What is Slurry Flow and how to do its CFD Modelling?

By

Dr. Sharad N. Pachpute ( PhD. IIT Delhi)

 

Introduction to Slurry Flows

 What is Slurry Flows?

• Slurry is a mixture of solid particles and liquid. Particles can be denser than liquid water
• slurry flow is used for transporting solid particles with the liquid being as a carrier medium
• The slurry mixture is generally pumped on a device such as a centrifugal pump.
• The size of solid particles typically varies in the range of 1 – 100 mm
• The particles may settle below a certain transport velocity and the mixture can behave as a Newtonian or non-Newtonian fluid. Depending on the mixture, the slurry may be abrasive and/or corrosive

Application of Slurry Flow

• The slurry flow through pipelines is wide applications in many industries such petroleum, mining, chemical industries and energy and nuclear

• Density meter is used to measure the operating density of slurries

• Sectional view of the density meter used for slurry flows

Types of Slurries

• Different forms of slurries are formed depending on applications
• In general, slurries are two types setting and  non-settling which are produced as per requirement of industrial applications

1) Coal Slurry

• Coal Slurry is a mixture of coal particles, minerals and water
• Minerals are mixed based of treatment of chemical processes

2) Food Slurries

• Food Slurry is a mixture of food material (from natural or animal extracts) and water
• Ingredients are mixed with food and water as per nutrients and deliciousness of final food products

3) Cement slurries

• Cement slurry is made of cement, water, and various chemical additives which has a certain density.
• Cement slurry is a runny (flow) form of concrete poured into forms for molding and results in the formation of strong construction
• It is used around for construction of large-scale building such as large slabs and columns

Cement slurries prepared for home construction

Cement slurries dumped from home construction

 

4) Slurry due to steel erosion

• Slurry erosion is a major problem for slurry handling devices, as it leads to considerable cost caused by failures of devices, replacement of material  and high downtime
•  Slurry erosion from steels depends on slurry properties, service conditions, and material properties
• The slurry comprises metal oxides, water and sand particles

5) Sand Slurry

• Sand Slurry is also called as a self-compacting form of Controlled Density Fill (CDF) which is mainly used for filling tanks and large voids in excavation.
• Sand slurry is made of a small portion of and large volume of water of sand

6) Ceramics Slurry in manufacturing industries

• The ceramic slurry is used in forming the mold about the pattern is usually a suspension of insoluble ceramic powders
• Ceramic slurry is used for casting and manufacturing industries
• A mixture of minerals, water, and additives used in the manufacture of ceramics. A bolus of chewed food mixed with saliva. A mixture of epoxy glue and glass microspheres used as a filler compound around core materials in sandwich-structured composite airframes.

 

7) Cow Dung Slurries

• Cow dung slurries consists of Cow dung (cow pats, cow pies or cow manure) and water and other waste residuals of plants
• Cow slurries are used for organic farming as well as for biogas plants

1.3 Complex Multiphase Problem

• The slurry flow is multiphase flow problem (two-phase liquid-solid flow)
• Understanding of slurry flow is highly complex due to the interactions between the phases as well interactions between the phases and surfaces of pipes
• Apart from basic variables of turbulent multiphase flow, other flow parameters such as solids concentration, pipe orientations add extra complexities Hence, CFD models and theories associated with slurry flow have been uncertain. Hence, development of CFD models and experimental understanding of slurry flow in labs are going on in universities and industries

Properties of Slurries

• Physical Properties of Slurry mixture depend upon composition. Slurries can be Newtonian or non-Newtonian in nature
• When the particle concentration of solid within the liquid is less than 10 % by volume, the slurry can consider a Newtonian fluid
• When the solid concentration is higher than 10 percent of liquid volume, it is generally considered as a non-Newtonian fluid
•  The following formulations are used for most of slurries like coal-water slurries, sand slurries,

1) Density of Slurry Mixture

The density of slurry can be calculated as:

ρ_m = 100 / (C_w/ρ_s) + [(100 – C_w) / ρ_L]

where:
ρ_m =density of slurry mixture (kg/m³)
C_w = solids concentration by weight (%)
ρ_s = density of solid in mixture (kg/m³)
ρ_L = density of liquid in mixture (kg/m³)

2) Volume Fraction

• • The term volume fraction is represented by the symbol Φ

Φ = C_v / 100

• • The term volume ratio represents the ratio of the volume of solid (Φ) to the volume of liquid (1- Φ)

Volume Ratio (VR) = Φ / 1 – Φ

where, C_v  is the concentration of solids by volume (%) and Φ is the volume fraction

3) The concentration of solids

• • In slurry flows, the concentration of solids particles by volume (C_v ) and the its weight ( C_w)   depend on  solid particle density and the mixture density which is given as C_v = C_w(ρ_m / ρ_s) where, C_v is the solid concentration by volume ( %)

4) Viscosity of slurry mixture

• • The viscosity of a dilute suspension consisting of solids in a liquid is calculated approximately based on volume fraction Φ and the viscosity of the liquid using the following expression:

µ_m = µ_L (1 + 2.5Φ)

where, µ_m is the viscosity of slurry mixture  and µ_L is the viscosity of liquid in slurry mixture

• • The above equation of the mixture viscosity is valid for only to laminar flow consering spherical particles. Also the equation is not valid if solid concentrations exceeds 1 percent by volume
  • For higher-concentration suspensions, the above equation of mixture viscosity is modified as

µ_m = µ_L [1 + 2.5Φ + 10.05Φ² + 0.00273 exp(16.6Φ)]

Rheology of Slurry 

• • Understanding the rheological properties of slurries are essential before CFD modeling
  • Adding more particles changes the physical properties of slurries like color, density and viscosity
  • Effect of volume fraction of particles on viscosity

• • The viscosity of slurries changes with a change in particle concentration ; 1) shear thickening, 2) shear thinning
  • The effect of particles on rheology of mixture

 Flow Features of Slurries

• Effect of particle concentration profiles on slurry flows are classifies as:
  • Homogeneous slurry: particles are uniformly distributed
  • Heterogeneous slurry: particles are not uniformly distributed
  • Moving bed slurry: the bed formed by particle moves with fluid flow
  • Stationary bed slurry: the bed formed by particle does not with fluid flow. Such a slurry flow can led to the scaling and blocking of fluid flows

• • The homogeneous and heterogeneous flows are also called a fully suspended flow

 

• Effect of Pressure gradient on slurries flow

 

• Effect of particle concentration profiles on slurry flows in pipes

Typical Liquid Properties Used in CFD

Slurry Classification Based on Solid Volume Fraction

Solid Volume Fraction	Classification	Typical Viscosity	CFD Recommendation
<5%	Very Dilute	1–2 cP	DPM
5–20%	Dilute	2–20 cP	Mixture Model
20–40%	Medium	20–200 cP	Mixture or Eulerian
40–60%	Dense	200–2000 cP	Eulerian
>60%	Paste Slurry	>2000 cP	Eulerian + Non-Newtonian Rheology

Typical Non-Newtonian Models for Slurries

Slurry Type	Rheological Model	Industrial Applications
Coal Slurry	Power Law	Coal gasification
Cement Slurry	Bingham Plastic	Cement pumping
Mine Tailings	Herschel-Bulkley	Thickened tailings
Sewage Sludge	Herschel-Bulkley	Wastewater treatment
Clay Slurry	Casson / Power Law	Ceramic industry
Biomass Slurry	Herschel-Bulkley	Biogas and biofuel plants
Food Slurry	Carreau-Yasuda	Food processing

Type of  Slurry and CFD Model selection and

• In Computational Fluid Dynamics (CFD), slurry flow is generally modeled as a multiphase flow consisting of a liquid phase and suspended solid particles.
• The choice of CFD model (Mixture, Eulerian, DPM, DEM, etc.) depends mainly on the solid concentration, particle size, and slurry viscosity 

Slurry Type	Liquid Phase	Typical Solid Particles	Solid Concentration (% wt)	Solid Concentration (% vol)	Particle Size	Dynamic Viscosity (mPa·s or cP)	Flow Characteristics	Recommended CFD Model
Dilute Slurry	Water	Sand, Ash	1–10	0.5–5	50–1000 µm	1–5	Newtonian	DPM (Discrete Phase Model)
Medium Slurry	Water	Coal, Ore	10–30	5–20	50–500 µm	5–30	Slightly Non-Newtonian	Mixture Model
Dense Slurry	Water	Mineral Concentrate	30–60	20–45	10–300 µm	30–500	Non-Newtonian	Eulerian Multiphase
Ultra Dense Slurry	Water	Tailings, Paste	60–80	45–65	1–200 µm	500–10000	Yield Stress Fluid	Eulerian + Herschel-Bulkley
Fine Clay Slurry	Water	Kaolin, Bentonite	20–50	10–35	<20 µm	50–5000	Shear Thinning	Non-Newtonian
Cement Slurry	Water	Cement Powder	40–70	25–50	1–100 µm	100–2000	Bingham Plastic	Bingham/Herschel-Bulkley
Fly Ash Slurry	Water	Fly Ash	20–60	10–40	5–100 µm	5–300	Slightly Non-Newtonian	Mixture/Eulerian
Coal-Water Slurry	Water	Pulverized Coal	40–70	30–55	10–300 µm	100–2000	Shear Thinning	Eulerian
Biomass Slurry	Water	Biomass Powder	5–30	5–20	50–5000 µm	2–100	Fibrous Suspension	Mixture Model
Sewage Sludge	Water	Organic Solids	2–10	2–8	Variable	10–5000	Non-Newtonian	Eulerian
Food Slurry	Water	Fruit Pulp, Starch	10–50	5–35	20–1000 µm	100–5000	Shear Thinning	Non-Newtonian
Lime Slurry	Water	Ca(OH)₂	10–30	5–20	1–100 µm	5–50	Newtonian to Slightly Non-Newtonian	Mixture Model

Case Study:  CFD Modelling of Slurry Flows

• For any CFD modelling, understanding mathematical equations are important
• The Eulerian-Eulerian model (two-fluid model) model is commonly used to CFD Modelling the slurry flow
• The in homogeneous Eulerian-Eulerian model (two-fluid model) considers continuous (liquid) and dispersed (solid) phases as an interpenetrating continuum.
• The Eulerian – Eulerian model is well suited for high-volume fractions of the dispersed phase (particle concentration) which is averaged over each control volume
• Each phase is governed by similar conservation equations and modeling is required for interaction between two phases, turbulent dispersion of particles, and collision of particle with walls.
• However, for that complex closure relations are required for the Eulerian – Eulerian model.
• The continuity (mass) and momentum equations for two-phase flow model are given below in brief
• To model slurry flows,  volume-averaged, isothermal, in-compressible, and transient Navier-Stokes continuity equations are solved numerically for both liquid and solid (particle) phases

 

 

4.1 Continuity Equations

The mass conservation equation without the mass exchange between the liquid and solid phases due to reaction is given as

where  h_l and  h_s are the volume fraction of liquid and solid, respectively, and  and are the velocity vector of liquid and solid, respectively.

4.2 Momentum Equations

The momentum equations for both liquid and solid phases which considers the interphase momentum exchange term that models the interaction between two phases is given as

Where,

g = gravity term,

p = thermodynamic pressure,

ρ_l , ρ_s = density of liquid and solid, respectively

M= sum of interfacial forces including drag force and lift force,

τ = the shear stress tensor (for liquid and solid)

The liquid phase and solid phase stress tensors 

 Bulk solid viscosity

Solid Pressure which represents the solids phase normal forces caused by particle-particle interactions

Here, the first term denotes the particle velocity fluctuations and the second term is due to the particle collisions.

In the above equations, kinetic and collisional components of the solids viscosity are given as

4.3 Interphase Models

Drag Force Model

• • For spherical particles, the drag force per unit volume is given as

• • The Gidaspow drag model is used for drag due to solid s particles

Lift Force Model

• • For spherical solid particles, select the Saffman and Mei lift force model as

4.4 Turbulence Model

• • Based on the literature, various turbulence models have used in predicting particle concentration profile. However, the k- ε turbulence model is very robust in predicting the particle concentration profile as compared to the other turbulence models
  • The k- ε turbulence model is well suited for robustness and general purpose of simulations
  • In multiphase flow, the transport equations for turbulent kinetic energy  (k) and dissipation rate (ε ) which are  are phase dependent and assume a similar form to the single-phase transport equations

The last terms in each equation are interphase transfer for k and ε

• The k- ε turbulence model, the turbulence viscosity is calculated based on the turbulence kinetic energy and dissipation rate

5. Geometry Modelling and Meshing

• • The three-dimensional (3D) horizontal pipe geometry was modeled
  • In order to ascertain  a fully developed turbulent flow, a hydrodynamic entrance length computed using the following equation

where N_Re is the Reynolds number of the liquids and D_h is the hydraulic diameter

    Boundary and Initial Conditions

• •  Inlet of the pipe: mixture velocity and volume fraction of both liquid and particles phases are  specified.
  • Outlet of the pipe:  pressure outlet is  specified.
  • Wall of the pipe,: no-slip condition is imposed on the liquid, but free-slip condition  is imposed on the particles.
  • Initialization of numerical solution:  average volume fractions and mixture velocity are specified as initial conditions.

Numerical Solution

• • Pressure-velocity coupling -SIMPLE algorithm momentum equations,
  • High resolution discretisation scheme : for the convective terms.
  • Time step: a fixed time-step of 0.001 s
  • The numerical solution was considered to be converged when the residuals of flow variables were less than  10⁻⁴

CFD Results:

• • Volume fraction of particles is presented for different cross section of pipe

• Effect of inlet volume fraction of particles is presented for different slurries

5. Case Studies of Slurry Flow using CFD Models

5.1 Slurry Flow Of Mineral Deposition 

Model assumptions and methodology

In three-phase Eulerian-Eulerian model,  the phase  is  defined individually for solid particles, water and air with different velocity fields:

• • Continuous  phase: water, air
  • Disperse  phase: solid particles
  • In-homogeneous flow,  turbulence is set for three phases
  • Each phase is coupled with two other phases through interfacial drag laws
  • A  power-law model or generic yield stress  are used to model  the slurry flow based on its rheological properties

The  slurry mixture viscositc  of slurry flow is calculated as follows:

• • Set the plastic  viscosity is separately defined, hence the mixture viscosity is given by the correlation: 
  • Liquid-phase viscosity   is set for water
  • The solid-phase (sand particles) viscosity   is a variable that will change as per its volume of fraction

This multi-phase model uses a velocity inlet  and pressure outlet for boundary conditions for better convergence.

• Free surface profile ; Sand Volume fractions

 

5.2 Erosion due to Slurry Flow through an Elbow

• Using CFD modeling, the particle concentration in pipe sections can be determined in order to find the erosion due to particles
• The erosion rate ( mm/s) is predicted using the erosion models
• CFD results show that with an increase in the number particles, the erosion rate of pipe increases. We can design  the optimum flow rate of slurry and life of pipe

 

Summary 

• Slurry flows have many practical applications in nature and industries
• Slurry flows cause erosion of pipes and decreases the fluid if concentration of solids is higher or particle size is not uniform
• Mluti-phase  model (Eulerian-Eulerian model) is used to predict the slurry flows in pipe
• Erosion  models  predict the depreciation of material due to erosion of solid particles
• CFD Modeling will help to design the complex slurry flows, how long the pipe or ducts will carry slurry flows within the design limit particles 

 

References

1. T. N. Ofei, A.Y. Ismai, Eulerian-Eulerian Simulation of Particle-Liquid Slurry Flow in Horizontal Pipe, Journal of Petroleum Eng, Hindawi Pub.( 2016) 5743471
2. S. K Lahiri, K.C.Ghanta, Slurry Flow Modelling by CFD , Chem. Ind. Eng., CI &CEO 16 (4) 295−308 (2010)
3.  S.K.Wee, Y.J. Yap, CFD study of sand erosion in pipeline”, J. Petrol. Sci. Eng., 176, 269–278 (2019).
4. B.T. Zengeni, Bingham Yield Stress and and Bingham Plastic Viscosity of Homogenous Non-Netwtonian Slurries, (Master Thesis) Cape Peninsula University of Technology, 2016
5. M. Swamy, N. González Díez, A. Twerd, Numerical modelling of the slurry flow
   in pipelines and prediction of flow regimes, Comp.Method Multiphase Flow, WIT Press (2015)
6. A. Kumar, CFD Modeling for Slurry Flow Through Bends and Straight Pipe Line, Springer