Commercial Flow Simulator Research Articles

Bi-Objective Optimization of Subsurface CO2 Storage with Nonlinear Constraints Using Sequential Quadratic Programming with Stochastic Gradients

Summary This study focuses on carbon capture, utilization, and sequestration (CCUS) via the means of nonlinearly constrained production optimization workflow for a CO2-enhanced oil recovery (EOR) process, in which both the net present value (NPV) and the net present carbon tax credits (NPCTC) are bi-objectively maximized, with the emphasis on the consideration of injection bottomhole pressure (IBHP) constraints on the injectors, in addition to field liquid production rate (FLPR) and field water production rate (FWPR), to ensure the integrity of the formation and to prevent any potential damage during the life cycle injection/production process. The main optimization framework used in this work is a lexicographic method based on the line-search sequential quadratic programming (LS-SQP) coupled with stochastic simplex approximate gradients (StoSAG). We demonstrate the performance of the optimization algorithm and results in a field-scale realistic problem, simulated using a commercial compositional reservoir simulator. Results show that the workflow can solve the single-objective and bi-objective optimization problems computationally efficiently and effectively, especially in handling and honoring nonlinear state constraints imposed onto the problem. Various numerical settings have been experimented with to estimate the Pareto front for the bi-objective optimization problem, showing the trade-off between the two objectives of NPV and NPCTC. We also perform a single-objective optimization on the total life cycle cash flow, which is the aggregated quantity of NPV and NPCTC, and quantify the results to further emphasize the necessity of performing bi-objective production optimization, especially when used in conjunction with commercial flow simulators that lack the capability of computing adjoint-based gradients.

Experimental study of liquid/dense-gas pipe flow

The pre-salt reservoirs play a significant role in the current Brazilian ultradeep water offshore scenario. Their importance is expected to increase soon. The fluids are transported through horizontal, inclined, and vertical wells of several kilometers, and due to the environmental conditions at the reservoir, dense-gas/liquid flow occurs in the pipelines. However, the literature lacks experimental data for gas-liquid flow with densities of the same order of magnitude, which affects the mechanistic model's accuracy for flow patterns, pressure gradients, and holdup predictions. To improve the understanding of that specific two-phase flow, an experimental apparatus was built, and an experimental study was carried out using sulfur hexafluoride (100 kg/m3) and mineral oil (850 kg/m3) at medium pressures. A density ratio lower than 10 was obtained for steady-state horizontal flow in a 50.8-mm-i.d. stainless-steel pipe, and flow patterns, pressure gradient, and holdup were measured. The experimental results show the effect of the low-density ratio on the stratified to non-stratified flow-pattern transition and the occurrence of the dual-continuous flow pattern at high mixture superficial velocity. Moreover, the pressure gradient and holdup data were compared with the results of a commercial multiphase flow simulator, showing good agreement.

Work Flow, Advisory System Optimizes Intelligent Production Network

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 205735, “A Digital Oil Field Comprehensive Study: Automated Intelligent Production Network Optimization,” by Aulia A. Naufal, SPE, and Sabrina Metra, Schlumberger. The paper has not been peer reviewed. _ Leveraging technologies from a flow-assurance simulator, a Python application programming interface (API) toolkit, open-source machine-learning (ML) packages in Python, and a commercial visualization dashboard, the complete paper proposes a series of work flows to simplify model deployment and set up an automatic advisory system to provide insight as a means of justifying day-to-day engineering decisions. The complete paper discusses this methodology and provides a case study of its implementation, although this synopsis concentrates on the former. Background The authors identify four steps necessary for a valid network model that can describe production-system fluid-flow behavior accurately and support day-to-day decision making. These four steps, detailed in the complete paper, include the following: - Well-model building and matching - Well-basis gas lift evaluation - Network modeling - Gas-lift-optimization scenarios Work Flow Objective The objectives of creating an automated, intelligent production-network-optimization work flow include the following: - Minimize risk for data-quality issues caused by human error - Quicken pre- and post-deployment stages of the work flow, thus saving time and resources - Increase the functionality of a digital-oilfield work flow, including adding a production-surveillance dashboard, extracting publicly available temperature data from a weather-service API, and adding an ML autocalibration work flow Theoretical Basis Multiphase Steady-State Flow Simulator. A commercial flow simulator is used to simulate multiphase flow simulation throughout the production system from the reservoir to the surface facilities to enable comprehensive production- (and injection-) system analysis. By the term “steady state,” the authors mean that the mass flow rate is conserved throughout the system, with no accumulation of mass in any system component. This simulator is used from design to the optimization period of the oil, gas, and water production and injection systems. It is most often used by reservoir, production, and facilities engineers to model well performance, design artificial-lift systems, model pipeline networks and facilities, analyze field-development plans, and optimize production. Network modeling is necessary if the interaction of different components (such as compressors, separators, and wells) producing into a common gathering system must be considered (Fig. 1); the wellhead pressure and the deliverability of any well are influenced by the backpressure imposed by the production system. Network modeling also allows engineers to determine the effects of adding new wells and compression, looping flowlines, and changing separation systems. To analyze all components, the network should be solved based on the boundary conditions set on each component. The network will be converged when the pressure balance and mass balance at each node are within the specified tolerance. Then, parameters along the flow path (profile) and at each node in the network will be output. The authors discuss simulation settings, a network optimizer, and a flow-simulation Python toolkit in the complete paper.

STEAM INJECTION NUMERICAL ANALYSES IN HEAVY OIL RESERVOIRS

Thermal recovery methods aim to reduce oil viscosity, thus, increasing its mobility and enhancing its recovery. Reservoir numerical simulation is a powerful tool for predicting reservoir production performance under different operational parameters. One critical point is understanding the relationship between flow rate and recovery factor. This study aims to analyze steam injection into the porous medium in heavy oil reservoirs by numerical simulation using a commercial multiphase flow simulator to simulate the continuous steam injection process. The homogeneous reservoir was built with 14,375 cells. The fluid model has characteristics of onshore Northeastern Brazilian fields. Simulations were performed over a period of 16 years, and results indicate that the steam injection promotes oil production anticipation but reaches a limit as the flow rate increases. The results presented can contribute to improve the understanding of the effects of flow rate in a heavy oil reservoir.

Evaluation of thermal stability of ultra-precision water-lubricated spindle

Minimizing spindle thermal deformation is of key importance for reaching high machining accuracy. In this study, the thermal stability of a spindle with water-lubricated hydrostatic bearings was investigated via simulation with experimental data for defining boundary conditions for the simulations. The simulation study was divided into two separate tasks. In the first stage, the temperature distribution in the water flowing through spindle bearings was determined using commercial FEM flow simulation software. The experimentally obtained temperatures of lubricant and spindle surfaces were used as boundary conditions for a finite volume problem that introduced the temperature distribution of the spindle body and water flowing around the spindle. Then, a thermal analysis of the spindle was performed using the temperature field obtained in the first stage to investigate thermal deformation of the spindle. Temperatures at specific parts of the spindle derived from the temperature distribution were used as boundary conditions for analysis in the second stage. The results were used to investigate the influence of spindle thermal deformation on the positioning accuracy of the end surface of the spindle rotor. The pattern of gap variations in journal and thrust bearings due to the thermal deformation of bearing surfaces was established. The thermal stability of a spindle under the influence of an external temperature field was evaluated using the bearing load capacity and stiffness as indicators. The bearing load capacity and stiffness were defined based on the pressure distribution on the bearing surfaces with consideration of the non-uniformity of the bearing gap due to thermal deformation. A separate study was conducted to investigate the effect of changing viscosity of increasing the temperature of lubricating fluid on bearing performance. Furthermore, the resulting displacement of the spindle rotor end, which directly affects machining error, is also discussed.

Modeling Conjugate Heat Transfer in an Anode Baking Furnace Using OpenFoam

The operation of large industrial furnaces will continue to rely on hydrocarbon fuels in the near foreseeable future. Mathematical modeling and numerical simulation is expected to deliver key insights to implement measures to further reduce pollutant emissions. These measures include the design optimization of the burners, the dilution of oxidizer with exhaust gasses, and the mixing of natural gas with hydrogen. In this paper, we target the numerical simulation of non-premixed turbulent combustion of natural gas in a single heating section of a ring pit anode baking furnace. In previous work, we performed combustion simulations using a commercial flow simulator combined with an open-source package for the three-dimensional mesh generation. This motivates switching to a fully open-source software stack. In this paper, we develop a Reynolds-Averaged Navier-Stokes model for the turbulent flow combined with an infinitely fast mixed-is-burnt model for the non-premixed combustion and a participating media model for the radiative heat transfer in OpenFoam. The heat transfer to the refractory brick lining is taken into account by a conjugate heat transfer model. Numerical simulations provide valuable insight into the heat release and chemical species distribution in the staged combustion process using two burners. Results show that at the operating conditions implemented, higher peak temperatures are formed at the burner closest to the air inlet. This results in a larger thermal nitric-oxide concentration. The inclusion of the heat absorption in the refractory bricks results in a more uniform temperature on the symmetry plane at the center of the section. The peak in thermal nitric-oxides is reduced by a factor of four compared to the model with adiabatic walls.

An analytical model for pressure behavior in multilayered radially composite reservoir with formation crossflow

The present work proposes an analytical model to calculate the pressure response for multilayered radially composite reservoirs considering the presence of formation crossflow along with all layers. The behavior of pressure transient during production tests in radially composite multilayered reservoirs with non-communicating layers has been widely studied, however there is still a lack of studies considering communicating layers, i.e., formation crossflow in such a model. In that sense, the main purpose of this work is to develop a novel analytical solution that can be used to accurately analyze production tests conducted in multilayered radially composite reservoirs considering communicating layers and multiple regions that can have different radii. An infinite reservoir is considered and the properties for each layer, such as permeability, oil viscosity, and porosity may be different. Moreover, the mathematical formulation for this model is presented in the Laplace domain and the Stehfest Algorithm is used to convert the pressure variation into the real-time domain. The results presented in this work show a close agreement when compared to the responses provided by a commercial flow simulator based on finite differences.

CLOSURE LAW MODEL UNCERTAINTY QUANTIFICATION

The prediction uncertainty in simulators for industrial processes is due to uncertainties in the input variables and uncertainties in specification of the models, in particular the closure laws. In this work, the uncertainty in each closure law was modeled as a random variable and the parameters of its distribution were optimized to correctly quantify the uncertainty in predictions. We have developed two methods for optimization, based on the integrated quadratic distance and the energy score. The proposed methods were applied to the commercial multiphase flow simulator LedaFlow with the liquid volume fraction and pressure gradient as output variables. Two datasets were analyzed. Both describe two-phase gas-liquid flow, but are otherwise fundamentally different. One is gas-dominated stratified/annular flow and the other is liquid-dominated slug flow. The closure law for the gas-wall friction factor is decisive for the gas-dominated predictions, and the estimated relative standard deviation is 4.5% or 8.0% depending on method. The liquid-dominated study showed that the liquid-wall friction factor and the slug bubble velocity are the closure laws with the greatest impact. Moreover, the estimated relative standard deviation in the liquid-wall friction factor is 5%, and the deviation in the slug bubble velocity is 4%. We used direct measurements of the slug bubble velocity to validate the estimated uncertainty.

Impulse functions applied to compute pressure change during injectivity tests

Analytical solutions to compute the pressure change during injectivity tests are desired, as they are useful to interpret pressure transient data. Currently, impulse functions (or Green’s functions) for single-phase flow are already known. However, these formulations are not applicable for injectivity tests, as they cannot handle two-phase flow. Instead, the existing analytical solutions for pressure change during injectivity tests assume that flow-rate within the swept region remains constant, which is not necessarily true for multilayer reservoirs. Therefore, the main novelty of this work is to obtain an impulse function for two-phase flow in single-layer reservoirs with vertical wells. The proposed formulation, which accounts for a flow-rate transient inside the flooded region, employs a radially composite reservoir approach to depict the waterfront propagation and assumes a piston-like fluid displacement. Then, we apply the proposed impulse function to determine pressure change in multilayer reservoirs with different layer properties and in single-layer reservoirs with horizontal wells. To the best of our knowledge, the solutions developed in this work have not been presented in literature before. This work also aims to estimate individual layer permeabilities based on the pressure and flow-rate data computed using the developed formulation. A computational implementation of the models proposed in this work was developed and compared to previously existing solutions and to a commercial flow simulator. Results showed a good agreement, and evidenced that a layer flow-rate transient occurs at the wellbore in multilayer reservoirs. Moreover, layer permeabilities were estimated with decent accuracy.

Onset of water accumulation in oil/water pipe flow – experiments and modelling with LedaFlow

In oil/water flows with very low water rates, the steady-state water fraction jumps discontinuously from a low value to a high value when the oil rate falls below the critical value. This jump is understood to be connected to the existence of multiple solutions, and generally takes place when the oil rate becomes too low to sustain a low water fraction. We refer to this critical oil flow rate as the onset of water accumulation. Water accumulation in oil transport lines is undesirable because it can lead to corrosion problems that can threaten the integrity of the installation, potentially leading to oil leaking undetected into the environment, jeopardizing nearby wildlife and ecosystems. It is therefore critical to maintain a flow rate that is high enough to prevent water from accumulating in oil lines, and the ability to predict the minimum allowable flow rate accurately is thus of great importance. To address this challenge, a new and unique set of experiments were conducted at the SINTEF Multiphase Laboratory. The experiments were specially designed to measure the critical conditions for water accumulation in oil/water flows and were performed with a pipe diameter of 8 inches (194 mm) and a pipe inclination of 2.5 degrees. The fluid system consisted of Exxsol D60 as the oil phase and regular tap water as the aqueous phase. In these experiments, the measured critical superficial water velocities were in the range 0.1-2.6 mm/s, while the critical superficial oil velocities were in the range 0.3-0.5 m/s. We found that the customary approach of modelling the oil/water interfacial shear stress as a smooth wall was inadequate for predicting these experiments, and that interfacial waves must be considered. The data analysis showed that the onset of interfacial waves is well predicted by Viscous Kelvin-Helmholtz theory, and that a model for the interfacial shear stress can be constructed with this theory as a starting point. A new model for oil/water interfacial shear stress was developed based on this data and the associated data analysis. The new model was able to match the experimental data well and a slightly modified version of it was ultimately implemented in the commercial multiphase flow simulator LedaFlow.

Experimental Characterization of Two-Phase Flow Through Valves Applied to Liquid-Assisted Gas-Lift

Abstract Liquid-assisted gas-lift (LAGL) is a recently developed concept to unload wells using a gas–liquid fluid mixture. The success deployment of the LAGL technology is related to the behavior of two-phase flow through gas-lift valves. For this reason, this work presents an experimental and numerical study on two-phase flow through orifice gas-lift valves used in liquid-assisted gas-lift unloading. To the knowledge of the authors, there is no investigation in the literature on experimental characterization of two-phase flow through gas-lift valves. Experimental data are presented for methane-water flow through gas-lift valves with different orifice port sizes: 12.7 and 17.5 mm. The experiments were performed for pressures ranging from 1.00 to 9.00 MPa, gas flow rates from 0 to 4.71 m3/h, and water flow rate from 0 to 0.68 m3/min. The experimental results are compared to numerical models published in the literature for two-phase flow through restrictions and to commercial multiphase flow simulators. It is observed that some models developed for two-phase flow through restrictions could successfully characterize two-phase flow thorough gas-lift valves with errors lower than 10%. However, it is first necessary to experimentally determine the discharge coefficient (CD) for each gas-lift valve. The commercial flow simulators showed a similar performance as the models available in the literature.

Development of a special connection fracture model for reservoir simulation of fractured reservoirs

The significant world oil and gas reserves related to naturally fractured carbonate reservoirs adds new frontiers to the development of upscaling and numerical simulation procedures for reducing simulation time. This work aims to accurately represent fractured reservoirs in reservoir simulators within a shorter simulation time when compared to dual porosity models, based on special connections between matrix and fracture mediums, both modeled in different grid domains of a single porosity flow model.For the definition of special connection fracture model (SCFM), four stages are necessary: (a) construction of a single porosity model with two symmetric structural grids, (b) geomodelling of fracture and matrix properties for the corresponding grid domain, (c) application of special connections through the conventional reservoir simulator to represent the fluid transfer between matrix and fracture medium, (d) calculation of the fracture-matrix fluid-transfer. For a proper validation, we apply our methodology in a fractured reservoir type II (tight matrix with flow controlled by fractures) and consider a probabilistic framework regarding geological and dynamic uncertainties.The probabilistic approach of SCFM under several static uncertainties revealed a good dynamic matching with DP. Under three rock-wettability scenarios (water-wet, oil-wet and intermediate-wet) the dynamic matching with DP is preserved. Furthermore, SCFM did not present convergence issues, considering all probabilistic realizations.The results revealed that the new method can be applied to commercial flow simulators in fractured reservoirs and it presents itself as a solution to reduce simulation time without disregarding the upscaling and dynamic representation of dual porosity flow models.

Modelling Leakage Risk Along a Fault Using Modified Discrete Elements

Capacity estimates for chosen CO2 storage reservoirs are limited by the prognosed maximum pore pressure, itself predicted to cause slippage of mapped faults and thus increase the risk of leakage from the site. In most simulation tools, shear failure criteria are checked for predicted pore pressure increased on inclined lines or surfaces representing faults; if the chosen criterion is met, the simulation stops and the pressure and stress distributions in the entire domain are recorded and assigned as critical values not to exceed. Here, we try a different approach, where instead of a line in 2D, a surface is delimited on both sides of a single fault, representing a fault process zone. An in-house model is used, Modified Discrete Element tool, capable of explicitly creating and propagating fractures. The model is coupled to the commercial flow simulator TOUGH2, thus enabling flow through the created fractures to be evaluated. A simple case is simulated, where a sandstone storage reservoir is bounded by a fault, continuing up through the caprock to the next sandstone layer. In the chosen case, the storage site undergoes depletion through gas production, before CO2 is stored in the reservoir, taking the pore pressure back to its initial level. Results show that during depletion, shear stresses may develop such that fractures run alongside the fault all the way up to the upper aquifer. By assigning a permeability value to the open fractured elements, a leakage rate along the fault can be computed. Thus, geological knowledge about the process zone of faults is translated in our tool into quantitative estimates of leakage rates as a function of stress path, historic and future, corresponding to injection plans.

A novel flow-based geometrical upscaling method to represent three-dimensional complex sub-seismic fault zone structures into a dynamic reservoir model

Most hydrocarbon reservoirs contain faults, which are highly complex heterogeneous and anisotropic three-dimensional (3D) volumes of deformed rock. A major technical challenge in full-field flow simulation is to represent the effects of 3D fault zone structure within the two-dimensional (2D) fault planar surfaces using the industry standard commercial reservoir flow simulator due to its limited functionality. Therefore, a new flow-based geometrical upscaling (FBGU) method has been developed for capturing the effects of 3D fault zone structures in conventional low-resolution upscaled flow simulation models. Geometrical upscaling (GU) is the process of calculating across-fault and up-fault transmissibility arising from 3D flow paths through fault zones, and expressing these transmissibilities as implicit connections in a low-resolution upscaled flow simulation model. The high accuracy of the method is demonstrated by comparing the flow responses of high-resolution (referred as truth model in this paper) simulation models in which the 3D fault zone structure is represented explicitly in the grid geometry, with that of conventional resolution models in which it is upscaled using FBGU method. The flow results show that the newly developed FBGU method is extremely accurate and geometrically flexible.

Smeared modeling of hydraulic fracture using partially coupled reservoir and geomechanics simulators

A smeared fracture type hydraulic fracture simulator is developed through numerical coupling between an in-house reservoir simulator and a geomechanical commercial software (FLAC2D). The new package falls within the category of partially decoupled model and is versatile, flexible and efficient. This approach can be used to couple any other advanced commercial fluid flow or geomechanical simulators for an accurate description of the initiation and propagation of hydraulic fractures.The paper contains a discussion of the partial coupling technique to link fluid flow and geomechanical calculations in modeling fracture initiation and propagation. The models use a common gridblock for the fracture and reservoir and use the deformation calculations to update the porosity and permeability. The method captures the interactive effects of the fracture on reservoir fluid flow and formation geomechanics through stress dependent permeability and porosity.The developed smeared fracture model can capture both tensile and shear fractures in the formation. Major features of this model include modeling poroelasticity and plasticity, matrix flow, shear and tensile fracturing with concomitant permeability enhancement, saturation-dependent permeability, stress-dependent stiffness and gradual degradation of oil sands due to dilatant shear deformation. The model has been applied to numerically simulate field size hydraulic fracturing in oil sands during cold-water injection to show the predictive capability of the simulator.

Experimental investigation of interfacial waves in stratified liquid-liquid flows in horizontal pipelines: Characteristics and pressure gradients

The increasing use of commercial flow simulators in the oil and gas industry provides the impetus to accurately model multiphase flows in pipelines. The current work investigates stratified oil-water flows in horizontal pipelines by experimentally measuring interfacial deformations, correlating them to interfacial friction. The derived interfacial model is then implemented into the two-fluid model to predict pressure losses in pipelines.An experimental campaign was undertaken using process oil (ρ=845kg/m3, μ=0.03Pa.s) and water as the test fluids in acrylic pipes of 40 mm diameter, with objectives of capturing interfacial deformations via image processing techniques, while also measuring pressure gradients in the pipe. The interfacial deformations were seen to increase with increasing flow velocities, plateauing with wave amplitudes of 3 mm. Further tests with identical fluids, conducted on larger diameter pipes (54.8 mm and 108.4 mm) also showed similar trend. Wave aspect ratios were correlated with a modified Froude number, linking the interfacial deformations to input flow variables.An empirical equation, utilizing the amplitude of interfacial deformations as roughness heights is derived for the interfacial friction factor. Incorporating the derived equation into the one dimensional two-fluid model, pressure losses were calculated and compared against experimental pressure drop measurements conducted in current work, as well as with those in literature. The performance of this model is also compared with existing prediction models and is found to provide improved accuracies across wide range of viscosity ratios and pipe diameters.

Application of hybrid adaptive neuro-fuzzy inference system in well placement optimization

Well placement optimization as a key factor in field development, is one of the reservoir management cycles, which aims to economize oil and gas production from the reservoir. One of the reservoir development scenarios is determining parts of the reservoir in which hydrocarbons have not been drained completely. After determination of these areas, some new wells are drilled to improve oil production. In this study, a new model based on adaptive neuro-fuzzy inference system (ANFIS) for optimum well placement is proposed. Also, an application of opportunity index (OI) concept is used to develop this model. Using particle swarm optimization (PSO) and genetic algorithm (GA) as population based algorithms, the ANFIS model was optimized. In order to develop and validate the proposed AFNIS-PSO model, a large number of simulation runs were performed in synthetic models. In this study, the proposed model was applied in both synthetic and standard models to find the best location for new production wells. The Tenth SPE model as a standard model was used to evaluate the performance and accuracy of ANFIS-PSO model. The performance of new method compared to well placement optimizer algorithms, which is the combination of commercial flow simulator and evolutionary algorithms, was investigated in terms of the number of simulations and maximum net present value (NPV). Finally, the simulation results show that the proposed ANFIS model was able to achieve better results with fewer simulation runs and therefore improving the computational efficiency.

Comparison of Analytical and Numerical Methods for the Evaluation of the Flow Forces in Conical Poppet Valves with Direct and Reverse Flow

Different methods for the evaluation of the flow forces in conical poppet valves are analyzed. The equation derived from the conservation of the fluid momentum is contrasted with a formulation obtained from the Bernoulli's equation and with computational fluid dynamics (CFD) simulations performed through two commercial codes, PumpLinx and Flow Simulation. Three different poppet angles and two flow directions are analyzed. In some operating conditions, a significant difference was found between the analytical formulation and the outcomes of the CFD simulations in case of reverse flow.

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150μm at solid concentrations of 0–40vol%, and superficial gas velocities of 0.02–0.034m/s in a slurry bubble column with a hydraulic diameter of 0.2m and height of 1.2m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.

CFD Modeling of Three-phase Flotation Column Incorporating a Population Balance Model

A Computational Fluid Dynamics (CFD) model was developed and validated against published experimental data to understand the effect of slurry concentration on bubbles’ coalescence process in flotation cell. The existing flow field was modelled for two- phase (gas-liquid) and three-phase (gas-liquid-solids). The simulations were carried out using the commercial flow simulation software AVL-FIRE 2009.2 for Jg= 0.94-5.01 cm s-1 Cs= 0-200 kg m-3, respectively. Modelling calculations have been conducted using Eulerian–Eulerian multiphase model with k-ɛ turbulence model for the liquid phase. In the present study, the population balance equation for bubble break-up and bubble coalescence rate and the interfacial exchange of mass and momentum as well as bubble-particles attachment and detachment have been included in the CFD code by writing subroutines in FORTRAN. Comparisons of the predicted results against measured gas holdups and axial pressure profile show reasonable agreement without using any fitting parameter. With the increase of slurry concentration, the gas holdup in a flotation column decreased. These results are in line with those of previous studies. The results also show that the addition of solid particles reduced the size of bubbles in a flotation column.