allow understanding how the environment behaves. This work confirms the usability of the drift-flux approach as an analysis tool for particle deposition in complex environments in a wide range of geometries.

Simulation of particulate matter ingress, dispersion and deposition in a historical building

Abstract In this work, we use a computational fluid dynamics (CFD) model to simulate the penetration, dispersion and deposition of particulate matter (mean particle size of 2.5 μm) in a historical house. We compare the simulation results with direct measurements of deposition in several rooms and with measurements of concentration in different conditions of wind direction. The computational model, based on the drift-flux approach, provides accurate predictions of the spatial distribution of deposition and the variation of the indoor/outdoor ratio, which display a good agreement with experimental measurements. Our analysis shows that while the ingress rate of particles is controlled by wind direction and pressure, the amount of particles that reaches every surface depends ultimately on the operation of the ventilation system. Concentration indoors is relatively homogeneous, however, the spatial arrangement of the rooms and the position of air inlets and outlets results in significant gradients of deposition rates, which has direct implications for cleaning and preservation. These findings illustrate the potential of CFD to produce meaningful predictions of yearly and monthly deposition in large, multi-room environments, and to offer site-specific evidence, which can inform heritage managers and enable risk assessment.

Analysis of Particle Transport and Deposition of Micron-Sized Particles in a 90° Bend Using a Two-Fluid Eulerian–Eulerian Approach

Two-phase flows involving dispersed particle and droplet phases are common in a variety of natural and industrial processes, such as aerosols, blood flow, emulsions, and gas-catalyst systems. For sufficiently dilute particle/aerosol phases, a simplified one-way coupling is often assumed, in which the continuous primary phase is unaffected by the presence of the dispersed secondary phase and standard CFD methods can be applied. To predict the transport and deposition of the particle phase, typically a Lagrangian particle-tracking or Eulerian one-fluid/two-phase drift-flux approach is used. Here, a full two-fluid Eulerian modeling approach is presented for coarse particles (>1 μm), in which transport equations are numerically solved for both particle-phase continuity and particle-phase momentum. Simulation results were obtained for a laminar flow regime (Re 100 and 1000) in a 90° elbow, and the effects of grid topology and resolution were investigated. Additionally, gravity effects were considered for both ...